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Nanoparticles of zirconia and titania prepared by Joule Quench Reactor
ISSN 0288-4534CODEN: KONAE7
KONAPOWDER AND PARTICLE
Published by Hosokawa Powder Technology Foundation
50 nmZrO2
20 nmTiO2
KONAPOWDER AND PARTICLE
Editorial BoardY. Kousaka Editor in Chief
(Emeritus Professor of Osaka Prefecture Univ.,JAPAN)
Asia / Oceania Editorial BoardY. Tsuji Vice Chairman
(Osaka Univ., JAPAN)Y. Morikawa (Emeritus Professor of Osaka Univ., JAPAN)K. Miyanami (Emeritus Professor of Osaka Prefecture Univ.,
JAPAN)H. Masuda (Kyoto Univ., JAPAN)H. Emi (Kanazawa Univ., JAPAN)K. Higashitani (Kyoto Univ., JAPAN)K. Nogi (Osaka Univ., JAPAN)Y. Fukumori (Kobe Gakuin Univ., JAPAN)J. Hidaka (Doshisha Univ., JAPAN)P. Arnold (Univ. of Wollongong, AUSTRALIA)S.H. Kang (Yeugnam Univ., KOREA)W. Tanthapani- (Chulalongkorn Univ., THAILAND)chakoonT. Yokoyama (Hosokawa Powder Technology Research Insti-
tute, JAPAN)K. Yoshida (Hosokawa Micron Corp., JAPAN)
SecretariatT. Kawamura (Hosokawa Powder Technology Foundation,
JAPAN)Europe / Africa Editorial Board
J. Schwedes Vice Chairman (Univ. Braunschweig, GERMANY)K. Schönert (Technische Univ. Clausthal, GERMANY)H. Schubert (TU Bergakademie Freiberg, GERMANY)E. Forssberg (Univ. Lulea, SWEDEN)H. Kalman (Ben Gurion Univ., ISRAEL)J.F. Davidson (Univ. of Cambridge, UNITED KINGDOM)J.F. Large (Univ. de Tech. de Compiégne, FRANCE)
SecretariatP. van der Wel (Hosokawa Micron B.V. NETHERLANDS)P. Krubeck (Hosokawa Micron GmbH, GERMANY)
Americas Editorial BoardD.W. Fuerstenau Chairman (Univ. of California, U.S.A.)R. Flagan (California Institute of Technology, U.S.A.)L. Augsburger (Univ. of Maryland School of Pharmacy, U.S.A.)S.F. Thames (Univ. of Southern Mississippi, U.S.A.)P.S. Santos (Univ. of São Paulo, BRAZIL)B.M. Moudgil (Univ. of Florida., U.S.A.)R. Hogg (Pennsylvania State Univ., U.S.A.)D.J.W. Grant (Univ. of Minnesota., U.S.A.)
SecretariatI. Pikus (Hosokawa Bepex Div., U.S.A.)D.A. Scott (Hosokawa Micron Inter., U.S.A.)
Publication OfficeHosokawa Powder Technology Foundation (Japan) in Hosokawa MicronCorporationNo. 9, 1-chome, Shoudai Tajika, Hirakata-shi, Osaka 573-1132 Japan
Notes Hosokawa Powder Technology Foundation has entrusted the editorial
duty to the editorial board organized by the Council of PowderTechnology, Japan.
(Complimentary Copy)Printed in Japan
KONA is a refereed scientific journal that pub-lishes articles on powder and particle sciences andtechnology. KONA has been published annuallysince 1983 in Japan. KONA is distributed toresearchers, members of the scientific community,universities and research libraries throughout theworld.
About the Cover of Journal “KONA”The Chinese character “粉” is pronounced “KONA” in Japanese, and means “Powder”. The hand written “ ” is after the late Mr. Eiichi Hosokawa, founder of the HosokawaMicron Corporation.
Hosokawa Micron Corporation and its R&D Center
On April, 29th. 2002, Professor Dr. Sunil de Silvadied, totally unexpected and fast. Towards the end ofa normal working day he felt some pain in his backand his stomach and they brought him by ambulanceinto a hospital. The physicians detected interiorbleeding. These were so strong, that no help was pos-sible. He died in an age of 59.
Sunil de Silva was borne in Colombo, Sri Lanka (atthat time: Ceylon), on January 13th. 1943. He got hiseducation up to university level in Colombo. Afterone year at Ceylon-University he went to the UK inEurope where he studied Chemical Engineering atthe University of Loughborough. Already at that timehe was aware of the effect that an education only inCeylon would make him very much dependent uponhis home-country. He stayed in Loughborough upto 1970 when he got his PhD with a thesis entitled“Transmission of Force through Particulate Systemswith Restricted Geometries”.
In 1970 Sunil moved on to the University of Karlsruhe in Germany, where he joined with ProfessorKurt Leschonski as a scientific assistant within theInstitute of Mechanical Process Engineering, headedby Professor Hans Rumpf. In 1972 he moved withKurt Leschonski to the Technical University ofClausthal (Germany), where they founded a newInstitute of Mechanical Process Engineering. Sunilstayed in Clausthal up to 1976. From 1976 to 1982he worked in industry with Donaldson Europe inBelgium. His experiences in air classification, sizeanalysis, jet mills and computer modelling of particu-late f lows, which he gained at the different places,
was an excellent basis to join Christian MichelsenInstitute in Bergen, Norway, as a Post-Doctoral Fel-low. In 1982 he was appointed as Head of Research inPowder Technology at Chr. Michelsen Institute.
In 1988 the management of the Chr. MichelsenInstitute decided to close ist activities in PowderTechnology. Sunil was appointed as an AdjunctProfessor in Powder Technology in the faculty ofTechnology of Telemark University College inPorsgrunn and he was asked to move POSTEC toPorsgrunn. POSTEC (POwder Science and TEChnol-ogy) was a research programme which Sunil startedin 1983 in Bergen together with his colleague andfriend Gisle Enstad. Gisle Enstad and K. Manjunathmoved with Sunil to Porsgrunn. Powder Science andTechnology Research Ltd. (still: POSTEC) wasfounded with Sunil as the Managing Director. Verysoon 25 companies got members of POSTEC. Sunilpossessed the talent to motivate people and to con-vince them to work with POSTEC and to give themthe necessary money. One of his mostly used sen-tence was “we don’t have to convince people, wehave to educate them”. Thus, POSTEC got researchmoney not only from companies but also from theEuropean Community, from Scandinavian founda-tions as well as from the Norwegian Government.
In 1994 POSTEC was integrated as a Departmentwithin the foundation Telemark Technological R&DCentre (Tel-Tec) with Sunil as the Head of the De-partment. In 1995 he was appointed a full Professor inPowder Technology at Telemark University College.He retained his responsibility within Tel-Tec up to theend of 2002, when this responsibility was handed overto Gisle Enstad. Now, Sunil could devote all his timeto the College, where he was Head of the Depart-ment, Pro-Dean and member of the College’s Senate.He concentrated his activities more and more onquestions of education, which following his ideas wasnot only teaching itself but more the formation andalteration of the existing teaching courses. He neverfollowed existing rules without asking for their signif-icance.
Sunil served on many international committees andworking parties, he was member of several editorialboards. He gave a number of courses in many coun-tries and he organised in Norway three well attendedinternational conferences RelPowFlo I, II, III (Reli-able Powder Flow). RelPowPlo IV should take place inSri Lanka in winter 2003/2004. With that conference
KONA No.20 (2002) 1
Obituary
Sunil wanted to retire. We all are very dispressed(sad) that it was not permitted to him to do so.
Sunil was a beloved and a requested partner inindustry, in university, in committees and in privatelife. His places of activity in four European countries,but most of all his open, friendly, direct and honestnature was the reason for the enormous number of
friends he had around the world. Sunil was a “charac-ter” whom we cannot forget.
J. SchwedesVice Chairman of Europe/Africa Editorial Board
(Prof., Univ. of Braunschweig, Germany)
2 KONA No.20 (2002)
KONA No.20 (2002) 3
The Fourth World Congress on Particle Technology(4WCPT) was successfully held in Sydney from July 21st
to 25th, 2002. There were approximately 500 participantsfrom 35 countries around the world and the number ofpapers including posters presented at the meeting wasabout 500. The number of participants was about 200 lessthan at the 3WCPT held in Brighton in 1998, whereasthe number of papers increased by about 100. This meet-ing was partially supported by the Hosokawa PowderTechnology Foundation. An informal KONA editorialboard meeting was held on July 23rd during the 4WCPTto exchange ideas among the several editors from theAmericas, Europe/Africa and Asia/Oceania Blocks. Aforthcoming particle related meeting, the Second AsianParticle Technology Symposium (APT2003), will be heldin Penang, Malaysia from December 17th to 19th, 2003.
The Hosokawa Powder Technology Foundation is nowconsidering electronic publication of this journal. It ishoped that we will have the ability to download this issuefrom the Internet.
This year we lost another member of the KONA editor-ial board, chairman of the Europe/Africa Block, Profes-sor S. de Silva in Postec-Research A/S, Norway. We allheartily lament his death and extend our sincere condo-lences.
In the past, issues of KONA have normally been pub-lished and distributed in February or March. However,the original KONA publication and distribution schedulewas intended for the end of December. This year we havemade an effort to advance the publication date, and I hopethis issue will be in your hands in December of 2002.
The Letter from the Editor
Yasuo KousakaEditor-in-Chief
4 KONA No.20 (2002)
HISTORY OF THE JOURNALKONA journal has been published by the Council of Powder
Technology, Japan. (CPT), from No.1 to No.12 issues, under thesponsorships of Hosokawa Micron Corporation (No.1 to No.9) and Hosokawa Powder Technology Foundation (No.10 to No.12).
The CPT has been established in 1969 as a non-profit organiza-tion to enhance the activities of research and development onpowder science and technology in Japan under the sponsorship ofHosokawa Micron Corporation. In 1983, the CPT has decided to issue an international journal named “KONA”, which publishesthe excellent articles appeared in Japanese journals concerningpowder science and technology, after translated into English,throughout the world. After the seventh volume issued in 1989, the CPT has changed its policy to internationalize the “KONA”from the 8th issue (1990) and on by incorporating the monographsoriginally written in English from the authors throughout theworld. Immediately, the present editorial board including Asian,Americas’ and European Blocks has been organized.
From the 13th issue and on, the Hosokawa Powder TechnologyFoundation has taken over the role of KONA publisher from theCPT in 1995 (No.13) and the Foundation has entrusted the editor-ial duty to the present KONA editorial board organized by the CPTwithout requesting any shift in our present editorial policies. Thisswitching of publisher has been simply and only to make the aimand scope of the Foundation definite. Essentially no change hasbeen observed in continuously editing and publishing this journalexcept in the designation on a part of the journal cover.
AIMS AND SCOPE OF THE JOURNALKONA Journal is to publish the papers in a broad field of
powder science and technology, ranging from fundamental princi-ples to practical applications. The papers discussing technologicalexperiences and critical reviews of existing knowledge in special-ized areas will be welcome.
These papers will be published only when they are judged, bythe Editor, to be suitable for the progress of powder science andtechnology, and are approved by any of the three Editorial Com-mittees. The paper submitted to the Editorial Secretariat shouldnot have been previously published except the translated paperswhich would be selected by the Editorial Committees.
CATEGORY OF PAPERS• Invited papers
Original research and review papers invited by the KONAEditorial Committees.
• Contributed papersOriginal research and review papers submitted to the KONAEditorial Committees, and refereed by the Editors.
• Translated papersPapers translated into English, which were previously publi-shed in other languages, selected by the KONA EditorialCommittees with the permission of the authors and / or thecopyright holder.
SUBMISSON OF PAPERSPapers should be sent to each KONA Editorial Secretariat.• Asia / Oceania Editorial Secretariat
T. KawamuraHosokawa Micron Corporation Micromeritics Laboratory 1-9,Shoudai Tajika, Hirakata 573-1132 JAPAN
• Europe / Africa Editorial SecretariatDr. P. van der Wel or Mrs. P. KrubeckHosokawa Micron GmbHWelserstr. 9-11, 51149 KölnP.O. Box 920262, 51152 KölnGERMANY
• Americas Editorial SecretariatDr. I. Pikus or D.A. ScortHosokawa Micron International Inc.10 Chatham Road, Summit, NJ 07901 USA
PUBLICATION SCHEDULEKONA is published once a year.
SUBSCRIPTIONKONA is distributed free of charge to senior researchers at
universities and laboratories as well as to institutions and librariesin the field throughout the world. The publisher is always glad toconsider the addition of names of those who wish to obtain thisjournal regularly to the mailing list. Distribution of KONA is madeby each Secretariat.
INSTRUCTIONS TO AUTHORS(1) Manuscript format
• Two copies should be submitted to the Editorial Secretariat, indouble-spaces typing on pages of uniform size.
• Authorship is to give author’s names, and the mailing addresswhere the work has been carried out on the title page.
• Abstract of 100-180 words should be given at the beginning ofthe paper.
• Nomenclature should appear at the end of each paper.Symbols and units are listed in alphabetical order with theirdefinitions and dimensions in SI units.
• Literature references should be numbered and listed togetherat the end of paper, not in footnotes. Please give informationas in the following examples:1) Carslaw, H.C. and J.C. Jaeger: “Conduction of Heat in
Solids”, 2nd ed., Clarendon Press, Oxford, England (1960).2) Howell, P.A.: US Patent, 3,334,603 (1963).3) Rushton, J.H., S. Nagata and D.L. Engle: AlChEJ., 10. 294
(1964).4) Seborg, D.E.: Ph.D. Dissertation, Princeton Univ., N.J., U.S.
A. (1969).• Original figures with each single copy should be submitted, on
separate sheets. Authors’ names and figure numbers aremarked in the corner.
• Figure numbers and captions are listed on a separate sheet.• Place of figure insertion is to be indicated in the margin of the
manuscript.• Tables should be typed on separated sheets.• Author’s short biography and photograph should be attached.• Submit an IBM-readable f loppy disk (31/2) with your
unformatted text file in ASCII code. If you use either WORDor WORD PERFECTas word processing system, please addthe formatted text file.
(2) Reprints• The authors shall receive 50 free reprints. Additional reprints
will be furnished when ordered with return of galley proofs.(3) Publication policy
• All papers submitted for publication become immediately theproperty of the CPT and remain so unless withdrawn by theauthor prior to acceptance for publication or unless releasedby the Editor. Papers are not to be reproduced or published inany form without the written permission of the CPT.
KONAGENERAL INFORMATION
Contents
＜Review＞
＊Motionless Mixers in Bulk Solids Treatments – A Review J. Gyenis...................................................................... 9
＊Gas-Phase Production of Nanoparticles A. Gutsch, M. Krämer, G. Michael,....................... 24H. Mühlenweg, M. Pridöhl and G. Zimmermann
＊A Century of Research in Sedimentation and Thickening F. Concha and R. Bürger ........................................ 38
＊Dry Powders for Pulmonary Delivery of Peptides and H. Okamoto, H. Todo, K. Iida ............................... 71Proteins and K. Danjo
＊Synthesis and Fabrication of Inorganic Porous Materials: M. Takahashi and M. Fuji ..................................... 84From Nanometer to Millimeter Sizes
＜Original Research Paper＞
＊The Feasibility of Ferro-alloy fines Recovery by using A.B. Nesbitt, S. Wanliss .......................................... 98Centrifugal Separator Technology and F.W. Petersen
＊Stochastic Aspects of Granular Flow in Vibrated Beds R. Wildman and J.M. Huntley.............................. 105
＊Low-Frequency Vibration Effects on Coarse Particle R.J. Wakeman and P. Wu...................................... 115Filtration
＊Effects of Wall Inclinations and Wall Imperfections on J. Tejchman ............................................................ 125Pressures during Granular Flow in Silos
＊X-Ray Analysis of Fluidized Beds and Other Multiphase J.G. Yates, D.J. Cheesman, P. Lettieri .................. 133Systems and D. Newton
＊Combination of SHS and Mechanochemical Synthesis T. Grigorieva, M. Korchagin ................................ 144for Nanopowder Technologies and N. Lyakhov
＊Performance and Cost-Effectiveness of Ferric and T.M. Scott, R.C. Sabo, J. Lukasik,........................ 159Aluminum Hydrous Metal Oxide Coating on Filter C. Boice, K. Shaw, L. Barroso-Giachetti,Media to Enhance Virus Removal H. El-Shall, S.R. Farrah, C. Park,
B. Moudgil and B. Koopman
＊Consolidation Behavior of Inhomogeneous Granular S. Zheng and A.M. Cuitiño .................................. 168Beds of Ductile Particles using a Mixed Discrete-Continuum Approach
＊Physical Properties of Supercritically-Processed and B.Y. Shekunov, J.C. Feeley, ................................... 178Micronised Powders for Respiratory Drug Delivery A.H.L. Chow, H.H.Y. Tong
and P. York
＊Particle Shape Modification in Comminution E. Kaya, R. Hogg and S.R. Kumar ...................... 188
＊Primary Segregation Shear Cell for Size-Segregation S.P. Duffy and V.M. Puri ...................................... 196Analysis of Binary Mixtures
＊A Load-Interactive Model for Predicting the Performance H. Delboni Jr. and S. Morrell ............................... 208of Autogenous and Semi-Autogenous Mills
KONA No.20 (2002) 5
KONA Powder and Particle No. 20 (2002)
＜Translated Research Paper＞
＊Development of an Apparatus for Measuring Adhesive Y. Shimada, Y. Yonezawa, H. Sunada,................ 223Force between Fine Particles R. Nonaka, K. Katou and H. Morishita
＊Continuous Synthesis of Monodispersed Alumina T. Ogihara and M. Nomura ................................. 231Particles by the Hydrolysis of Metal Alkoxide Using a Taylor Vortex
＊Production of Silica Particles by Electrostatic Y. Mori and Y. Fukumoto ..................................... 238Atomization
＊Flocculation Mechanism of Suspended Particles Using S. Sakohara, T. Kimura ....................................... 246the Hydrophilic/Hydrophobic Transition of a and K. NishikawaThermosensitive Polymer
＊Development of Agglomerated Crystals of Ascorbic Acid Y. Kawashima, M. Imai, H. Takeuchi, ............... 251by the Spherical Crystallization Technique for Direct H. Yamamoto and K. KamiyaTableting, and Evaluation of Their Compactibilities
＊Dispersion and Flocculation Behavior of Fine Metal J. Shibata, K. Fujii, N. Murayama...................... 263Oxide Particles in Various Solvents and H. Yamamoto
6 KONA No.20 (2002)
KONA No.20 (2002) 7
Explanation of the Cover Photographs
Nanoparticles of zirconia and titania prepared by Joule Quench Reactor
The photographs show TEM images of zirconia (ZrO2) and titania (TiO2) particles produced using a nanoparti-
cle generator, called “Joule Quench Reactor (JQR)”. JQR produces the nanoparticles by the chemical reaction of
organic compounds including inorganic or metal components to generate core particles using plasma followed by
rapid quenching. The ZrO2 particles made by JQR have an average particle size calculated from BET specific sur-
face area of 37 nm and a crystal size measured by X-ray diffraction method of 32 nm. The good agreement of
these two means each particle consists of a single crystal, which is also presumed from the fact that the particles
have polygonal shape. It is also remarkable that the ZrO2 particles have higher whiteness than the conventional
ones.
On the other hand, JQR also produces TiO2 of anatase phase showing photocatalytic properties. The TiO2
particles made by JQR have a BET equivalent particle size of 58 nm and a XRD crystal size of 38 nm. The parti-
cles have spherical shape and higher whiteness compared with the conventional TiO2.
50 nmZrO2
20 nmTiO2
KONA No.20 (2002) 9
1. Introduction
Motionless or static mixers are widely known andapplied in process technologies for the mixing of liq-uids, especially for highly viscous materials, and tocontact different phases to enhance heat and masstransfer. Producing dispersions in two- and multi-phase systems such as emulsions, suspensions,foams, etc., is also the common aim of using motion-less mixers. Far less information is known on theirbehavior, capabilities and applications in bulk solidstreatments. Although investigations started morethan thirty years ago in this field, research and devel-opment is still under way even now. Recent studiesand applications gave evidence on the beneficial fea-tures of such devices in powder technology for mix-ing and other treatments of bulk solids.
Motionless or static mixers are f low-modifyinginserts, built into a tube, duct or vessel. These toolsdo not move themselves, but using the pressure dif-ference or the kinetic and potential energy of thetreated materials, create predetermined f low patternsand/or random movements, causing velocity differ-ences and thus relative displacements of various partsof the moving material. In this way, motionless mixerscan considerably improve the process to be carriedout. In f luids, motionless mixers work efficientlyboth in turbulent and laminar regions. Splitting, shift-ing, shearing, rotating, accelerating, decelerating and
recombining of different parts of materials are com-mon mechanisms in this respect, both in f luids andbulk solids.
Motionless mixers eliminate the need for mechani-cal stirrers and therefore have a number of benefits:No direct motive power, driving motor and electricalconnections are necessary. The f low of materials(even particulate f low) through them may be inducedeither by gravity, pressure difference or by utilizingthe existing potential or kinetic energy. The spacerequirement is small, allowing a compact design ofequipment in bulk solids treatments. Installation iseasy and quick, e.g. by simple replacement of a sec-tion of tube or by fixing inserts into a tube or vessel.Set-up and operating costs are much lower than thoseof mechanical mixers, while maintenance is practi-cally superf luous. Motionless mixers are available ina number of different types, shapes and geometries,made from a great variety of materials. The mixer cantherefore easily be matched to process requirementsand to the features of the processed materials. Phys-ical properties, e.g. f low behavior, particle size,mechanical strength, abrasive effects, safe prescrip-tions. e.g. for food and pharmaceutical industries, canbe taken into account by the proper design of mixers.Applications in powder technology are equally feasi-ble in gravity and pneumatic conveying tubes, inchutes, hoppers and silos, or even in rotating, vi-brated or shaken containers.
The greatest advantages of motionless mixers inbulk solids treatment are: high performance, continu-ous operation, energy and manpower savings, mini-mum space requirement, low maintenance costs,
J. GyenisUniversity of KaposvarResearch Institute of Chemical and Process Engineering*
Motionless Mixers in Bulk Solids Treatments – A Review†
Abstract
In this paper the general features, behavior and application possibilities of motionless mixers inmixing and treatments of bulk solids are overviewed, summarizing the results published during thelast three decades. Working principles, mechanisms, performance, modeling and applications ofthese devices are described. Related topics, such as use in particle coating, pneumatic conveying,contacting, f low improvement, bulk volume reduction, and dust separation are also summarized.
* Veszprem, Egyetem u. 2, Hungary† Accepted: June 28, 2002
trouble-free operation, easy measurement and con-trol, and improvement of product quality.
There are a number of different types of motionlessmixers available from a number of manufacturers,most of them are applicable for bulk solids, too. Themost widely known types are, e.g. Sulzer SMX andSMF mixers, Ross ISG and LPD mixers, Komaxmixer, Kenics and FixMix mixers, etc. Fig. 1 showssome examples of these devices.
The Sulzer SMX mixer (Fig. 1a) is a typical formof lamellar mixer, composed of narrow strips or lamel-las placed side by side within a tube section. Thesestrips decline from axial direction alternately by posi-tive and negative angles, crossing the planes of eachother, and thus constituting a 3-D series of X forms.During f low, the material is split into several streamsor layers corresponding to the number of strips,shifted to opposite directions relative to each other.Flow cross-sections contract along its up-f low sidesand expand at the down-f low sides. Thus, the materialis forced laterally from the contracting to the neigh-boring expanding channels. One SMX element, i.e.one series of crossing strips, mixes principally in twodimensions along the plane of the X forms. Therefore,the next series of X forms is aligned at 90° to ensurethree-dimensional mixing. Sulzer SMX is thus charac-terized by excellent cross-sectional (transversal) mix-ing and a high dispersing effect with a small space
requirement and a narrow residence time distribu-tion. In multiphase f lows no deposits and blockagesoccur, due to the high turbulence caused by the sharpedges and crossings. But, a drawback of this mixeralso comes from this, because sharp edges and thesudden changes in f low directions increases pressuredrop. In bulk solids f low, troubles can arise, especiallyfor cohesive materials, for larger particles or broadsize distributions.
Fig. 1b shows the Ross LPD mixer which consistsof a series of slanted semi-elliptical plates positionedin a discriminatory manner in a tubular housing.When the material f lows through this mixer, the inputstream is split and diverted repeatedly in differentdirections along the cross-section of the tube, untila homogeneous mixture is achieved. This type ofmotionless mixer is generally used for the turbulentf low of low-viscosity liquids to enhance macro- andmicro-mixing and/or to improve the heat transfercoefficient in heat exchangers. It is also feasible forparticulate f lows. But, since the f low at a given tubesection is divided into two streams only, shear andmaterial exchange takes place in one plane onlybetween the two half-tube cross-sections, thus themixing effect along a given length is weaker than inSMX mixers, especially for viscous materials or bulksolids. Naturally, the pressure drop is also less. Forbulk solids, the maximal throughput in a Ross LPD
10 KONA No.20 (2002)
Fig. 1 Examples for motionless mixers also applicable for bulk solids(a) lamellar (Sulzer SMX) mixer, (b) Ross LPD mixer, (c) Komax mixer, (d ) Kenics static mixer, (e) FixMix mixer, ( f ) a - taper and(g) b - skewness of a FixMix element
(a) (b) (c) (d) (e) ( g)
a
( f )
b
b
mixer is higher than in SMX, and the risk of pluggingfor cohesive powders or large particle sizes is consid-erably reduced. Another difference is that, due to thenon-uniform axial velocity profile, the longitudinalmixing effect of the LPD mixer may be higher thanthat of the SMX mixer.
The Komax mixer (see Fig. 1c) consists of f latplates arranged essentially in axial direction in a tube,but at both ends of these plates they are hatched,rounded and bent in opposite directions. The neigh-boring mixer plates are arranged at 90° in radialdirection, touching each other with the tips of thebent f laps. This mixer is also called a “Triple-ActionMixer”, because it provides (i) two-by-two division,(ii) cross-current mixing and (iii) back mixing ofcounter-rotating vortices. Each mixing element set incombination sweeps approximately two-thirds of thecircumference of the pipe and directs the f low to theopposite side, providing very strong wall-to-wall radialtransfer. Between the sets of generally four mixer ele-ments, inter-set cavities provide space for intensivecontacting of the sub-streams of material by strongmomentum reversal and f low impingement. For mul-tiphase f low, this mixer is resistant to fouling or clog-ging, because the f lips of the mixer elements aresmoothly contoured with a large radius. Intersectionsbetween the element ends with the wall are alloblique angles, eliminating corners that can trap solidor fibrous materials and promote material accumula-tion. Momentum reversal and f low impingement pro-vide a self-cleaning environment.
The Kenics static mixer shown in Fig. 1d pos-sesses almost all the advantages of the Komax mixer.It consists of a long cylindrical pipe containing a num-ber of helical elements twisted by 180° alternately inleft-hand and right-hand directions, perpendicular tof low direction. The adjacent elements are set by 90°in radial direction, therefore the outlet edge of a givenelement and the inlet edge of the next one are perpen-dicular to each other. The smooth helical surfacedirects the f low of material towards the pipe wall andback to the center, due to secondary vortices inducedby the spiral-form twist of the f low channels. Addi-tional velocity reversal and f low division results fromshearing of the material along the tube cross-sectionbetween the adjacent elements. The systematic divi-sion of streams and their recombination in anotherway enhance the mixing effect proportionally to 2n,where n is the number of the applied mixer elements.For f luids or in multiphase f lows, a relatively narrowresidence time is ensured, in addition to excellentradial mixing. Due to the smooth and mildly bending
surfaces of the helices, the pressure drop along aKenics mixer is very low, while it provides continuousand complete mixing and eliminates radial gradientsin temperature, velocity and composition. For bulksolids, because of the non-uniform axial velocity pro-file, a certain degree of longitudinal mixing also takesplace. Due to the smooth surfaces and relatively widef low channels, the risk of plugging or blockage isvery limited.
The FixMix motionless mixer shown in Fig. 1e isvery similar to the Kenics static mixer, with the essen-tial difference that the individual elements are slantedrelative to the tube axis and are tapered along theirlength. It results in several benefits: the slightlyincreasing gap between the mixer element and thetube wall eliminates the corners or contact pointsbetween them. Therefore, there are no dead zones,and deposition or blockage cannot occur. On theother hand, the cross-section of the f low channels onthe two sides of a mixer element changes continu-ously along its length: the cross-sectional area on oneside expands while on the other side it contracts. Dueto the tangential f low at the wall and the pressure dif-ference between the two sides, an intensive cross-f low takes place between the neighboring f lowchannels. These features provide improved mixingefficiency, lower pressure drop with suitable cross-sectional turbulence, and more uniform radial andtangential velocity fields. The higher velocity and theturbulence close to the tube wall results in higherheat transfer coefficients and a cleaner surface. Inaddition to this self-cleaning effect, the lack of cor-ners makes the cleaning easier for difficult materials.This mixer provides higher mixing efficiency per unitmixer length and reduces the risk of blockage in bulksolids treatment.
During the past three decades, quite a number ofpapers were published on the application of motion-less mixers in this latter field, and it is worth survey-ing these results to initialize further studies andpractical applications.
2. Motionless Mixers in Bulk Solids Mixing
The mixing of bulk solids is an important operationin many industries, such as in the chemical and phar-maceutical industries, mineral processing, food in-dustry and for treatments of agricultural materials.Uniform composition in these processes is of primaryimportance, as well as to eliminate segregation. Be-sides mechanical mixers and silo blenders, motion-less mixers represent a viable solution for this task,
KONA No.20 (2002) 11
especially if continuous operation is possible or nec-essary. The application to homogenize solids wasalready envisaged as early as in 1969 by Pattison [1].
A crucial condition of such an application is thetrouble-free f low of the bulk solids to be treated.Therefore, motionless mixers can only be used forfree-f lowing particles, but cohesiveness to some ex-tent is tolerable even in gravity f low of such materials.
In addition to the devices conventionally known asmotionless mixers, any other tools inserted into atube or vessel or the intentional changes of tube orchute cross-sections can modify the f low pattern ofsolids. Therefore, they may also be considered assome kind of motionless mixer. Various inserts insilos or hoppers, or cascade chute assemblies causingthe multiple division and recombination or modifica-tion of bulk solids f lows can also be ranked here.
2.1 Mixing Mechanisms of Motionless MixersSeveral workers investigated the mixing mecha-
nisms of particulate solids in motionless mixers act-ing in transversal [2] and longitudinal directions [3].Observing the interactions between the particles andmixer elements, four kinds of mixing actions weredistinguished [3, 4]. Namely: (a) multiple division andrecombination of the particle f low, (b) interaction ofparticles with other particles, with the surface ofmixer elements and the tube wall, (c) changes in f lowdirection, and (d) differences in velocity profile.Three main mechanisms, namely diffusive, convec-tive and shear mixing were attributed to theseactions. Shear: certain particle regions are shearedduring particle f low, creating velocity differencesbetween the adjacent layers. Convection: multiple divi-sion and recombination of the particle f low, as it issplit into sub-streams and diverted to different ductsor directions, and then unified with other sub-streams. Dispersive or dif fusive-type mixing: stochasticmovements with interchanges of different particles. Agreat deal of experience accumulated in the lastdecades indicates that these mixing mechanisms actmore or less together in any type of motionless mixer,and therefore they are hardly separable from eachother.
The majority of experimental studies carried outuntil now used helical mixer elements such as Kenicsor FixMix-type devices. In a few works, other types ofmotionless mixers such as Sulzer (Koch) mixers andmixer grids composed of helices, rods or lamellas,were investigated.
For certain types of mixers, the mixing mecha-nisms inf luence the characteristic direction of mixing.
There is a general belief that motionless mixers per-form mainly radial (transversal) mixing, and that axial(longitudinal) mixing is negligible. But, according toour experience, also seen from the results of otherworkers, this is not entirely valid even for viscous liq-uids or plastic materials, due to non-uniform axialvelocity profiles. Depending on their shape, arrange-ment and operational conditions, and in addition to ahigh radial dispersion [2], motionless mixers maycause effective axial mixing [3, 4], too. This latter fea-ture is of crucial importance in equalizing concen-tration variations in time and space in continuousparticle f lows caused either by segregation or by non-uniform feeding.
2.2 Mixing Kinetics and PerformanceThe performance of a bulk solids mixer is charac-
terized by its throughput, i.e. the treatable mass perunit volume and time, and by the degree of homo-geneity achieved. These features are in close relationwith the mixing kinetics, i.e. with the rate of homo-geneity improvement, characterizing how fast theconcentration uniformity is getting better as a func-tion of time or mixer length. The mixing kineticsdetermines the number of motionless mixers neces-sary to achieve a given degree of homogeneity or itsequilibrium. The latter may be the result of two com-peting processes: mixing and segregation. In otherwords: whilst the mixing mechanism tells us in whatmanner, the mixing kinetics characterizes by whichrate and how far the process is going on.
From a practical point of view, the performance of amixer is the most important feature, if we disregardthe actual mechanism of mixing. However, the mech-anism gives an explanation of the mixing kineticsexperienced, thus also serving as a starting point forfurther improvements. Therefore, almost all studiescarried out in this field aimed at determining the rateof process [5-14], and only a few works dealt with themechanism. The kinetics of the mixing and segrega-tion processes competing with each other can becharacterized by the equation [14]:
Km(1M)KsΦ (1)
where M denotes the actual degree of mixedness, Km
and Ks are the kinetic constants of mixing and segre-gation, respectively, while Φ is the so-called segrega-tion potential [14]. Although there are a number ofvarious definitions for the degree of mixedness [15],the most simple and well applicable one was definedby Rose [16] as
dMdt
12 KONA No.20 (2002)
M1 (2)
where s and s0 are the estimated standard deviationsof the sample concentrations taken from the actualmixture and in a totally segregated state, respectively.
Among the earliest works carried out in this field,the mixing performance of the Kenics [2-4, 8] andSulzer (Koch) motionless mixers [6, 7] was reportedby the team of L. T. Fan. In some studies, the mixingof wheat, sorghum grains and f lour was determinedboth in axial and radial directions. Among differentexperimental methods, the radioactive tracer tech-nique was used to observe the rate of the process.The practical purpose of these investigations was toupgrade low-quality products by adding high-qualityones during continuous blending. Motionless mixerswere proposed, e.g. to feed mills with a controlledquality of raw material. The kinetics of simultaneousmixing and segregation processes was investigatedexperimentally with free-f lowing particles which dif-fered in particle size or in particle density, or both.Under given conditions, comparison showed thatdifferences both in particle size and density gavesubstantially faster mixing and segregation ratescompared to systems where differences took place ineither particle size or particle density alone [8].
The mixing of materials of different particle sizes,shapes and densities is generally accompanied bysegregation. After quite a long mixing time, theseconcurrent processes result in a balanced degree ofmixedness which is lower than it would be in a totallyrandom distribution of the component particles.Depending on the initial positions of the components,equilibrium is approached gradually from below, orvery often, after going through a maximum. In thislatter case, the uniformity of a mixture decreases inthe final period of the process, in spite of continuedmixing action. Boss and his co-workers [10, 11] inves-tigated the balanced degree of mixedness in systemsof different particle sizes. Two types of motionlessmixers were tested: (a) lamellar mixers composed ofslanted metal strips crossing each other similarly toSulzer SMX mixers, and (b) roof mixers consisting ofgrids of angle profiles arranged in horizontal rows atdifferent cross-sections. Similarly to the works of Fanand his co-workers, these experiments showed signif-icant segregation after certain passes through themotionless mixer. (In these experiments, increasingmixer lengths were simulated by repeated f lowsthrough a given length of mixer tube.)
ss0
2.3 Modeling and SimulationsTo describe a process or equipment theoretically, or
to predict the characteristic features and results oftheir applications under different conditions, math-ematical modeling and simulation proved to be widelyapplied and useful tools. To investigate motionlessmixers in solids mixing, various modeling principlesand simulation methods were used till now. Chen etal. [4] adapted the concepts of an axially dispersedplug-f low model, commonly used at that time todescribe the mixing of f luids in various unit opera-tions. In their work, a quasi-continuous deterministicmodel was applied to describe the axial dispersion ofparticles in a gravity mixer tube containing motion-less mixer elements. Residence time distributionswere measured by the stimulus-response technique,and apparent Peclet numbers and axial dispersioncoefficients were determined for three different kindsof solid particles, after different number of passesthrough the mixer tube.
Apparent Peclet numbers (Pe′) and axial dispersioncoefficients (K ′ax) have similar definitions here tothose used in f luids to characterize the intensity oflongitudinal mixing. Their values can be determinedfrom the residence time distribution of tracer parti-cles in the mixer tube determined by discrete sam-pling at the outlet at different times after they areintroduced at the inlet in the form of a plug [17]. Thesecond central moment m2 of the residence time dis-tribution is as follows:
m2∑i
(tit— )2 · xi (3)
where ti is the residence time of tracer particles inthe mixer tube taken off by the i-th sample, and xi isthe mass fraction of tracer particles in the i-th sample.The mean residence time of all tracer particles alongthe mixer tube corresponds to the first moment of theresidence time distribution as:
t— ∑i
ti · xi (4)
The apparent Peclet number is determined fromthe mean residence time t— and the second centralmoment m2 of the residence time distribution, cor-rected by m2,0, which is the second central momentobtained in a plain tube, i.e. without motionless mixerelements:
Pe′ (5)
and the axial dispersion coefficient:
2t— 2
m2m2,0
KONA No.20 (2002) 13
K ′ax (6)
where Lmix is the length of the studied mixer section.The intensity of mixing, i.e. the achievable mixingeffect of motionless mixer elements per unit length isthe higher the lower Pe′ is or the higher K ′ax is.
Chen et al. [4] pointed out that smaller particleshad a higher apparent axial dispersion coefficientthan the bigger ones. By increasing the linear velocityof solids through the motionless mixers, an almostexponential improvement was obtained in the axialdispersion coefficient. A similar technique and modelwas used by Gyenis et al. [17] to investigate the influ-ence of different f low regimes, particle propertiesand length-to-diameter ratios of helical motionlessmixers on the resultant axial dispersion coefficient.
In mixing processes, especially in particulate sys-tems, stochastic behavior is a common feature whichcauses random variations both in f low characteristicsand in the local concentrations of components. Suchbehavior in gravity mixer tubes containing motionlessmixers was already recognized by the team of L. T.Fan [3, 7]. To interpret the experimental findings, adiscrete stochastic model was applied [3, 7, 9, 18]. Forthis, prior knowledge of the one-step transition proba-bilities of the particles was necessary, which weredetermined experimentally. This model seemed to besuitable to predict concentration distributions afterdifferent passes through the mixers. However, onexamining the results of experiments and thoseobtained by the stochastic model, two kinds of dis-crepancies can be recognized. One is that, in spite ofidentical particle properties, segregation and a spa-tially non-uniform mixing rate could be recognized[3]. Gyenis and Blickle proposed a possible theoreti-cal explanation of this behavior [19]. It was assumedthat spatially non-uniform transitions of particlesbetween the adjacent layers were caused by thechanging conditions during the non-steady-state f low.A correlation was proposed between the mixing rateand the energy dissipation caused by the interactionsof the particles and the mixer elements.
The other discrepancy came from the fact that ear-lier stochastic models used only expected values tocharacterize the one-step transition probabilities, to-tally ignoring their possible random variation. Thiscan be quite high if large-scale f low instabilities occur,especially in larger mixer volumes. Gyenis and Kataiproposed [20] a new type of stochastic model toexplain and describe the high random variationsexperienced in repeated experiments in an alterna-
Lmix2
t— · Pe′
tively revolving tumbler mixer, with and withoutmotionless mixer grids. Some years later, this modelwas simplified for simulation purposes [21], and wasthen made more exact by Mihalyko and his co-worker[22], introducing the concept of a so-called doublestochastic model.
DEM simulations based on a Lagrangian approachalso helped to understand the features and workingmechanisms of motionless mixers in particulate sys-tems [23].
2.4 Application Studies for Bulk Solids MixingThe mixing of free-f lowing particle systems in grav-
ity f low through motionless mixers was investigatedby several workers [2-12]. Most of these studiesresulted in suitable homogeneity after a few passes,but in some cases, depending on the physical proper-ties of the components, considerable segregation alsoemerged. Herbig and Gottschalk [24] applied hori-zontal bars serving as motionless mixers built into agravity mixer. It was found that assuring the smallestpossible shear action is essential to suppress segrega-tion.
A special, alternatively revolving bulk solids mixerequipped with motionless mixer elements shown inFig. 2 was studied by Gyenis and Arva [13, 14, 25,26] and provides practically segregation-free mixing.This device consists of two cylindrical containers (1)and a mixer section between them containing hori-zontal mixer grids (2) composed of a number of
14 KONA No.20 (2002)
Fig. 2 Schematic diagram of the alternating revolving bulk solidsmixer(a) outline of the mixer, 1 - containers, 2 - grids composedof motionless mixer elements, 3 - components to be mixed,4 - mount with rotating shaft, (b) helical motionless mixersarranged in grids
(b)
3
4
1
2
1
(a)
ordered FixMix elements. The material to be mixed(3) is filled into the lower container, then the mixer isrotated intermittently. In other words, the mixer bodyis turned through 180° in one direction, then stoppedto allow the bulk solids that are meanwhile at the topenough time to f low down through the mixer ele-ments. After this, the mixer is turned again through180° but in the opposite direction. The whole proce-dure is then repeated till the required homogeneity isobtained. Because of the periodically reversing direc-tions of particle f low and the changing direction ofacceleration and deceleration of the particles, segre-gation can be almost totally avoided.
By this method, a considerable improvement of themixing rate was achieved, resulting in a short mixingtime and a high homogeneity at a reasonably lowpower consumption [27]. This was evidenced byexamining the mixing kinetics of particle systemscomposed of materials with extremely different physi-cal properties, listed in Table 1. The density ratios ofthe component particles were varied from 1.2 : 1 to2.9 : 1, while the particle size ratios were changedfrom 1 : 2.7 to 1 : 110 as seen from Table 2. Kineticcurves, i.e. the variation of the degree of mixednessas a function of mixer turns are plotted in Fig. 3. Itshows that this mixer provides rapid and segregation-free mixing. The degrees of mixedness were deter-mined from the concentration variations of 65 spotsamples taken after different numbers of mixer turnsor mixing times by metal templates according to aregular pattern. A detailed description of this sam-
pling method was given by Gyenis and Arva [13]. Themass of each sample was 20 g, and the compositionsof samples were determined from 32.5 g materialtaken off from each sample, by dissolving the sodiumchloride tracer particles and measuring the conduc-tivity of the solution, or in other cases, by weighingthe polypropylene tracer particles after mechanicalseparation of the samples.
Theoretical considerations gave an explanation ofthis segregation-free operation and of the high achiev-able equilibrium homogeneity [14].
Bauman [29] studied three different types of mo-tionless mixers (Kenics, Komacs and Sulzer SMX) tomix particulate materials differing in mean particlesize and size distribution, in bulk density and in massratio. It was concluded that the mass ratio of the com-ponents, as well as the shape and number of motion-less mixers played a significant role in the achievablehomogeneity. Kenics-type mixers proved to be thebest when mass ratios were equal. But, when thesediffered significantly, Komacs and Sulzer SMX mixersgave much better results.
Motionless mixers are now increasingly appliedin various process technologies to mix particulatesolids. An interesting example for this is, e.g. the indus-trial standard of Tennessee [30], which mandates theuse of Komax, Ross, Koch (Sulzer) or similar com-monly accepted motionless mixers to manufacturehydraulic cement.
3. Bulk Solids Flow through Motionless Mixers
3.1 Gravity Flow StudiesThe continuous f low of bulk solids in vertical tubes
through Kenics-type motionless mixers was studied
KONA No.20 (2002) 15
Component Mean particle size, Density, mm kg/m3
Quartz sand 0.17 2650
Sodium chloride 0.46 2160
Wheat f lour 0.05 1510
Polypropylene granules 5.50 0910
Table 1 Particle sizes and densities of the constituents in mixesshown in Fig. 3.
Component Size ratio, Density ratio,
Quartz sand - Sodium chloride 1 : 2.7.. 1.2 : 1
Quartz sand - Polypropylene 1 : 32.4 2.9 : 1
Wheat f lour - Polypropylene 1 : 110. 1.7 : 1
Table 2 Size and density ratios of the constituent particles inmixes shown in Fig. 3.
wheat flour - polypropylene granules
quartz sand - polypropylene granules
quartz sand - sodium chloride
0 2 4 6 8 10 12
Number of mixer turns
Deg
ree
of m
ixed
ness
, M
14 16 18 20 22 240,0
0,2
0,4
0,6
0,8
1,0
Fig. 3 Kinetic curves obtained by the mixer shown in Figure 2with extreme particle systems (particle sizes, densities,and their ratios are given in Tables 1 and 2)
by Gyenis and his co-workers [12, 31, 32] under dif-ferent conditions. These mixer tubes consisted ofthree sections: (1) a plain feeding tube at the top, (2)motionless mixers in the middle, and (3) anotherplain tube below the motionless mixers. The massf low rate of solids was controlled by two means: (a)by adjusting the feeding rate at the inlet, or (b) bycontrolling the particle discharge at the bottom. Localparticle velocities were measured by fiber-opticalprobes that captured light ref lection signals. Averageand local solids hold-ups were determined by weigh-ing the material remaining in the tube after closingboth ends, and by gamma-ray absorption during oper-ation at different cross-sections, respectively. Theaxial mixing intensity was characterized by apparentPeclet numbers and dispersion coefficients calculatedfrom residence time distributions of tracer particles.The details of experiments and the applied experi-mental devices were described in several papers ofGyenis and his co-workers [12, 31, 32].
Experiments [12, 31, 32] and DEM simulations [23]equally revealed that, depending on the feeding anddischarging conditions, three characteristic f lowregimes could be distinguished in such gravity mixertubes, shown schematically by visualized simulationresults in Fig. 4.
A first type of f low regime takes place, shown inFig. 4a, if a solids f low withdrawn from the bottom,e.g. by a belt or screw conveyor, is less than the maxi-mal possible throughput of the gravity mixer tube,determined by its diameter and the configuration ofmotionless mixers. Naturally, the inf low of particles atthe tube inlet must be unlimited in this case, e.g.directly from a hopper. This 1st f low regime is charac-terized by dense f low, i.e. high solids hold-up in allthe three tube sections.
By increasing the discharged f low rate in this 1st
f low regime, the solids hold-up in the mixer tubedecreases slightly, mainly due to the growing “gasbubbles” just below the lower surface of the motion-less mixer elements. After reaching the maximalthroughput, which is achieved by unlimited outf low,the solids hold-up suddenly drops to a well-deter-mined value, resulting in a second f low regime shownin Fig. 4b. It is characterized by a dense sliding parti-cle bed in the upper tube, accelerating particle f lowalong the mixer elements and almost free-falling parti-cles in the lower plain tube section below the mixersection. The transition between the 1st and 2nd f lowregimes can be well recognized from the snap-shotsin Fig. 4d, obtained by DEM simulation, showing theactual situations at successive moments in time.
Another f low regime evolves when the solids f lowrate is controlled at the inlet of the tube, with free out-f low at the bottom. In this case, the f low rate of bulksolids fed into the tube must be lower than the maxi-mal attainable throughput of the motionless mixers.This 3rd f low regime, shown in Fig. 4c, is character-ized by almost free-falling particles in the upper andbottom plain tube sections with very low and progres-sively decreasing solids concentration. In the mixersection, however, a rapid sliding particle f low takesplace along the surface of the mixer elements with amuch higher solids hold-up compared to the upperand lower tube sections. When the solids f low rate inthis f low regime is increased from zero to the maxi-mal attainable capacity, the average solids volumefraction in the tube also increases from zero to a maxi-mal value. Reaching this latter stage, the upper tube
16 KONA No.20 (2002)
Fig. 4 Characteristic f low regimes in gravity mixer tubes withmotionless mixers in the middle tube section(a) 1st f low regime, (b) 2nd f low regime, (c) 3rd f low regime,(d) transition between the 1st and 2nd f low regimes
(a) (b)
0.0s
limited discharge
unlimited inf low unlimited inf low limited inf low
free outf low free outf low
0.4s 0.8s 1.2s 1.4s 1.8s
(c)
(d)
section above the motionless mixers suddenlybecomes choked with this sliding particle bed. Thiscauses a rapid transformation from the 3rd to the 2nd
f low regime.Visual observations and experimental data revealed
that in these f low regimes, a different and well-defined correlation exists between the solids hold-upin the mixer tube and the mass f low rate of particlestaken off at the bottom or fed into the tube.
As seen from Figs. 4a-d, the particle concentrationand thus solids volume fraction changes from place toplace along the length of the tube. However, since theusual mixer tubes are composed of several sections(e.g. feeding, mixing and post-mixing sections) and,very frequently, free tube sections (inter-element dis-tances) can be present between the individual mixerelements, it is reasonable to characterize operationconditions by the mean solids volume fraction aver-aged within the whole tube.
Plotting this mean solids volume fraction vs. themass f low rate, important characteristics of theabove-described f low regimes can be recognized, alsoindicating the conditions of transitions between them,as is shown in a general status diagram in Fig. 5.
The upper, slightly slanted curves of this diagramcorrespond to the changes in the 1st f low regime.Namely: by increasing the discharged mass f low rateat the tube bottom, the solids volume fraction aver-aged within the whole mixer tube also decreasesslightly, mainly due to the increasing void fractionwithin the section containing motionless mixers.Decreasing the l/d ratio of the mixer elements alsodecreases the mean solids volume fraction, making
these curves steeper.Achieving the maximum throughput of the given
mixer tube, the average solids volume fraction sud-denly drops to a distinct point shown in Fig. 5, whichcharacterizes the 2nd f low regime in the given system.It should be emphasized in this respect that localsolids volume fractions in this f low regime changesfrom place to place, generally decreasing in down-wards direction from the inlet of the mixer section,and especially in the plain tube below the mixer ele-ments. However, the average solids volume fraction isa well-determined distinct value, belonging to themaximal possible mass f low rate of particles underthis condition. This mass f low rate and average solidsvolume fraction depend on the diameter of tube, onthe physical properties of material, e.g. particle size,density, shape, surface properties, particle-particleand particle-wall frictions, as well as on the geometri-cal and other properties of the motionless mixer ele-ments, on the length ratios of feeding, mixing andpost-mixing sections, on the distance between themixer elements, etc. From Fig. 5, it is clearly seenthat by decreasing the l/d ratio of the helical mixerelements, the maximal throughput of the tube belong-ing to the 2nd f low regime also decreases. The gapbetween the solids volume fraction at the end point ofthe 1st f low regime curves and at the 2nd f low regimemainly depends on the length of the plain tube belowthe mixing section and on the distances between themixer elements: the gap diminishes if these plain tubesections are shorter.
In the 3rd f low regime, shown by the lower curvesin Fig. 5, the mean solids volume fraction increasesas the mass f low rate of solids fed into the tube inletis increased. The higher the retaining effect of themixer elements against the particulate f low, i.e. thelower their l/d ratio, the higher the mean solids vol-ume fraction in the tube will be: i.e. the slope of thecorresponding curves becomes steeper. After achiev-ing the maximum throughput of the mixer tube fromthis side, the feeding section becomes choked andthe mean solids volume fraction in the tube suddenlyincreases: i.e. the 3rd f low regime transforms to the2nd f low regime. This transformation is reversible, butsome hysteresis loop was experienced here. The gapsbetween the ends of the 3rd f low regime curves andthe data point of the 2nd f low regime mainly dependon the length of the feeding section.
It should be noted that Fig. 5 is a general diagramonly and therefore does not give precise quantitativedata on given particle systems or mixer tube configu-rations. It is a summary of our experiences and mea-
KONA No.20 (2002) 17
Fig. 5 General status diagram of f low regimes in gravity mixertubes containing motionless mixers
1st f low regime
l/d1
l/d1
00,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
500 1000 1500
Mass f low rate, kg/h
Mea
n so
lids
volu
me
frac
tion,
(1-
ε)
2000 2500
l/d1.5
l/d1.5
l/d2
l/d2
2nd f low regime
3rd f low regime
surements carried out with different particle systemsand mixer tubes under different conditions [12, 31,32]. However, this is a quite realistic diagram regard-ing the scales of its axes and tendencies of its curves,since they are close to the results obtained for thegravity f low of quartz sand of 0.17 mm mean particlesize in a gravity mixer tube of 1.6 m length and 0.05 minner diameter, with about 0.6 m total length of helicalmixer elements. Very similar curves were obtained byrecent DEM simulations for polymer particles with 3mm diameter and 1190 kg/m3 density [23], with thedifference that the corresponding mass f low rateswith similar mean solids fractions are somewhatlower compared to those of quartz sand.
Measurements [12] and DEM simulations [23]revealed a periodic variation of the local solids volumefractions along the motionless mixers in the middletube section. As typical examples, Figs. 6a,b,c showthe results obtained by the DEM simulation of partic-ulate f low in a mixer tube of 0.05 m ID and 0.80 mlength, composed of a feeding, a mixing and a post-mixing section of 0.20, 0.30 and 0.30 m length, respec-tively. The number of spherical model particles in thetube used for the DEM simulation was changed from10,000 to 65,000, with 3.0 mm diameter and 1190kg/m3 density. Other parameters such as stiffness,restitution coefficients, particle-particle and particle-wall frictions, and inlet velocity were described indetail by Szepvolgyi [23]. The mass f low rate con-trolled at the inlet or at the outlet of the tube to gener-ate different f low regimes was varied between 300and 1500 kg/h. From this diagram, it is seen that peri-odicity of local solids volume fractions took place inall the three f low regimes, due to the multiple interac-tion with the motionless mixers, which caused peri-odic deceleration and acceleration of the f low alongthe mixer lengths. These diagrams also show signifi-cant differences between the three f low regimesregarding the change of local solids volume fractionalong the various sections of the mixer tube.
Experimental studies revealed that these f lowregimes had a great inf luence on the mixing perfor-mance, too. Fig. 7 shows some examples for resi-dence time distributions of tracer particles measuredduring gravity f lows through Kenics-type motionlessmixers [12]. The model material for these experi-ments was quartz sand, the same as used for thesolids volume fraction measurements, and a shortplug of sodium chloride or polypropylene granuleswas used as the tracer. It was found that residencetime distributions were somewhat broader in the 1st
f low regime relative to the 2nd or 3rd f low regimes,
especially for smaller length-to-diameter (l/d) ratios.However, due to the higher throughput and lowermean residence time, the apparent Peclet numbersand axial dispersion coefficients were more beneficialin the 2nd and 3rd f low regimes, mainly for higher l/dratios. The best homogeneity values were obtained inthe 2nd f low regime and, at higher mass f low rates inthe 3rd f low regime, close to its transition point [12].
18 KONA No.20 (2002)
Fig. 6 Variation of the local cross-sectional solids volume frac-tions along the tube length in the three characteristic f lowregimes(a) 1st f low regime, (b) 2nd f low regime, (c) 3rd f low regime
3rd f low regime
motionless mixerspost mixing
sectionfeedingsection
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80Length from the inlet, l
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0Cro
ss-s
ectio
nal s
olid
s ho
ld-u
p, (
1-ε)
2nd f low regime
post mixing section
feedingsection
motionlessmixers
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80Length from the inlet, l
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0Cro
ss-s
ectio
nal s
olid
s ho
ld-u
p, (
1-ε)
1st f low regime
motionless mixerspost mixing
sectionfeedingsection
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80Length from the inlet, l
(a)
(b)
(c)
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0Cro
ss-s
ectio
nal s
olid
s ho
ld-u
p, (
1-ε)
3.2 Gas-solids two-phase flows Experiments were carried out by Gyenis et al. [12]
in a concurrent downward gas-solids two-phase f lowin a test device where the f low rates of both phasescould be controlled more or less independently. Byincreasing the gas f low rate, the mass f low rate andthus the solids hold-up could be enhanced consider-ably, which is generally beneficial to the performance
of in-line mixers and other operations by effective gas-solids contacting.
Motionless mixers can also be applied in counter-current gas-solids two-phase f low for more effectivephase contacting. It is known that f luidized bedprocesses often use various types of inserts in theparticle bed to improve the f luidization behavior [33].Motionless mixers can replace the usual inserts,favorably inf luencing the minimum f luidization gasvelocity, solids hold-up, and heat and mass transferbetween the phases by enhancing the relative veloci-ties and avoiding f luidization abnormalities.
4. Other Applications in Bulk Solids Handling
4.1 Improvement of Bulk Solids Flow andReduction of Bulk Volumes
In handling bulk solids, motionless mixers are wellsuited to eliminate problems in the bulk solids f low,and to decrease the bulk density in storage and trans-port.
In silos, inserts are frequently used to enhance f lowuniformity in space and/or time [34], avoiding pulsa-tion and bridging, which may totally stop the f low.Concentric, inverted or double cones, slanted platesor rods are frequently used for this purpose. In thisway, funnel f low can be transformed to mass f low,avoiding segregation during discharge. For this pur-pose, various forms of motionless mixers can also beused, but before their application, careful design workis necessary with preliminary investigation of mater-ial properties and its f low behavior through themotionless mixers to avoid potential troubles.
According to our experiences, motionless mixers ingravity tubes make the f low of fine powders more sta-ble, even if they are cohesive to some extent, such asf lour or ground coffee. It should be noticed, however,that this is true only for continuous or non-inter-rupted f lows. If continuous discharge is stopped, trou-bles can arise in re-starting the f low. This difficultycan be avoided by applying quasi-motionless mixers,connected to each other elastically, joining them bysprings, thus making the individual mixer elementsmobile to a certain extent [35]. Stresses inside thebulk solids column cause some passive movements ofthe mixer elements, which is enough to start or to sta-bilize the f low, therefore avoiding choking.
In loading a container, silo, truck or railroad boxcarfrom a spout or hopper, the bulk volume of solids mayexpand. Therefore, during storage or transportation,a considerable part of the available space is occupiedby air. However, if particulate materials are passed
KONA No.20 (2002) 19
Fig. 7 Residence time distribution curves obtained with Kenics-type motionless mixers in different f low regimes(a) 1st f low regime, (b) 2nd f low regime, (c) 3rd f low regime
3rd f low regime
0,0 1,0 2,0 3,0 4,0 5,0 6,0Residence time, τ
3,0
2,5
2,0
1,5
1,0
0,5
0,0
Freq
uenc
y, f(
τ)
without motionless mixer, G2000 kg/hl/d2, G1760 kg/hl/d1.5, G470 kg/hl/d1.5, G1700 kg/hl/d1, G700 kg/h
2nd f low regime
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0Residence time, τ
3,0
2,5
2,0
1,5
1,0
0,5
0,0
Freq
uenc
y, f(
τ)
without motionless mixer, G2000 kg/hl/d2, G2300 kg/hl/d1.5, G1500 kg/hl/d1, G950 kg/h
1st f low regime
3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0Residence time, τ
(a)
(b)
(c)
3,0
2,5
2,0
1,5
1,0
0,5
0,0
Freq
uenc
y, f(
τ)
no mixer, G830 kg/hl/d2, G830 kg/hl/d1, G710 kg/h
through motionless mixers, the expansion of bulk vol-ume can be reduced by 20-40 percent compared toloading via plain tube, as was proven by experimentswith wheat grains [36]. When bulk solids, which wereexpanded already, are passed through motionlessmixers, absolute reduction can also be achieved. Bythis method, as much as 4-10 percent more bulksolids can be stored or transported in a given volumeof a container or ship. To this end, motionless mixerelements should be well designed to avoid attrition orbreakage of the grains or particles.
4.2 Coating, Size Enlargement, Size ReductionMotionless mixers are applicable not only to blend
particulate solids, but also to contact different parti-cles effectively with each other. In a suitably designedgravity mixer tube supplied continuously with twoparticulate solids differing in size, a coating of the big-ger particles with the smaller ones can be realized ifsuitable binding material is also supplied. Gyenis etal. [37, 38] reported on a coating process of jellybon-bons with crystalline sugar, applying motionlessmixers. Similar equipment was used for coatingammonium nitrate fertilizer granules with limestonepowder to avoid sticking during storage. Granulationor controlled agglomeration of particulate solids isalso conceivable by this method, but a crucial point isto ensure proper conditions to avoid sticking of solidsor deposition of the binding material onto the surfaceof the mixers. Disintegration or size reduction, as wellas controlled attrition [39], can also take place duringinteraction between the particles and motionless mix-ers, especially at higher velocities ensured by gas-solids two-phase f lows.
4.3 Applications in Pneumatic ConveyingAs was mentioned above, concurrent gas-solids
f low in vertical tubes containing motionless mixersincreases the f low rate and solids hold-up, alsoenhancing the mixing process compared to simplegravity f lows of particles [12]. Because of the retain-ing effect of motionless mixers, the velocity differ-ence between the phases and also the residence timeof the particles can be increased considerably, com-pared to a plain tube. Such conditions are favorablefor heat and mass transfer processes or chemicalreactions in gas-solids contactors, thus decreasing thenecessary dimensions. This makes the realization ofvarious operations during pneumatic conveying [39]conceivable. But for this, carefully planned pilot-scaleexperiments and caution in design are needed toavoid troubles, e.g. choking or damage of the parti-
cles.Motionless mixers may be useful tools in pneumatic
conveying lines, e.g. in horizontal tube sections. DEMsimulation studies revealed that particles that tendedto settle downwards could be re-dispersed into thegas stream again by suitably designed motionlessmixer elements [23, 40]. This may reduce the salta-tion velocity, thus diminishing the required gas f lowrate. By using motionless mixers, a given section ofpneumatic conveying system can also serve as aneffective gas-solids contactor, too, or to realize othertypes of solids treatments simultaneously with con-veying. Caution and preliminary experiments men-tioned above are also recommended here.
4.4 Heat Treatment of Particulate SolidsHeat transfer processes in particulate solids can be
improved by motionless mixers built in a cooler orheater, due to the multiple transmissions of particlesfrom the bulk material to the heating or cooling sur-face and back. In some cases, heat-transmitting tubesor lamellas themselves, arranged, e.g. in a hopper,can modify the f low pattern of the solids, similarly tomotionless mixers.
Very often, heat treatment is carried out in rotaryheater or kiln, as is frequently used in the cementindustry or, in smaller dimensions, in food process-ing. Motionless mixers fixed inside a rotating unit,shown in Fig. 8, enhance the heat transfer betweenparticles and a streaming gas, or between the par-ticles and the heated surface, as was patented byBucsky et al. [41]. It also ensures uniform tempera-ture distribution throughout the cross-section of theparticle bed, which is of crucial importance in thetreatment of heat-sensitive materials. Such a device isalso applicable for drying particulate solids.
20 KONA No.20 (2002)
motionlessmixersgas
out
hot gas inroastedproductout
grains in
Fig. 8 Rotary heater with motionless mixers to roast agriculturematerials
4.5 DryingGodoi et al. [42] used a vertical tube equipped with
helical motionless mixers with perforations on theirsurface for the continuous drying of agriculturalgrains. The particulate materials to be dried were fedcontinuously at the top, and slid or rolled down a-long the surface of the mixer elements. Heated gasstreamed up along the f low channel between themixer elements and through their perforations. Dueto the interactions between the grains, the motionlessmixers and the gas, an effective mass and heat trans-fer was achieved. The rotary equipment in Fig. 8 alsocan be used for such a purpose.
4.6 Dust SeparationMotionless mixers are applicable for the separation
of particles from gases. The dust or volatile solidscontent of hot industrial gases often causes troublesin pipeline operation due to deposition onto the tubewall, especially at critical sections. Based on labora-tory- and pilot-scale experiments, Ujhidy et al. [43]described a new gas purification method and equip-ment applying helical motionless mixers shown inFig. 9. Solid particles are captured by a liquid filmtrickling down along the surface of mixer elements,totally avoiding plugging and thus extra maintenanceof the gas pipeline system. Applying proper condi-tions, i.e. optimal superficial gas velocity and suitablemotionless mixer geometry, the dry separation ofsolids is also feasible, especially above one hundredor several hundred microns particle size. This effectis due to the centrifuging and collision of particleswith the motionless mixers.
Concluding Remarks
As was seen from this review, motionless mixersare useful tools for process improvements: not onlyfor f luid treatments, but also in bulk solids technolo-gies. In this latter field, the most detailed knowledgeis available in bulk solids mixing, discussed in a greatnumber of papers. Investigations started more thanthirty years ago, elucidating the kinetics and mecha-nisms of this operation, mainly in gravity mixingtubes, but also in a special alternatively rotating bulksolids mixer. Modeling and simulations helped tounderstand experimental findings and to predict thebehavior and results of such equipment.
Particulate f lows in motionless mixer tubes showexiting phenomena which greatly inf luence theprocesses taking place in these devices. Other appli-cations such as to improve the bulk solids f low intubes, chutes and silos, or to reduce the bulk volumeexpansion led to significant results. In gas-solids two-phase f lows, namely in pneumatic conveying andsimultaneous treatment of bulk solids, their use offersnew possibilities for realization and process improve-ment. Coating, size enlargement, size reduction andattrition, heat treatment, drying, wet dust removaland dry particle separation are also promising fieldsof applications.
Acknowledgement
The author wishes to acknowledge the support ofthe Hungarian Scientific Research Fund (OTKAT29313).
Nomenclature
d diameter or width of motionless mixer element m
K ′ax axial dispersion coefficient, Eqn.6 m2/sKm kinetic constant of mixing Ks kinetic constant of segregation Lmix total length of the studied mixer section mL length, measured from the inlet ml length of one motionless mixer element ml/d length-to-diameter ratio of a motionless
mixer element M degree of mixedness, defined by Eqn.2
[15, 16] s estimated standard deviations of sample
concentrations taken from a mixture s0 estimated standard deviations of sample
concentrations taken in a totally segregated
KONA No.20 (2002) 21
Slurry collecting basin
Dusty gas inlet
Purified gas outlet
Slurry outlet
Droplet separationunit with motionlessmixers
Dust separationtubes with wettedmotionless mixers
Washing liquid inlet
Fig. 9 Dust removal unit applying motionless mixers
state xi mass fraction of the tracer particles within
the i-th sample taken at the outlet of the mixer tube
Pe′ apparent Peclet number, Eqn.5 m2 second central moment of the residence
time distribution of the tracer particles, Eqn.3 s2
ti the residence time of tracer particles within the i-th sample s
t— the mean residence time of all tracer particles in the mixer tube, Eqn.4 s
Φ segregation potential [14]
Bibliography
1) Pattison D, A.: Motionless Inline Mixers Stir Up BroadInterest, Chem. Eng., May 19, 1969, 94-96.
2) Wang R, H.; Fan L, T.: Contact Number as an Index ofTransverse Mixing in a Motionless Mixer, ParticulateScience and Technology, 1, 1983, 269-280.
3) Chen S, J.; Fan L, T.; Watson C, A.: The Mixing of SolidParticles in a Motionless Mixer A Stochastic Approach,AIChE J., 18 (5), 1972, 984-989.
4) Chen S, J.; Fan L, T.; Watson C, A.: Mixing of Solid Par-ticles in Motionless Mixer Axial-Dispersed Plug-FlowModel, Ind. Eng. Chem. Process Des. Develop., 12 (1),1973, 42-47.
5) Fan L, T.; Chen S, J.; Eckhoff N, D.; Watson C, A.: Evalu-ation of a Motionless Mixer Using a Radioactive TracerTechnique, Powder Technol., 4 (6), 1971, 345-350.
6) Lai F, S.; Fan L, T.: A Study on the Mixing of Flour in aMotionless Sulzer (Koch) Mixer Using a RadioactiveTracer, Powder Technol., 13 (1), 1975, 73-83.
7) Wang R, H.; Fan L, T.: Axial Mixing of Grains in aMotionless Sulzer (Koch) Mixer, Ind. Eng. Chem.,Process Des. Dev., 15 (3), 1976, 381-388.
8) Fan L, T.; Gelves-Arocha H, H.; Walawender W, P.; Lai F,S.: A Mechanistic Kinetic Model of the Rate of MixingSegregating Solid Particles, Powder Technol., 12 (2),1975, 139-156.
9) Lai F, S.; Fan L, T.: Application of a Discrete MixingModel to the Study of Mixing of Multicomponent SolidParticles, Ind. Eng. Chem. Process Des. Dev., 14 (4),1975, 403-411.
10) Boss J.; Knapik A, T.; Wegrzyn M.: Segregation of Het-erogeneous Grain System during Mixing in Static Mix-ers, Bulk Solids Handling, 6 (1), 1986, 145-149.
11) Boss J.; Wegrzyn M.: The Effect of the Tracer ParticlesDistribution on the Equilibrium Degree of Mixture,Powder Handling and Processing, 3 (3), 1991, 253-255.
12) Gyenis J.; Arva J.; Nemeth L.: Steady State ParticleFlow in Mixer Tubes Equipped with Motionless MixerElements, Industrial Mixing Technology: Chemical andBiological Applications. Eds.: Gaden E. L; Tatterson G.B., AIChE Symp. Ser. Vol. 90, New York, 1994, 144-160.
13) Gyenis J.; Arva J.: Improvement of Mixing Rate ofSolids by Motionless Mixer Grids in Alternately Re-volving Mixers, Powder Handling and Processing, 1 (2),1989, 165-171.
14) Gyenis J.: Segregation-Free Particle Mixing, Handbookof Powder Technology, Vol. 10 [Eds. A. Levy and H.Kalman]. Elsevier, Amsterdam-Tokyo, 2001, 631-645.
15) Fan L, T.; Wang R, H.: On Mixing Indices, Powder Tech-nol., 11, 1975, 27-32.
16) Rose H, H.: A Suggested Equation Relating to the Mix-ing of Powders and its Application to the Study of Per-formance Certain Types of Machines, Trans. Instn.Chem. Engrs., 37 (2), 1959, 47-56.
17) Gyenis J.; Nemeth J.; Arva J.: Gravity Mixing of SolidParticle Systems in Steady State Static Mixer Tubes,Swiss Chem., 13 (5), 1991, 51-55.
18) Wang R, H.; Fan L, T.: Stochastic Modeling of Segrega-tion in a Motionless Mixer, Chem. Eng. Sci., 32, 1977,695-701.
19) Gyenis J.; Blickle T.: Simulation of Mixing During Non-Steady State Particle Flow in Static Mixer Tubes, ActaChimica Hungarica Models in Chemistry, 129 (5),1992, 647-659.
20) Gyenis J.; Katai F.: Determination and Randomness inMixing of Particulate Solids, Chem. Eng. Sci., 45 (9),1990, 2843-2855.
21) Gyenis J.; Diaz E.: Simulation of the Stochastic Behaviorduring Bulk Solids Mixing, Proc. 5th World Congress ofChemical Engineers, San Diego, CA, U.S.A. July 14-18,1996, 321-326.
22) Mihalyko Cs.; Mihalyko E, O.: A Double StochasticModel of the Mixing of Solid Particles, Handbook ofPowder Technology, Vol. 10 [Eds. A. Levy and H.Kalman]. Elsevier, Amsterdam-Tokyo, 2001, 659-664.
23) Szepvolgyi J.: Lagrangian Modelling of ParticulateFlows in Static Mixer Tubes, Ph.D. Theses, Universityof Veszprem, 1999. p. 119.
24) Herbig R.; Gottschalk I.: Mixing of Segregating SolidParticles in a Static Mixer, J. Powder and Bulk SolidsTechnol., 10 (2), 1986, 7-12.
25) Gyenis J.; Arva J.: Mixing Mechanism of Solids in Alter-nately Revolving Mixers I. Change of the Local Concen-trations and Concentration Profiles, Powder Handlingand Processing, 1 (3), 1989, 247-254.
26) Gyenis J.; Arva J.: Mixing Mechanism of Solids in Alter-nately Revolving Mixers II. The Role of Convection andDiffusion Mechanisms, Powder Handling and Process-ing, 1 (4), 1989, 365-371.
27) Gyenis J.; Nemeth J.: Power Consumption of an Alter-nately Revolving Bulk Solids Mixer, Hung. J. Ind.Chem., 19, 1991, 69-73.
28) Gyenis J.; Arva J.; Nemeth J.: Mixing and Demixing ofNon Ideal Solid Particle Systems in Alternating BatchMixer, Hung. J. Ind. Chem., 19, 1991, 75-82.
29) Bauman I.: Solid-Solid Mixing with Static Mixers,Chemical and Biochemical Engineering Quarterly, 15(4), 2001, 159-165.
30) Supplemental Specification of the Standard Specifica-
22 KONA No.20 (2002)
tion for Road and Bridge Construction. State of Ten-nessee. Section 900. March 3, 1995. Sheet of 5 of 19.
31) Gyenis J.: Strömungseigenschaften von Schüttgüternim statischen Mischrohr, Chem.-Ing.-Tech. 64 (3), 1992,306-307.
32) Nemeth J.; Gyenis J.; Nemeth J.: Gravity and Gas-SolidFlow in Static Mixer Tubes, PARTEC 95, Preprints of3rd European Symposium Storage and Flow of Particu-late Solids (Janssen Centennial), 21-23 March 1995,Nürnberg, 459-467.
33) Hilal N.; Ghannam M, T.; Anabtawi M, Z.: Effect of BedDiameter, Distributor and Inserts on Minimum Fluidiza-tion Velocity, Chem. Eng. Technol., 24 (2), 2001, 161-165.
34) Yang S, C.; Hsiau S, S.: The Simulation and Experimen-tal Study of Granular Materials Discharged from a Silowith the Placement of Inserts, Powder Technology, 120(3), 2001, 244-255.
35) Bucsky Gy.; et al.: Method and Equipment for Mixing ofContinuous Streams of Particulate Materials, Hung. Pat.No. 22/90, 1990. (in Hungarian)
36) Chen S, J.; Fan L, T.; Chung D, S.; Watson C, A.: Effectof Handling Methods on Bulk Volume and Homogene-ity of Solid Materials, J. Food Science, 36, 1971, 688-691.
37) Gyenis J.; Farkas I.; Németh J.; Hollósi S.: Energy Sav-
ing Coating of Grains with Smaller Particles, MagyarKemikusok Lapja, 44 (1), 1989, 16-21. (in Hungarian)
38) Gyenis J.; Arva J.; Nemeth J.: Coating of Grains withFine Particles, Preprints of 9th International Congress ofChemical Engineering, CHISA’ 87, Prague, 30 August 4 September, 1987, 1-10.
39) Kalman H.: Personal communications.40) Gyenis J.; Ulbert Zs.; Szepvolgyi J.; Tsuji Y.: Discrete
Particle Simulation of Flow Regimes in Bulk Solids Mix-ing and Conveying, Powder Technol., 104, 1999, 248-257.
41) Bucsky Gy.; et al.: Method and Equipment for Continu-ous Gentle Heat Treatment of Heat Sensitive ParticulateMaterials, Hung. Pat. No. 209 661 A, 1995, 1-7. (in Hun-garian)
42) Godoi L, F, G.; Park K, J.; Alonso L, F, T.; Correa W, A,Jr.: Particle Flow in an Annular Static Mixer Dryer,Proc. 5th World Congress of Chemical Engineers, Vol.VI, 14-18 July 1996, San Diego, CA, U.S.A., 356-361.
43) Ujhidy A.; Bucsky Gy.; Gyenis J.: Application of Motion-less Mixers in Gas Purification A Case Study, Proc.Joint Symposium (Korea/Hungary) on Energy andEnvironmental Technology for 21st Century, November16, 2001, Taejon, Korea, 3-15.
KONA No.20 (2002) 23
Author’s short biography
Janos Gyenis
Professor Janos Gyenis graduated in Chemical Engineering at the University ofVeszprem, Hungary. He received Dr. Habil and Ph.D. degrees at the Technical Uni-versity of Budapest, and a D.Sc. title at the Hungarian Academy of Sciences. Atpresent, he is a full professor at the University of Kaposvar, Department of Engi-neering, and director of the Research Institute of Chemical and Process Engineer-ing. Since 1971, he has been involved in a number of collaborative research workswith leading laboratories and university departments in Europe, the United Statesand Asia. He is now working with the mixing and f low of particulate solids and theapplication of motionless mixers for various purposes. Up to now, he has publishedabout 120 papers and he is co-inventor of 22 patents.
24 KONA No.20 (2002)
1. Introduction
Nanomaterials and ultra-thin functional coatings ofnanoparticles will determine the utility of many prod-ucts in the future: superhard materials and superfastcomputers, dirt-repellent surfaces and new cancertreatments, scratch-proof coatings and environmen-tally friendly fuel cells with highly effective catalysts.The market for products manufactured by nanotech-nology is already registering double-digit growthrates and will amount to hundreds of billions US$ by2002.
Nanoparticles are at the core of this technology.These are particles ranging in size from 1 millionth to100 millionths of a millimetre more than 1,000 timessmaller than the diameter of a hair. In this order ofmagnitude, it is not only the chemical compositionbut also the size and the shape of the particles thatdetermine their properties. Optical, electric and mag-netic properties, but also hardness, toughness orthe melting point of nanomaterials dif fer substantial-ly from the properties of the macroscopic solids.
Table 1 gives an overview of effects associated withdecreasing particle size.
Degussa possesses many years of experience in themanufacture and marketing of extremely fine pow-ders. Examples are the pyrogenic silica (AEROSIL®),titania, alumina and industrial carbon black. Fumed
A. Gutsch, M. Krämer, G. Michael, H. Mühlenweg, M. Pridöhl and G. ZimmermannDegussa AGProject House Nanomaterials*
Gas-Phase Production of Nanoparticles†
Abstract
Gas-phase synthesis is a well-known chemical manufacturing technique for an extensive variety ofnano-sized particles. Since the potential of ultra-fine and especially nano-sized particles in high-per-formance applications has been identified, the scientific and commercial interest has increasedimmensely, disclosing this field as a most important technology of the future.
The paper will present the basics of the gas-phase synthesis and particle formation process includ-ing the relation between the principal process conditions and the product characteristics.
Moreover, several reactor technologies such as f lame, hot-wall, plasma and laser reactors will beintroduced and their specific advantages will be pointed out. Precise process control is crucial inorder to meet stringent specifications regarding the particles’ chemical composition and morphology.
In addition, the paper will deal with some special nanoscaled gas-phase products of high innova-tive potential and their functional contribution in various applications.
* Rodenbacher Chaussee 4, 63457 Hanau, Germany† Accepted: June 28, 2002
The smaller the particles, the ...
• higher the catalytic activity (Pt@Al2O3)
• higher the mechanical reinforcement (carbon black in rubber)
• higher the electrical conductivity of ceramics (CeO2)
• lower the electrical conductivity of metals (Cu, Ni, Fe, Co, Cualloys)
• initially increasing and later decreasing magnetic coercivity,finally superparamagnetic behaviour (Fe2O3)
• higher the hardness and strength of metals and alloys
• higher the ductility, hardness and formability of ceramics; thelower the sintering and superplastic forming temperature ofceramics (TiO2)
• higher the blue-shift of optical spectra of quantum dots (quan-tum confinement of Si)
• higher the luminescence of semiconductors (Si, GaAs,ZnS:Mn2)
Table 1 General effects of decreasing particle size.
KONA No.20 (2002) 25
silica, for which Degussa is the world market leader,is used in particular as a reinforcing filler in siliconerubber and to control the rheology of coatings andcolorants. Industrial carbon black, in which Degussaranks second in the world, is used particularly in thetyre industry and as a pigment in printing inks, coat-ings and plastics.
In industrial products, primary nanoscale particlesare normally not isolated but build up aggregates andagglomerates. In aggregates, the primary particlescontact each other at surfaces or edges and as arule they cannot be broken down further by shearforces applied in the application. Agglomerates areformed when aggregates and/or primary particlescontact each other at points. If nanoparticles are dis-persed in a liquid, the agglomerates are destroyedand the surface chemical groups of the aggregatesinteract with each other (see Fig. 1).
Fig. 1 Interaction of aggregates (schematically).
Parameter to control aggregate size Application effects
residence time
pressure
loading rheology
nature of precursor optical effects
thermal treatment reinforcement
densification scratch resistance
surface chemistry
structure modification
dispersing energy
Table 2 Morphology control parameters and resultant effects inthe application.
In the case of fumed silica, this affinity is attributedto the hydrogen bridge linkages and results in a tem-porary, three-dimensional lattice structure becomingmacroscopically “visible” in the form of thickeningand thixotropy. To control the application behaviouroften means to generate tailor-made aggregates witha tailor-made surface chemistry. In Table 2, someparameters during and “after” production are shownwhich have an inf luence on the aggregates andhereby also an inf luence on the application effects.
2. Project House Nanomaterials
2.1 Scope and structureDegussa utilises the know-how from years of expe-
rience and the resultant market knowledge to developthe global, technology- and innovation-driven marketfor nanoscale materials.
This is done in the research groups of the businessunits Silica & Silanes and Advanced Fillers & Pig-ments, which are focusing on developing new or im-proved types of fumed silica, titania, alumina, carbonblack and dispersions thereof.
The Project House Nanomaterials was created todevelop new nanomaterials and also new gas phaseprocesses. To this end, an interdisciplinary team withexperienced people from different business units wasformed. Chemists, materials scientists, process engi-neers and industrial management experts from theProject House Nanomaterials develop together withcustomers and universities innovative technologiesand novel nanoscale materials such as special types ofcarbon black, zirconia, indium tin oxide, zinc oxide,ceria and superparamagnetic composite materials.Some examples are described in Chapter 5.
These new materials are manufactured in the gasphase at temperatures up to 10,000 K. The manufac-turing process and conditions determine size andmorphology of the particles and hence their applica-tion properties. Seven new pilot plants have been builtcomprising three f lame reactors, two hot-wall reac-tors, a plasma reactor, and very new, a laser evapora-tion reactor. They are described in detail later on (seeChapter 4). One special feature of the Project HouseNanomaterials is the close cooperation both withpotential customers and with academia, the latter pro-viding results from fundamental research. Some pro-jects carried out together with the universities aredescribed in the following section.
2.2 Cooperation with universitiesThe Project House Nanomaterials has nine cooper-
Staupendahl from the University of Jena. See Chapter4.4. for details.
Prof. Ebert evaluates the feasibility of an adiabaticquench system in the low-pressure f lame reactor torapidly cool particle-gas mixtures by adiabatic expan-sion. This system also affects particle morphology.
Prof. Fissan further develops his SMPS (scanningmobility particle sizer) with respect to corrosion re-sistance against chlorine-containing atmospheres andoperation of the SMPS connected to reactors, whichare operated at reduced pressure.
Prof. Hahn is checking the scalability of his conceptto synthesise non-aggregated oxidic nanoparticlesusing hot-wall reactor technology at reduced pres-sure. The experiments are done in a dedicated pilotreactor mainly producing SiO2.
Prof. Roth is proving the feasibility of the TEM-gridsampling system to take samples out of running reac-tors. The particles deposited by thermophoresis canbe directly investigated by means of transmissionelectron microscopy (TEM). Thus particle size andmorphology can be correlated with reactor settingsand the particle formation can be monitored as a func-tion of residence time and chemical conversion rate.
3. Gas-Phase Synthesis of Nanoparticles
Although a number of variations exist for gas-phasesynthesis processes, they all have in common the fun-damental aspects of particle formation mechanismsthat occur once the product species is generated [2],[3], [4]. Product quality and application characteris-tics of nanoscaled particles depend strongly on theparticle size distribution and on the morphology ofthe particles, i.e. the size and number of primary par-ticles defining the degree of aggregation. In gas-phase reactors, the final characteristics of particulateproducts are determined by f luid mechanics and par-ticle dynamics within a few milliseconds at the earlystages of the synthesis process. Within this shorttime frame, three major formation mechanisms domi-nate the particle formation.
Chemical reaction of the precursor leads to the for-mation of product monomers (clusters) by nucleationor direct inception, and to the growth of particles byreaction of precursor molecules on the surface ofnewly formed particles; this is called surface growth[5], [6]. Coagulation is an intrinsic mechanism whichinevitably occurs at high particle concentrations andtherefore in all industrial aerosol processes. Particlesdispersed in a f luid move randomly due to Brownianmotion and collide with each other along their trajec-
ation partners from eight universities (see Fig. 2).This tight cooperation is funded by the DeutscheForschungsgemeinschaft, DFG (German ScienceFoundation).
The universities provide state-of-the-art measuringtechnology and the results from their fundamentalresearch in the fields of particle synthesis and pro-cessing, particle characterisation and simulation ofparticle formation. On the other hand, the universitiesare granted access to dedicated pilot reactors to testtheir equipment or to prove their results on larger,industrial-scale equipment. Following are some exam-ples:
Prof. Bockhorn’s aim is to model the formation ofparticles, especially of soot, in f lames. To gather basicinformation on particle formation, he developed theRAYLIX method, which combines laser-induced in-candescence (LII), Rayleigh scattering and extinctionmeasurement, whereas the Rayleigh scattering andthe LII-signal are detected in two dimensions. Thisset-up provides locally resolved information on sootvolume fractions and on the size of the soot particlesin f lames [1].
Prof. Leipertz uses time-resolved laser-inducedincandescence to monitor on-line the average particlesize of just-formed soot particles. Both systems havebeen successfully transferred to monitor the carbonblack formation in a plasma reactor. We also success-fully adapted both systems to monitor the particle for-mation of carbon-free systems such as titania andzirconia in our laser evaporation reactor. This uniquereactor is the result of the cooperation with Dr.
26 KONA No.20 (2002)
Fig. 2 Project partners from universities.
Prof. RothCombustionGas dynamic
Kinetic
Prof. BockhornChemical technology
Flame analytics
Dr. SchmidProcess technology
Sintering
Dr. MoritzCeramics
Granulation
Project HouseNanomaterials
Prof. HahnMaterial ScienceParticle synthesis
Prof. FissanDr. Kruis
Analytic of aerosols
Prof. Ebert/BüttnerProcess technology
Dr. StaupendahlCeramics
Laser ablation
Prof. Leipertz/WillThermodynamics Process analytics
tories. Assuming strong adhesive forces, characteris-tic for small particles, or chemical bonds, these colli-sions result in coagulation [7], [8]. Coalescence andfusion are sufficiently fast in the high-temperaturezones of the reactor to effect a reduction in the levelof aggregation or even the formation of spherical par-ticles due to sintering processes [9], [10]. Figure 3shows the mechanisms’ inf luence on particle forma-tion, growth, and final morphology.
According to these particle formation mechanisms,the product quality can be inf luenced by a sensibleselection of the process parameters. However, linkingprocess parameters such as temperature, reactantstate or reactor geometry to product characteristicsrequires a good understanding of the physico-chemi-cal fundamentals of gas-phase synthesis. Measure-ments in gas-phase reactors are quite problematic astime scales are extremely small, temperatures veryhigh and the gaseous atmosphere is often aggressive.Therefore, process simulation is a useful tool and cansignificantly improve the general understanding ofparticle formation and moreover can support productand process optimisation.
Numerous models based on the so-called particlepopulation balance have been developed and appliedto the simulation of particle formation and growth[11], [12]. A robust and time-efficient model is thesimple monodisperse model developed by Kruis et al.[13], which has been coupled to f luid dynamics(CFD) successfully by Schild et al. [14]. While CFD-coupled simulations of the particle formation revealspecific reactor characteristics, the plain applicationof population balances, i.e. simulations reduced totime-temperature calculations for particle trajectories,is also very helpful in terms of increasing the basicunderstanding of the synthesis process.
As an example, the particle formation in a premixedf lame reactor has been modelled by approximatingthe average time-temperature history of the particles’trajectories. The calculated particle size evolution wasthen compared to experimental data obtained by ther-mophoretic sampling on a TEM grid which enablesdirect measurements of particle sizes and morphol-ogy in the f lame at various distances (residencetimes) from the burner mouth [15]. Figure 4 pre-sents the principle of the sampling device, sectionsof the TEM pictures taken and the correspondingaverage aggregates obtained from simulation. Withincreasing residence time, the expected advancingdegree of aggregation can clearly be seen. Both re-sults, from experiment and simulation, are in excel-lent conformity and validate the simulation technique.
KONA No.20 (2002) 27
4. Reactor Technologies
Researchers of the Project House Nanomaterialshave improved existing processes and developednew technologies for the production of tailor-madenanoscaled materials.
4.1 Flame reactorFlame reactors are one of the most common reactor
designs for the production of high-purity nanoscalepowders in large quantities [16-20]. The capability forfull-production scale has been demonstrated for manymetal oxides such as silica, titania, alumina and oth-ers. Powders, liquids and vapours can be used as pre-cursors. The f lame provides the energy to evaporate
Fig. 3 Formation mechanisms relevant in gas-phase synthesis ofparticles.
Fig. 4 Schematic of the TEM-grid sampling system mounted to af lame reactor, sampled TEM images, and correspondingsimulation results.
Chem. Reaction
Chem. Reaction
Coagulation
Coalescence
burner
TEMgrid
reactor
experimental set-up TEM-images simulation
t20msdprim21.5nmnprim20
t50msdprim21.6nmnprim66
t90msdprim21.6nmnprim114
pneumaticpiston
Surface Growth
Nucleation Inception
the precursors and to drive the chemical reactions.Due to the high energy density in the f lame, the pre-cursor concentration can be quite high. In the flames,temperatures from 1000°C up to 2400°C can be rea-lised. The residence time in the highest temperatureregion is very short and usually ranges between 10and 100 ms. This region is crucial for the formation ofthe primary particles. After this zone only the sizeand the morphology of the aggregates can be inf lu-enced. With f lame synthesis, primary particle sizesfrom a few nm up to 500 nm are accessible. The spe-cific surface areas of these powders can go up to 400m2/g and higher.
The shape of the f lame can be inf luenced by using“premixed” or “diffusion” f lames. In premixed f lamesthe fuel and the air/oxygen are already mixed andthe reaction takes places right at the burner mouth.These premixed f lames are typically very short. Indiffusion f lames the fuel and the air/oxygen are fedseparately to the burner mouth. The reactants have todiffuse together and combust in the diffusion zone[21].
The control of the three reactor parameters tem-perature profile, reactor residence time and reactantconcentration is of great importance to generate tai-lor-made particles. Unfortunately, these parameterscannot be changed in f lame reactors independently.Every adjustment of the feed f low causes a change inall three parameters.
The Project House Nanomaterials runs two f lamereactors (Fig. 5, 6). One of these f lame reactors isespecially designed for low pressures down to pmin20 kPa. The control of the reactor pressure is interest-ing for two reasons: 1. Decreasing the pressure causes a dilution effect,
which allows for the synthesis of less aggregatedparticles.
2. By controlling the pressure one can change theresidence time independently from the f lame tem-perature.
Fig. 7 shows the f low sheet of a f lame reactor.Flame reactors consist usually of the burner, a f lametube, a particle collection unit (e.g. a bag filter) andan off-gas treatment unit (e.g. an alkaline scrubber).
28 KONA No.20 (2002)
Fig. 5 Low-Pressure Flame Reactor.
Fig. 6 Flame Reactor.
Product
BurnerT1000-2400°Cp20-100kPa
Filter
PRECURSOR
FUELAIR
VacuumPump Off-
gas
Scrub-ber
Fig. 7 Flow sheet of a f lame reactor.
4.2 Hot-wall reactorHot-wall systems employ tubular furnace-heated
reactors for initiating the synthesis reaction [20]. Theconstruction is relatively simple and process parame-ters are moderate in comparison to other gas-phasereactors. Temperatures range below 1700°C, concen-trations are variable, the gas composition is freelyselectable and the system pressure is usually atmos-pheric but can also be used as a process parameter.The technique allows for precise process control andtherefore allows for particle production with specificcharacteristics. Due to their high energy require-ments, hot-wall systems have mainly been investi-gated on a lab scale. But there are also industrialapplications. One important example is the produc-tion of Al-doped TiO2 as a pigment. Precursors thatare most often used for particle formation are metalchlorides and organometallic precursors. The mixingof the reactants and the carrier gas is, besides theabove-mentioned process parameters, the most im-portant instrument for controlling product character-istics. A variety of mixing arrangements has beeninvestigated on a laboratory and industrial scale. Pre-mixed systems, often used on a lab scale, are avoidedin industrial applications as the reactant streamscould react spontaneously before entering the reactor.The feeding location is also crucial. The reactants canbe introduced concurrently at the reactor entrance orsomewhat downstream, thus inf luencing the resi-dence time within the reaction zone. Alternatively, thereactants can be fed separately at different locations,affecting the particle formation mechanisms and en-abling even composites or coated particles.
To summarise, the hot-wall technology involves thefollowing Advantages: Disadvantages:
Figure 8 presents the schematic set-up of a pilot-scale hot-wall reactor developed in cooperation with
the Department of Material Science of the TechnicalUniversity of Darmstadt (Prof. Hahn) and operated atthe Project House Nanomaterials. The hot zone isdivided into three parts, allowing for specific tempera-ture profiles, various precursor feeding locations andalso for product sampling during particle formation.
KONA No.20 (2002) 29
Fig. 8 Schematic of the pilot-scale hot-wall reactor operated bythe Project House Nanomaterials.
Fig. 9 Photograph of the pilot-scale hot-wall reactor operated bythe Project House Nanomaterials.
carrier gas
N2
LPDS
precursor
preheater
furnace
sampling
sampling
sampling
filter
fan
product
quench gas
• often requires volatileprecursors with signifi-cant vapour pressureand stability belowreaction temperature,often resulting in highprecursor costs
• high degree of aggrega-tion at high aerosol con-centrations
• high energy require-ment
• simplicity of design• precise control of pro-
cess parameters andf lexibility with respectto gas composition andsystem pressure
• production of oxides,non-oxides, semicon-ductors and metals inthe range from atomicto micrometre dimen-sions
The carrier gas is preheated and the precursor isvaporised by a commercial liquid precursor deliverysystem (LPDS). Exiting the last furnace section, theaerosol stream is quenched and the powder is col-lected in a bag filter. So far, the pilot plant has beeninvestigated intensely for the production of tailor-made silica particles and will be tested for mixedmetal oxides in the near future (Fig. 9).
4.3 Plasma reactorThermal or hot plasmas are in or close to the local
thermodynamic equilibrium, i.e. the temperature ofheavy species in the plasma and the temperature ofthe electrons are mostly identical. Hot plasmas arecharacterised by a high electron density of 10211026
m3. These plasmas can be generated by gaseous dis-charge between electrodes, by microwaves, by laseror high-energy particle-beams or by electrodeless ra-dio frequency (RF) discharge. An RF discharge canbe maintained either by capacitive or by inductivecoupling. The most widely used electrical methodsfor producing plasmas are high-intensity arcs andinductively coupled high-frequency discharge. An in-ductively coupled high-frequency discharge is main-tained by a time-varying magnetic field operated at 3MHz to 30 MHz [22].
Today, the plasma deposition of coatings and filmsby plasma spraying, thermal plasma chemical vapourdeposition (TPCVD) and thermal plasma physicalvapour deposition (TPPVD) is quite common. Theproduction of nanoparticles by means of thermal plas-ma is a less evaluated field. One investigated exampleis the production of carbon black by means of high-intensity arc plasmas [23].
The electrodes necessary for arc discharge are typ-ically made from thermally quite stable graphite.They are nevertheless eroded or evaporated within ashort time, thus polluting the desired product. Toavoid product contamination, plasma processes whichdo not use electrodes can be used, e.g. „cold“ micro-wave plasma or the thermal RF plasma. But the mi-crowave plasma requires reduced pressure, thusstrongly limiting production rate and particle temper-ature. Therefore we started to evaluate the nanoparti-cle synthesis by means of an inductively coupledplasma. Due to the missing electrodes, contaminationin the product can be minimised.
Our high-frequency plasma reactor is operated atnormal pressure with a frequency of 34 MHz, pro-viding 40 kW of thermal power (efficiency 3040%)and yielding locally up to 10 000 K. Particles are col-
lected by means of a cyclone or a filter, the waste gascan be washed with alkaline or acidic solutions. Up to6 Nm3/h of typical plasma gases such as nitrogen orargon as well as air can be used; solid, liquid orgaseous precursors can be fed up- or downstream ofthe plasma f lame. The residence time in the hot zoneis less than 1 s; cooling rates of 106109 K/s are fea-sible. Depending on the gas composition the pre-cursors are physically or chemically converted tonanoparticles. The reactor set-up and a picture there-of are given in Figures 10 and 11.
4.4 Laser reactorIn cooperation with the German Science Founda-
tion (DFG) and the University of Jena, the Project
30 KONA No.20 (2002)
Fig. 10 Plasma reactor set-up.
Fig. 11 Plasma reactor during operation.
Waste gas
Waste water
Waste gastreatment
Blower
Filter
Reactor
Cooling gas
Plasma gas
Plasma burner
Samplingdevice
Frequencygenerator
Cyclone
Product
Precursor
150kVA
NaOH
House Nanomaterials has built a pilot-scale laser evap-oration reactor (see Fig. 12 ab). The reactor is ascale-up of the reactor from the University of Jena[24, 25] and features three CO2 lasers of 2 kW laserpower each at a wavelength of 10.59 mm, a reactionchamber and a product separation unit. Figure 13shows the schematic process f low diagram. The laser
beams are directed and focused into the reactionchamber, resulting in an intensity of 6 kW in a volumeof only a few cubic millimetres. This high-intensityvolume is located in the centre of the reaction cham-ber where the precursor, typically a coarse metaloxide powder, is f luidised. The gas-dispersed precur-sor powder is evaporated by the focused laser, andnanopowder is formed by condensation of thevapours. Figure 14 is the view into the reactor dur-ing operation. The so-formed particles are separatedfrom the gas stream by conventional filtration meth-ods. Figure 15 shows a TEM image of laser-synthe-sised particles.
The high-power intensity of the laser opens a widefield of solid precursor options having high vaporisa-tion temperatures, e.g. ceramics and metal oxides,which are not suitable for the synthesis of nanoscaledpowders by standard gas-phase processes. Due to the
KONA No.20 (2002) 31
a) Laser unit with reaction chamber to the right and filter to the left.
b) Reaction chamber.
Fig. 12
Fig. 13 Schematic process f low diagram of the laser reactor.
Fig. 14 Focus zone during operation.
Fig. 15 TEM image of laser-synthesised particles.
Product
Filter
Blower
Air
Precursor
Lasergas(He, N2, CO2)
Resonator
ReactionChamber
CycloneLaser beam
32 KONA No.20 (2002)
high cooling rates, the morphologies of the laser-synthesised particles differ significantly from typicalpyrogenic oxides, which opens new fields of potentialapplications.
5. Products New Pyrogenic Oxides
5.1 ZirconiaThe production of pyrogenic oxides by means of
f lame hydrolysis of metal chloride vapours is wellknown. Degussa has been using this approach success-fully for decades producing, e.g. silica (AEROSIL®),alumina and titania. The synthesis of pyrogenic zirco-nia via the chloride route on a large scale is difficultand very costly. The chloride precursors make highdemands on the materials of construction for thereactors, especially for the evaporation unit. Further-more, the chloride in the product hinders its suitabil-ity toward several potential fields of applications.To reduce the chloride in the powder, a lot of efforthas to be put into the process. One cannot use exces-sive temperatures for the deacidification becausehigh temperature equals loss of specific surface area(BET). To overcome all these disadvantages, a newprocess was developed for the production of low-chloride (500ppm) high-BET (30m2/g) zirconia.In contrast to the existing chloride route, the newgas-phase process is based on metallorganic or non-chloride salt solutions.
The process uses a f lame spray pyrolysis techniqueto yield nanoscaled high-purity (mixed) metal oxides.The precursor is sprayed into a f lame reactor wherethe conversion into the oxide material takes place fol-lowed by the particle separation. Variations in the
time-temperature history of the particles in the com-bustion zone and the spraying parameters result indifferent product grades, e.g. specific surface area(BET). With this reactor set-up, various metal oxidesand mixed metal oxide nanopowders are accessible.Zirconia and different yttrium-stabilised forms thereof(YSZ) but also indium tin oxide (ITO), alumina, etc.have been synthesised in the pilot-scale reactor. Fig-ure 16 shows a TEM image of ZrO2 with a BET of 74m2/g. In Table 2 typical physico-chemical data ofZrO2 and YSZ are listed. As the average primary parti-cle size is in the 12-nm region, the sintering processstarts at low temperatures (see also Fig. 17).
There are various applications for high-puritynanoscaled ZrO2, e.g. dental, catalysts, ceramic mem-branes, thermal barrier coatings, gas sensors, opticalconnectors and polishing agents.
Fig. 16 TEM image of EP Zirconium Dioxide PH with a BET of74 m2/g.
Properties Units ZrO2 YSZ
Specific surface area (BET) m2/g 4575 4575
Tapped density (approx. value) g/l 100 100
Moisture % 2.0 2.0
Ignition loss % 3.0 3.0
pH-value 4.0 6.0 4.0 6.0
Y2O3 content (based on ignited material) % 5
HfO2 content (based on ignited material) % 1.02.5 1.02.5
ZrO2 content (based on ignited material) % 97.0 92.0
HCl content (based on ignited material) % 0.05 0.05
Average primary particle size nm 12 12
Table 3 Typical physico-chemical data of EP Zirconium Dioxide PH (ZrO2) and stabilised EP Zir-conium Dioxide 3-YSZ.
100 nm
KONA No.20 (2002) 33
5.2 Indium tin oxideFor the production of transparent electrically con-
ductive polymer composites, nanoscaled indium tinoxide (ITO) is being developed for use as a raw mate-rial. The ITO nanoparticles should be characterisedby the following parameters:
• Colourless or slightly blue• Specific resistance: 102108 Ωcm• Average primary particle size: 20 nm• Aggregate size: 100 nm• Good dispersibility• Anisotropic self-organisation in the matrix
Such an ITO can be produced by spray pyrolysis(see Figure 18). It was demonstrated that the con-ductivity could be clearly improved by doping theITO samples. Therefore the technical term DITO(doped indium tin oxide) is reasonable and may beapplied. Under optimal circumstances it is possible to
reduce the specific resistance from 660 cm to 400cm with DITO. Further post-treatment additionallyreduces the resistance to 10 cm, whilst BET surfacearea remains constant. The colour of the material canalso be controlled by the addition of certain dopants.
5.3 Superparamagnetic nanocompositesSuperparamagnetic nanocomposites show the char-
acteristic magnetic properties of paramagnetic as wellas of ferromagnetic materials. Like paramagnets, thesematerials possess no permanently aligned structureof the elementary magnetic dipoles when no mag-netic field is applied. Otherwise, the shape of themagnetisation curve looks like a ferromagnetic curvewithout hysteresis (see Fig. 19). Nanoscale magneticparticles display this superparamagnetic behaviourbecause the tiny magnetic domains are small enoughto immediately become disordered due to entropy[26, 27].
A TEM image of a superparamagnetic material isshown in Fig. 20. Via f lame synthesis, nanoscalediron oxide particles were embedded in an amorphoussilica matrix. The dark dots represent the iron oxidecrystals. The TEM picture indicates that the magneticdomains of iron oxide are well distributed throughthe silica matrix and that they are smaller than 20 nm.These are important requirements to obtain single-domain and well-decoupled magnetic centres.
X-ray diffraction of the produced powders showsmainly the magnetic iron oxide phases magnetite andmaghemite with a low content of non-magnetic hem-atite (Fig. 21). The specific surface area of the com-posite (BET) was varied from 114 m2/g to 214 m2/g
80
70
60
50
40
30
20
10
00 200 400 600 800 1000 1200
2h at temperature °C
Fig. 18 TEM images of ITO (left: powder; right: in a polymer matrix).
100 nm
BE
T m
2 /g
Fig. 17 Sintering behaviour of EP Zirconium Dioxide PH.
by adjusting process parameters. A SQUID magne-tometer was used for magnetic characterisation. Theparticles display superparamagnetic behaviour above50 K and the iron oxide domains are magneticallywell decoupled. The so far highest saturation mag-netisation achieved was 18 Am2/kg.
The advantage of the described superparamagneticnanocomposites is their high chemical, mechanicaland thermal stability, which is often well beyond thatof traditional superparamagnetic materials with organiccoatings.
6. Conclusion
Gas-phase synthesis is a well-known technique forthe production of an extensive variety of nano-sizedparticles. The “original” commercial nanopowdersgenerated by this method comprise the largest shareof the market, e.g. as reinforcing fillers, for rheologycontrol and as pigments. The growing need for multi-functional materials (scratch-resistanttransparent,transparentconductive, etc.) drives the transitionfrom powders to highly specialised functional materi-als.
Based on fundamental research, the detailed analy-sis of particle size and morphology together with agood understanding of the particle formation mecha-nisms, it is possible to design reactors and to pre-cisely control the processes. Results thereof aretechnical innovations consisting of new synthesisroutes and new forms of nanoparticles with custom-tailored characteristics which provide distinct perfor-mance advantages for specific applications.
The development of such technical innovations,however, comprises only the first step of the route tosuccessful commercialisation of new nanoscale prod-ucts. The real challenge lies in the discovery anddevelopment of markets and applications that canbenefit from the technology. In practice, this requiresa focused and dedicated marketing and applied tech-nology effort, coupled with the willingness and abilityto precisely fit your product to the needs of the cus-tomer. Degussa plans to implement such an approachin order to fully realise the commercial potential oftheir innovative nanomaterials and synthesis tech-nologies resulting from their strategic research.
Acknowledgements
The authors want to thank the German ScienceFoundation (DFG) for the financial support and alluniversity partners for the excellent cooperation.
34 KONA No.20 (2002)
Fig. 19 Magnetisation curves of ferro-, para- and superparamag-netic materials.
Fig. 20 TEM of iron oxide/ silica nanocomposite.
Fig. 21 XRD graph of iron oxide/ silica nanocomposite.
400.0
350.0
300.0
250.0
200.0
150.0
100.0
50.0
0.030.0 32.0 34.0 36.0 38.0 40.0 42.0 44.0
Abs
olut
e In
tens
ity
2Theta
HematiteMaghemiteMagnetite
Magnetisation
Magnetic Field
Paramagnetic
Ferromagnetic
Superparamagnetic
α -Fe2O3γ-Fe2O3Fe3O4
KONA No.20 (2002) 35
Nomenclature
BET specific surface area (m2/g)CFD computational f luid dynamicsDFG Deutsche Forschungsgemeinschaft
(German Science Foundation)DITO doped indium tin oxidedprim primary particle diameter (nm)ITO indium tin oxideLII laser-induced incandescenceLPDS liquid precursor delivery systemnprim particle number ()pmin minimum pressure (kPa)RF radio frequencySMPS scanning mobility particle sizerSQUID superconducting quantum interference devicet residence time (ms)T Temperature (°C)TEM transmission eletron microscopyTPCVD thermal plasma chemical vapour depositionTPPVD thermal plasma physical vapour depositionXRD x-ray diffractionYSZ yttria-stabilised zirconia
References
[1] Geitlinger, H.; Streibel, T.; Suntz, R.; Bockhorn, H.:27th Symposium (international) on Combustion/ TheCombustion Institute, 1998, 1613-1621.
[2] Ulrich, G. D.: Theory of Particle Formation andGrowth in Oxide Synthesis Flames, Combustion Sci-ence and Technology, 4, 1971, 47.
[3] Pratsinis, S. E.; Vemury, S.: Particle Formation inGases A Review, Powder Technology, 88, 1996, 267.
[4] Kodas, T. T.; Hampden-Smith, M.: Aerosol Processingof Materials, Wiley-VCH, New York, 1999.
[5] Schaefer, D. W.; Hurd, A. J.: Growth and Structure ofCombustion Aerosols, Aerosol Science and Technol-ogy, 12, 1990, 876.
[6] Pratsinis, S. E.; Spicer, P. T.: Competition between GasPhase and Surface Oxidation of TiCl4 during Synthesisof TiO2 Particles, Chemical Engineering Science, 53,1998, 1861.
[7] Fuchs, N. A.: The Mechanics of Aerosols, PergamonPress, Oxford, 1964.
[8] Hinds, W. C.: Aerosol Technology Properties, Behav-ior and Measurement of Airborne Particles, JohnWiley & Sons, New York, 1999.
[9] Koch, W.; Friedlander, S. K.: The Effect of Particle Coa-lescence on the Surface Area of a Coagulating Aerosol,J. Colloid Interface Science, 140, 1990, 419.
[10] Johannessen, T.; Pratsinis, S. E.; Livbjerg, H.: Computa-
tional Fluid-Particle Dynamics for the Flame Synthesisof Alumina Particles, Chemical Engineering Science,55, 2000, 177.
[11] Ramkrishna, D.: Population Balances Theory andApplications to Particulate Systems in Engineering,Academic Press, 2000.
[12] Mühlenweg, H.; Gutsch, A.; Schild, A.; Pratsinis, S. E.:Process Simulation of Gas-to-Particle-Synthesis viaPopulation Balances: Investigation of Three Models,Chemical Engineering Science, in press.
[13] Kruis, F. E.; Kusters, K. A.; Scarlett, B.; Pratsinis, S. E.:A Simple Model for the Evolution of the Characteristicsof Aggregate Particles Undergoing Coagulation andSintering, Aerosol Science and Technology, 19, 1993,514.
[14] Schild, A.; Gutsch, A.; Mühlenweg, H.; Pratsinis, S. E.:Simulation of Nanoparticle Production in PremixedAerosol Flow Reactors by Interfacing Fluid Mechanicsand Particle Dynamics, J. Nanoparticle Research, 1,1999, 305.
[15] Arabi-Katbi, O.I.; Pratsinis. S.E.; Morrison, P.W.;Megaridis, C.M.: Monitoring Flame Synthesis of TiO2-Particles by in-situ FTIR Spectroscopy and Ther-mophoretic Sampling, Combustion and Flame, 124,2001, 560.
[16] Degussa, DE 762 723, 1942 (H. Klöpfer).[17] Degussa, Schriftenreihe Pigmente, Paper No. 11, Frank-
furt 1992.[18] Degussa, Schriftenreihe Pigmente, Paper No. 56, Frank-
furt 1990.[19] Ullmann’s Encyclopedia of Industrial Chemistry, Vol.
A23, 635ff.[20] Kodas, T. T.; Hampden-Smith, M.: Aerosol Processing
of Materials, Wiley-VCH, New York, 1999.[21] Fristrom, R. M.: Flame Structure and Processes,
Oxford University Press, 1995.[22] Boulos, I. B.; Fauchais, P.; Pfender, E.: Thermal Plas-
mas, Fundamentals and Applications, Plenum PressNew York, Vol. 1, 1994, 1-19.
[23] Fulcheri, L.; Probst, N.; Flamant, G.; Fabry, F.; Grivei,E.: 3rd Int. Conf. on Carbon Black, Mulhouse, 2000, 11-20.
[24] Michel. G., Müller, E., Oestreich, Ch., Staupendahl, G.,Henneberg, K.-H.: Ultrafine ZrO2 Powder by LaserEvaporation: Preparation and Properties, Materialwis-senschaft und Werkstofftechnik, 27, 1996, 345-349.
[25] Michel. G., Staupendahl, G., Eberhardt, G., Vogelsberger,W.: Ultrafine ceramic powder by laser evaporation
Nanosized ceramic particles by laser evaporation andrecondensation, Fine Solid Particles, Shaker VerlagAachen, 1997, 127-135.
[26] Cullity, B. D.: Introduction to magnetic materials,Adison-Wesley, 1972.
[27] Kneller, E.: Ferromagnetismus, Springer Verlag, 1962.
36 KONA No.20 (2002)
Author’s short biography
Andreas Gutsch
Dr. Gutsch studied chemical engineering in Karlsruhe, Germany, and began hiscareer working as a free-lance consultant in the power engineering field. While hewas doing his doctorate, he gained international experience at the University ofCincinnati, Ohio. In 1995, he joined former Degussa. Here he worked in theprocess engineering field, where he was appointed Chief of Section in 1998. He hasbeen head of the Nanomaterials Project House since 2000. In April 2002 Dr. Gutschhas been appointed head of Creavis Technologies & Innovation. Dr. Gutsch be-longs to a number of advisory committees at the German Research Union, acts asspecial adviser for the Land North Rhine-Westphalia, and is an appointed memberof various scientific organisations.
Heike Mühlenweg
Heike Mühlenweg received her PhD-degree in Mechanical Process Engineeringfrom the Technical University of Clausthal in 1995. The following year sheaccepted a scholarship from the German National Science Foundation (DFG) andspent eighteen month as a Post-Doc researcher at the Department of Mechanicaland Aerospace Engineering, Arizona State University, USA. In 1998 she started atthe Degussa AG. Following nine month of scientific work concerning populationbalances at the University of Cincinnati, USA, she worked as R&D engineer inDegussa’s Department of Process Technology and Engineering. Her main topicwas the simulation of particle synthesis in gas-phase reactors and the collaborationin preparation of the Project House Nanomaterials as a new strategic project forthe development of advanced nano-scaled powders. In January 2000 she has beentransferred to the starting Project House Nanomaterials and since she is respon-sible as R&D manager for the coordination of a joint venture project with nineleading German Universities funded by the DFG. Furthermore, based on her sim-ulation know-how she developed and constructed a gas-phase reactor that is nowoperated for the generation of new nano-scaled powders.
Günther Michael
Dr. Michael studied chemistry at the University of Kaiserslautern where hereceived his PhD-degree on “Agostic complexes of chromium” in 1986. From 1987on he has been working with the Aerosil Applied Technology Group of DegussaAG. He was also the quality supervisor for Aerosil. Since 2000 he is working withthe Project House Nanomaterials as senior manager.
Markus Pridöhl
Dr. Pridöhl studied chemistry at the Technical University of Berlin where hereceived his PhD-degree on “Synthesis, 77Se-NMR spectroscopy and HPLC analy-sis of Bis-organyl-sulfur-selen-chains” in 1995. In the same year he started with theformer Cerdec AG in Frankfurt as a quality control manager. After a trainee assign-ment in the field of carbon black production and site management with DegussaAG in 1996 he worked as R&D manager with Degussa’s Fillers and Pigments Divi-sion from 1998 on. In 2000 Dr. Pridöhl joined the Project House Nanomaterials asR&D manager.
KONA No.20 (2002) 37
Author’s short biography
Guido Zimmermann
Guido Zimmermann got his chemical engineering degree from the university ofapplied science of Cologne in 1997. In the same year he started at the department„Process Technology and Engineering“ at DEGUSSA in a research group fordeveloping ultra-fine particles as R&D engineer. Since 2000 he works for the Pro-ject House Nanomaterials as R&D manager and is responsible for the developmentand construction of novel types of gas-phase reactors and for the generation of newnanoscale powders.
Michael Krämer
Michael Krämer graduated in Chemical Engineering at the University of Karls-ruhe, Germany, in 1999. He started his career at Degussa AG within the ProcessTechnology and Engineering Department in the field of particle technology. Since2000 he is working as R&D manager in Degussa’s Project House Nanomaterials.Amongst his areas of expertise are the design and scale-up of gas-phase processesfor the synthesis of new tailor-made nanoscaled powders.
38 KONA No.20 (2002)
1. Introduction
The invention of the Dorr thickener in 1905 and itsintroduction in the mining concentrators of SouthDakota can be regarded as the starting point of themodern era of thickening research. Therefore, thehistory of thickening can be associated with thebeginning of the 20th century. Thus the beginningof the 21st century provides a good opportunity toreview the steps of progress of those almost one hun-dred years of research and development of industrialthickeners. A second prominent reason for publishingthis review just now is the 50th anniversary of thepublication of Kynch’s celebrated paper A theory ofsedimentation in 1952, which can be considered as theorigin of modern sedimentation and thickening re-search in numerous disciplines.
Thickening is not a modern undertaking and wascertainly not discovered as a process in the Americas.
Whenever an ore was dressed to obtain a concentrate,two processes were used in an unseparable form:crushing and washing. There is evidence that in the IVEgyptian dynasty, some 2500 years BC, the ancientEgyptians dug for and washed gold. There is also evi-dence of gold washing in Sudan in the XII dynasty.Nevertheless, the earliest written reference for crush-ing and washing in Egypt is that of Agatharchides, aGreek geographer who lived 200 years before Christ.Ardaillon, author of the book Les Mines du Lauriondans l’Antiquité, described in 1897 the process used inthe extensive installations for crushing and washingores in Greece between the V to the III century BC.A.J. Wilson (1994) describes in his book The LivingRock mining of gold and copper in the Mediterraneanfrom the fall of the Egyptian dynasties right to theMiddle Ages and the Renaissance.
The development of mineral processing from un-skilled labor to craftsmanship and eventually to anindustry governed by scientific discipline is largelydue to the Saxons in Germany and Cornishmen inEngland in the beginning of the 16th century. Aninternational exchange of technology began betweenthese two countries and continued for a long time.However, it was in Saxony where Agricola wrote hisDe Re Metallica, the first major contribution to thedevelopment and understanding of the mining indus-
Fernando Conchaa,* and Raimund Bürgerb
a Department of Metallurgical Engineering, University of Concepción
b Institute of Applied Analysis and Numerical Simulation, University of Stuttgart
A Century of Research in Sedimentation and Thickening†
Abstract
This paper provides a concise review of the contributions to research in sedimentation and thick-ening that were made during the 20th century, starting from the invention of the Dorr thickener in1905. The different steps of progress that were made in understanding batch sedimentation and con-tinuous thickening processes in mineral processing are reviewed. A major breakthrough was Kynch’skinematic sedimentation theory published in 1952. The authors’ own contributions to sedimentationand thickening research are summarized, including the development of the appropriate mathemati-cal framework for Kynch’s theory and its extensions to continuous sedimentation and to polydispersesuspensions of spheres. An even more general model framework is provided by the phenomenologicaltheory of sedimentation, which permits the description and simulation of the transient behavior off locculent suspensions.
a Casilla 53-C, Correo 3, Concepción, ChileFax: +56-41-230759, E-mail: [email protected]
b Pfaffenwaldring 57, D-70569 Stuttgart, GermanyFax: +49-711-6855599E-mail: [email protected]* Corresponding author† Accepted: April 16, 2001
try, published in Latin in 1556, and shortly after trans-lated to German and Italian.
Agricola’s book describes several methods of wash-ing gold, silver, tin and other metallic ores. Hedescribes settling tanks used as classifiers, jigs andthickeners and settling ponds used as thickeners orclarifiers, see Figures 1 and 2. These devices oper-ated in a batch or semi-continuous manner. A typicaldescription is as follows: “To concentrate copper at theNeusohl mine in the Carpathians the ore is crushed andwashed and passed through three consecutive washer-sifters. The fine particles are washed through a sieve ina tub full of water, where the undersize settles to the bot-tom of the tub. At a certain stage of f illing of the tub
with sediment, the plug is drawn to let the water runaway. Then the mud is removed with a shovel andtaken to a second tub and then to a third tub where thewhole process is repeated. The copper concentrate whichhas settled in the last tub is taken out and smelted.”
It is evident from these references that, by usingthe washing and sifting processes, the ancient Egyp-tians and Greeks and the medieval Germans and Cor-nishmen knew the practical effect of the difference inspecific gravity of the various components of an oreand used sedimentation in operations that can now beidentified as classification, clarification and thicken-ing. There is also evidence that in the early days noclear distinction was made between these three oper-ations.
Agricola’s book had a tremendous impact, not onlyin the mineral industry but also on society in general,and continued to be the leading textbook for minersand metallurgists outside the English speaking worldfor at least another three hundred years. Apart fromits immense practical value as a manual, the greatestinf luence of De Re Metallica was in preparing theground for the introduction of a system of miningeducation which, with various modifications to suitthe local conditions, was later to be adopted interna-tionally.
While in Russia the first mining school was openedin 1715 in Petrozavodsk, the most important miningacademic institution, the Freiberg Mining Academy,was founded in Germany in 1765. Twenty years laterthe Ecole des Mines was established in Paris, but it didnot become an important institution until severalyears later. Regardless of the intense and prolongedtechnological transfer that was established betweenSaxony and Cornwall, the British were backward intechnical mining education and in the 19th centurycould virtually offer no facilities for the study of thisdiscipline. The Royal School of Mines was founded inLondon in 1851 and the Camborn School of Mines,whose prospectus was presented in 1829, was notestablished until 1859. The irony is that by that timethe school was properly established, the mining pro-duction of Cornwall was declining and emigration ofminers was in full swing to North America, Australia,and later to South and Central Africa (Wilson 1994).
The discovery of gold in California in 1848 andin Nevada a few years later caught Americans ill-equipped to make the best of these resources. Theyworked with shovels and pans, digging out gravelfrom the stream-beds and washing it in much thesame way as Egyptians had done five thousand yearsbefore them. The only professional mining engineers
KONA No.20 (2002) 39
Fig. 1 Settling tanks described by Agricola (1556).
Fig. 2 Washing and settling according to Agricola (1556).
found in the North American continent until after thecivil war were those which came from Freiberg orother European schools. The first American univer-sity to establish mining was the Columbia Universityin New York in 1864 (Wilson 1994).
It is the purpose of this review to describe thedevelopment of the science and technology of thick-ening during the 20th century, and to present the cur-rent accepted theory. This paper is therefore organ-ized as follows: in Section 2, we present an overviewof the most important contributions to thickeningresearch that were made during the 20th century.This period can be subdivided into five phases: thatof the invention of the Dorr thickener and initialresearch of thickener design (1900-1940, Sect. 2.1),that of the discovery of the operating variables in acontinuous thickener (1940-1950, Sect. 2.2), the KynchEra, during which the theory of sedimentation wasdeveloped (1950-1970, Sect. 2.3), the phase of the phe-nomenological theory (1970-1980, Sect. 2.4), and thecurrent one of the mathematical theory (1980-pre-sent, Sect. 2.5). The year numbers are of course to acertain degree arbitrary and not meant in a precisesense. We shall discuss a few example of researchwork that either lagged behind or was far ahead of itssurrounding current status of knowledge, and wouldtherefore have merited to fall within a prior or subse-quent phase than determined by the respective publi-cation year. We will also mention a few instances inwhich historic achievements have turned out to bestill important to contemporary research. In Sections3 and 4, the authors’ contribution to thickening re-search are summarized. In Section 3, results relat-ed to ideal suspensions, including the extension ofKynch’s theory to continuous sedimentation and poly-disperse mixtures are presented, while Section 4focuses on the recent phenomenological theory ofsedimentation of f locculated suspensions. In Section 5,we comment some of the results of Sections 3 and 4,and discuss approaches by other current researchgroups. This paper closes with a concluding remark(Section 6).
2. Historical perspective
2.1 The invention of the Dorr thickener andthickener design (1900-1940)
Classification, clarification and thickening all in-volve the settling of one substance in solid particulateform through a second substance in liquid form, butthe development of each one of these operations hasfollowed different paths. While clarification deals with
very dilute suspensions, classification and thickeningare forced to use more concentrated pulps. This isprobably the reason for which clarification was thefirst of these operations amenable to a mathematicaldescription. The work by Hazen in 1904 was the firstanalysis of factors affecting the settling of solid parti-cles from dilute suspensions in water. It shows thatdetention time is not a factor in the design of settlingtanks, but rather that the portion of solid removedwas proportional to the surface area of the tank andto the settling properties of the solid matter, andinversely proportional to the f low through the tank.At the beginning, classification equipment mimickedclarification settling tanks, adding devices to dis-charge the settled sediment. Therefore, the firsttheories of mechanical classification were based onHazen’s theory of settling basins. The introduction ofhydraulic classifiers led to theories of hindered set-tling in gravitational fields, and finally the introduc-tion of the hydrocyclone moved away from gravitysettling and used hindered settling in centrifugalfields as a mechanism.
The invention of the Dorr thickener in 1905 (Dorr,1915) can be mentioned as the starting point of themodern thickening era. John V.N. Dorr, D.Sc., achemist, cyanide mill owner and operator, consultingengineer and plant designer, tells (Dorr, 1936): “Thefirst mill I built and operated was turned into a prof-itable undertaking by my invention of the Dorr classi-fier in 1904 and, in remodeling another mill in thesame district, the Dorr thickener was born in 1905.[…] Its recognition of the importance of mechanicalcontrol and continuous operation in fine solid-liquidmixtures and the size of its units have opened the wayfor advances in sewage and water purification andmade wet chemical processes and industrial mineralprocesses possible.”
The invention of the Dorr thickener made the con-tinuous dewatering of a dilute pulp possible, wherebya regular discharge of a thick pulp of uniform densitytook place concurrently with overf low of clarifiedsolution. Scraper blades or rakes, driven by a suitablemechanism, rotating slowly over the bottom of thetank, which usually slopes gently toward the center,move the material as fast as it settles without enoughagitation to interfere with the settling.
It is well known that in many mineral processingoperations, applications appear and are utilized farahead of their scientific understanding. This is thecase in thickening. The first reference on variablesaffecting sedimentation is due to Nichols (1908).Authors who studied the effects of solids and elec-
40 KONA No.20 (2002)
trolytes concentration, degree of f locculation, andtemperature in the process also include Ashley(1909), Forbes (1912), Mishler (1912, 1918), Clark(1915), Ralston (1916), Free (1916), and the fre-quently cited work of Coe and Clevenger (1916).
Several of these studies introduced confusion in thecomprehension of the settling process and Mishler(1912), an engineer and superintendent at the TigreMining Company in the Sonora desert in Mexico, wasthe first to show by experiments that the rate of set-tling of slimes is different for dilute than for concen-trated suspensions. While the settling speed of diluteslimes is usually independent of the depth of thesettling column, a different law governed extremelythick slimes, and sedimentation increases with thedepth of the settling column. He devised a formula bymeans of which laboratory results could be used incontinuous thickeners. These formulas representmacroscopic balances of water and solids in the thick-ener and can be written as
FD, (1)FDFDDDO, (2)
where F and D are the solid mass f low rates in thefeed and the discharge respectively, O is the watermass f low rate in the overf low, and DF and DD arethe dilutions of the feed and the underf low, respec-tively. The volume f low rate of water at the overf lowQOO/ρf, where ρf is the mass density of water, isgiven by
QOF(DFDD)/ρf . (3)
Mishler (1912) assumed that the f low rate of waterper unit area in a continuous thickener should beequal to the rate of formation of the column of waterin a batch column, where a suspension with the sameconcentration as the thickener feed is allowed to set-tle. Since this rate of water formation is equal to therate of descent of the water-suspension interface,Mishler equated this rate, QO/S, with the settlingrate, which we denote by sI(DF). Then the cross-sec-tional area S of the thickener required to treat a feedrate of F is
S . (4)
Clark (1915) carefully measured concentrations in athickener with conical bottom, a configuration thatclearly gives rise to at least a two-dimensional f low.Clark’s note unfortunately is little more than half apage long but displays three diagrams of thickenerswith the sample locations and the respective mixture
F(DFDD)ρf sI(DF)
densities. The brevity of the note ref lects that at thetime of its writing the phenomena of settling were farfrom being understood, let alone in more than onespace dimension. This also becomes apparent inClark’s introductory statement: “Whatever interestthey may possess lies in the fact that few determinations[the specific gravity of pulp] of this nature have beenrecorded, rather than in any unusual or unexpectedconditions developed by the determinations themselves.”Clark’s measurements have received little attentionas presented in his note, but it seems that they inpart stimulated the well-known paper by Coe andClevenger, which appeared in 1916, since Coe andClevenger explicitly acknowledge Clark’s experimen-tal support.
Coe and Clevenger’s paper was importance in tworespects. On one hand, they were the first to recog-nize that the settling process of a f locculent suspen-sion gives rise to four different and well-distinguishedzones. From top to bottom, they determined a clearwater zone, a zone in which the suspension is presentat its initial concentration, a transition zone and acompression zone, see Figure 3. Coe and Clevengerreported settling experiments with a variety of materi-als showing this behaviour.
On the other hand, they were also the first to usethe observed batch settling data in a laboratory col-umn for the design of an industrial thickener. Theyargued that the solids handling capacity, today calledsolids f lux density, has a maximum value in the thick-ener at a certain dilution Dk between the feed and dis-charge concentration. They developed, independentlyfrom Mishler, an equation similar to (4) but with thefeed dilution DF replaced by a limiting dilution Dk:
S , (5)
where sI(Dk) is the settling velocity of a pulp with thelimiting dilution Dk. They recommend the determina-tion of the limiting dilution by batch experiments forthe desired underf low dilution DD. Equation (5), withminor sophistications, continues to be the most reli-able method of thickener design to date.
After the important contributions made in the de-velopment of thickening technology in the first twodecades of the 20th century, the invention of the Dorrthickener and the development of thickener designprocedures, the next two decades surely saw theexpansion of this technology. Several authors madeefforts to model the settling of suspensions by ex-tending Stokes’ equation or postulated empirical equa-tions (Adamson and Glasson 1925, Robinson 1926,
F(DkDD)ρf sI(Dk)
KONA No.20 (2002) 41
Egolf and McCabe 1937, Ward and Kammermeyer1940, Work and Kohler 1940), but no further impor-tant contributions were made until the forties. It isinteresting to note that Robinson’s paper was of minorinf luence for the development of sedimentation the-ory in the context of mineral processing, but that itsapproach seems to have been of great interest toinvestigators in the area of blood sedimentation halfa century later (Puccini et al. 1977).
Stewart and Roberts (1933) give, in a review paper,a good idea of the state of the art of thickening in thetwenties. They say: “The basic theory is old but limita-tions and modifications are still but partially developed.Especially in the realm of f locculent suspensions is theunderlying theory incomplete. Practical testing methodsfor determining the size of machines to be used areavailable, but the invention and development of newmachines will no doubt be greatly stimulated by furtherinvestigation of the many interesting phenomena ob-served in practice and as fresh problems are uncov-ered.”
2.2 The discovery of the operating variables ina continuous thickener (1940-1950)
The University of Illinois became very active inthickening research in the forties, shortly afterComings’ paper Thickening calcium carbonate slurrieshad been published in 1940. It should be pointed outthat this paper is the first to recognize the importanceof local solids concentration and sediment composi-tion for the thickening process, since it shows mea-surements of solids concentration profiles in acontinuous thickener, while all previous treatmentshad been concerned with observations of the suspen-
sion-supernate and sediment-suspension interfaces,with the exception of Clark (1915).
At least nine B.Sc. theses were made underComings’ guidance, mainly on the effect of operatingvariables in continuous thickening. Examples of the-sis subjects were: settling and continuous thickeningof slurries; continuous thickening of calcium carbon-ate slurries; thickening of clay slurries and limitingrates of continuous thickening. These theses weresummarized in an important paper by Comings,Pruiss and De Bord (1954).
The mechanism of continuous sedimentation wasinvestigated in the laboratory in order to explain thebehaviour of continuous thickeners. Comings et al.(1954) show four zones in a continuous thickener: theclarification zone at the top, the settling zone under-neath, the upper compression zone further down andthe rake action zone at the bottom. The most interest-ing conclusion, expressed for the first time, was thatthe concentration in the settling zone is nearly con-stant for a thickener at steady state, and that itdepends on the rate at which the solids are fed intothe thickener, and not on the concentration of thefeed suspension. At low feed rate, the solids settledrapidly at a very low concentration, regardless of thefeed concentration. When the feed rate was in-creased, the settling zone concentration increasedand approached a definite value when the maximumsettling capacity of the equipment was reached. If thefeed rate was increased further, the settling zonestayed constant and the solids fed in excess of the set-tling handling capacity left the thickener by the over-f low. It was verified that in most cases the feedsuspension was diluted to an unknown concentration
42 KONA No.20 (2002)
Fig. 3 Settling of a f locculent suspension as illustrated by Coe and Clevenger (1916), showing the clear water zone (A), the zone in which thesuspension is at its initial concentration (B), the transition zone (C) and the compression zone (D).
E F G H I J
BB
DC
A
B
C
D
A
BC
DD
D
AA
CriticalPoint
A
on entering the thickener. Another finding was that,for the same feed rate, increasing or decreasing thesediment depth could adjust the underf low concentra-tion.
It is worth mentioning that the paper by Comings etal. (1954) did not yet take into account Kynch’s sedi-mentation theory published two years earlier (Kynch1952), which is discussed below.
Another contribution of practical importance is thework of Roberts (1949), who advanced the empiricalhypothesis that the rate at which water is eliminatedfrom a pulp in compression is at all times proportionalto that amount left, which can be eliminated upto infi-nite time:
DD(D0D)exp(Kt), (6)
where D0, D and D are the dilutions at times zeroand t and at infinite time, respectively. The equationhas been used until today for the determination of thecritical concentration.
2.3 Theory of sedimentation (1950-1970)From the invention of the Dorr thickener to the
establishment of the variables controlling the equip-ment, the only quantitative knowledge that was ac-complished was Coe and Clevenger’s (1916) designprocedure. This method was solely based on a macro-scopic balance of the solid and the f luid and on theobservation of the different zones in the thickener.No underlying sedimentation theory existed.
The first attempts to formulate a theory of sedimen-tation in the sense of relating observed macroscopicsedimentation rates to microscopic properties of solidparticles were made by Steinour in a series of papersthat appeared in 1944 (Steinour 1944a-c). But it wasKynch, a mathematician at the University of Birming-ham in Great Britain, who presented in 1952 his cele-brated paper A theory of sedimentation. He proposed akinematical theory of sedimentation based on thepropagation of sedimentation waves in the suspen-sion. The suspension is considered as a continuumand the sedimentation process is represented by thecontinuity equation of the solid phase:
0, 0zL, t0, (7)
where f is the local volume fraction of solids as afunction of height z and time t, and
f bk(f)fvs
is the Kynch batch f lux density function, where vs isthe solids phase velocity. The basic assumption of
∂ f bk(f)∂ z
∂f∂ t
Kynch’s theory is that the local solid-liquid relativevelocity is a function of the solids volumetric concen-tration f only, which for batch sedimentation in aclosed column is equivalent to stating that vsvs(f).Equation (7) is considered together with the initialcondition
0 for zL,f(z, 0)f0 for 0zL, (8)
fmax for z0,
where it is assumed that the function f bk satisfies
f bk(f)0 for f0 or ffmax,0 for 0ffmax,
where fmax is the maximum solids concentration.Kynch (1952) shows that knowledge of the functionf bk is sufficient to determine the sedimentationprocess, i.e. the solution ff(z, t), for a given initialconcentration f0, and that the solution can be con-structed by the method of characteristics.
Kynch’s paper had the greatest inf luence in thedevelopment of thickening thereafter. The period oftwenty years after this paper may be referred to asthe Kynch Era. When Comings moved from Illinois toPurdue, research on thickening continued there foranother ten years. Although Comings soon moved onto Delaware, work continued at Purdue under thedirection of P.T. Shannon. A Ph.D. thesis by Tory(1961) and M.Sc. theses by Stroupe (1962) and DeHaas (1963) analyzed Kynch’s theory and proved itsvalidity by experiments with glass beads. Their re-sults were published in a series of joint papers bythese authors (Shannon et al. 1963, 1964, Tory andShannon 1965, Shannon and Tory 1965, 1966).
Batch and continuous thickening was regarded asthe process of propagating concentration changesupwards from the bottom of the settling vessel as aresult of the downward movement of the solids. Equa-tions were derived and experimental results for thebatch settling of rigid spheres in water were foundto be in excellent agreement with Kynch’s theory.Experiments aiming at verifying the validity ofKynch’s theory have repeatedly been conducted up tothe present (Davis et al. 1991, Chang et al. 1997).
Kynch’s paper also motivated industry to explorethe possibilities of this new theory in thickener de-sign. Again the Dorr Co. went a step further in theircontribution to thickening by devising the Talmageand Fitch method of thickener design (Talmage andFitch 1955). They affirmed that one settling plot con-tained all the information needed to design a thick-ener. Since the water-suspension interface slope (in a
KONA No.20 (2002) 43
z versus t diagram) gave the settling rate of the sus-pension, the slope at different times represented thesettling velocity at different concentrations. Theyused this information in conjunction with the citedMishler-Coe and Clevenger method to derive a for-mula for the unit area, that is, the thickener arearequired to produce a sediment of given concentra-tion at a given solids handling rate. Talmage andFitch’s method is described in detail in our previousreview article (Concha and Barrientos 1993) and inChapter 11 of Bustos et al. (1999), so the resulting for-mulas and related diagrams are not explicitly statedhere. Although Kynch’s theory can not be regardedas an appropriate model for f locculent suspensions,thickener manufacturers still use and recommendTalmage and Fitch’s method, which is based on thistheory, for design calculations (Outukumpu Mintec1997).
Yoshioka et al. (1957) and Hassett (1958, 1964,1968) used the solid f lux density function to interpretthe operation of a continuous thickener and devisea method for thickener design (see Concha andBarrientos (1993) for details).
Experience by several authors, including Yoshiokaet al. (1957), Hassett (1958, 1964, 1968), Shannon etal. (1963), Tory and Shannon (1965), Shannon andTory (1965, 1966) and Scott (1968a,b), demonstratedthat while Kynch’s theory accurately predicts the sed-imentation behaviour of suspensions of equally sizedsmall rigid spherical particles, this is not the case forf locculent suspensions forming compressible sedi-ments.
An interesting paper that seems to have been over-looked by the thickening literature is that of Behn(1957). This paper by its nature was ahead of its timeand would have been well received in the seventies.Behn was the first writer to relate thickening com-pression with the consolidation process. Therefore heapplies the following consolidation equation for theexcess pore pressure pe, that is, the pressure in thepores of the sediment in excess of the hydrostaticpressure:
, (9)
where k is the average sediment permeability, ρs isthe solids density, ∆ρ is the solid-liquid density differ-ence, and hc is the initial height of the consolidatingregion. Unfortunately without explicitly mentioningthe boundary conditions or presenting any detail ofthe derivation, Behn (1957) obtained the solution
∂ 2pe
∂ z2k∆ρhc
ρs
∂pe
∂ t
DD(D0D)exp(Kt), K . (10)
Equation (10) is identical to Roberts’ equation (6) andgives some theoretical support to it, although Roberts’equation is essentially empirical (Fitch 1993).
Although Behn’s paper is valuable in providing aconcise review of the mathematical models of sedi-mentation that had been advanced until 1957 and inrecognizing that the settling velocity formulas postu-lated in some of them in fact furnish the Kynch batchf lux density function f bk, it ref lects at the same timethat the implications of Kynch’s theory had still notyet been well understood. This becomes apparent inBehn’s conclusion that “ the Kynch theory does extendinto the compression zone, although Kynch did not soindicate.” It has already been pointed out that Kynch’stheory does not apply to the compression zone. Thisbecomes obvious by the fact that the compressionzone is characterized by rising curved iso-concentra-tion lines, which finally become horizontal, while inthe framework of Kynch’s theory concentration val-ues always propagate along straight lines if cylindricalvessels are considered.
To describe the batch settling velocities of particlesin a suspension several equations for vsvs(f) orf bk(f)fvs(f) were proposed, all of them extensionsof the Stokes equation. The most frequently used wasthe two-parameter equation of Richardson and Zaki(1954):
f bk(f)uf(1f)n, n1, (11)
where u is the settling velocity of a single particle inquiescent, unbounded f luid. This equation has theinconvenience that the settling velocity becomes zeroat a solids concentration of f1, while experimentallythis occurs at a maximum concentration fmax between0.6 and 0.7.
Michaels and Bolger (1962) proposed the followingthree-parameter alternative:
f bk(f)uf1 n, n1, (12)
where the exponent n4.65 turned out to be suitablefor rigid spheres.
For equally sized glass spheres, Shannon et al.(1963) determined the following equation by fittinga forth-order polynomial to experimental measure-ments, see Figure 4:
f bk(f)f(0.338431.37672f1.62275f2
0.11264f30.902253f4)102 m/s.
ffmax
k∆ρhcρs
44 KONA No.20 (2002)
A paper that still belongs to the Kynch era, al-though it was published later, is the one by Petty(1975). He extended Kynch’s theory from batch tocontinuous sedimentation. If q is defined as the vol-ume f low rate of the mixture per unit area of the sedi-mentation vessel, Kynch’s equation for continuoussedimentation can be written as
(qff bk(f))0. (13)
Petty (1975) also discussed, for the first time, theproper boundary conditions at the bottom of the set-tling vessel, which is a non-trivial problem.
2.4 The phenomenological theory (1970-1980)Although Behn (1957) was the first writer to apply
consolidation theory for the settling of compressibleslurries, it was Shirato and his co-workers (1970) whosolved the consolidation problem taking into accountthe effect of sediment growth and compression due todeposition of solid particles from the hindered set-tling zone. The latter is, however, not explicitly mod-eled due to the use of material coordinates in thecompressible sediment. The result were sedimentconcentration and excess pore pressure profiles.
If Behn’s work had received greater attention, thedevelopment of a phenomenological theory wouldhave started about fifteen years earlier. It took an-other five years for Adorján (1975, 1977) to presenthis ad-hoc theory of sediment compression, givingthe first satisfactory method of thickener design, andfor Smiles (1976a,b) to present his integral approach.
At about the same time, a group of researchers inBrazil made great efforts to give the phenomenologi-cal sedimentation theory a proper framework. Strongand important research on thickening, and in generalin the field of f low through porous media, was goingon in Brazil in the decade of the 1970s. At the Engi-
∂∂ z
∂f∂ t
neering Graduate School of the Federal University ofRio de Janeiro, COPPE, several researchers and grad-uate students, among them Giulio Massarani, AffonsoSilva Telles, Rubens Sampaio, I-Shih Liu, JoséTeixeira Freire, Liu Kay, João D’Avila and SatoshiTobinaga, were involved in the application of a newlydeveloped mathematical tool, the Theory of Mixturesof continuum mechanics, to particulate systems. Un-fortunately these findings were rarely published inmainstream international journals, but are well docu-mented in local publications and conference volumes,see for example D’Avila (1976, 1978), D’Avila andSampaio (1977), D’Avila et al. (1978), Liu (1978) andTobinaga and Freire (1980).
With strong ties with the Brazilian researchers, agroup led by the first author of this review at the Uni-versity of Concepción in Chile worked in the samedirection. Findings were presented in the B.Sc. thesesby O. Bascur (1976) and A. Barrientos (1978), at theXII International Mineral Processing Congress in SãoPaulo, Brazil in 1977 (Concha and Bascur 1977) andat the Engineering Foundation Conference on Parti-cle Technology in New Hampshire, USA, in 1980.
Independently, Kos (1975) used the theory of mix-tures to set up boundary value problems for batchand continuous sedimentation. Thacker and Lavelle(1977) used the same theory for incompressible sus-pensions.
2.5 Mathematical theory (1980-present)At the end of the seventies and during the eighties
several papers, for example Concha and Bustos(1985), Buscall and White (1987), Auzerais et al.(1988), Landman et al. (1988), Bascur (1989) andDavis and Russel (1989) show that the phenomeno-logical model, based on the theory of mixtures, waswell accepted by the international scientific commu-nity.
In spite of the fact that the theory of mixtures did agreat job in unifying the sedimentation of dispersedand f locculated suspensions and, once appropriateconstitutive equations were formulated, gave rise to arobust framework in which the sedimentation of anysuspension could be simulated, the mathematicalanalysis of these models did not exits. Furthermoreno adequate numerical method existed for solving theinitial-boundary value problems for batch and contin-uous thickening.
While it is common that mathematics is needed insolving specific problems, many engineers regard thebasic principles of mineral processing as purely physi-cal and mathematical treatment as belonging only to a
KONA No.20 (2002) 45
Fig. 4 Flux density function for glass beads with two inflectionpoints a and b, after Shannon et al. (1963).
0.0 0.1 0.2 0.3 0.4 0.5 0.60.0
f bk(f)
f[]
[104 m/s]
2.0
1.0
a0.3391
b0.5515
later stage in the development of a theory. Whenfinally mathematics get started, it could be precise,but setting up the theory is for them an extra-math-ematical operation. Truesdell (1966) stated that thecharacteristics of a good theory are that the physicalconcepts themselves are made mathematical at theoutset, and mathematics is used to formulate the the-ory and to obtain solutions.
At the beginning of the eighties, followingTruesdell’s ideas and convinced that the only way inestablishing a rigorous theory of sedimentation con-sisted in the cooperation of engineers with math-ematicians, the first author, together with MaríaCristina Bustos, then a staff member of the Depart-ment of Mathematics at the University of Concepción,and Wolfgang Wendland, professor of mathematics atthe University of Darmstadt, started a fruitful cooper-ation on the topic of mathematical analysis of sedi-mentation models. After Wendland moved to theUniversity of Stuttgart in Germany in 1986, firstMatthias Kunik and then the second author joinedthis cooperation, which now also includes ElmerTory, Professor Emeritus at Mount Allison Universityin Sackville, New Brunswick, Canada. The results ofthis cooperation, which has lasted for two decadesnow, are summarized in the following Sections 3 and4.
3. Sedimentation of ideal suspensions
3.1 Kynch’s sedimentation model and mathematical preliminaries
For batch sedimentation, equation (7) is solvedtogether with the initial condition (8). Note that, dueto the assumptions on f bk, the initial condition (8)could be replaced by the initial condition
f(z, 0)f0(z) for 0zL,
combined with the boundary conditions
f(0, t)fmax, f(L, t)0 for 0 tT.
To construct the solution of the initial value prob-lem (7), (8), the method of characteristics is employed.This method is based on the propagation of f0(z0),the initial value prescribed at zz0, at constant speedf ′bk(f0(z0)) in a z versus t diagram. These lines mightintersect, which makes solutions of equation (7) dis-continuous in general. This is due to the nonlinearityof the f lux density function f bk. In fact, even forsmooth initial data, a scalar conservation law with anonlinear f lux density function may produce discon-tinuous solutions, as the well-known example of
Burgers’ equation illustrates, see Le Veque (1992).On the other hand, one particular theoretically andpractically interesting initial-value problem for ascalar conservation law is the Riemann problem wherean initial function
f0(z)f0 for z0,
f0 for z0
(14)
consisting just of two constants is prescribed. Obvi-ously, the initial-value problem (7), (8) consists of twoadjacent Riemann problems producing two ‘fans’ ofcharacteristics and discontinuities, which in this casestart to interact after a finite time t1.
At discontinuities, equation (7) is not satisfiedand is replaced by the Rankine-Hugoniot condition(Bustos and Concha 1988, Concha and Bustos 1991),which states that the local propagation velocity s(f,f) of a discontinuity between the solution values f
above and f below the discontinuity is given by
s(f, f) . (15)
However, discontinuous solutions satisfying (7) atpoints of continuity and the Rankine-Hugoniot condi-tion (15) at discontinuities are in general not unique.For this reason, an additional selection criterion, orentropy principle, is necessary to select the physicallyrelevant discontinuous solution, the entropy weak solu-tion.
One of these entropy criteria, which determine theunique entropy weak solution, is Oleınik’s jump en-tropy condition requiring that
s(f, f)
for all f between f and f (16)
is valid. This condition has an instructive geometricalinterpretation: it is satisfied if and only if, in an f bk ver-sus f plot, the chord joining the points (f, f bk(f))and (f, f bk(f)) remains above the graph of f bk forff and below the graph for ff, see Figure 5.
Discontinuities satisfying both (15) and (16) arecalled shocks. If, in addition,
f ′bk(f)s(f, f) or f ′bk(f)s(f, f) (17)
is satisfied, the shock is called a contact discontinuity.In that case, the chord is tangent to the graph of f bk inat least one of its endpoints.
A piecewise continuous function satisfying theconservation law (7) at points of continuity, the initialcondition (8), and the Rankine-Hugoniot condition
f bk(f)f bk(f)ff
f bk(f)f bk(f)ff
f bk(f)f bk(f)ff
46 KONA No.20 (2002)
(15) and Oleınik’s jump entropy condition (16) at dis-continuities is unique.
Consider equation (7) together with the Riemanndata (14). If we assume (for simplicity) that f0
f0
and that f ′′bk(f)0 for f0ff0
, it is easy to see thatno shock can be constructed between f0
and f0. In
that case, the Riemann problem has a continuoussolution
f0 for zf ′bk(f0
)t,f(z, t)( f ′bk)1(z/t) for f ′bk(f0
) tz f ′bk(f0)t, (18)
f0 for z f ′bk(f0
)t,
where ( f ′bk)1 is the inverse of f ′bk restricted to theinterval [f0
, f0]. This solution is called a rarefaction
wave and is the entropy weak solution of the Riemannproblem.
For details on entropy weak solutions of scalar con-servation laws, we refer to the books by Le Veque(1992), Godlewski and Raviart (1991, 1996), Kröner(1997) or Dafermos (2000).
3.2 Solutions of the batch sedimentation problem
We now consider entropy weak solutions for theproblem of equation (7) with the initial condition (8),where we set f0≡const. corresponding to an initiallyhomogeneous suspension and consider a f lux densityfunction f bk with at most two inf lection points. Usingthe method of characteristics and applying the theorydeveloped by Ballou (1970), Cheng (1981, 1983) andLiu (1978), Bustos and Concha (1988) and Concha
and Bustos (1991) construct entropy weak solutionsof this problem in the class of piecewise continuousfunctions, in which zones of constant concentrationsare separated by shocks, rarefaction waves or combi-nations of these. Therefore, it is necessary to solvethe two Riemann problems given at t0, zL and att0, z0 and to treat the interaction of the two solu-tions at later times. For f lux density functions with atmost two inf lection points, they obtain five qualita-tively different entropy weak solutions or modes of sed-imentation.
Their classification turned out to be not yet com-plete, since they had considered only functions withtwo inf lection points similar to our Figure 4, and twoinf lection points can also be located in a different way,producing two additional modes of sedimentation. Inthese two new modes of sedimentation, the super-nate-suspension interface is not a sharp shock but ararefaction wave. The mathematically rigorous, de-tailed construction of the complete set of sevenmodes of sedimentation MS-1 to MS-7 is presented inChapter 7 of Bustos et al. (1999). In this review, theconstruction of the seven different entropy solutionsis outlined in Figures 6 and 7.
The solutions constructed by Bustos and Concha(1988) and Concha and Bustos (1991) were notnew and had been published decades earlier byStraumann (1962) and Grassmann and Straumann(1963). However, at that time the mathematical con-cept of entropy solutions had not yet been developed,and Grassmann and Straumann (1963) had to intro-duce new physical arguments and insights in everycase in order to obtain their solutions of the sedimen-tation process. Their paper certainly would havedeserved greater attention, and should have beenquoted by those who were active in thickening re-search in the 1960s, such as P.T. Shannon and hisco-workers, but unfortunately was published inGerman.
The simplest case is that of a mode of sedimenta-tion (MS) MS-1, in which the supernate-suspensionand the suspension-sediment interfaces are bothshocks, see Figure 6 a). These shocks meet at thecritical time tc to form a stationary clear water-sedi-ment interface. In an MS-2, the rising shock isreplaced, from top to bottom, by a contact discontinu-ity followed by a rarefaction wave, see Figure 6 b).In the f lux plot, the contact discontinuity is repre-sented by a chord joining the points (f0, f bk(f0)) and(f0*, f bk(f0*)) which is tangent to the graph of f bk in thesecond point. If we take the same f lux function andstill increase f0, this chord can no longer be drawn
KONA No.20 (2002) 47
Fig. 5 Geometrical interpretation of Oleınik’s jump entropy con-dition, applied to five jumps between ffi
and ffi,
i1, …, 5. For i1, 3 the condition is satisfied (solidchords), for i2, 4, 5 it is violated (dashed chords).
f bk(f)
ff1
f2 f3
f4 f1
f5 f4
f3 f2
f5
and the contact discontinuity becomes a line of conti-nuity. This situation corresponds to an MS-3, seeFigure 6 c). Note that the modes of sedimentationMS-2 and MS-3 can occur only with a f lux densityfunction f bk with exactly one inf lection point (werecall that we always assume that f ′′bk(0)0).
With a f lux density function f bk having exactly twoinf lection points, four additional modes of sedimenta-tion are possible, which are collected in Figure 7.Clearly, an MS-1 is also possible with two inf lectionpoints. Bustos and Concha (1988) and Concha andBustos (1991) obtained two of the four additionalmodes of sedimentation, namely the modes MS-4 andMS-5 shown in Figure 7 a) and b). These modes aresimilar to an MS-2 and MS-3 respectively, but the sec-ond inf lection point produces an additional contact
discontinuity, denoted by C2 in Figure 7 a) and by C1
in Figure 7 b), which separates the lower rarefactionwave (R1) from the rising sediment.
Of course, the shape of a given f lux density func-tion determines which modes of sedimentation areactually possible. In Chapter 7 of Bustos et al. (1999),a corresponding geometrical criterion to decide thisis presented. It is quite obvious that f lux density func-tions that are similar to that shown in Figure 4 makean MS-4 or MS-5 possible. However, it is also possibleto place the inf lection points a and b in such a waythat f ′bk(a)0, f ′bk(b)0, and that there exists a pointaftb such that the tangent to the graph of f bk at(ft, f bk(ft)) also goes through the point (0, fbk(0)0).This situation is shown in the f lux plots of Fig-ure 7 c) and d). If the initial concentration f0 is then
48 KONA No.20 (2002)
Fig. 6 Modes of sedimentation MS-1 to MS-3. From the left to the right, the f lux plot, the settling plot showing characteristics and shock lines,and a representative concentration profile taken at time tt* are shown for each mode. Chords in the f lux plots and shocks in the set-tling plots having the same slopes are marked by the same symbols. Slopes of tangents to the flux plots occurring as slopes of charac-teristics in the settling plots are also indicated (Bürger and Tory, 2000).
0 f0 fmaxL
z
0
L
z
0t* tc t 0 f0 fmax f
0f bk(f)
f
S1 S1
S1
S2
S2 S2
S3
a) MS-1:
clear liquid
sediment
0 f0 α f0* fmax L
z
0
L
z
0t* t1 tc t 0 f0 f0* fmax f
0f bk(f)
f
S1 S1
S1
C1
C1 C1
R1
S2
R1
R1
S3
b) MS-2:
clear liquid
sediment
0 α f0 fmax L
z
0
L
z
0t* t1 tc t 0 f0 fmax f
0f bk(f)
f
S1S1
S1
S2
R1
S3
c) MS-3:
clear liquid
sediment
chosen between ft and the second inf lection point b, anew mode of sedimentation, called MS-6, is produced,see Figure 7 c): the supernate-suspension interfaceis no longer sharp, that is, a shock; rather, an upperrarefaction wave R1 emerges from zL at t0, whichis separated from the supernate by a contact discon-tinuity and from the bulk suspension by a line ofcontinuity. That line of continuity meets the risingsediment-suspension interface, the shock S1, at tt1.
After that a curved, convex shock S2 forms, separat-ing the rarefaction wave from the sediment. At thecritical time ttc, the shock S2 meets the upper end ofthe rarefaction wave, that is, the contact discontinuityC1, and the stationary shock S3 forms, which denotesthe sediment-supernate interface located at the sedi-ment height zc.
A similar construction applies if f0b is chosensuch that there exists a point ftf0*b with f ′bk(f0*)
KONA No.20 (2002) 49
Fig. 7 Modes of sedimentation MS-4 to MS-7.
a) MS-4: 0 f0 f0* f t fmaxf0
f bk(f)S1
S1
S2
S3
S3
S2
S1
S1 C1
C2
R1
C1C1
C1
C1
C2
R1
R1
C2 clear liquid
sediment
t*t1 tc t 0 f0f0*ft fmax f
Lz
0
Lz
0
b) MS-5: 0 f0 f t fmaxf0
f bk(f)S1
S1
C1
R1
clear liquid
sediment
t* t1 tc t 0 f0ft fmax f
Lz
0
Lz
0
c) MS-6: 0 ft f0 fmaxf0
f bk(f)C1
S1
S1
S1
R1
C1
C2
S2
S3
S2
S3R1
C1
S1
C1 R1clear liquid
sediment
t* t1 tc t 0 ftf0 fmax f
Lz
0
Lz
0
d) MS-7: 0 ftf0* f0 fmax
f0f bk(f)
S1
C1
C2
S1
C1C2
R1clear liquid
sediment
t* t1 tc t 0 ftf0*f0 fmax f
Lz
0
Lz
0
s(f0*, f0), see Figure 7 d). The resulting entropyweak solution is an MS-7, differing from an MS-6 inthat the bulk suspension is separated from the upperrarefaction wave by a contact discontinuity instead ofa line of continuity.
All modes of sedimentation terminate in a station-ary sediment of the maximum concentration fmax andof height zcf0L/fmax. This stationary state is at-tained at the critical time tc.
3.3 Continuous sedimentation of ideal suspensions
Similar solutions of standardized initial-boundaryvalue problems can be constructed by the method ofcharacteristics for continuous sedimentation of idealsuspensions (Bustos et al. 1990b, Concha and Bustos1992). These solutions satisfy the equation (13) wher-ever f is discontinuous. At discontinuities betweentwo solution values f and f, the Rankine-Hugoniotcondition
s(f, f)q(t) (19)
and Oleınik’s jump entropy condition
q(t) s(f, f)
q(t) (20)
for all f between f and f
are satisfied. Conditions (19) and (20) are naturalextensions of conditions (15) and (16) to the case of af lux density function with a convection term q(t)fadded to the Kynch batch f lux density function fbk(f).
The standard initial function for continuous sedi-mentation, where q(t) is a negative constant, is
f(z, 0)f0(z)fL for AzL,fmax for 0zA,
(21)
where 0AL is the initial sediment height and fL isthe concentration in the thickener to which the feedf lux f F is diluted. The value fL is obtained ny solvingthe equation
qfLf bk(fL) f F. (22)
In case Eq. (22) admits several solutions fL, the rele-vant one is selected by the physical argument that thefeed suspension should always be diluted on enteringthe thickener, as shown by Comings et al. (1954), seeChapter 2 of Bustos et al. (1999).
It is assumed that the feed f lux f F and the volume
f bk(f)f bk(f)ff
f bk(f)f bk(f)ff
f bk(f)f bk(f)ff
average f low velocity q are kept constant during thecontinuous sedimentation process. This suggests for-mulating the boundary conditions as
f(L, t)fL, t0, (23)f(0, t)fmax, t0. (24)
However, the boundary conditions (23) and (24) canbe imposed only in that special case where no char-acteristics carrying solution values intersect theboundary zL from below and z0 from above,respectively. This case is exceptional, since the usualsolution picture of the Riemann problem given byEq. (13) and the initial datum (21) will be a centredwave, a so-called Riemann fan, emerging from (zA,t0), consisting of characteristics and discontinuities,which after some finite time reach zL or z0. If theentire Riemann fan cuts the boundary zL, we saythat the thickener overf lows; if it cuts z0, the thick-ener empties.
When such intersections with the boundaries occur,the boundary conditions (23) and (24) are no longervalid. The appropriate mathematical concept to main-tain well-posedness of the initial-boundary value prob-lem is that of set-valued entropy boundary conditions.This means that boundary conditions (23) and (24)are replaced by
f(L, t)εL(fL; f ), t0, (25)f(0, t)ε0(fmax; f ), t0, (26)
where eL(fL; f )[0, fmax] and e0(fmax; f )[0, fmax]are particular sets of admissible boundary values thatcan be constructed using the graph of the compositef lux function f defined by
f(f):qff bk(f),
see Bustos and Concha (1992), Bustos et al. (1996),Bürger and Wendland (1998b) and Chapters 6 and 8of Bustos et al. (1999) for details.
For a f lux density function f bk with exactly oneinf lection points (note that f bk and f have the sameinf lection points), there exist three different modes ofcontinuous sedimentation (Concha and Bustos 1992)depending on the structure of the Riemann fan. Thesolution is called a mode of continuous sedimentationMCS-1 if it consists of two constant states separatedby a shock; an MCS-2 if it consists of two constantstates separated by a contact discontinuity; and anMCS-3 if the solution is continuous and consists oftwo constant states separated by a rarefaction wave.
Note that we have to distinguish less modes of sedi-mentation in the continuous than in the batch casesince we have to solve only one Riemann problem,
50 KONA No.20 (2002)
and no wave interactions occur at positive times. How-ever, in each of these modes the thickener can eitheroverf low, empty, or attain a steady state, i.e. approxi-mates a stationary solution for t→, so that there arenine qualitatively different solution pictures.
For a detailed construction of the complete set ofthese solutions we refer to Chapter 8 of Bustos et al.(1999), and for a particularly concise overview toConcha and Bürger (1998). In this review, we presentthree examples from Chapter 8 of Bustos et al.(1999), see Figure 8, in which the left column showsplots of the composite f lux function f, and the rightone the corresponding settling plots. In Figures 8and 9, j≡f and jfmax.
The construction method for exact entropy solu-tions of the problem of batch and continuous sedi-mentation of ideal suspensions with standardizedinitial and boundary data, and in particular the factthat the exact location and propagation speed ofthe sediment-suspension interface level are alwaysknown, have led Bustos et al. (1990b) to formulate asimple control model for continuous sedimentation. Itis shown that steady states corresponding to an MCS-1 can always be recovered after a perturbation of thefeed f lux density f FqfLf bk(fL) by solving two ini-tial-boundary value problems at known times andwith parameters q and fL that can be calculated a pri-ori, see Figure 9.
KONA No.20 (2002) 51
Fig. 8 Modes of continuous sedimentation (Bustos et al. 1999). Top: MCS-1 with emptying ICT; Middle: MCS-2 attaining a steady state; Bot-tom: MCS-3 causing the ICT to overf low.
jL j** j j
j** jLjM** jM j j
j** a jL j j
f F
f F
f
0
f F
f
0
L
z
A
00 t1 t
L
z
A
0
L
z
A
0
0 t2 t
0 t1 t2 t
jL
jL
j
j
j
jL z1 z2
z1
z1
z2
3.4 Sedimentation of polydisperse suspensionsof spheres
In this section we consider polydisperse mixtures,i.e. suspensions of rigid spheres with particles be-longing to a finite number of species differing in sizeor density. For simplicity, the mathematical model isoutlined here for the case of different sizes only; seeBürger et al. (2000a) for the general case.
If we denote by vi and fifi(z, t) the phase velocityand the local volumetric concentration of particlespecies i, respectively, the mass balances for thesolids can be written as
0, i1, …, N, (27)
where
f ifivi, i1, …, N.
These balances lead to a solvable system of N scalarequations if either the solid phase velocities vi or thesolid-f luid relative velocities uivivf, where vf
denotes the f luid phase velocity, are given as func-tions of f1 to fN. The former approach is due toBatchelor (1982) and Batchelor and Wen (1982),while the latter has been advocated by Masliyah(1979). For sake of brevity, we present here only themodel due to Masliyah, and refer to Concha et al.(1992), Bürger et al. (2000a) and Bürger et al. (2001c)for extensive treatments.
The settling of a polydisperse suspension in a col-umn of height L can be described by a system of Nconservation laws
0, 0zL, t0; f(Φ)( f 1(Φ), …, fN(Φ))T,(28)
∂ f(Φ)∂ z
∂ Φ∂ t
∂ fi
∂ z∂fi
∂ t
where Φ(f1, …, fN)T denotes the vector of concen-tration values, together with prescribed initial concen-trations and the zero f lux conditions
fi(z, 0)fi0(z), 0zL, 0f1
0(z)…fN0(z)fmax;
f z00, f xL0.
It is well known that solutions of equation (28) are dis-continuous in general. The propagation speed of a dis-continuity in the concentration field fi is given by theRankine-Hugoniot condition
si(Φ, Φ): , i1, …, N, (29)
where Φ, fi, Φ and fi
denote the limits of Φ andfi above and below the discontinuity, respectively.This condition can readily be derived from first princi-ples by considering the f lows to and from the inter-face.
For batch sedimentation in a closed column, thevolume average velocity
q:(1f)vff1v1…fN vN
vanishes, which can be seen easily by summing equa-tion Eq. (27) over i1, …, N and by taking intoaccount the continuity equation of the f luid,
((1f)vf )0, (30)
and that q0 at z0. In terms of the relative velocitiesui:viv f, i1, …, N, we can rewrite q0 as
vf(f1u1…fNuN).
Noting that
f ifi(uivf),
we obtain
fifi(Φ)fi(ui(f1u1…fNuN)).
Including in his analysis the momentum equations foreach particle species and that of the f luid and usingequilibrium considerations, Masliyah (1979) derivedthat the constitutive equation for the solid-f luid rela-tive velocity ui should be
uiuiV(f),
where ui denotes the Stokes settling velocity of asingle particle of species i with respect to a f luid ofdensity
ρ(f)fρs(1f)ρf ,
i.e.,
∂∂ z
∂f∂ t
fi(Φ)fi(Φ)fi
fi
52 KONA No.20 (2002)
Fig. 9 Control of continuous sedimentation, after Bustos et al.(1990b) and Chapter 8 of Bustos et al. (1999).
L
z
A
00 t1 tB t2 tD tE t
jL2
jL1
jL1
j
z1
z2
z4 z8
B
C D E
z6
z7
z5
z3
jj
jL0
ui , i1, …, N,(31)
and where V(f) can be chosen as one of the hinderedsettling functions known in the monodisperse case,for example as the ubiquitous Richardson and Zaki(1954) formula V(f)V RZ(f)(1f)n, with parame-ters n1, for 0ffmax. With the parameters
m , di , i1, …, N,
we finally obtain
f i(Φ)m(1f)V(f)fi
N∑j1
djfjdifi. (32)
The mathematical theory of systems of conserva-
di2
d12
gd12
18mf
2(1f)∆ρgr i2
9mf
2(ρsρ(f))gr i2
9mf
tion laws is significantly more complicated, and muchless developed, than that of scalar equations. For ini-tial-boundary value problems of nonlinear coupledsystems such as that given by (28), supplementedwith the f lux density function (32), no general exis-tence and uniqueness result is available. In fact, theanalysis of these polydisperse sedimentation equa-tions is just starting. It is, however, possible to obtainnumerical solutions of these equations by the appli-cation of modern shock-capturing finite differenceschemes for systems of conservation laws.
We present here a numerical example from Bürgeret al. (2000a). Consider the experiment performed bySchneider et al. (1985) with glass beads of the samedensity ρs2790 kg/m3 and of the diameters d10.496 mm and d20.125 mm in a settling column ofheight L0.3 m. The f luid density and viscosity areρf1208 kg/m3 and mf0.02416 kgm1s1, respec-tively. The initial concentrations are f1
00.2 and f20
0.05, and the simulated time here is T1200 s. Fol-lowing Schneider et al. (1985), we employ Richardson
KONA No.20 (2002) 53
Fig. 10 Settling of a bidisperse suspension of heavy particles oftwo different sizes: iso-concentration lines (a) of thelarger particles and (b) of the smaller particles, corre-sponding to the values of fi 0.02, 0.04, 0.06, 0.08, 0.1,0.15, 0.25, 0.3, 0.4, 0.5 and 0.6. The circles and thedashed lines correspond to experimental measurementsof interface locations and shock lines, respectively,obtained by Schneider et al. (1985). Concentration pro-files taken at the times t1, t2 and t3 are given in Figure 11.
Fig. 11 Settling of a bidisperse suspension of heavy particles oftwo different sizes: concentration profiles (a) of thelarger particles and (b) of the smaller particles (index 2)at t151.9 s, t2299.8 s and t3599.7 s.
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.30
0.25
0.20
0.15
0.10
0.05
0.00
z[m]
z[m]
a)
t1 t2 t3a)
0 600 t[s] 1200
0 0.1 0.2 0.3 0.4 0.5 f1 0.7
0.30
0.25
0.20
0.15
0.10
0.05
0.00
z[m]
b)
0 0.1 0.2 0.3 0.4 0.5 f2 0.7
0.30
0.25
0.20
0.15
0.10
0.05
0.00
z[m]
t1 t2 t3b)
0 600 t[s] 1200
t1
t1
t2, t3
t2
t3
and Zaki’s f lux density function with n2.7, which iscut at fmax0.68, see Concha et al. (1992).
Figure 10 displays the simulated iso-concentra-tion lines for each species, together with the exper-imental measurements of interface locations andcomputed shock lines made by Schneider and co-authors, while Figure 11 shows concentration pro-files of both species at three selected times.
4. Phenomenological theory of thickening
4.1 The Theory of MixturesThe Theory of Mixtures (Bowen 1976) states that a
mixture of continuous media with components α maybe described by the following quantities: the apparentcomponent densityρα , the component velocity vα , thecomponent stress tensor Tα , the component bodyforce, and the interaction force between componentsmα . These quantities constitute a dynamic process if,in regions where the field variables are continuous,they obey the following f ield equations:
∇ ·(ραvα)0, (33)
ρα ∇ vα · vα∇ ·Tαραbmα. (34)
In regions with discontinuities, the field equationsmust be replaced by the following jump conditions:
[ρα vα ·e I][ρα vI ·e I], (35)[ρα vα vα · e I][ρα vα vI · e I][Tα ·e I], (36)
where e I is the normal vector of a jump discontinuityand [ · ] (bold square brackets) denotes the jump of aquantity across a discontinuity. The jump balances(35) and (36) can be derived from the appropriateintegral or macroscopic mass and momentum bal-ances (33) and (34) and do not involve nor providesupplementary information. More details can befound in Chapter 1 of Bustos et al. (1999).
4.2 Solid-fluid particulate systemsA particulate system, consisting of a finely divided
solid in a f luid, can be regarded as a mixture of con-tinuous media if the following assumptions are met(Concha et al. 1996):
1. The solid particles are small with respect to thecontaining vessel, and have the same density,size and shape.
2. Particles and f luid are incompressible.3. There is no mass transfer between the solid and
the f luid.
∂ vα
∂ t
∂ρα
∂ t
4. Gravity is the only body force.For such a system, we let αs denote the solid com-ponent and αf the f luid component. Equations (33)and (34) then produce the following balance equa-tions: the solid mass balance
∇ · (fvs)0, (37)
the f luid mass balance
∇ · ((1f)vf)0, (38)
the solid linear momentum balance
ρsf ∇ vs · vs∇ · Tsρsfbm (39)
and the f luid linear momentum balance
ρf(1f) ∇ vf · vf∇ · Tfρf(1f)bm. (40)
Here f denotes the local volume solid concentration, ttime, vs and vf the respective solid and f luid phasevelocity, ρs and ρf the respective solid and f luid massdensities, Ts and Tf the corresponding Cauchy stresstensors, b the body force and m the solid-f luid inter-action force per unit volume.
In the cases of practical interest, the accelerationterms are small and can be neglected; the solid-f luidinteraction force m can be decomposed into a staticterm mb and a dynamic term md; and both stressescan be written as a pressure term and a viscous extrastress. For sake of simplicity, we limit the treatmenthere to one space dimension, in which the viscousextra stress tensors are unimportant, and introducethe constitutive assumption
5. Particles and f luid are contained in an impervi-ous vessel with frictionless walls, in which allvariables are constant across any cross-sectionalareas.
The viscosity terms of the extra stress tensors play,however, a decisive role for the stability of the result-ing model equations in two or three space dimensions(Bürger and Kunik 2001, Bürger et al. 2001d), seealso the discussion in Section 5 of this review. Detailson the justification of these assumptions and on thefollowing deduction can be found in Concha et al.(1996) and Bürger and Concha (1998) for one spacedimensions and in Bürger et al. (2000e) for severalspace dimensions.
Inserting the present assumptions into the linearmomentum balances (39) and (40), we obtain
∂ vf
∂ t
∂ vs
∂ t
∂f∂ t
∂f∂ t
54 KONA No.20 (2002)
ρf(1f)gmbmd, (41)
ρsfgmbmd. (42)
The quantities ps and pf are theoretical variableswhich we now express in terms of measurable vari-ables, namely the pore pressure p and the effectivesolid stress se. Assuming that the local surface poros-ity of every cross section of the network formed bythe solid f locs equals the volume porosity, we canexpress pf and ps in terms of p and se via the formulas
pf(1f)p(1f)[peρf g(Hz)],psf[peρf g(Hz)]se(f),
where pe is again the excess pore pressure, that is,the pore pressure minus the hydrostatic pressure,
pepρf g(Hz). (43)
It can be shown (Concha et al. 1996) that the hydro-static interaction force is proportional to the porepressure and the concentration gradient:
mbp , (44)
and the hydrodynamic interaction force may be mod-eled by a Stokes-like (or Darcy-like) equation as a lin-ear function of the solid-f luid relative velocity:
mdα(z, t)(vsvf), (45)
where α(z, t) is the resistance coefficient of the sus-pension or the sediment.
Collecting all these results, and introducing theminto equations (41) and (42), reduces Eqns. (37)-(40)to
0, (46)
0, (47)
∆ρgf (vsvf), (48)
∆ρgf. (49)
At discontinuities, equations (46)-(49) have to bereplaced by the appropriate jump conditions.
Three important steps have to be taken to trans-form Equations (46) to (49) into a usable mathemati-cal model. First, observe that we consider six scalar
∂se
∂ z∂pe
∂ z
α(f)1f
∂se
∂ z
∂(1f)vf
∂ z∂f∂ t
∂(fvs)∂ z
∂f∂ t
∂f∂ z
∂ps
∂ z
∂pf
∂ z
variables, but have only four scalar equations avail-able to specify them. Thus two quantities should bespecified by constitutive equations. We therefore as-sume that the resistance coefficient α and the effec-tive solid stress function se are given as constitutivefunctions of the types αα(f) and sese(f).
Second, we observe that the volume average veloc-ity of the mixture,
q:fvs(1f)vf≡vs(1f)(vsvf ) (50)
satisfies the simple equation
0 (51)
obtained from summing Equations (46) and (47). It isuseful to replace Eq. (47) by (51).
Finally, we express the solid-f luid relative velocityvsvf from (50) in the form
vsvf (vsq). (52)
Substituting (52) into (48) and (49), we can nowdefine a Dynamic Process for a Particulate System as aset of four unknown field variables: the volumetricsolids concentration f, the excess pore pressure pe,the volume average velocity q and the solids volumef lux
f :fvs, (53)
if in any regions of continuity, these four variables sat-isfy the four scalar field equations
0, (54)
0, (55)
∆ρgf ( ffq), (56)
∆ρgf, (57)
where se and α are given as functions of f. At discon-tinuities Equations (54)-(57) have to be replaced bythe appropriate jump conditions.
4.3 Kinematical sedimentation processAn ideal suspension can be defined as a suspension
of equally sized rigid spherical particles, such as glassbeads, for which the effective solid stress is constant,i.e.
∂se
∂ z∂pe
∂ z
α(f)f(1f)2
∂se(f)∂ z
∂q∂ z
∂f∂ z
∂f∂ t
11f
∂q∂ z
KONA No.20 (2002) 55
≡0. (58)
Introducing (58) into (56), we obtain
fqf .
Defining the Kynch batch f lux density function f bk
f bk(f) by
f bk(f) , (59)
we can rewrite f in the form
ff (f, t)fqf bk(f),
and Eq. (54) turns into the equation (13) of a continu-ous sedimentation process of an ideal suspension.
4.4 Dynamic sedimentation processesIn applying the phenomenological model of a par-
ticulate system to the sedimentation of a f locculentsuspension forming compressible sediments, the fol-lowing two assumptions are made:
6. The suspension is entirely f locculated at thebeginning of the sedimentation process.
7. The solid and the liquid can perform a one-dimensional simple compression motion only.
For f locculent suspensions we consider again theequations (54)-(57) defining a Dynamic Process fora Particulate System, together with two constitutiveequations for the resistance coefficient αα(f) (or,equivalently, for the Kynch batch f lux density func-tion f bkf bk(f)), and for the effective solid stresssese(f).
Isolating f from Eq. (56) and using the definition ofq yields
fqf 1 .In view of Eq. (59), this can be rewritten as
fqff bk(f)1 , (60)
hence the solids mass balance equation can be writ-ten as
(q(t)ff bk(f)) . (61)
Observe that f is now a function of f(z, t ), (∂ f/∂ z)(z, t) and t. However, for the definition of boundaryconditions, it is more convenient to simply refer toff(z, t).
∂f∂ z
f bk(f)s′e(f)∆ρgf
∂∂ z
∂∂ z
∂f∂ t
∂f∂ z
s′e(f)∆ρgf
∂f∂ z
s′e(f)∆ρgf
∆ρf2(1f)2
α(f)
∆ρgf2(1f)2
α(f)
∆ρgf(1f)α(f)
∂se
∂ z
Defining the diffusion coefficient
a(f):
and its primitive
A(f):0
fa(s)ds,
we can rewrite Eq. (61) in the form
(q(t)ff bk(f)) . (62)
We assume here that the effective solid stress is givenas a function of the volumetric solids concentration fsatisfying
se(f)const. for ffc,s′e(f)0 for ffc,
0 for ffc, 0 for ffc,
where fc is the critical concentration or gel point atwhich the solid f locs begin to touch each other. Acommon constitutive equation is the power law (Tillerand Leu 1980, Landman and White 1994)
se(f) 0 for ffc,s0 [(f/fc)n1] for ffc,
n1, s00. (63)
Due to the constitutive assumptions concerning thefunctions f bk and se, we see that
a(f)0 for 0ffc and ffmax,0 for fcffmax.
(64)
Consequently, Eq. (61), or equivalently Eq. (62) is ofthe first-order hyperbolic type for ffc and ff andof the second-order parabolic type for fcffmax.Summarizing, we say that (62) is a quasilinear stronglydegenerate parabolic equation, where the attributestrongly states that the degeneration from parabolic tohyperbolic type not only takes place at isolated val-ues, but on the whole interval [0, fc] of concentrationvalues.
4.5 Initial and boundary conditionsIn one space dimension, we see that the volume
average velocity of the mixture is given by boundaryconditions, and we are left with the quasilinearstrongly degenerate parabolic equation (62) for (z, t)(0, L)(0, T ), together with the equation (57).
Obviously, only Eq. (62) has actually to be solved,since by Eq. (57) the excess pore pressure can alwaysbe calculated from the concentration distribution. It istherefore sufficient to consider initial-boundary valueproblem of Eq. (62) only.
For batch sedimentation of a f locculated suspen-
∂ 2A(f)∂ z 2
∂∂ z
∂f∂ t
f bk(f)s′e(f)∆ρgf
56 KONA No.20 (2002)
sion of initial concentration f0 in a closed column weconsider the initial-boundary value problem of Eq.(62) with q≡0 on QT and the initial and boundary con-ditions f(0, t)f(z, t)0, that is
f(z, 0)f0(z), z[0, L], (65a)
f bk(f) (L, t)0, t[0, T], (65b)
f bk(f) (0, t)0, t[0, T]. (65c)
For continuous sedimentation we assume that thesolids f lux at z0, f(0, t) reduces to its convectivepart q(t)f(0, t), and that the concentration does notchange when the concentrated sediment leaves thethickener. This implies the equation
f(0, t)≡q(t)ff bk(f) (0, t)q(t)f(0, t),
from which we deduce that boundary condition (65c)is valid also in the continuous case. At zL, we pre-scribe in the continuous case a solids feed f lux fF(t),i.e. f(L, t)f F(t), which leads to the following bound-ary condition replacing (65b):
f bk(f)q(t)f (L, t) fF(t), t[0, T]. (66)
4.6 Mathematical analysis of the initial-boundary value problems
It is well known that, due to both the type degener-acy and to the nonlinearity of the function f bk, solu-tions of (62) are discontinuous and have to be definedas entropy solutions. The basic ingredient of theappropriate solution concept of entropy weak solu-tions is an entropy inequality, which can be formu-lated by suitably modifying the well-known results ofthe pioneering papers by Kruzkov (1970) and Vol’pert(1967) for first-oder partial differential equations andby Vol’pert and Hudjaev (1969) for second-order par-tial differential equations.
By the vanishing viscosity method using a mollifiertechnique, Bürger et al. (2000c) showed that an en-tropy solution of the initial-boundary value problem(62), (65) exists, even if the function aa(f) has ajump at ffc, which in turn is a consequence of thefact that the vast majority of effective solid stressfunctions sese(f) suggested in the literature havediscontinuous derivatives s′e at ffc. In that case, theintegrated diffusion coefficient A(f) will only be con-tinuous, but not differentiable at ffc.
The existence proof for this case is a fairly straight-
∂A(f)∂ z
∂A(f)∂ z
∂A(f)∂ z
∂A(f)∂ z
forward extension of the previous proof presented byBürger and Wendland (1998a). However, to showuniqueness of entropy solutions for a discontinuousdiffusion function, new arguments have to be in-voked. In fact, the uniqueness proof by Bürger andWendland (1998a) is based on a particular jump con-dition derived by Wu and Yin (1989), which is validonly for Lipschitz continuous diffusion functions a(f)and is limited to one space dimension. Fortunately, arecent result by Carrillo (1999) made it possible toavoid these limitations. He utilized a technique knownas “doubling of the variables”, introduced by Kruzkov(1970) as a tool for proving the L1 contraction prin-ciple for entropy solutions of scalar conservationlaws, in order to establish the uniqueness result.Most notably, Carrillo’s approach is not based onjump conditions and only presupposes that A(f) isLipschitz continuous, i.e. a(f) may have discontinu-ities. Carrillo’s results were employed by Bürger et al.(2000c) to show uniqueness of entropy solutions ofthe initial-boundary value problem (62), (65).
4.7 Numerical methods for sedimentation-consolidation processes
A numerical scheme that approximates entropysolutions of the initial-boundary value problem (62),(65) (or one of its variants) should have the built-inproperty to reproduce discontinuities of the entropysolutions, most notably the suspension/sedimentinterface where the equation changes type, appropri-ately without the necessity to track them explicitly,i.e. the scheme should posses the shock capturingproperty. Moreover, an obvious requirement is thatthe scheme should approximate (converge to) thecorrect (entropy) solution of the problem it is tryingto solve. This clearly rules out classical schemesbased on naive finite differencing for strictly parabolicequations, which otherwise work well for smoothsolutions, see Evje and Karlsen (2000).
In this section we present an example of a work-ing finite difference scheme having all these desiredproperties, and which is moreover easy to implement.This scheme is presented for the application to batchor continuous sedimentation. There also exist vari-ants of the scheme for the simulation of batch cen-trifugation of a f locculated suspension (Bürger andConcha 2001) or of pressure filtration (Bürger etal. 2001b). For alternative schemes, in particularschemes that are based on operator splitting and fronttracking, that are equally suitable for the sedimenta-tion-consolidation model we refer to Bürger et al.(2000d) and the references cited therein.
KONA No.20 (2002) 57
The scheme considered here can be referred to asgeneralized upwind scheme with extrapolation. Weconsider a rectangular grid on QT with mesh sizes∆zL/J, ∆tT/N and let fj
n( j∆z, n∆t). The calcul-ation starts by setting
fj0f0( j∆z), j0, …, J.
The partial differential equation to be solved, Eq.(62), is approximated by the explicit scheme
q(n∆t)
, j1, …, J1. (67)
The boundary condition at z0 is inserted into Eq.(67) for j0:
q(n∆t) .
For boundary condition (65b), we obtain for jJfjn
f1(n∆t), while boundary condition (65c) turns theinterior scheme (67) into the boundary formula
q(n∆t)
.
The numerical f lux function of the generalized up-wind or Engquist-Osher method (Engquist and Osher,1981) is given by
fbkEO(u, v):fbk(0)0
umin f ′bk(s), 0ds0
vmax f ′bk(s), 0ds.
The quantities fjL and fj
R are given by extrapolation:
fjL :fj
n sjn, fj
R:fjn sj
n,
which makes the scheme second order accurate inspace. The slopes are given by s0
ns1ns n
J1s nJ 0 and
are otherwise calculated using a limiter function, e.g.
s nj MMθ(fj
nfnj1), , θ(fn
j1fjn),
θ[0, 2], j2, …, J2
using the so-called minmod limiter function
mina, b, c if a, b, c0,MM(a, b, c)maxa, b, c if a, b, c0,
0 otherwise,
in order to ensure that the total variation of the
fnj1fn
j1
21∆z
∆z2
∆z2
A(f Jn1)A(fn
J )∆z2
fbkEO(f j
R, fLj1)fbk
EO(f Jn1, fn
J )∆z
Ψ(n∆t)fJn
∆zfJ
n1fJn
∆t
A(f1n)A(f0
n)∆z2
fbkEO(f0
n, f1n)
∆zf1
nf0n
∆zf0
n1f0n
∆t
A(fnj1)2A(fn
j )A(fnj1)
∆z2
fbkEO(f j
R, fLj1)fbk
EO(f jR1, fL
j )∆z
fLj1f j
R
∆zfj
n1fjn
∆t
numerical solution is bounded. The scheme con-verges to the entropy solution if the following stabilitycondition is satisfied:
maxt[0, T]q(t) max
f[0, fmax] f ′bk(f) maxf[0, fmax]a(f) 1.
The Engquist-Osher method has also been used byother authors for the simulation of sedimentation pro-cesses, see e.g. Amberg and Dahlkild (1987).
4.8 Numerical examples4.8.1 Simulation of batch sedimentation
As a first example of the use of the numerical tech-nique, we present in the sequel four different simu-lations of batch sedimentation in which publishedsettling experiments were utilized to compare thenumerically predicted settling behaviour with therespective experimental findings. In every case, therequired model functions se and f bk had to be deter-mined or constructed from the published experimen-tal information. We refer to Bürger et al. (2000b) andGarrido et al. (2000) for details.
The simulation of a settling experiment by Holdichand Butt (1997), as presented by Bürger and Karlsen(2001b), shall be discussed here in detail (Figures12 and 13). For simulations of experiments per-formed by Shirato et al. (1970), Shih et al. (1986) andBergström (1992), we present here only the numeri-cal results (Figures 14, 15 and 16), and refer to thepaper by Garrido et al. (2000) for details.
Holdich and Butt (1997) performed sedimentationexperiments with a suspension of talc in tap water(∆ρ1690 kg/m3) and obtained settling plots fromconductivity measurements. From the published ex-perimental data, Garrido et al. (2000) obtained the fol-lowing constitutive functions:
v(a2f2a1f) for ffM: ,
f bk(f)v for fMffmax:b1/b2,
se(f)0 for ffc:0.04,2.14107f7Pa for ffc,
where the constants have the values v4.4106
m/s, a13.0693, a228.5004, b112 and b232.5.The remaining parameters are L0.331 m and ∆zL/300. We considered three different initial concen-trations, f00.052, 0.072 and 0.112. Figures 12 and13 show the corresponding numerical simulations.Observe that essentially due to the presence of thediffusion term, the settling process can be simulated
(1f)3
b1b2f
3b1b2
2b2
2∆t∆z2
∆t∆z
58 KONA No.20 (2002)
KONA No.20 (2002) 59
Fig. 12 Simulation of batch sedimentation of a talc suspension in a column (Bürger and Karlsen 2001, Garrido et al. 2000, Holdich and Butt1997): concentration profiles at different times for three different initial concentrations.
Fig. 13 Simulation of batch sedimentation of a talc suspension in a column, after Bürger and Karlsen (2001): settling plots for three differentinitial concentrations (0.052, top left, 0.072, top right, and 0.112, bottom). The symbols denote the measured iso-concentration lines.
f00.052
t1
t1
t1
t2
t3
t3
t2
t1
t4t5 t6
t2
t3
t3
t2
t1
t4
t2
t2
t4, t5, t6
t5, t6
t1
t3
f00.072 f00.1120.3
0.25
0.2
0.15
0.1
0.05
0
z[m]
0 0.1 0.2 0 0.1 0.2 0 0.1 0.2 f[]
0.300
0.250
0.200
0.150
0.100
0.050
0.0000 2000 4000 6000 8000 t[s] 10000
z[m]0.300
0.250
0.200
0.150
0.100
0.050
0.0000 2000 4000 6000 8000 t[s] 10000
z[m]
0.300
0.250
0.200
0.150
0.100
0.050
0.0000 2000 4000 6000 8000 t[s] 10000
z[m]
0.04
0.120.10
0.080.06
0.140.16
0.04, 0.06
0.12 0.140.16
0.18
0.20
0.21
0.100.08
0.18
0.20
0.10
0.12
0.18
0.20
0.21
0.22
0.160.140.04, 0.06, 0.08
interface height0.060.080.100.120.140.160.18
interface height0.080.100.120.140.160.180.200.21
interface height0.120.160.200.22
by the numerical algorithm although the f lux densityfunction has a singularity at f0.3692.
The simulations of these four experimental casesillustrate that the phenomenological model is ableto predict the most important features normallyobserved during batch settling of initially unnet-worked suspensions in a column, which are the fol-lowing:
• Before sedimentation begins, the suspension ishomogenized by stirring to obtain a homoge-neous concentration. When sedimentation starts,all the solid f locs have the same settling velocity
so that they form a sharp water-suspension inter-face in the upper portion of the column. Thisstage is called hindered settling.
• Particles at the bottom of the column rapidlyoccupy the entire surface available. Immediately,new f locs start to accumulate over the depositedsediment pressing over them and, in that way,squeezing out some of its retained water. Fromthat point on the sediment is under compressionor consolidation. The sediment surface, that is thesuspension-sediment interface, moves upward asnew particles incorporate into the sediment.
60 KONA No.20 (2002)
Fig. 14 Simulation of the experiment by Shirato et al.: comparison of simulated with measured concentration (left) and excess pore pressureprofiles (right); after Garrido et al. (2000).
Fig. 15 Comparison of concentration profiles measured by Shihet al. (1986) with numerical simulation of the settlingexperiment, after Garrido et al. (2000).
Fig. 16 Comparison of concentration profiles measured byBergström (1992) with numerical simulation of the set-tling experiment, after Garrido et al. (2000).
1.00
0.80
0.60
0.40
0.20
0.00
z/zc[]
z[m]
z[m]30[s]
90[s]
180[s]
300[s]
420[s]
5[d]8[d]13[d]26[d]55[d]
0.14 0.16 0.18 0.20 0.22 0.24 0.26 f[]
1.00
0.80
0.60
0.40
0.20
0.00
z/zc[]
0.0 0.2 0.4 0.6 0.8 1.0 pe/pemax[]
4[h]
8[h]
16[h]
24[h]
32[h]
t0
8[h]
16[h]
24[h]
32[h]
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.20
0.15
0.10
0.05
0.000.00 0.05 0.10 0.15 f[] 0.00 0.10 0.20 0.30 0.40 f[]
• In the case of suspensions with ffc, at eachpoint in the column under the supernate-suspen-sion interface the concentration either stays con-stant or increases.
• Utilizing X-ray, γ-ray or conductivity measure-ment instruments, one can generate data fromwhich it is possible to track determined concen-tration values as they move upward in the col-umn. For dilute concentrations, that is in regionswhere ffc, these iso-concentration curves formstraight lines which in cylindrical vessels areidentical to the characteristics of the scalar conser-vation law (7). In the compression zone, that is inthe sediment, the iso-concentration lines for con-centrations greater than the critical emerge fromthe bottom z0 at positive slope, and becomehorizontal as the consolidation process proceeds.Experiments in which this behaviour is particu-larly well visible have been reported by Scott(1968a), Been and Sills (1981) and Tiller et al.(1990).
• At a given instant and a certain height in the col-umn, the water-suspension and the suspension-sediment interfaces meet, leaving an area ofapproximately triangular shape to their left in asettling plot, in which the concentration equalsthe constant initial concentration f0. The coordi-nates of this event are the critical time tc and thecritical height zc, forming the critical point atwhich simultaneous hindered settling and consol-idation end and only consolidation perdures. Thenew suspension-sediment interface moves down-ward at a diminishing (in absolute value) speed.
• After a sufficiently large finite time, consolidationends and a constant concentration gradient isestablished from the critical concentration at thetop to a greater concentration at the bottom. Con-sequently, the entire sedimentation-consolidationprocess terminates after a finite time. In spite ofthe fact that this observation has been made by aseries of numerical experiments, it is still to beshown that it is an inherent property of the math-ematical model.
4.8.2 Continuous thickening of f locculated suspensionsThe second example presents a simulation of the
dynamic behaviour of a f locculated suspension anIdeal Continuous Thickener from Bürger et al.(2000d). The numerical algorithm employed for thissimulation is not based on the one presented in Sec-tion 4.7, but rather on an equally suited three-stepoperator splitting method, see Bürger et al. (2000d)
and Chapter 9 of Bustos et al. (1999) for details. We use a Kynch batch f lux density function of the
well known Richardson and Zaki type (1954),
f bk(f)6.05104f(1f)12.59 m/s,
and the effective solid stress function
se(f) 0 for ffc0.23,5.35exp(17.9f) Pa, for ffc
determined by Becker (1982) based on experimentalmeasurements on Chilean copper ore tailings. Notethat this choice of the function se(f) leads to a diffu-sion function a(f) that is discontinuous. Further-more, we use the parameters ∆ρρsρf1500 kg/m3
and g9.81 m/s2. We consider continuous sedimentation with piece-
wise constant average f low velocity q(t) and feed f luxf F(t). We start with a steady state, that is, a stationaryconcentration profile, and then attain two new steadystates by manipulating f F and q appropriately. Steadystates are obtained as stationary solutions of equation(62). It is assumed that a desired discharge concen-tration fD is prescribed. Then the discharge f lux isf DqfD. The requirement that at steady state the dis-charge f lux must equal the feed f lux, f Df F, leads toan equation from which the concentration value fL atzL can be computed:
qfLf bk(fL)qfD. (68)
The sediment concentration profile is then calculatedfrom
, z0, f(0)fD. (69)
The boundary value problem (69) is solved until thecritical concentration is reached at a certain height zc
denoting the sediment level. Above this level, the con-centration assumes the constant value fL calculatedfrom (68). The choice of fD is subject to the require-ment that the concentration increases downwards.See Bürger et al. (1999) and Bürger and Concha(1998) for details. Consider the three steady stateswith parameters given in Table 1. We now prescribethe steady state f1(z) as the initial concentration pro-
qf(z)f bk(f(z))qfD
a(f(z))dfdz
KONA No.20 (2002) 61
i qi[104 m/s] f iD fi
L f iF[104 m/s] zc[m]
1 0.10 0.41 0.0072993552 0.041 3.10
2 0.15 0.38 0.0104589127 0.057 1.77
3 0.05 0.42 0.0036012260 0.021 2.49
Table 1 Parameters of the steady states considered in Figure 17.
file. After operating the ICT at this steady state forsome time, we then change successively to the steadystates f2(z) and f3(z). The changes in fL(t) and q(t)will be described in detail now.
The ICT is operated at the steady state f1(z) for0t t250000 s. At tt2, we change the volumeaverage velocity q to the next smaller value q2. How-ever, the value of the feed f lux density should remainconstant during this operation, therefore the bound-ary concentration value fL
1 has to be changed to a newvalue f12
L , which is calculated from the feed f lux conti-
nuity condition
q2f12L fbk(f12
L ) f F1,
yielding f12L 0.0076397602. The change from fL
1 tof12
L should be performed at such a time that the newvalue f12
L is present above the sediment level at tt2.The change propagates as a rarefaction wave into thevessel. This rarefaction wave is marked by R1 in Fig-ure 17 b). We assume that the relevant speed is
s2q1f ′bk(f12L )5.0607104 m/s,
62 KONA No.20 (2002)
Fig. 17 Simulation of transitions between three steady states in an ICT: a) prescribed values of fL, b) settling plot (the iso-concentration linescorrespond to the annotated values), c) prescribed values of q(t), d) the numerically calculated discharge concentration, together withthe discharge concentrations of the target steady states, e) the numerically computed solids discharge f lux, compared with prescribedvalues of the feed f lux.
4.00
3.20
2.40
1.60
0.80
0.00
0.015
0.000
0.00
0.20
0.45
0.35
0.00
1.00
fL1
fL(t)
z[m]
q104[m/s]
fD105[m/s]
f(0, t)
t1
R1 R2 R3 S1
t2
q1
fD10.41
fD20.38
fD30.42
q2
f F1 f F
1f F12
f F2 f F
2f F23 f F
3
q3
t3 t4
t5 t[h]
0.410.38
0.35
0.32
0.29
0.26
0.10, 0.20
0 60 120 180 240 300
fc0.23
t6
fL2
fL3
fL23
f12L
a)
b)
c)
d)
e)
therefore the change from fL1 to f12
L is performed at
t1t2 48222 s13.4 h.
It should be noted that the feed f lux does not remainprecisely constant; it is different from f F
1 in the smalltime interval [t1, t2], during which we have
f F f F12q1f12
L f bk(f12L )f F
1(q1q2)f12L
0.04138104 m/s.
From Figure 17 e) it becomes apparent that for tt2,the actual solids discharge f lux density f D(t )q2f(0, t) is larger than the feed f lux f F prescribed. Thisleads to a slow emptying of the vessel and the sedi-ment level falls at almost constant speed. It may there-fore be estimated that it will have fallen to the heightz c
2 of the next target steady state by t316560 s87.9h. At that time, the concentration value fL
2 corre-sponding to the new feed f lux density f F
2 should havepropagated to the sediment level. Again, this changepropagates downwards as a rarefaction wave (markedby R2 in Figure 17 b)). The relevant propagationvelocity may be taken as
s4q2f ′bk(fL2)4.7746104 m/s,
hence we change fL again from f12L to fL
2 at
t3316560 s 311854 s86.6 h.
For tt3, both the value of q and the feed f lux fF
correspond to the steady state f2(z) given in Table 1.Although this value is not prescribed explicitly, weobserve in Figures 17 d) and e) that both the dis-charge f lux and the discharge concentration convergeto the appropriate values pertaining to the targetsteady state f2(z). At t5600000 s166.7 h we wish tochange to the next steady state by changing q from q2
to q3. The feed f lux above the sediment is assumed toremain constant. Therefore fL
2 is changed to the valuefL
230.0113417003 which is calculated from
q3fL23f bk(fL
23)f F2.
Again, the change from fL2 to fL
23 propagates as a rar-efaction wave into the vessel (marked by R3 in Fig.17 b)). The value fL
23 propagates at speed
s6q2f ′bk(fL23)4.6338104 m/s,
hence the change is performed at
t4t5 595182 s165.3 h.
Similar to the change from fL1 to f12
L , the feed f lux
Lz c2
s6
Lz c2
s4
Lzc1
s2
assumes a value in the time interval [t4, t5] which isslightly different from f F
2; namely, there we have
fFf F23q2fL
23f bk(fL23) f F
2(q3q2)fL23
0.0559104 m/s.
After tt5, the feed f lux exceeds the discharge f luxin absolute value, as can be conceived from Fig. 17e). This causes a rise of the sediment level, again tak-ing place at apparently constant speed, and it will haveattained the last desired level z c
3 when t672240 s186.7 h. At that time, the last value of the feed flux f F
3
should be valid above the sediment level. In contrastto the previous changes of fL, the change from fL
23 tofL
3 propagates as a shock (marked by S1 in Fig. 17b)) with the speed
s7q3 5.1391104 m/s.
This discontinuity reaches the sediment level at thedesired time if the change from fL
23 to fL3 is done at
t7672240 s 669301 s185.9 h.
After tt7, no more changes are made. Figures 17b), d) and e) indicate convergence to the third steadystate. The simulation is terminated after a simulatedtime of T300 h1080000 s.
5. Discussion
We now comment some of our results that are out-lined in Sections 3 and 4, and put them in the appro-priate perspective of current research efforts, bothour own and those of other groups. We begin witha remark related to the way Petty (1975) extendedKynch’s theory to continuous sedimentation by mod-eling feed and discharge by boundary conditions.This description was the starting point for the treat-ment presented in Section 3.3 and gave rise to theinvestigation of conservation laws with boundary con-ditions. However, this model still has severe short-comings, among them the neglected clarificationzone, that is the zone above the feed level to whichsolids may pass in the case of overf low, and the viola-tion of conservation of mass principles due to thechoice of boundary conditions, since entropy bound-ary conditions lead to mathematical well-posedness,but may be physically incorrect. More appropriatemodels for continuous sedimentation within Kynch’stheory were studied by Diehl in a recent series ofpapers (Diehl 1995, 1996, 1997, 2000, 2001), in whichhe analyses a model of continuous sedimentation in a
Lzc3
s7
f bk(fL23)f bk(fL
3)fL
23fL3
KONA No.20 (2002) 63
so-called settler-clarifier, in which the feed, dischargeand overf low mechanisms are merely expressed bydiscontinuities of the f lux-density function at the bot-tom, at the (intermediate) feed level and at the top ofthe vessel, and an additional singular source term atthe feed level. Conservation of mass yields jump con-ditions valid across these discontinuities. The appar-ent advantages of this elegant model consist in thecompleteness of the treatment (since the overf lowzone above the feed level, zL, has so far not beenconsidered in our work) and in the avoidance ofboundary conditions, such that only initial conditionsneed to be considered. Although exact solutions canbe constructed for all practically relevant cases, aglobal existence and uniqueness result is not yetavailable, so we do not yet wish to elaborate on thissedimentation model here, but recommend studyingDiehl’s original papers.
We now discuss some issues related to the phenom-enological theory of sedimentation. It should be men-tioned that the postulate of a constitutive equation ofthe type sese(f) follows widespread usage in theengineering literature, see Bustos et al. (1999) andthe references cited therein and recent handbooks onsolid-liquid separation such as Rushton et al. (2000),Wakeman and Tarleton (1999) and Concha (2001).One should, however, bear in mind that this relation-ship is a strong (albeit in many cases useful) simplifi-cation, and that different approaches for se, althoughaltering the nature of the resulting model equation,could possibly describe better observed consolidationbehaviour. In fact, several researchers recently pro-posed alternate equations for the effective solid stressfunction. Some of them suggest expressing se as anintegral (with respect to height) of a new concentra-tion-dependent phenomenological function (Dreher1997, Toorman and Huysenstruyt 1997, Toorman1999). It can be easily seen that in the present modelframework this will lead again to a first-oder equation,i.e. one essentially falls back to the equation (7) ofKynch’s kinematic sedimentation theory, with all itswell-known shortcomings. A different, and to ourview potentially more promising approach was ad-vanced by Zheng and Bagley (1998, 1999), who pro-posed an effective stress equation (Eq. 18 of Zheng,1998) that depends on both the value of the localsolids concentration and its rate of change. Therebythe necessity to refer to a critical concentration is re-moved. However the appropriate mathematical frame-work, in which the resulting mathematical modelshould be studied, still remains to be explored.
Another natural question arising from the presenta-
tion of Section 4 is whether the phenomenologicalmodel extends to several space dimensions and if so,under which extensions. The constitutive assump-tions introduced in Section 4 remain valid if the one-dimensionality of the motion is no longer imposed,that is, if a truely multidimensional framework is con-sidered. It is then straightforward to derive the follow-ing field equations, which replace (54)-(57):
∇ · (fqf bk(f)k)∇ ·(a(f)∇ f), (70)
∇ ·q0, (71)
∇ pe∆ρgfk∇ se(f). (72)
In two or three space dimensions, the unknown f lowvariables are the concentration j, the volume averagef low velocity field q and the excess pore pressure pe.The latter can be calculated a posteriori from the con-centration distribution. In one space dimension, how-ever, qq(t) is determined by a boundary condition,and only solving the scalar equation (62) for f re-quires computational effort.
Schneider (1982, 1985) was the first to observe aremarkable property of equations (70)-(72): takingthe curl of equation (72) reveals that f depends onlyon the vertical space coordinate and on time wher-ever it is continuous. The same will then be true forthe vertical component of q. Under specific assump-tions on the geometry of the vessel considered, thevelocity field q can be determined from suitableboundary conditions. However, since equation (72)does not depend on q, equations (70)-(71) are in mostcircumstances not sufficient to determine that quan-tity, and in any case the resulting mathematical modelis not well posed and seems to be of little practical use(Bürger and Kunik 2001).
The independence of equation (72) from q is, ofcourse, a result of the simplifications performedbased on the dimensional analysis. As mentionedbefore, the more general phenomenological sedimen-tation-consolidation theory, in the sense that not onlyseveral space dimensions but also viscous stressesare considered, and that fewer terms are neglected, isdeveloped by Bürger, Wendland and Concha (2000e).That analysis leads to a set of equations that are simi-lar to (70)-(72), but in which the analogue of equa-tion (72) contains additional viscous and advectiveacceleration terms. That equation, together with (71),represents a nonlinear version of the well-knownNavier-Stokes equations for an incompressible f luid,to which (in the proper sense) they reduce in the caseof a pure f luid (f≡0). The model equations derived
∂f∂ t
64 KONA No.20 (2002)
by Bürger et al. (2000e) (see also Bürger 2000) aresufficient for the computation of f, q and pe. However,some new source terms describing the interactionbetween the evolution of the concentration distribu-tion, or kinematic waves, and the average f low fieldappear. In one space dimension, these terms affectonly the excess pore pressure distribution, so that theinteraction they describe becomes effective only ina truly two- or three-dimensional setup. Schneider(1985) pointed out that this interaction makes thetwo- or three-dimensional treatment qualitatively dif-ferent from what is known in one space dimension.
The significance of these terms and their actualmagnitude has not yet been analysed. Moreover, ifthe viscous stress tensors are not neglected, addi-tional difficulties arise from the necessity to relate thesolid and f luid phase viscosities, which are theoreticalvariables, to the effective viscosity of the mixture,which can be measured experimentally. Obviouslyadditional steps of progress in the theoretical under-standing of the phenomenological framework have tobe made before a definite multidimensional model forsedimentation with compression can be advocated.Having said this, some recent results by Bürger et al.(2001d) are available.
Finally, we mention that the phenomenologicalframework has led to a variety of similar mathemati-cal models of spatially one-dimensional solid-liquidseparation processes of f locculent suspensions suchas centrifugation (Bürger and Concha 2001, Bürgerand Karlsen 2001a) pressure filtration (Bürger et al.2001b, Garrido et al. 2001) of f locculated suspensions,and can be regarded as the foundation of a robust andunified theory of solid-liquid separation of f locculatedsuspensions (Bürger et al. 2001a, Garrido et al. 2002).
6. Concluding remark
This paper has outlined the development of re-search in sedimentation and thickening during thelast century from the invention of the Dorr thickenerin 1905 onwards. The development that took place inthe first half of that period was perhaps best charac-terized in the introduction of Roberts’ paper (1949):“Prior to 1916, thickening was an art, and any accu-rate decision as to what size of machine to install tohandle a given tonnage of a specific ore must have beenone of those intuitive conclusions, based on both inti-mate and extensive acquaintance with thickeners andore pulps. Then in 1916 “knowledge of acquaintance,”became “knowledge about” with the publication of theCoe and Clevenger paper. The unit operation of thicken-
ing had graduated to the status of an engineering sci-ence.” He concludes that “Thickening has long held thestatus of an engineering science but it is still long wayfrom being an exact science. On the other hand there isconsiderable “art” involved in deciding certain points;namely, what safety factor to specify to take care of pos-sible changes in feed characteristics; whether to use thecompression depth indicated or to increase the area toget a lower compression depth; how to prophesy islandformation; what to do about island formation if it doesoccur, and so on. Careful, planned observation and re-porting on part of operators is needed before some ofthese items can be reduced to the engineering sciencestatus.”
Roberts’ statements show that the title of his paper,Thickening Art or Science?, must be understood asa serious question thrown up from the status ofknowledge of 1949. He could not foresee that onlythree years later, Kynch’s paper would definitely turnsedimentation and thickening not only into an engi-neering science, but eventually also into a topic ofprofound and still very active research in a variety ofdisciplines, such as chemistry, biology medicine and,most notably from the authors’ viewpoint, mechanicsand mathematics.
Acknowledgements
The preparation of this work was made possiblethrough Fondef Project D97-I2042 at the Universityof Concepción and through the Sonderforschungs-bereich 404 at the University of Stuttgart.
References
Adams, W.H. Jr. and Glasson, P.S. (1925) MIT Thesis, citedby Robinson (1926).
Adorján, L.A. (1975) ‘A theory of sediment compression’, XIInternational Mineral Processing Congress, Cagliari,Italy, Paper 11:1-22.
Adorján, L.A. (1977) Determination of thickener dimensionsfrom sediment compression and permeability test re-sults, Trans. Inst. Min. Met. 85, C157-C163.
Agricola, G. (1556) De Re Metallica. Translated from Latinby H.C. Hoover, Dover Publications, Inc., New York1950.
Amberg, G. and Dahlkild, A.A. (1987) Sediment transportduring unsteady settling in an inclined channel, J. FluidMech. 185, 415-436.
Ashley, H.H. (1909) Theory of the settlement of slimes,Min. Scient. Press, 831-832, June 12.
Ardaillon, E. (1897) Les Mines du Laurion dans l’Antiquité.Paris.
Auzerais, F.M., Jackson, R. and Russel, W.B. (1988) The res-
KONA No.20 (2002) 65
66 KONA No.20 (2002)
olution of shocks and the effects of compressible sedi-ments in transient settling, J. Fluid Mech. 195, 437-462.
Ballou, D.P. (1970) Solutions to non-linear hyperbolicCauchy problems without convexity conditions, Trans.Amer. Math. Soc. 152, 441-460.
Barrientos, A. (1978) Modelo Fenomenológico de la sedi-mentación: obtención de parámetros y aplicación, M.Sc.Thesis, University of Concepción, Chile.
Bascur, O. (1976) Modelo fenomenológico de suspensiones ensedimentación, B.Sc. Thesis, University of Concepción,Chile.
Bascur, O. (1989) A unified solid-liquid separation frame-work. Presented at the First Regional Meeting of theAmerican Filtration Society, Houston, Texas, Oct. 30-Nov. 1, 1989, 11 pp.
Batchelor, G.K. (1982) Sedimentation in a dilute polydis-perse system of interacting spheres. Part 1. Generaltheory, J. Fluid Mech. 119, 379-408.
Batchelor, G.K. and Wen. C.S. (1982) Sedimentation in adilute polydisperse system of interacting spheres. Part2. Numerical results, J. Fluid Mech. 124, 495-528.
Becker, R. (1982) Espesamiento continuo, diseño y simu-lación de espesadores, M.Sc. Thesis, University of Con-cepción, Chile.
Been, K. and Sills, G.C. (1981) Self-weight consolidation ofsoft soils: An experimental and theoretical study,Géotechnique 31, 519-535.
Behn, V.C. (1957) Settling behavior of waste suspensions, J.San. Engrg. Div. ASCE 83 No. SA 5, 1423-11423-20.
Bergström, L. (1992) Sedimentation of f locculated aluminasuspensions: γ-ray measurements and comparison withmodel predictions, J. Chem. Soc. Farad. Trans. 88,3201-3211.
Bowen, R. (1976) Theory of mixtures. In: Eringen, A.C.(Ed.), Continuum Physics Vol. 3, Academic Press, NewYork, pp. 1-127.
Bürger, R. (1996) Ein Anfangs-Randwertproblem einer quasi-linearen parabolischen entarteten Gleichung in der Theo-rie der Sedimentation mit Kompression, Doctoral Thesis,University of Stuttgart, Germany.
Bürger, R. (2000) Phenomenological foundation and mathe-matical theory of sedimentation-consolidation proc-esses, Chem. Eng. J. 80, 177-188.
Bürger, R., Bustos, M.C. and Concha, F. (1999) Settlingvelocities of particulate systems: Phenomenologicaltheory of sedimentation: 9. Numerical simulation ofthe transient behaviour of f locculated suspensions inan ideal batch or continuous thickener. Int. J. MineralProcess. 55, 267-282.
Bürger, R. and Concha, F. (1998) Mathematical model andnumerical simulation of the settling of f locculated sus-pensions, Int. J. Multiphase Flow 24, 1005-1023.
Bürger, R. and Concha, F. (2001) Settling velocities of partic-ulate systems: 12. Batch centrifugation of f locculatedsuspensions, Int. J. Mineral Process., 63, 115-145.
Bürger, R., Concha, F., Fjelde, K.-K. and Karlsen, K.H.(2000a) Numerical simulation of the settling of polydis-perse suspensions of spheres. Powder Technol. 113, 30-
54.Bürger, R., Concha, F. and Garrido, P. (2001a) A unified
mathematical model of thickening, filtration and cen-trifugation of f locculated suspensions. In: da Luz, A.B.,Soares, P.S.M., Torem, M.L. and Trinidade, R.B.E.(eds.), Proceedings of the VI Southern Hemisphere Meet-ing on Mineral Technology, Rio de Janeiro, Brazil, 2001,vol. 1, CETEM/MCT, Rio de Janeiro, 123-129.
Bürger, R., Concha, F. and Karlsen, K.H. (2001b) Phenome-nological model of filtration processes: 1. Cake forma-tion and expression. Chem. Eng. Sci. 56, 4537-4553.
Bürger, R., Concha, F. and Tiller, F.M. (2000b) Applicationsof the phenomenological theory to several publishedexperimental cases of sedimentation processes, Chem.Eng. J. 80, 105-117.
Bürger, R., Evje, S. and Karlsen, K.H. (2000c) On stronglydegenerate convection-diffusion problems modelingsedimentation-consolidation processes, J. Math. Anal.Appl. 247, 517-556.
Bürger, R., Evje, S., Karlsen, K.H. and Lie, K.-A. (2000d)Numerical methods for the simulation of the settling off locculated suspensions, Chem. Eng. J. 80, 91-104.
Bürger, R., Fjelde, K.-K., Höf ler, K. and Karlsen, K.H.(2001c) Central difference solutions of the kinematicmodel of settling of polydisperse suspensions and three-dimensional particle-scale simulations, J. Eng. Math.41, 167-187.
Bürger, R. and Karlsen, K.H. (2001a) A strongly degenerateconvection-diffusion problem modeling centrifugationof f locculated suspensions. In: Freistühler, H. and Warnecke, G. (eds.), Hyperbolic Problems: Theory,Numerics, Applications. Birkhäuser Verlag, Basel, 207-216.
Bürger, R. and Karlsen, K.H. (2001b) On some upwindschemes for the phenomenological sedimentation-con-solidation model, J. Eng. Math. 41, 145-166.
Bürger, R. and Kunik, M. (2001) A critical look at thekinematic-wave theory for sedimentation-consolidationprocesses in closed vessels, Math. Meth. Appl. Sci. 24,1257-1273.
Bürger, R., Liu, C. and Wendland W.L. (2001d) Existenceand stability for mathematical models of sedimentation-consolidation processes in several space dimensions. J.Math. Anal. Appl. 264, 288-310.
Bürger, R. and Tory, E.M. (2000) On upper rarefactionwaves in batch settling. Powder Technol. 108, 74-87.
Bürger, R. and Wendland, W.L. (1998a) Existence, unique-ness and stability of generalized solutions of an initial-boundary value problem for a degenerating quasilinearparabolic equation. J. Math. Anal. Appl. 218, 207-239.
Bürger, R. and Wendland, W.L. (1998b) Entropy boundaryand jump conditions in the theory of sedimentation withcompression. Math. Meth. Appl. Sci. 21, 865-882.
Bürger, R., Wendland, W.L. and Concha, F. (2000e) Modelequations for gravitational sedimentation-consolidationprocesses, Z. Angew. Math. Mech. 80, 79-92.
Buscall, R. and White, L.R. (1987) The consolidation of con-centrated suspensions, Part 1. The theory of sedimenta-
KONA No.20 (2002) 67
tion, J. Chem. Soc. Faraday Trans. 1 83, 873-891.Bustos, M.C. and Concha, F. (1988) On the construction of
global weak solutions in the Kynch theory of sedimenta-tion, Math. Meth. Appl. Sci. 10, 245-264.
Bustos, M.C. and Concha, F. (1992) Boundary conditions forthe continuous sedimentation of ideal suspensions,AIChE J. 38, No. 7, 1135-1138.
Bustos, M.C., Concha, F., Bürger, R. and Tory, E.M. (1999)Sedimentation and Thickening: Phenomenological Foun-dation and Mathematical Theory, Kluwer AcademicPublishers, Dordrecht, The Netherlands.
Bustos, M.C., Concha, F. and Wendland, W.L. (1990a)Global weak solutions to the problem of continuous sed-imentation of an ideal Suspension, Math. Meth. Appl.Sci. 13, 1-22.
Bustos, M.C., Paiva, F. and Wendland, W.L. (1990b) Controlof continuous sedimentation of ideal suspensions as aninitial and boundary value problem, Math. Meth. Appl.Sci. 12, 533-548.
Bustos, M.C., Paiva, F. and Wendland, W.L. (1996) Entropyboundary conditions in the theory of sedimentation ofideal suspensions, Math. Meth. Appl. Sci. 19, 679-697.
Carrillo, J. (1999) Entropy solutions for nonlinear degener-ate problems, Arch. Rat. Mech. Anal. 147, 269-361.
Chang, D., Lee, T., Jang, Y., Kim, M. and Lee, S. (1997) Non-colloidal sedimentation compared with Kynch theory,Powder Technol. 92, 81-87.
Cheng, K.S. (1981) Asymptotic behaviour of solutions of aconservation law without convexity conditions, J. Diff.Eqns. 40, 343-376.
Cheng, K.S. (1983) Constructing solutions of a single con-servation law, J. Diff. Eqns. 49, 344-358.
Clark, A. (1915) A note on the settling of slimes, Eng. Min. J.99, 412.
Coe, H.S. and Clevenger, G.H. (1916) Methods for deter-mining the capacity of slimesettling tanks, Trans. AIME55, 356-385.
Comings, E.W. (1940) Thickening calcium carbonate slur-ries, Ind. Eng. Chem. 32, 663-640.
Comings, E.W., Pruiss, C.E. and De Bord, C. (1954) Contin-uous settling and thickening, Ind. Eng. Chem. 46, 1164-1172.
Concha, F. (2001) Manual de Filtración & Separación, Cen-tro de Tecnología Mineral, Universidad de Concepción/Fundación Chile, Concepción, Chile.
Concha, F. and Barrientos, A. (1993) A critical review ofthickener design methods, KONA 11, 79-104.
Concha, F. and Bascur, O. (1977) Phenomenological modelof sedimentation. Proceedings of the 12th InternationalMineral Processing Congress (XII IMPC), São Paulo,Brazil, 4, 29-46.
Concha, F. and Bürger, R. (1998) Wave propagation phe-nomena in the theory of sedimentation. In: Toro, E.F.and Clarke, J.F. (Eds.), Numerical Methods for WavePropagation, Kluwer Academic Publishers, Dordrecht,The Netherlands, pp. 173-196.
Concha, F. and Bustos, M.C. (1985) Theory of sedimenta-tion of f locculated fine particles. In: Moudgil, B.M. and
Somasundaran, P. (Eds.), Proceedings of the Engineer-ing Foundation Conference on Flocculation, Sedimenta-tion and Consolidation, Sea Island, GA, AIChE, NewYork, pp. 275-284.
Concha, F. and Bustos, M.C. (1991) Settling velocities of par-ticulate systems: 6. Kynch sedimentation processes:Batch settling, Int. J. Mineral Process. 32, 193-212.
Concha, F. and Bustos, M.C. (1992) Settling velocities ofparticulate systems: 7. Kynch sedimentation processes:Continuous thickening, Int. J. Mineral Process. 34, 33-51.
Concha, F., Bustos, M.C. and Barrientos, A. (1996) Phenom-enological theory of sedimentation. In: Tory, E.M.(Ed.), Sedimentation of Small Particles in a Viscous Fluid,Computational Mechanics Publications, Southampton,UK, pp. 51-96.
Concha, F., Lee, C.H. and Austin, L.G. (1992) Settling veloci-ties of particulate systems: 8. Batch sedimentation ofpolydispersed suspensions of spheres, Int. J. MineralProcess. 35, 159-175.
Dafermos, C.M. (2000) Hyperbolic Conservation Laws inContinuum Physics, Springer Verlag, Berlin.
D’Avila, J.S. (1976) Uma análise da teoria de Kynch parasedimentação, Revista Brasileira de Tecnologia 7, 447-453.
D’Avila, J.S. (1978) Um modelo matemático para a sedi-mentação, Doctoral Thesis, Federal University of Rio deJaneiro.
D’Avila, J.S., Concha, F. and Telles, A.S. (1978) Um modelofenomenológico para sedimentação bidimensionalcontínua, Anais VI Encontro de Escoamento em MeiosPorosos, Rio Claro, Brasil, 11-13 outubro 1978, II, pp.III-1-1III-1-19.
D’Avila, J.S. and Sampaio, R. (1977) Equações de estadopara a pressão no sólido, Revista Brasileira de Tecnolo-gia 8, 177-191.
Davis, K.E. and Russel, W.B. (1989) An asymptotic descrip-tion of transient settling and ultrafiltration of colloidaldispersions, Phys. Fluids A 1, 82-100.
Davis, K.E., Russel, W.B. and Glantschnig, W.J. (1991) Set-tling suspensions of colloidal silica: observations andX-ray measurements, J. Chem. Soc. Faraday Trans. 87,411-424.
De Haas, R.D. (1963) Calculation of the Complete Batch Set-tling Behavior for Rigid Spheres in a Newtonian Liquid,M.Sc. Thesis, Purdue University, West Lafayette, IN,USA.
Diehl, S. (1995) On scalar conservation laws with pointsource and discontinuous f lux function, SIAM J. Math.Anal. 26, 1425-1451.
Diehl, S. (1996) A conservation law with point source anddiscontinuous f lux function modelling continuous sedi-mentation, SIAM J. Appl. Math. 56, 388-419.
Diehl, S. (1997) Dynamic and steady-state behaviour of con-tinuous sedimentation, SIAM J. Appl. Math. 57, 991-1018.
Diehl, S. (2000) On boundary conditions and solutions forideal clarifier-thickener units, Chem. Eng. J. 80, 119-
68 KONA No.20 (2002)
133.Diehl, S. (2001) Operating charts for continuous sedimenta-
tion I: Control of steady states, J. Eng. Math. 41, 117-144.
Dorr, J.V.N. (1915) The use of hydrometallurgical apparatusin chemical engineering, J. Ind. Eng. Chem. 7, 119-130.
Dorr, J.V.N. (1936) Cyanidation and Concentration of Goldand Silver Ores. McGraw-Hill Book Co. Inc., New York.
Dreher, T. (1997) Non-intrusive measurement of particleconcentration and experimental characterization of sedi-mentation. Preprint 97/34, Sonderforschungsbereich404, University of Stuttgart, Germany.
Egolf, C.B. and McCabe, W.L. (1937) Rate of sedimentationof f locculated particles, Trans. Amer. Instn. Chem. Engrs.33, 620-640.
Engquist, B. and Osher, S. (1981) One-sided difference ap-proximations for nonlinear conservation laws, Math.Comp. 36, 321-351.
Evje, S. and Karlsen, K.H. (2000) Monotone difference ap-proximation of BV solutions to degenerate convec-tion-diffusion equations, SIAM J. Numer. Anal. 37,1838-1860.
Fitch, E.B. (1993) Thickening theories an analysis, AIChEJ. 39, 27-36.
Forbes, D.L.H. (1912) The settling of mill slimes, Eng. Min.J. 93, 411-415.
Free, E.E. (1916) Rate of slimes settling, Eng. Min. J. 101,681-686.
Garrido, P., Bürger, R., and Concha, F. (2000) Settling veloci-ties of particulate systems: 11. Comparison of the phe-nomenological sedimentation-consolidation model withpublished experimental results, Int. J. Mineral Process.60, 213-227.
Garrido, P., Concha, F. and Bürger, R. (2001) Application ofthe unified model of solid-liquid separation of f loccu-lated suspensions to experimental results. In: da Luz,A.B., Soares, P.S.M., Torem, M.L. and Trinidade, R.B.E.(eds.), Proceedings of the VI Southern Hemisphere Meet-ing on Mineral Technology, Rio de Janeiro, Brazil, 2001,vol. 1, CETEM/MCT, Rio de Janeiro, 117-122.
Garrido, P., Concha, F. and Bürger, R. (2002) Settling veloci-ties of particulate systems: 14. Unified model of sedi-mentation, centrifugation and filtration of f locculatedsuspensions. Int. J. Mineral Process., to appear.
Godlewski, E. and Raviart, P.-A. (1991) Hyperbolic Systems ofConservation Laws, Mathématiques et Applications,Ellipses, Paris, France.
Godlewski, E. and Raviart, P.-A. (1996) Numerical Approxi-mation of Hyperbolic Systems of Conservation Laws,Springer Verlag, New York, Berlin, Heidelberg.
Grassmann, P. und Straumann, R. (1963) Entstehen undWandern von Unstetigkeiten der Feststoffkonzentrationin Suspensionen, Chem.-Ing.-Techn. 35, 477-482.
Hassett, N.J. (1958) Design and operation of continuousthickeners, Ind. Chemist 34, 116-120, 169-172, 489-494.
Hassett, N.J. (1964) Mechanism of thickening and thickenerdesign, Trans. Inst. Min. Met. 74, 627-656.
Hassett, N.J. (1968) Thickening in theory and practice, Min.
Sci. Engrg. 1, 24-40.Hazen, A. (1904) On sedimentation, Trans. ASCE 53, 45-71.Holdich, R.G. and Butt, G. (1997) Experimental and numeri-
cal analysis of a sedimentation forming compressiblecompacts, Separ. Sci. Technol. 32, 2149-2171.
Kos, P. (1977) Fundamentals of gravity thickening, Chem.Eng. Prog. 73, 99-105.
Kröner, D. (1997) Numerical Schemes for Conservation Laws,Wiley-Teubner, Chichester & Stuttgart.
Kruzkov, S.N. (1970) First order quasilinear equations inseveral independent variables, Math. USSR Sb. 10, No.2, 217-243.
Kynch, G.J. (1952) A theory of sedimentation, Trans. Fara-day Soc. 48, 166-176.
Landman, K.A. and White, L.R. (1994) Solid/liquid separa-tion of f locculated suspensions, Adv. Colloid Interf. Sci.51, 175-246.
Landman, K.A., White, L.R. and Buscall, R. (1988) The con-tinuous-f low gravity thickener: steady state behavior,AIChE J. 34, 239-252.
Liu, I. (1978) On chemical potential and incompressibleporous media, Preprint Memórias de Matemática 108,Instituto de Matemática, UFRJ, Rio de Janeiro, Brazil.
Liu, T.P. (1978) Invariants and asymptotic behavior of solu-tions pf a conservation law, Proc. Amer. Math. Soc. 71,227-231.
Masliyah, J.H. (1979) Hindered settling in a multiple-speciesparticle system, Chem. Eng. Sci. 34, 1166-1168.
Michaels, A.S. and Bolger, J.C. (1962) Settling rates and sed-iment volumes of f locculated Kaolin suspensions, Ind.Eng. Chem. Fund. 1, 24-33.
Mishler, R.T. (1912) Settling slimes at the Tigre Mill, Eng.Min. J. 94, 643-646.
Mishler, R.T. (1918) Methods for determining the capacityof slime-settling tanks, Trans. AIME 58, 102-125.
Outukumpu Mintec (1997) Supaf lo Thickeners & Clarifiers,brochure distributed at the XX International MineralProcessing Congress, Aachen, Germany, September 1997.
Petty, C.A. (1975) Continuous sedimentation of a suspensionwith a nonconvex f lux law, Chem. Eng. Sci. 30, 1451-1458.
Puccini, C., Stasiw, D.M. and Cerny, L.C. (1977) The ery-throcyte sedimentation curve: a semi-empirical ap-proach, Biorheology 14, 43-49.
Ralston, O.C. (1916) The control of ore slimes II, Eng.Min. J. 101, 890-894.
Richardson, J.F. and Zaki, W.N. (1954) Sedimentation andf luidization: Part I. Trans. Instn. Chem. Engrs. (London)32, 35-53.
Roberts, E.J. (1949) Thickening art or science? MiningEng. 1, 61-64.
Robinson, C.S. (1926) Some factors inf luencing sedimenta-tion, Ind. Eng. Chem. 18, 869-871.
Rushton, A., Ward, A.S., and Holdich, R.G. (2000) Solid-liquid Filtration and Separation Technology, SecondEdition, Wiley-VCH, Weinheim, Germany.
Schneider, W. (1982) Kinematic-wave theory of sedimenta-tion beneath inclined walls, J. Fluid Mech. 120, 323-346.
KONA No.20 (2002) 69
Schneider, W. (1985) Kinematic wave description of sedi-mentation and centrifugation processes. In: Meier,G.E.A. and Obermaier, F. (Eds.), Flow of Real Fluids,Lecture Notes in Physics, Springer-Verlag, Berlin, pp.326-337.
Schneider, W., Anestis, G. and Schaf linger, U. (1985) Sedi-ment composition due to settling of particles of differ-ent sizes, Int. J. Multiphase Flow 11, 419-423.
Scott, K.J. (1968a) Theory of thickening: factors affectingsettling rate of solids in f locculated pulps, Trans. Inst.Min. Met. 77, C85-C97.
Scott, K.J. (1968b) Experimental study of continuous thick-ening of a f locculated silica slurry, Ind. Engrg. Fund. 7,582-595.
Shannon, P.T., Dehaas, R.D., Stroupe, E.P. and Tory, E.M.(1964) Batch and continuous thickening, Ind. Eng.Chem. Fund. 3, 250-260.
Shannon, P.T., Stroupe, E.P. and Tory, E.M. (1963) Batchand continuous thickening, Ind. Eng. Chem. Fund. 2,203-211.
Shannon, P.T. and Tory, E.M. (1965) Settling of slurries, Ind.Eng. Chem. 57, 18-25.
Shannon, P.T. and Tory, E.M. (1966) The analysis of contin-uous thickening, SME Trans. 235, 375-382.
Shih, Y.T., Gidaspow, D. and Wasan, D.T. (1986) Sedimenta-tion of fine particles in nonaqueous media: Part I Experimental, Part II Modeling, Colloids and Surfaces21, 393-429.
Shirato, M., Kato, H., Kobayashi, K. and Sakazaki, H. (1970)Analysis of settling of thick slurries due to consolida-tion, J. Chem. Eng. Japan 3, 98-104.
Smiles, D.E. (1976a) Sedimentation: integral behaviour,Chem. Eng. Sci. 31, 273-275.
Smiles, D.E. (1976b) Sedimentation and filtration equilibria,Sep. Sci. 11, 1-16.
Steinour, H.H. (1944a) Rate of sedimentation. Nonf loccu-lated suspensions of uniform spheres. Ind. Eng. Chem.36, 618-624.
Steinour, H.H. (1944b) Rate of sedimentation. Suspensionsof uniform-size angular particles. Ind. Eng. Chem. 36,840-847.
Steinour, H.H. (1944c) Rate of sedimentation. Concentratedf locculated suspensions of powders. Ind. Eng. Chem.36, 901-907.
Stewart, R.F. and Roberts, E.J. (1933) The sedimentation offine particles in liquids, Trans. Instn. Chem. Engrs. 11,124-141.
Straumann, R. (1962) Über den Einf luß der Sedimentationauf die Filtration. Doctoral Thesis ETH Prom. Nr. 3187,Swiss Federal Polytechnical Institute (ETH), Zurich.
Stroupe, E. (1962) Batch Sedimentation of Rigid Spheres ina Newtonian Liquid, M.Sc. Thesis, Purdue University,West Lafayette, IN, USA.
Talmage, W.P. and Fitch, E.B. (1955) Determining thickenerunit areas, Ind. Eng. Chem. 47, 38-41.
Thacker, W.C. and Lavelle, J.W. (1977) Two-phase f lowanalysis of hindered settling, Phys. Fluids 20, 1577-1579.
Tiller, F.M., Hsyung, N.B., Shen, Y.L. and Chen, W. (1990)
CATSCAN analysis of sedimentation and constant pres-sure filtration. Proceedings of the V World Congress onFiltration, Société Française de Filtration, Nice, France,2, pp. 80-85.
Tiller, F.M. and Leu, W.F. (1980) Basic data fitting in filtra-tion, J. Chin. Inst. Chem. Engrs. 11, 61-70.
Tobinaga, S. and Freire, J.T. (1980) Escoamento de agua emsolos não-saturados: Uma descrição pela teoria de mis-turas. Revista Brasileira de Tecnologia 11, 105-115.
Toorman, E.A. (1999) Sedimentation and self-weight consol-idation: constitutive equations and numerical modeling,Géotechnique 49, 709-726.
Toorman, E.A. and Huysenstruyt, H. (1997) Towards a newconstitutive equation for effective stress in self-weightconsolidation. In: Burt, N., Parker, R. and Watts, J.(Eds.), Cohesive Sediments, Wiley, Chichester, UK, pp.121-132.
Tory, E.M. (1961) Batch and Continuous Thickening of Slur-ries, PhD Thesis, Purdue University, West Lafayette,USA.
Tory, E.M. and Shannon, P.T. (1965) Reappraisal of the con-cept of settling in compression, Ind. Engrg. Chem. Fund.4, 194-204.
Truesdell, C. (1966) Method and taste in Natural Philoso-phy. In: Truesdell, C., Six Lectures on Modern NaturalPhilosophy, Springer-Verlag, Berlin.
Truesdell, C. and Noll, W. (1965) The nonlinear field theo-ries of mechanics. In: Flügge, S. (ed.), Handbuch derPhysik, Vol. III/3, Springer-Verlag, Berlin.
Ungarish, M. (1993) Hydrodynamics of Suspensions, Springer-Verlag, Berlin.
Vol’pert, A.I. (1967) The spaces BV and quasilinear equa-tions, Math. USSR Sb. 2, No. 2, 225-267.
Vol’pert, A.I. and Hudjaev, S.I. (1969) Cauchy’s problem fordegenerate second order quasilinear parabolic equa-tions, Math. USSR Sb. 7, No. 3, 365-387.
Wakeman, R.J. and Tarleton, E.S. (1999) Filtration: Equip-ment Selection, Modelling and Process Simulation, Else-vier Science, Oxford, UK.
Ward, H.T. and Kammermeyer, K. (1940) Sedimentation inthe laboratory: Design data from laboratory experimen-tation, Ind. Eng. Chem. 32, 622-626.
Wilson, A.J. (1994) The Living Rock, Woodhead PublishingLimited, England.
Work, L.T. and Kohler, A.S. (1940) Sedimentation of suspen-sions, Ind. Eng. Chem. 32, 1329-1334.
Wu, Z. and Yin, J. (1989) Some properties of functions inBVx and their applications to the uniqueness of solutionsfor degenerate quasilinear parabolic equations, North-east. Math. J. 5, 395-422.
Yoshioka, N., Hotta, Y., Tanaka, S., Naito, S. and Tsugami, S.(1957) Continuous thickening of homogeneous f loccu-lated slurries, Chem. Eng. Japan 21, 66-75.
Zheng, Y. and Bagley, D.M. (1998) Numerical simulation ofbatch settling process, J. Environ. Eng. 124, 953-958.
Zheng, Y. and Bagley, D.M. (1999) Dynamic model for zonesettling and compression in gravity thickeners, J. Envi-ron. Eng. 125, 1007-1013.
70 KONA No.20 (2002)
Author’s short biography
Fernando Concha Arcil
Fernando Concha Arcil, obtained a Batchelor degree in Chemical Engineering atthe University of Concepcion in Chile in 1962 and a Ph.D. in Metallurgical Engi-neering from the University of Minnesota in 1968. He is professor at the depart-ment of Metallurgical Engineering, University of Concepción. His main researchtopic is the application of transport phenomena to the field of Mineral Processing.He has published four books: Modern Rational Mechanics, Design and Simulationof Grinding-Classification Circuits and Filtration and Separation, all in Spanish andSedimentation and Thickening: Phenomenological Foundation and MathematicalTheory, in English and more than 90 technical papers in international journals. Forhis work in sedimentation with applications to hydrocyclones and thickeners heobtained the Antoine Gaudin Award-1998, presented by the American Society forMining Metallurgy and Exploration, SME.
Raimund Bürger
Raimund Bürger is a scientific assistant at the Institute of Applied Analysis andNumerical Simulation of the University of Stuttgart, Germany. He has specializedin the formulation, analysis and numerics of mathematical models of solid-liquidseparation processes. This includes in particular the mathematical analysis of thenonlinear partial differential equations involved, which frequently exhibit non-stan-dard properties such as type degeneracy and discontinuous coefficients. He studied Mathematics at the Technische Universität Darmstadt in Germany andreceived his diploma degree in 1993. From 1995 to 2001 he held a position as re-search fellow within the Collaborative Research Center (Sonderforschungsbereich)404 “Multifield Problems in Continuum Mechanics” at the University of Stuttgart.He obtained his doctoral degree in Applied Mathematics in 1996 under guidance ofProfessor Wolfgang L. Wendland and finished his habilitation in 2002. In 1997 he was awarded a scholarship by Fundación Andes, Chile, which he usedfor a post-doctoral research visit to Fernando Concha’s group at the Department ofMetallurgical Engineering of the University of Concepción during the period fromJuly 1997 to August 1998. Raimund Bürger is co-author of the monograph Sedimentation and Thickening,more than 30 articles in refereed journals and 15 contributions to proceedings vol-umes. He is married, has a little son, and lives in Stuttgart, Germany.
KONA No.20 (2002) 71
1. Introduction
Recent advances in biotechnology have made it pos-sible to use macromolecules such as peptides andproteins as therapeutic agents. At this time intra-venous, intramuscular, and subcutaneous injectionsare the practical routes for administering such macro-molecules. One would expect peroral administrationto be the most convenient for patients, but the peroralbioavailability of macromolecules is extremely lowdue to their large molecular size and high susceptibil-ity to enzymes in the gastrointestinal tract. Mean-while, it has been suggested that the lungs are usefulfor administering macromolecules, which are poorlyabsorbed from the intestines.
So far, inhalation therapy has been used with low-molecular-weight drugs to treat local lung diseasessuch as asthma and infections. Recombinant humandeoxyribonuclease (rhDNase) is the first protein ap-proved for inhalation therapy (1). Patients with cysticfibrosis are given 2.5 ml of a 1 mg/ml solution ofrhDNase by nebulization (2).
In the area of systemic therapy, insulin is the pep-
tide that is expected to be the first approved forinhalation therapy. Exubera® is a rapid-acting drypowder insulin being developed through a collabora-tion between Pfizer Inc. and Aventis Pharma. The six-month Phase III studies involving 328 patients withtype 1 diabetes and 309 patients with type 2 diabeteswere completed in 2002 (3, 4). The AERx® PulmonaryDrug Delivery System is a broadly applicable tech-nology platform that converts large or small mole-cules into fine-particle aerosols. AERx®iDMS (in-sulin Diabetes Management System) was developedthrough a collaboration between Novo Nordisk andAradigm Co. A 12-week-long Phase II study including107 non-smoking patients with type 2 diabetes hasbeen completed (5).
The three main delivery systems used for aerosolinhalation in humans are pressurized metered-doseinhalers (MDI), nebulizers, and dry powder inhalers(DPI) (6). DPIs appear to be the most promising ofthese for future use because the device is small andrelatively inexpensive, no propellants are used, andbreath actuation can be used successfully by manypatients with poor MDI technique (6, 7).
This review will focus on the dry powder peptidesand proteins for inhalation. The success of inhalationtherapy with dry powders is determined by the activeingredient’s biological aspects, by the physicochemi-cal aspects of formulation, and by inhaler perfor-mance (Fig. 1). Here we brief ly review some of the
Hirokazu Okamoto*, Hiroaki Todo, Kotaro Iida,and Kazumi DanjoFaculty of Pharmacy, Meijo University **
Dry Powders for Pulmonary Delivery of Peptides and Proteins†
Abstract
Because proteins and peptides are poorly absorbed through the gastrointestinal tract, the lungs area promising organ for administering these substances because of their large inner surface area, thinepithelium, and relatively low protease activity. Pulmonary absorption rate constants are inverselyrelated to molecular weights. Adding an absorption enhancer is a promising method to increase sys-temic bioavailability of inhaled peptides and proteins. The local lung toxicity of soluble powder seemsto be minimal. Spray drying is a useful and widely applied technique to prepare powders for inhala-tion, and supercritical f luids have recently been used for producing such powders. Selecting operat-ing conditions and adding proper additives such as sugars yields hollow porous particles, which areeasily dispersed and avoid phagocytic clearance in the lungs, with maximized chemical and physicalstability.
* Corresponding author.Phone: 81-52-832-1781 (ext. 359); Fax: 81-52-834-8090; E-mail: [email protected]**150 Yagotoyama Tempaku-ku, Nagoya 468-8503, Japan† Accepted: July 31, 2002
biological and physicochemical aspects of inhalationtherapy with dry powder peptides and proteins. Ex-tensive reviews on inhalers are available elsewhere(8, 9).
2. Biological aspects of the pulmonary absorption of peptides and proteins
This section summarizes the histological features ofthe lungs, drug permeability through the lung epithe-lium, the metabolism of proteins and peptides in lungtissue, and the safety of peptides and proteins admin-istered through the lungs. It also reviews how chemi-cals and enzyme inhibitors enhance the pulmonaryabsorption of peptides and proteins.
2.1 Histological features of the lungsThe respiratory tract can be divided into upper air-
ways (the nose, mouth, larynx, and pharynx) andlower airways (from the trachea to the alveoli) (10).The average weight of human lungs is 0.6 kg. Be-cause the lungs receive the entire cardiac output, theirblood f low is as high as 5,700 ml/min, more thanfive times that of the portal system (1,125 ml/min),including the stomach and the small and large intes-tines (11).
Airway diameter decreases and surface area in-creases according to the successive branching of theairways. The cross sectional area of the trachea isabout 2.5 cm2, while that of the respiratory zone ismuch wider (10). The total cross sectional area of thealveoli is about 104 cm2. The total surface are of theairway tubes also increases and that of alveoli is morethan 100 m2 as large as that of the small intestine.
The epithelial layer of the trachea is composedmainly of columnar ciliated cells. The thickness fromthe airway surface to blood vessels is on the order of30 to 40 µm (12). Particulates deposited in the upperairways are rapidly carried away by mucociliarytransport, resulting in a short of residence time (13).
The alveolar surface is populated by two majorepithelial cell types: the terminally differentiated typeI cell and its progenitor type II cell (14). The alveolarepithelium is quite thin. In the alveoli drugs have totravel only 0.5 to 1.0 µm to enter the blood stream.Total f luid volume in the human lungs is approxi-mately 10 ml (15). Lung pH at the site of drug absorp-tion has been estimated at about 6.6 using pulmonaryabsorption data for several weak electrolytes in rats(16). The alveolar surface is lined by a surface-activematerial called the lung surfactant, which is a mixtureof lipids, proteins, and carbohydrates (17). Phospho-lipids account for 75-80% of the total weight, and di-palmitoyl phosphatidylcholine accounts for nearly halfof that. The lung surfactant reduces alveolar surfaceactivity and stabilizes alveolar structure.
Lavage of a normal adult lung yields a cell countthat is 93% macrophages, 7% lymphocytes, and lessthan 1% neutrophils, eosinophils, or basophils (18).Alveolar macrophages interact with microorganismsor particulates, act as effector and accessory cells ininf lammatory and immune reactions, and protect al-veolar structures to form a protease attack (18).
2.2 Drug absorption through the lungsThe pulmonary absorption of small molecules basi-
cally obeys pH-partition theory, i.e., drugs are likelyabsorbed by diffusion across a lipid membrane (19,
72 KONA No.20 (2002)
Inhalation therapy
Chemical stabilityPhysical stabilityAerodynamic diameterAdhesion forcePhagocytosis
PermeabilityMetabolismSafetyImmunogenicity
Biological aspects of active ingredient
Physicochemical aspects of formulation
Performance of inhaler
Fig. 1 Factors determining successful inhalation therapy with dry powders.
20). In vivo rat lung absorption data for saccharides ofvarious molecular weights (122 to 75,000) showedthat the absorption rate constants were inversely re-lated to molecular weight and directly related to thediffusion coefficients of the compounds (21). Thetransport of dextrans (4 to 150 kDa) across culturedrat alveolar epithelial cell monolayers suggested thatmacromolecules with radii under 5 µm traverse thealveolar epithelial barrier via paracellular pathways,while macromolecules with radii of 6 µm or largercross the barrier via other pathways such as pinocyto-sis (22). The penetration of hydrophilic compoundsthrough excised rabbit trachea sacs also inverselycorrelates to molecular weight (23). When severalhydrophilic and lipophilic drugs were administeredthrough rat trachea as aerosols, the absorption rateswere roughly twice as rapid as when administered bythe intratracheal injection of drug solutions. Theseresults suggest that drug absorption is more rapidin the alveolar region than in the tracheobronchialregion of the lungs (24). The distal or deep lung is theoptimal site for the high absorption of proteins. In-haler systems should be designed to maximize depo-sition in this region (12).
It is known that peptides or proteins could be ab-sorbed through the lungs (25, 26). The pulmonarybioavailability of peptides can be easily evaluatedwith small animals by the method proposed by Ennaand Schanker (21). The pulmonary bioavailability ofinsulin administered as a pH 7.0 solution was 13 to14% better than subcutaneous administration in rats(27).
2.3 Metabolism in the lungsIn general, the metabolic activity of the lungs is
much lower than that of the intestinal wall and liver.In the lungs there is no first-pass conjugation ofsalbutamol, which undergoes extensive first-pass con-jugation in the intestinal wall and liver. The systemicbioavailability of orally administered budesonide is11%, whereas that when inhaled is 73%. Fluticasonpropionate’s hepatic first-pass metabolism is 99%, butit is zero in the lungs (28).
However, it is known that peptides such as insulinare subjected to enzymatic degradation in the lungs(29-31). The degradation of insulin in lung cytosolfrom diabetic rats was significantly less than in thatfrom normal rats (30). An experiment with synthe-sized model peptides suggested that the lung has theability to metabolize peptides through pathways notobserved in the rat intestine. However, avoiding thehepatic first-pass effect through the pulmonary route
would eliminate the disadvantage of pulmonarymetabolism (32). Type II cells have higher metabolicactivity than type I cells. The degradation rate con-stant of luteinizing hormone releasing hormone(LHRH) in type II cells was higher than that of type Icells but lower than that of nasal and rectal epithelialmembranes. The transformation of type II cells intotype I cells resulted in a more than 10-fold decrease inLHRH proteolytic activities (14).
2.4 Safety of inhaled proteinsResearchers have investigated the systemic toxicity
of therapeutic peptides and proteins following subcu-taneous administration. When discussing the safetyaspect of inhaled proteins, interest focuses on localtoxicity to the lungs and on adverse immune reac-tions. Assaying bronchoalveolar lavage is useful inscreening lung injuries from inhaled substances (33).An increase in the extracellular activity of lactate de-hydrogenase (LDH), a cytosol enzyme, indicates celllysis or cell membrane damage. An increase in thenumber of phagocytic cells suggests an inflammationreaction in the lungs. When a suspension of superfinesilica was intratracheally instillated in rats, the LDHactivity and number of cells recovered in the lavageincreased at 4 hr and reached a maximum at 24 hr.The LDH activity and number of cells declined there-after for a week, then gradually increased over thesucceeding two months (34, 35).
However, the local lung toxicity of soluble powderseems to be minimal. When insulin dry powder for-mulated with mannitol was intratracheally adminis-tered in rats, the LDH level (36) and number of cells(unpublished data) in the lavage did not increase over24 hr. Clinical studies for inhaled DNase, insulin,interferon α, interferon γ, leuprolide acetate, and α-1-antitrypsin showed virtually no adverse lung reac-tions (12).
2.5 Additives for improving bioavailability ofinhaled peptides and proteins
One of the reasons of the low bioavailability of largemolecules relates to low diffusivity through the epi-thelial barrier. To overcome this, several chemicalsand enzyme inhibitors were examined as pulmonaryabsorption enhancers. In the 1990s there were manyreports on the enhancement of the pulmonary ab-sorption of peptides and proteins. These reportsexamined bile acids, surfactants, fatty acids, citricacid, and protease inhibitors (Tables 1 and 2).
Glycocholate and bacitracin had higher enhancingactivity for the pulmonary absorption of peptide so-
KONA No.20 (2002) 73
lutions. Yamamoto et al. intravenously injected EvansBlue and examined the leakage of Evans Blue in thelung. Although increasing calcitonin activity, 5 mMN-Lauryl-β-D-maltopyranoside increased Evans Blueleakage, suggesting lung toxicity. On the other hand,1 mM N-Lauryl-β-D-maltopyranoside, 10 mM glyco-cholate, and 10 mM mixed micelles of linoleic acid
and HCO60 were safe and effective enhancers (42).Citrate is a potent pulmonary absorption enhancerfor peptides formulated as dry powders. When insulindry powder containing 0.036 mg/dose of citric acidwas administered to rat lungs, bronchoalveolar lavagewas as low as that for saline administration, suggest-ing that citric acid is a safe additive (36). Adding an
74 KONA No.20 (2002)
Peptide/Protein Enhancer DFa ERb Ref.
insulin 50 mM glycocholate SL 5.1 27, 37
insulin 10 mM glycocholate SL 4.2 38
eel calcitonin 10 mM glycocholate SL 4.0 38
eel calcitonin 20 mM glycocholate SL 3.1 39
TSH 50 mM glycocholate SL 6.3 37
FSH 50 mM glycocholate SL 5.9 37
HCG 50 mM glycocholate SL 20 37
salmon calcitonin 250 µg/dose taurocholic acid SL 1.4 40
salmon calcitonin 250 µg/dose taurocholic acid DP 1.9 40
insulin 1% Span 85 SL 3.1 27
insulin 1% Span 85 SL 7.2 36
insulin 160 µg/dose Span 85 DP 0.7 36
insulin 10 mM MMc SL 2.5 38
eel calcitonin 10 mM MM SL 4.0 38
salmon calcitonin 250 µg/dose dimethyl-β-cyclodextrin SL 2.4 40
salmon calcitonin 250 µg/dose dimethyl-β-cyclodextrin DP 2.1 40
salmon calcitonin 250 µg/dose lecithin SL 1.5 40
salmon calcitonin 250 µg/dose lecithin DP 1.8 40
salmon calcitonin 250 µg/dose octyl-β-glucoside SL 1.4 40
salmon calcitonin 250 µg/dose octyl-β-glucoside DP 1.6 40
insulin 5 mM LMd SL 7.1 38
eel calcitonin 5 mM LM SL 5.7 38
salmon calcitonin 0.5% palmitoleic acid SL 2.5 41
salmon calcitonin 0.5% linoleic acid SL 2.4 41
salmon calcitonin 0.5% oleic acid SL 2.2 41
salmon calcitonin 250 µg/dose oleic acid SL 1.6 40
salmon calcitonin 250 µg/dose oleic acid DP 2.8 40
insulin 100 mM EDTA SL 0.6 27
eel calcitonin 10 mM EDTA SL 1.8 38
insulin 100 mM salicylate SL 0.5 27
insulin citrate (pH5.0) SL 3.4 36
insulin citrate (pH3.0) SL 4.5 36
insulin 36 µg/dose citric acid DP 2.1 36
insulin citrate (pH 3.0) SL 3.2 37
insulin 0.5 mg/dose citrate DP 2.7 37
TSH citrate (pH 3.0) SL 3.2 37
FSH citrate (pH 3.0) SL 3.9 37
HCG citrate (pH 3.0) SL 26 37
salmon calcitonin 250 µg/dose citric acid SL 1.5 40
salmon calcitonin 250 µg/dose citric acid DP 2.2 40
Table 1 Effect of absorption enhancers on pulmonary absorption of peptides and proteins
a Dosage form. SLsolution and DPdry powder.b Enhancement ratio. Ratio of AUC or biological response between a dosage form with absorption enhancer and
that without absorption enhancer.c Mixed micelles of linoleic acid and HCO60 at a molar ratio of 30:4 in phosphate buffered saline.d N-Lauryl-β-D-maltopyranoside.
absorption enhancer is a promising method forincreasing the systemic bioavailability of inhaled pep-tides and proteins, but long-term safety should beexamined for application to humans.
It should be noted that the effect of absorptionenhancers depends on their formulation. Bacitracinand Span 85 increased pulmonary insulin absorptionfrom solutions in rats, but were not effective when for-mulated as dry powders with insulin (36).
In research on protease inhibitors, a relatively fa-vorable correlation was observed between the cal-citonin absorption-enhancing activity and membraneenzyme inhibition activity of 18 protease inhibitors(41).
3. Physical aspects of dry powder peptides andproteins
Spray drying is a useful and widely applied tech-nique to prepare powders for inhalation. Supercriticalf luids have recently been applied for producing pow-ders for inhalation. In this section, we briefly reviewthese techniques, stability of the produced dry pow-der peptides and proteins, and aerodynamic diameterbeing one of the most critical factors to determine thesuccess of inhalation therapy.
3.1 Spray dry for preparation of dry powderpeptides and proteins
Spray drying is a useful and widely applied tech-nique for one-step preparation of powders for in-halation with a drug solution or suspension. Theindependent variables of spray drying processes areliquid feed rate, atomizing air f low rate, drying air
f low rate, and inlet air temperature. Outlet tempera-ture linearly depends on each of these variables (43),suggesting that it can be estimated if the regressionlines between outlet temperature and the independentvariables are available for a spray drier. The inlet tem-perature is usually several tens of degrees higherthan the outlet temperature. Determining the temper-ature variation within a drying chamber revealed thatthe temperature at 5 cm below the nozzle was muchcloser to the outlet temperature than the inlet temper-ature, and that the temperature at 17 cm below thenozzle, midway between the nozzle and outlet, wasapproximately the same as the outlet temperature(43). This means that during spray drying, droplets inthe drying chamber were exposed to the temperatureswayed by the outlet temperature.
It is likely that proteins are susceptible to degrada-tion upon spray drying due to the relatively high tem-peratures (44). Table 3 summarizes the effect of inletand outlet temperatures on spray-dried peptides andproteins. Spray drying of a 5 mg/ml aqueous insulinsolution caused minor degradation of insulin at outlettemperatures below 120°C. However, degradation ofhigh-molecular-weight proteins, A-21 desamido insu-lin, and other insulin-related compounds increasedwith outlet temperature above 120°C (47). β-galactosi-dase activity is susceptible to spray drying tempera-ture, and only half of its activity remained after spraydrying without additives at an outlet temperature of50°C. When 6% β-galactosidase was spray-dried with5% mannitol, no activity was lost at outlet tempera-tures below 50°C, but it deceased above 50°C. Replac-ing mannitol with trehalose stabilized the spray-driedβ-galactosidase, and its activity was maintained at
KONA No.20 (2002) 75
Peptide/Protein Enzyme inhibitor DFa ERb Ref.
insulin 1 mM bacitracin SL 0.9 27
insulin 20 mM bacitracin SL 6.8 38
eel calcitonin 20 mM bacitracin SL 19 39
salmon calcitonin 0.2 mM bacitracin SL 2.2 41
insulin 10 mM bacitracin SL 7.0 36
insulin 420 µg/dose bacitracin DP 1.0 36
insulin 13 mM nafamostat SL 2.1 27
eel calcitonin 20 mM nafamostat SL 3.9 39
insulin 10 mM surfactin SL 6.1 27
insulin 10 mg/mL aprotinin SL 2.0 38
insulin 10 mg/mL STI SL 2.5 38
salmon calcitonin 0.2 mM chymostatin SL 2.1 41
Table 2 Effect of enzyme inhibitors on pulmonary absorption of peptides and proteins
a Dosage form. SLsolution and DPdry powder. b Enhancement ratio. Ratio of AUC or biological response between a dosage form with absorption enhancer and
that without absorption enhancer.
100% at an outlet temperature of 100°C (45).Surface denaturation at the air-liquid interface of
sprayed droplets may play a significant role in proteindegradation. Spray drying of mannitol-formulatedhuman growth hormone (hGH) at room temperatureresulted in increased protein degradation by increas-ing the atomizing air rate, which suggested degrada-tion at the air-liquid interface during spray drying(48). Adding polysorbate-20 into the liquid feed signif-icantly reduced the formation of insoluble hGH aggre-gates, and adding divalent metal zinc ions effectivelysuppressed the formation of soluble hGH aggregates(49).
3.2 Application of supercritical fluids to preparation of dry powder proteins
Fluids at temperatures and pressures above criticalvalues are called supercritical f luids (SCFs). SCF den-sities of similar to those of liquids, while their vis-cosities and diffusivities are in the range of gases(50). The application of SCFs to particle design hasrecently emerged as a promising techniques for pro-ducing powders for inhalation. Carbon dioxide is themost widely used supercritical solvent because it ischeap and nontoxic, and because of its easily accessi-ble critical parameters (Tc31.1°C and Pc73.8 bar)(50).
When a substrate has a reasonable solubility in aSCF, dry powders are obtained by depressurizingthe SCF solution through an adequate nozzle. Thisprocess is called the rapid expansion of supercriticalsolutions (RESS). However, the solubility of manypeptides and proteins in SCFs is relatively low. When
a SCF is a poor solvent for the substrate, it can beused as an anti-solvent to precipitate the substrate dis-solved in a good solvent (51).
Dimethylsulfoxide (DMSO) is a good solvent forlysozyme. When CO2 is put into lysozyme dissolved inDMSO, and the CO2 mole fraction reaches a criticalvalue, the solution becomes saturated and causesthe catastrophic precipitation of lysozyme (52). Thisprocess is called the gas-antisolvent (GAS) precipita-tion process.
Other techniques to produce powders with SCFs asanti-solvents are the aerosol solvent extraction sys-tem (ASES) (53, 54), precipitation with a compressedf luid antisolvent (PCA) (55, 56), the supercritical anti-solvent technique (SAS) (57-60), and solution en-hanced dispersion by supercritical f luids (SEDS) (61,62). These techniques introduce protein solutionsthrough a nozzle at a relatively low f low rate into thef low of a SCF in a vessel. The SCF removes the sol-vent of the protein solution and precipitates the pro-tein in the vessel.
Yeo et al. applied the SAS technique to a 5 mg/mlinsulin solution in DMSO. The slow CO2 injection ratefavored the growth of larger particles (57). A signifi-cant increase in β-sheet content and a correspondingdecrease in α-helix content were observed for theprecipitated insulin relative to a commercial powder.However, the precipitated insulin solution in 0.01 MHCl yielded a solution structure similar to that ofthe dissolved commercial powder (58). Intravenousadministration to rats revealed that the processedinsulin maintained its biological activity (57). Theincrease in β-sheet content and the concomitant de-
76 KONA No.20 (2002)
Peptide/ProteinTemperature (°C) Activity Degradation Moisture Da
Ref.Inlet Outlet (%) (%) (%) (µm)
050 100β-galactosidase 070 080 45
090 030
050 2.00oxyhemoglobin 080 2.90 46
120 5.00
091 053 8.3 2.0rhDNase 120 072 7.6 2.2 43
150 090 6.1 2.3
100 050 0.36b 5.1 3.2b
100 074 0.44 3.1 3.1insulin 160 100 0.49 3.1 2.2 47
220 120 0.77 3.3 2.1220 150 3.32 1.9 4.2
Table 3 Effect of inlet and outlet temperatures on spray-dried peptides and proteins
a Geometric or aerodynamic diameter.b High-molecular-weight protein.
crease in α-helix content, which were reversible uponreconstitution, were also observed in lysozyme andtrypsin precipitated by the SAS technique (60).
When the solubility of the solvent (for instance,water) in the SCF (for instance, CO2) is very low, amodifier (for instance, ethanol) is employed in thesystem. Powders of lysozyme, albumin, insulin, andrecombinant human deoxyribonuclease (rhDNase)were prepared by the ASES process. An aqueoussolution of a protein was put into a precipitation cham-ber through the inside tube of a coaxial nozzle. Super-critical CO2 modified by ethanol was fed through theoutside tube of the coaxial nozzle. The mole fractionof ethanol in CO2 was 0.2 and the volumetric f low rateratio of the aqueous solution to CO2 was 0.4/12. TheASES process at 35 or 45°C and at 80 to 90 bar pro-duced lysozyme powder without activity loss. Someaggregation was observed for insulin and albuminpowders. rhDNase was substantially denatured dur-ing the processing (63).
A new supercritical CO2-assisted aerosolization cou-pled with bubble drying was recently reported (64).This process involves mixing a stream of drug solu-tion and a SCF stream inside a low dead-volume tee.The emulsion is allowed to expand out of a capillaryrestrictor, resulting in the aerosolization of the drugsolution.
3.3 Stability of peptides and proteinsA crystalline solid of small molecule drugs is gen-
erally less prone to chemical decomposition thanthe amorphous form. In some cases, however, thecrystalline state may not be more stable for proteinand peptide formulations (65). The primary degrada-tion pathways of biosynthetic human insulin involvedeamidation at the AsnA21 site and covalent dimer for-mation. When storing at 25°C and 40°C at relativehumidities between 0 and 75%, amorphous insulin wasfar more stable than crystalline insulin under all con-ditions (66).
The hydration state of proteins affects their solid-state stability. The aggregation of humanized mono-clonal antibodies and rhDNase in mannitol-for-mulated spray-dried powders increased as storagehumidity rose (67). Deamidation at the AsnA21 site ofcrystalline insulin increased sharply as moisture con-tent increased, while that of amorphous insulin wasalmost independent of moisture (66).
It is known that the chemical stability of proteins inthe solid state is enhanced by the presence of certainamorphous sugars. Two hypotheses have been pro-posed for the mechanism of protein stabilization by an
amorphous sugar (68). The water substitution hy-pothesis supposes that sugar molecules form hydro-gen bonds with dried proteins in place of watermolecules to maintain higher-order protein structure.The glassy state theory supposes that the high viscos-ity of an amorphous sugar prevents proteins fromdegrading physically or chemically by retarding mole-cular movement. Table 4 summarizes the effect ofsugars on spray-dried peptides and proteins.
Izutsu et al. examined the stabilizing effect ofmannitol during the freeze-drying of L-lactate dehy-drogenase, β-galactosidase, and L-asparaginase. Theactivities of the freeze-dried enzymes depended onthe content of amorphous mannitol in the cake. Thestabilizing effect of mannitol decreased as mannitolcrystallinity increased, suggesting that amorphousmannitol protected proteins against degradation (72).
The physical state of sugars used as an excipient forprotein powder plays a role not only in maintainingprotein stability but also in providing suitable aerosolperformance. When recombinant humanized anti-IgE monoclonal antibodies (rhuMAbE25) were spray-dried with 10, 20, and 30% mannitol, the spray-driedpowders with 10 and 20% mannitol remained amor-phous during storage, while the powder with 30%mannitol crystallized. The fine-particle fraction (FPF)for the powder with 10 and 20% mannitol was main-tained at 30-40% during storage for 36 weeks at30°C. However, the fraction of the powder with 30%mannitol exhibited a dramatic decrease upon storagedue to mannitol crystallization and an increase in par-ticle size (44).
Moisture mediates the crystal growth of sugars indry protein powders. Spray drying rhDNase with lac-tose produced spherical powders with noncrystallinesubstances. However, α-lactose monohydrate crystalswere identified in the powders stored at high humidi-ties (73).
3.4 Mass median aerodynamic diameterParticle size and its distribution affect particle
retention in the lungs (70, 74). Particles larger than20 µm likely fail to go beyond the terminal bron-chioles. Those larger than 6 µm fail to reach the alve-olar ducts. The optimum particle size to reach and bedeposited in the alveolar region seems to be 1 to 5 µm(70, 71, 74, 75). Submicrometer-size particles areexhaled, deposited, or both by random Brownianmotion in distal regions. It should be noted that theparticle size referred to in this context is not geomet-ric diameter but aerodynamic diameter.
The theoretical aerodynamic diameter, daer, of indi-
KONA No.20 (2002) 77
vidual particles is calculated according to the follow-ing definition (76):
daer(ρ/F)0.5d (1)
Where:d is mass median particle diameter as measured bylight microscopy,ρ is particle density, andF is the dynamic shape correction factor.
The F values for spheres and cubes are 1.00 and 1.08,respectively (76). The tap density could be an esti-mate of the particle density, ρ, although it remains anapproximately 20% systemic underestimate of ρ (15).
The experimental mass median aerodynamic diam-eter (MMAD) of the particles is obtained as followswith an Andersen cascade impactor (70, 71). Thecumulative mass of powder less than the stated size ofeach stage of the impactor is calculated and plotted ona log probability scale, as the percent of total massrecovered in the impactor against the effective cut-offdiameter. The MMAD of the particles is defined fromthis graph as the particle size at which the linecrosses the 50% mark. The geometric standard devia-tion (GSD) is calculated as GSD(X/Y)0.5, where Xand Y are the particle sizes at which the line crossesthe 84.13% mark and the 15.87% mark, respectively.
Fine particle fraction (FPF) is defined as the mass
78 KONA No.20 (2002)
Peptide/Protein Sugara Activity Degradation FPF Moisture DbRef.
(%) (%) (%) (%) (µm)
nonec 042 4.5.. 03.9
β-galactosidase10% mannitol 081 1.5.. 04.3
4510% sucrose 102 2.8.. 04.310% trehalose 109 4.0.. 04.0
none 197d 05.8catalase 50% lactose 153 06.4 69
50% mannitol 107 04.4
none 018d 02.9insulin 50% lactose 024 03.9 69
67% mannitol 018 05.0
nonee 50
oxyhemoglobin0.01M sucrose 40
460.10M sucrose 100.20M sucrose 02
Albumin/DPPC 20% sucrose 53.0 04.8c
(20/60) 20% mannitol 11.3 10.470
Albumin/DPPC20% lactoseb 38.0 01.2
(20/60)20% trehalose 34.0 01.1 7120% mannitol 11.0 01.5
none 46.0 03.450% mannitol 14.0 06.1
rhDNase20% trehalose 29.0 02.9
6340% trehalose 36.0 02.660% trehalose 20.0 03.240% sucrose 27.0 02.8
none 27.0 03.3
anti-IgE MAb10% mannitol 25.0 03.8
6320% mannitol 29.0 04.040% trehalose 31.0 03.3
none 27.0 2.23f
10% mannitol 35.0 1.31rhuMAbE25 20% mannitol 28.0 0.86 44
30% mannitol 27.0 1.0040% mannitol 08.5 1.11
Table 4 Effect of sugars on spray-dried peptides and proteins
a Percentage stands for the sugar content in dry powder except for β-galactosidase and oxyhemoglobin.b Geometric or aerodynamic diameter.c Concentration in feed solution. β-Galactosidase concentration was 6%.d Activity relative to that of raw material.e Concentration in feed solution. Oxyhemoglobin concentration was 10%.f Pseudo first-order degradation rate constant at 30°C.
fraction of particles smaller than a certain aero-dynamic diameter (for instance, 5 µm). The twinimpinger is often used to estimate FPF values and isvaluable for the routine quality assessment of aerosolsduring product development, stability testing, and forquality assurance and comparison of products (77).The particles captured in stage 2 are considered to bethe FPF. The aerodynamic cutoff diameter betweenstages 1 and 2 of the twin impinger with an air streamof 60 l/h is 6.4 µm (78). The cutoff size of theimpinger stage can easily be changed because it isinversely proportional to the square root of the airf low (79).
3.5 Hollow porous particlesEquation 1 predicts that a large and light particle
may have the same aerodynamic diameter as a smalland heavy particle. Edwards et al. showed in 1997that the FPF for large porous particles was muchhigher than that for small nonporous particles, eventhough the aerodynamic diameters were nearly iden-tical. Large porous particles also increased systemicbioavailability of insulin in rats (80). The advantage oflarge porous particles can be attributed to the smallersurface-to-volume ratio for the porous particles,which results in less particle aggregation.
Another benefit to the use of large particles is thatthey can avoid phagocytic clearance from the lungs.Radiolabeled polystyrene microspheres of 3, 9, and 15µm in diameter administered into rat lungs werecleared with biphasic patterns. The half lives for thelate phases of the 3 and 9 µm microspheres were 69and 580 days, respectively, while that for the 15 µmmicrosphere was found not measurable during the106-day study (81).
Spray drying produced hollow porous powders con-sisting of albumin, DPPC, and lactose. The solutionfeed rate and pressure of the compressed air had littleimpact on powder properties. Increasing the inlettemperature tended to make the powders heavier(15). The lower the bulk powder tap density, thehigher the FPF. Removing albumin or DPPC from thecomposition led to denser and smaller particles.Replacing lactose with mannitol resulted in a poorFPF value. The FPF was maximized at albumin/DPPC/lactose10/60/30 (71).
Large porous particles composed of albuterol sul-fate (4%), a short-acting bronchodilator, and humanserum albumin (18%), lactose (18%), and DPPC (60%)were prepared by spray drying. Inhalation of thealbuterol particles obtained produced a significantinhibition of carbachol-induced bronchoconstriction
for at least 16 hr in guinea pigs, while small non-porous albuterol particles were effective for up to 5hr. It is possible that the long-lasting action observedin the large porous particles was at least partly due tothe slower clearance by phagocytosis (82).
PulmoSphere™ particles are hollow porous parti-cles with geometric diameters between 3 and 5 µmand tap densities of about 0.1 g/cm3 prepared by aspray-drying method. A submicrometer f luorocar-bon-in-water emulsion stabilized by a monolayer ofphospholipid at the f luorocarbon-water interface iscombined with a second aqueous phase containingthe drug and any wall-forming excipients desired.Spray drying the aqueous dispersion produces hollowporous powders. The f luorocarbon serves as a blow-ing agent or inf lation agent during the spray-dryingstep (83). Deposition of PulmoSphere™ particles ofalbuterol sulfate in the human respiratory tract deliv-ered by pMDI was double the deposition of a conven-tional micronized drug pMDI formulation (84).
The spray freeze-drying technique has been pro-posed as a method to produce light and porous pro-tein particles (63). A protein solution with excipient issprayed in liquid N2. After spraying, the whole con-tent of the liquid N2 was lyophilized to harvest pow-ders. This technique produced powders of DNase andanti-IgE MAb with a high FPF up to 70% (63).
When the GAS process with supercritical carbondioxide is used to produce protein powders, the oper-ating temperature or rate of CO2 addition had a minoreffect on the morphology and size of the powders.Large porous particles were obtained at a high con-centration of proteins, while agglomeration of the pre-cipitated particles occurs at dilute concentrations(52). ASES processing at higher temperatures withhigher concentrations of the protein reduced theagglomeration of primary particles due to a higherdegree of supersaturation and a higher nucleationrate (85).
4. Conclusion
Although pulmonary absorption of peptides andproteins is much better than that through the gas-trointestinal tract, the bioavailability of inhaled pep-tides and proteins is still below that administeredintravenously or subcutaneously. The success of in-halation therapy with dr y powders is determinedby the biological aspects of active ingredients, thephysicochemical aspects of formulation, and inhalerperformance. The bioavailability of inhaled peptidesand proteins will be improved by considering these
KONA No.20 (2002) 79
factors. The application of hollow porous particleshas opened a new avenue for inhalation therapy inhumans. We now expect groundbreaking success inincreasing permeability, reducing metabolic degrada-tion, maximizing the FPF, and in other areas that willmake inhalation therapy with peptides and proteinsmore effective and economical.
References
1) Cipolla, D. C., Clark, A. R., Chan, H. K., Gonda, I. andShire, S. J. “Assessment of aerosol delivery system forrecombinant human deoxyribonuclease,” STP PharmaSciences 4, 50-60 (1994).
2) Chan, H. K., Clark, A., Gonda, I., Mumenthaler, M. andHsu, C. “Spray dried powders and powder blends ofrecombinant human deoxyribonuclease (rhDNase) foraerosol delivery,” Pharm Res 14, 431-437 (1997).
3) Pfizer Inc. Press Release, June 15, 2002. “Study showsExubera® (inhaled insulin) provides glycemic controlequal to insulin injections in patients with type 1 dia-betes,” http://www.pfizer.com/pfizerinc/about/press/exubera0615.html
4) Pfizer Inc. Press Release, June 15, 2002. “Exubera®
(inhaled insulin) provides better glycemic control thanoral therapy for patients with type 2 diabetes, new datashow,” http://www.pfizer.com/pfizerinc/about/press/exubera0615b.html
5) Aradigm Co. News Release, June 17, 2002. “New datashow first electronic inhalation insulin system compara-ble to multiple injections in controlling glucose,” http://www.aradigm.com/
6) Timsina, M. P., Martin, G. P., Marriott, C., Ganderton,D. and Yianneskis, M. “Drug delivery to the respiratorytract using dry powder inhalers,” Int J Pharmaceut 101,1-13 (1994).
7) Newman, S. P., Hollingworth, A. and Clark, R. “Effect ofdifferent modes of inhalation on drug delivery from adry powder inhaler,” Int J Pharmaceut 102, 127-132(1994).
8) Dunbar, C. A., Hickey, A. J. and Holzner, P. “Dispersionand characterization of pharmaceutical dry powderaerosols,” Kona 16, 7-45 (1998).
9) Chew, N. Y. K. and Chan, H. K. “Pharmaceutical drypowder aerosol delivery,” Kona 19, 46-56 (2001).
10) Suarez, S. and Hickey, A. J. “Drug properties affectingaerosol behavior,” Respiratory Care 45, 652-666 (2000).
11) Benowitz, N., Forsyth, R. P., Melmon, K. L. andRowland, M. “Lidocaine disposition kinetics in monkeyand man I. Prediction by a perfusion model,” ClinPharmacol Ther 16, 87-98 (1974).
12) Wolff, R. K. “Safety of inhaled proteins for therapeuticuse,” Journal of Aerosol Medicine 11, 197-219 (1998).
13) McConville, J. T., Patel, N., Ditchburn, N., Tobyn, M. J.,Staniforth, J. N. and Woodcock, P. “Use of a novel modi-fied TSI for the evaluation of controlled-release aerosol
formulations,” I. Drug Dev Ind Pharm 26, 1191-1198(2001).
14) Ang, X. D., Ma, J. K. A., Malanga, C. J. and Rojanasakul,Y. “Characterization of proteolytic activities of pul-monary alveolar epithelium,” Int J Pharmaceut 195, 93-101 (2000).
15) Vanbever, R., Mintzes, J. D., Wang, J., Nice, J., Chen, D.H., Batycky, R., Langer, R. and Edwards, D. A. “Formu-lation and physical characterization of large porous par-ticles for inhalation,” Pharm Res 16, 1735-1742 (1999).
16) Schanker, L. S. and Less, M. J. “Lung pH and pul-monary absorption of nonvolatile drugs in the rat,”Drug Metabol Dispos 5, 174-178 (1977).
17) Fisher, A. B. and Chander, A. “Introduction: Lung sur-factant phospholipids and apoproteins,” Exp Lung Res6, 171-174 (1984).
18) Hunninghake, G. W., Gadek, J. E., Kawanami, O.,Ferrans, V. J. and Crystal, R. G. “Inflammatory andimmune processes in the human lung in health and dis-ease: evaluation by bronchoalveolar lavage,” Am JPathol 97, 149-206 (1979).
19) Lanman, R. C., Gillilan, R. M. and Schanker, L. S. “Ab-sorption of cardiac glycosides from the rat respiratorytract,” J Pharmacol Exp Ther 187, 105-111 (1973).
20) Enna, S. J. and Schanker, L. S. “Absorption of drugsfrom the rat lung,” Am J Physiol 223, 1227-1231 (1972).
21) Enna, S. J. and Schanker, L. S. “Absorption of saccha-rides and urea from the rat lung,” Am J Physiol 222,409-414 (1972).
22) Matsukawa, Y., Lee, V. H. L., Crandall, E. D. and Kim,K. J. “Size-dependent dextran transport across rat alveo-lar epithelial cell monolayers,” J Pharm Sci 86, 305-309(1997).
23) Morimoto, K., Uehara, Y., Iwanaga, K. and Kakemi, M.“Tracheal barrier and the permeability of hydrophilicdrugs and dipeptides,” Biol Pharm Bull 22, 510-514(1999).
24) Brown, R. A. J. and Schanker, L. S. “Absorption ofaerosolized drugs from the rat lung,” Drug MetabDispos Biol Fate Chem 11, 355-360 (1983).
25) Yoshida, H., Okumura, K., Hori, R., Anmo, T. andYamaguchi, H. “Absorption of insulin delivered to rabbittrachea using aerosol dosage form,” J Pharm Sci 68,670-671 (1979).
26) Patton, J. S., Trinchero, P. and Platz, R. M. “Bioavail-ability of pulmonary delivered peptide and proteins: α-interferon, calcitonins and parathyroid hormones,” JControlled Release 28, 79-85 (1994).
27) Okumura, K., Iwakawa, S., Yoshida, T., Seki, T. andKomada, F. “Intratracheal delivery of insulin Absorptionfrom solution and aerosol by rat lung,” Int J Pharmaceut88, 63-73 (1992).
28) Lipworth, B. J. “Pharmacokinetics of inhaled drugs,” BrJ Clin Pharmacol 42, 697-705 (1996).
29) Lie, F. Y., Kildsig, D. O. and Mitra, A. K. “Pulmonarybiotransformation of insulin in rat and rabbit,” LifeScience 51, 1683-1689 (1992).
30) Shen, Z., Zhang, Q., Wei, S. and Nagai, T. “Proteolytic
80 KONA No.20 (2002)
enzymes as a limitation for pulmonary absorption ofinsulin: in vitro and in vivo investigations,” Int JPharmaceut 192, 115-121 (1999).
31) Hsu, M. C. P. and Bai, J. P. F. “Investigation into thepresence of insulin-degrading enzyme in cultured typeII alveolar cells and the effects of enzyme inhibitors onpulmonary bioavailability of insulin in rats,” J PharmPharmacol 50, 507-514 (1998).
32) Hoover, J. L., Rush, B. D., Wilkinson, K. F., Day, J. S.,Burton, P. S., Vidmar, T. J. and Ruwart, M. J. “Peptidesare better absorbed from the lung than the gut in therat,” Pharm Res 9, 1103-1106 (1992).
33) Henderson, R. F. “Use of bronchoalveolar lavage todetect lung damage,” Environ Health Perspect 56, 115-129 (1984).
34) Morgan, A., Moores, S. R., Holmes, A., Evans, J. C.,Evans, N. H. and Black, A. “The effect of quartz, admin-istered by intratracheal instillation, on the rat lung. I.The cellular response,” Environ Res 22, 1-12 (1980).
35) Moores, S. R., Black, A., Evans, J. C., Evans, N.,Holmes, A. and Morgan, A. “The effect of quartz,administered by intratracheal instillation, on the ratlung. II. The short-term biochemical response,”Environ Res 24, 275-285 (1981).
36) Todo, H., Okamoto, H., Iida, K. and Danjo, K. “Effect ofadditives on insulin absorption from intratracheallyadministered dry powders in rats,” Int J Pharmaceut220, 101-110 (2001).
37) Komada, F., Iwakawa, S., Yamamoto, N., Sakakibara, H.and Okumura, K. “Intratracheal delivery of peptide andprotein agents: Absorption from solution and dry pow-der by rat lung,” J Pharm Sci 83, 863-867 (1994).
38) Yamamoto, A., Umemori, S. and Muranishi, S. “Absorp-tion enhancement of intrapulmonary administered in-sulin by various absorption enhancers and proteaseinhibitors in rats,” J Pharm Pharmacol 46, 14-18 (1993).
39) Morita, T., Yamamoto, A., Takakura, Y., Hashida, M.and Sezaki, H. “Improvement of the pulmonary absorp-tion of (Asu1,7)-eel calcitonin by various proteaseinhibitors in rats,” Pharm Res 11, 909-913 (1994).
40) Kobayashi, S., Kondo, S. and Juni, K. “Pulmonary de-livery of salmon calcitonin dry powders containingabsorption enhancers in rats,” Pharm Res 13, 80-83(1996).
41) Kobayashi, S., Kondo, S. and Juni, K. “Study on pul-monary delivery of salmon calcitonin in rats: Effects ofprotease inhibitors and absorption enhancers,” PharmRes 11, 1239-1243 (1994).
42) Yamamoto, A., Okumura, S., Fukuda, Y., Fukui, M.,Takahashi, K. and Muranishi, S. “Improvement of thePulmonary Absorption of (Asu1,7)-eel Calcitonin byVarious Absorption Enhancers and Their PulmonaryToxicity in Rats,” J Pharm Sci 86, 1144-1147 (1997).
43) Maa, Y. F., Costantino, H. R., Nguyen, P. A. T. and Hsu,S. S. “The effect of operating and formulation variableson the morphology of spray-dried protein particles,”Pharmaceut Dev Technol 2, 213-223 (1997).
44) Costantino, H. R., Andya, J. D., Nguyen, P. A., Dasovich,
N., Sweeney, T. D., Shire, S. J., Hsu, C. C. and Maa, Y. F.“Effect of mannitol crystallization on the stability andaerosol performance of a spray-dried pharmaceuticalprotein, recombinant humanized anti-IgE monoclonalantibody,” J Pharm Sci 87, 1406-1411 (1998).
45) Broadhead, J., Rouan, S. K. and Rhodes, C. T. “Theeffect of process and formulation variables on theproperties of spray-dried β-galactosidase,” J PharmPharmacol 46, 458-467 (1994).
46) Labrude, P., Rasolomanana, M., Vigneron, C., Thirion,C. and Chaillot, B. “Protective effect of sucrose on spraydrying of oxyhemoglobin,” J Pharm Sci 78, 223-229(1989).
47) Tahl, K., Claesson, M., Lilliehorn, P., Linden, H. andBackstrom, K. “The effect of process variables on thedegradation and physical properties of spray driedinsulin intended for inhalation,” Int J Pharmaceut 233,227-237 (2002).
48) Mumenthaler, M., Hsu, C. C. and Pearlman, R. “Feasi-bility study on spray-drying protein pharmaceuticals:Recombinant human growth hormone and tissue-typeplasminogen activator,” Pharm Res 11, 12-20 (1994).
49) Maa, Y. F., Nguyen, P. A. and Hsu, S. W. “Spray-dryingof air-liquid interface sensitive recombinant humangrowth hormone,” J Pharm Sci 87, 152-157 (1998).
50) Donsi, G. and Reverchon, E. “Micronization by meansof supercritical f luids: possibility of application to phar-maceutical field,” Pharm Acta Helv 66, 170-173 (1991).
51) Jung, J. and Perrut, M. “Particle design using supercrit-ical f luids: Literature and patent survey,” J SupercriticalFluids 20, 179-219 (2001).
52) Thiering, R., Dehghani, F., Dillow, A. and Foster, N. R.“The inf luence of operating conditions on the densegas precipitation of model proteins,” J Chem TechnolBiotechnol 75, 29-41 (2000).
53) Steckel, H. and Muller, B. W. “Metered-dose inhaler for-mulation of f luticasone-17- propionate micronized withsupercritical carbon dioxide using the alternative pro-pellant HFA-227,” Int J Pharmaceut 173, 25-33 (1998).
54) Steckel, H., Thies, J. and Muller, B. W. “Micronizing ofsteroids for pulmonary delivery by supercritical carbondioxide,” Int J Pharmaceut 152, 99-110 (1997).
55) Bodmeier, R., Wang, H., Dixon, D. J., Mawson, S. andJohnston, K. P. “Polymeric microspheres prepared byspraying into compressed carbon dioxide,” Pharm Res12, 1211-1217 (1995).
56) Falk, R., Randolph, T. W., Meyer, J. D., Kelly, R. M. andManning, M. C. “Controlled release of ionic compoundsfrom poly (L-lactide) microspheres produced by precip-itation with a compressed antisolvent,” J ControlledRelease 44, 77-85 (1997).
57) Yeo, S. D., Lim, G. B., Debenedetti, P. G. and Bernstein,H. “Formation of microparticulate protein powdersusing a supercritical f luid antisolvent,” BiotechnolBioeng 41, 341-346 (1993).
58) Yeo, S. D., Debenedetti, P. G., Patro, S. Y. andPrzybycien, T. M. “Secondary structure characteriza-tion of microparticulate insulin powders,” J Pharm Sci
KONA No.20 (2002) 81
83, 1651-1656 (1994).59) Winters, M. A., Debenedetti, P. G., Carey, J., Sparks, H.
G., Sane, S. U. and Przybycien, T. M. “Long-term andhigh-temperature storage of supercritically-processedmicroparticulate protein powders,” Pharm Res 14, 1370-1378 (1997).
60) Winters, M. A., Knutson, B. L., Debenedetti, P. G.,Sparks, H. G., Przybycien, T. M., Stevenson, C. L. andPrestrelski, S. J. “Precipitation of proteins in supercriti-cal carbon dioxide,” J Pharm Sci 85, 586-594 (1996).
61) Palakodaty, S., York, P. and Pritchard, J. “Supercriticalf luid processing of materials from aqueous solutions:The application of SEDS to lactose as a model sub-stance,” Pharm Res 15, 1835-1843 (1998).
62) Ghaderi, R., Artursson, P. and Carlfors, J. “Preparationof biodegradable microparticles using solution- en-hanced dispersion by supercritical f luids (SEDS),”Pharm Res 16, 676-681 (1999).
63) Maa, Y. F., Nguyen, P. A., Sweeney, T., Shire, S. J. andHsu, C. C. “Protein inhalation powders: Spray drying vsspray freeze drying,” Pharm Res 16, 249-254 (1999).
64) Sellers, S. P., Clark, G. S., Sievers, R. E. and Carpenter,J. F. “Dry powders of stable protein formulations fromaqueous solutions prepared using supercritical CO2-assisted aerosolization,” J Pharm Sci 90, 785-797 (2001).
65) Lai, M. C. and Topp, E. M. “Solid-state chemical stabil-ity of proteins and peptides,” J Pharm Sci 88, 489-500(1999).
66) Pikal, M. J. and Rigsbee, D. R. “The stability of insulinin crystalline and amorphous solids: observation ofgreater stability for the amorphous form,” Pharm Res14, 1379-1387 (1997).
67) Maa, Y. F., Nguyen, P. A., Andya, J. D., Dasovich, N.,Sweeney, T. D., Shire, S. J. and Hsu, C. C. “Effect ofspray drying and subsequent processing conditions onresidual moisture content and physical/biochemical sta-bility of protein inhalation powders,” Pharm Res 15,768-775 (1998).
68) Imamura, K., Iwai, M., Ogawa, T., Sakiyama, T. andNakanishi, K. “Evaluation of hydration states of proteinin freeze-dried amorphous sugar matrix,” J Pharm Sci90, 1955-1963 (2001).
69) Forbes, R. T., Davis, K. G., Hindle, M., Clarke, J. G. andMaas, J. “Water vapor sorption studies on the physicalstability of a series of spray-dried protein/sugar pow-ders for inhalation,” J Pharm Sci 87, 1316-1321 (1998).
70) Bosquillon, C., Lombry, C., Preat, V. and Vanbever, R.“Comparison of particle sizing techniques in the case ofinhalation dry powders,” J Pharm Sci 90, 2032-2041(2001).
71) Bosquillon, C., Lombry, C., Preat, V. and Vanbever, R.“Inf luence of formulation excipients and physical char-acteristics of inhalation dry powders on their aerosoliza-tion performance,” J Controlled Release 70, 329-339(2001).
72) Izutsu, K., Yoshioka, S. and Terao, T. “Effect of mannitol
crystallinity on the stabilization of enzymes duringfreeze-drying,” Chem Pharm Bull (Tokyo) 42, 5-8(1994).
73) Chan, H. K. and Gonda, I. “Solid state characterizationof spray-dried powders of recombinant human deoxyri-bonuclease (RhDNase),” J Pharm Sci 87, 647-654(1998).
74) Kanig, J. L. “Pharmaceutical aerosols,” J Pharm Sci 52,513-535 (1963).
75) Gonda, I. “A semi-empirical model of aerosol depositionin the human respiratory tract for mouth inhalation,” JPharm Pharmacol 33, 692-696 (1981).
76) Crowder, T. M., Rosati, J. A., Schroeter, J. D., Hickey, A.J. and Martonen, T. B. “Fundamental effects of particlemorphology on lung delivery: predictions of Stokes’ lawand the particular relevance to dry powder inhaler for-mulation and development,” Pharm Res 19, 239-245(2002).
77) Hallworth, G. W. and Westmoreland, D. G. “The twinimpinger: a simple device for assessing the delivery ofdrugs from metered dose pressurized aerosol inhalers,”J Pharm Pharmacol 39, 966-972 (1987).
78) Kawashima, Y., Serigano, T., Hino, T., Yamamoto, H.and Takeuchi, H. “Effect of surface morphology of car-rier lactose on dry powder inhalation property of pran-lukast hydrate,” Int J Pharmaceut 172, 179-188 (1998).
79) Chew, N. Y. K. and Chan, H. K. “Inf luence of particlesize, air f low, and inhaler device on the dispersion ofmannitol powders as aerosols,” Pharm Res 16, 1098-1103 (1999).
80) Edwards, D. A., Hanes, J., Caponetti, G., Hrkach, J.,Ben-Jebria, A., Eskew, M. L., Mintzes, J., Deaver, D.,Lotan, N. and Langer, R. “Large porous particles for pul-monary drug delivery,” Science 276, 1868-1871 (1997).
81) Snipes, M. B. and Clem, M. F. “Retention of micros-pheres in the rat lung after intratracheal instillation,”Environ Res 24, 33-41 (1981).
82) BenJebria, A., Chen, D. H., Eskew, M. L., Vanbever, R.,Langer, R. and Edwards, D. A. “Large porous particlesfor sustained protection from carbachol-induced bron-choconstriction in guinea pigs,” Pharm Res 16, 555-561(1999).
83) Dellamary, L. A., Tarara, T. E., Smith, D. J., Woelk, C.H., Adractas, A., Costello, M. L., Gill, H. and Weers, J.G. “Hollow porous particles in metered dose inhalers,”Pharm Res 17, 168-174 (2000).
84) Hirst, P. H., Pitcairn, G. R., Weers, J. G., Tarara, T. E.,Clark, A. R., Dellamary, L. A., Hall, G., Shorr, J. andNewman, S. P. “In vivo lung deposition of hollow porousparticles from a pressurized metered dose inhaler,”Pharm Res 19, 258-264 (2002).
85) Bustami, R. T., Chan, H. K., Dehghani, F. and Foster, N.R. “Generation of micro-particles of proteins for aerosoldelivery using high pressure modified carbon dioxide,”Pharm Res 17, 1360-1366 (2000).
82 KONA No.20 (2002)
KONA No.20 (2002) 83
Author’s short biography
Hirokazu Okamoto
Dr. Hirokazu Okamoto is an associate professor in the Faculty of Pharmacy, MeijoUniversity. He received his Ph.D. from the Faculty of Pharmaceutical Sciences,Kyoto University in 1989. He worked at Upjohn Pharmaceuticals Limited, theJapanese branch of The Upjohn Co., as a research scientist in Pharmacy ResearchGroup from 1989, and was transferred to Pharmacia & Upjohn as a PharmacyResearch Group leader in 1996 upon the merger of Pharmacia Co. and The UpjohnCo. He has occupied his present position since 1998. His research interests are inthe development of drug delivery systems to improve bioavailability. His recentmain research theme is the development of dry powder proteins and dry powdergenes for inhalation.
Hiroaki Todo
Hiroaki Todo is a graduate student in the Faculty of Pharmacy, Meijo University.He received his B.S. from the same university in 1999. His research theme isimproving the bioavailability of dry powder insulin prepared by spray-drying andSCF techniques.
Kotaro Iida
Dr. Kotaro Iida is a lecturer in the Faculty of Pharmacy, Meijo University. Hereceived his Ph.D. from Meijo in 1992. He was a post doctoral fellow in the Schoolof Pharmacy, University of Basel from 1997 to 1999. His research interests are thedesign of dry powders for inhalation with carrier particles. His recent mainresearch theme is the characterization of powder systems for pulmonary applica-tion.
Kazumi Danjo
Dr. Kazumi Danjo is a professor in the Faculty of Pharmacy, Meijo University. Hereceived his Ph.D. from the same institute in 1981. He was a post doctoral fellow inthe School of Pharmacy, University of Wisconsin in 1986. His research interestsare in the development of composite particles using the spray-drying technique.One of his recent research projects is a study on the dissolution of drugs with poorwater solubility from porous particles.
84 KONA No.20 (2002)
Introduction
Porous materials are widely used in everyday life,whether one is aware of them or not. The silica gel asa dehumidifying agent and the activated carbon as adeodorant are traditional porous materials. Anotherexample is traditional Japanese houses, which aremade of wood, earth, and paper. Such architectureresulted from long years of innovation through in-sights that these materials would function to insulateand adjust humidity in Japanese climate, whose tem-perature and humidity vary over broad ranges. It isamazing how people unconsciously worked out theuse of materials with various pore sizes. Tightlysealed modern housing holds in humidity, which hascreated problems such as molds and bacteria, andthere are also concerns about the many illnesses thatcould result from these. This has focused attention onbuilding materials that incorporate porous materials,and many such materials are being developed. [1, 2]As this shows, porous materials are closely integratedinto our lives. Here we shall attempt to classify theporous materials reported to date while taking theirfunction expression mechanisms, and then, based onthat classification, describe the synthesis and fabrica-
tion methods for some representative porous materi-als.
Functions and Classification of Porous Materials
Typical porous ceramics and the range of their poresizes are shown in Fig. 1, [3]. There are currentlymany porous materials with pore sizes from about0.1 nm to 10 mm. When considering these functionexpression mechanisms of these materials, the levelat which we see pores is important. The functionexpression of Angstrom-order pores is likely relatedto interaction with ions, atoms, and molecules, whilethose in micrometer and millimeter ranges are proba-bly related to the adhesion of solid particles on filter.It is assumed that pores size in the middle of thisrange are related to molecular aggregates and con-densed liquids.
In this session, the relationship between pore sizeand function expression mechanisms is reviewed.Fig. 2 shows the mechanisms of porous materials inrelation to gas permeation. [4] When pore size is 10µm or larger, the mechanism can be regarded as thef low passing through an equivalent packed bed, andfor that reason the relationship between a porousmaterial and function can be forecast from the Darcyequation and other relational equations for f low veloc-ity and pressure loss. Molecular diffusion controls the
Minoru Takahashi and Masayoshi FujiCeramics Research Laboratory, Nagoya Institute ofTechnology*
Synthesis and Fabrication of Inorganic Porous Materials: From Nanometer to Millimeter Sizes†
Abstract
In recent years, the functions of porous ceramics such as light weight, thermal insulation, perme-ability, separation, adsorption, and sound absorption have been paid attention. They are applied tomaterials for environmental improvement, materials for energy system, biomechanical materials,spatial materials and so on. In conjunction with this, many synthesis and fabrication methods fornot only porous ceramics in the usual macropore range, but also those in the mesopore and micro-pore ranges were reported. The functions and fabrication methods of porous materials are closelyrelated to pore size and structure. In this paper we reviewed recent synthesis and fabrication methodsfor porous materials across a wide range from nanometer to millimeter pore sizes while also touch-ing upon material functions.
* 10-6-29 Asahigaoka, Tajimi, Gifu 507-0071 Japan† Accepted: June 27, 2002
permeation mechanism of porous materials whosepore sizes are in the approximate range of 0.1 to 10µm. When pore size and molecular mean free path fallbelow that range, they are governed by Knudsen dif-fusion. Permeation f low velocity then is proportionalto molecular weight to the 0.5 power. At smaller poresizes below several nm, an activation process causedby interaction between pore wall surfaces and mole-cules contributes to the permeation phenomenon,which is called “activation diffusion” or “surfacef low.” This is a pore size range in which capillary con-densation governs when the gas is a condensing gassuch as water vapor. At still smaller pore sizes, perme-ation selectivity is expressed due to difference inmolecule sizes, and one can expect the so-called“molecular sieve effect.” From these examples, thecorrespondence between pore size and function isapparent. It is in fact clear that properties includingporosity, pore shape, interpore networks, pore open-ing, and pore closing contribute to various func-tion expressions. Table 1 presents the relationshipbetween these pore properties and functions. [5]These are sufficient for considering rough designguidelines of porous materials, but owing to the com-plex connections between function expression andpore properties such as pore size, porosity, and pore
KONA No.20 (2002) 85
micropore
zeolite
FSM-16, M41S
sol-gel method (colloidal process)
sol-gel method (cat. NH3)
phase separation glass
sintered powder
auto filter
honeycomb ceramics
humidity sensor
enzyme carrier filter
microbe carrier
sol-gel method (cat. HCl3)
mesopore macropore
1 Å 1 nm 10 nm 100 nm 1 µm 10 µm 100 µm 1 mm
Fig. 1 Pore size of typical porous ceramics.
Surface diffusion
Molecular sieve
Knudsen diffusion
Capitally condensation
Fig. 2 Permeation model of gas in porous materials (modifiedfrom Matsukata [4]).
shape, or between function expression and materialproperties, a method of cataloging them more care-fully is desirable from the standpoint of materialdesign.
One method of classifying pores is the Internation-al Union of Pure and Applied Chemistry (IUPAC)method, which is internationally recognized. [6] It isbased on the Russel classification, in which pores areclassified mainly according to the results of nitrogenadsorption experiments. [7, 8] One should be wellaware that classification is based on nitrogen adsorp-tion, meaning that the relative sizes of nitrogen mole-cules and pores must be taken into account. Withmolecules larger than nitrogen, adsorption resem-bling micropore filling will occur in the mesoporerange. Additionally, caution is needed when workingwith molecules smaller than nitrogen molecules, suchas hydrogen and water. For example, even if materialsare non-porous to nitrogen molecules, it is often the
case that they are not necessarily non-porous to thesesmaller molecules. Therefore we think that an indexsuch as the relative pore sizes shown in Table 2 isneeded in pore classification. However nitrogen mole-cules are quadrupole interactive, generally in nitro-gen adsorption they can be seen as often forming amultilayer structure as in BET theory, but compara-ble phenomena do not necessarily occur with othermolecules. Thus at this time classification by thepresence of molecules in pores is perhaps a practicalmethod.
Based on the foregoing, and using the IUPAC clas-sification as the standard, Table 2 presents the classi-fication based on the function expression discussedabove and the phenomena occurring in pores, as wellas the pore classification organized by consideringthe synthesis methods for existing porous materials,discussed below.
86 KONA No.20 (2002)
Porosity dependence Examples of properties
No dependence on porosity Lattice parameter, unit cell volume, thermal expansion, heat capacity per unit weight, density
Dependence only on the amount of porosity Apparent density, dielectric constant, heat capacity per unit volume
Dependence both Flux or stress dominant Mechanical properties, Electrical and thermal conductivity at low to moderate the amount and in the solid phase temperature and porosity character of porosity
All f lux in the pore Surface area and tortuosity, e.g., for catalysisphase and filtration
Flux in both pore and Thermal conductivity, with larger and more open pores at higher temperaturesolid phase
Table 1 Inf luence of porosity on properties (From Rice [5])
Pore State of atoms or Characterization
Relative Category radius Origin of pore pore
rangemolecules in pore methods
radius*
Atom and Micropore 2 nm Space among atoms or ions, Microporefilling, Atom, Gas adsorption, 6molecule pore Crystal lattice, Trace of Ion, Molecule TEM, XRD
solvent molecules after drying
Aggregate Mesopore I 2-10 nm Micelle or liquid crystal Intermediate state of Gas adsorption, 6-30Molecules pore templating microporefilling and TEM, XRD
condensation, Molecules interact with pore wall
Liquid phase Mesopore II 2-50 nm Phase separation, Space Capillary condensation, Gas adsorption, 30-141pore among particles Liquid phase SEM, TEM
Spatial pore Macropore 50 nm Bubble, Cavity, Space among The same on a f lat surface, Porosimetry SEM 141particles, Particle templating Pore is just a space
* Pore radius divided by diameter of nitrogen molecule (0.354 nm)
Table 2 Classification of porous materials
Synthesizing Atom and Molecule Pore
Zeolite is a typical material in this pore range. Itwas in 1756 that the Swedish minerologist A. F.Cronstedt was the first to observe that steam wasemitted when a mineral called stilbite was heated. Onaccount of this he coined the term “zeolite,” which isa combination of the Greek “zeo” for boil and “lithos”for stone. Since then about 40 kinds of such mineralshave been discovered. Today zeolite is understoodto be a hydrous crystallized aluminosilicate mineral.Many of these materials are tectoaluminosilicateswhich, as illustrated in Fig. 3, are MO4 tetrahedra (Mmeans the Si, Al, or other atom of a tetrahedron) thatshare their apex oxygen atoms with a neighboringtetrahedron. This means the atomic ratio O/M in theframe is 2.
Zeolite is characterized by its uniform pores, whichare about the same size as its molecules. Because zeo-lite can be classified by the size of its molecules, it isalso called a molecular sieve. [9] Many types of zeo-lite have been synthesized, as seen in the industrial-ization of ZSM-5 (MFI) as a catalyst. In addition toaluminosilicate, zeolite with many different composi-tions and structures have been synthesized. VPS-5,with pore sizes between 1.2 and 1.3 nm, is the firstaluminophosphate zeolite with pore sizes over 1 nm.Its pore walls have an 18-ring structure comprising 18MO4 (M: Al, P) units. Gallium phosphate zeolite,which has a 20-ring structure have been synthesizedrecently. A characteristic is that although the poreentrance size is about the same as that of VPI-5, crys-
tal interiors have voids called supercages as large as 3nm.
Generally zeolite is made by hydrothermal synthe-sis. Si and Al sources and crystallizing agents are putinto an autoclave, where the materials are dissolvedand recrystallized. Any number of different zeolitetypes may result depending on the ingredient ratios,crystallization temperature, and crystallization time.Table 3 gives the conditions for synthesizing zeolitemembranes, which are of particular interest. [10-16].
At the center of attention in recent years is zeolitethat can change its pore size in accordance with exter-nal fields. Reported types of variable-pore-size zeolitethat can adjust its pore size by temperature are alumi-nosilicate of RHO type, and a type of titanosilicatezeolite. In particular, the titanosilicate whose ETS-4(Engelhard titanosilicate-4) counter cations have beenreplaced by strontium is stable under heat treatmentand can reversibly and precisely adjust its pore sizebetween 0.427 and 0.394 nm. [17] Further, recentenvironmental problems underlie frequent reportsincluding those on the synthesis of zeolite fromwastes, and there are expectations for increasing re-search advances in the field of zeolite synthesis.
In contrast with the three-dimensional spaces ofzeolite, various attempts are underway to find ways touse the unique two-dimensional spaces of stratifiedsubstances, of which the clay minerals are representa-tive. The water-caused swelling of montmorillonite,which has long been known, is a phenomenon that isclosely connected to the plasticity of clay. While thedistance between layers in dry montmorillonite is
KONA No.20 (2002) 87
CaA
NaX
etc.
O
O O
O
0
Si4
O
O O
O
1
Al3
Si Al
O O Sodalite cage : Oxygen : Aluminum or Silicon
OOOO
Na
O
Fig. 3 Synthesis process and frame structure of zeolite.
about 0.95 nm, it changes by steps from 0.95, 1.24,1.54, and 1.90 nm as relative humidity rises. [18]These distances correspond to a compound in whichwater molecule layers each about 0.3 nm thick maketheir way between montmorillonite layers in numbersof 0, 1, 2, and 3 water layers, respectively. The inter-layer energy balance depends on: 1) inter-layer ionsand silicate layer coulomb energy, 2) hydrationenergy of inter-layer cations, and 3) energy of wateradsorption between layers in relation to humidity.[19] Hence, the behavior of change in inter-layerdistance is controlled by the types of inter-layercations and the nature of the silicate layers. [20]Montmorillonite with Na ions between its layersswells without limit under circumstances with muchwater, as in aqueous solutions, [18, 21] and there arereports that montmorillonite with Li ions betweenits layers undergoes similar unlimited swelling. [22]Additionally, various organic compounds becomethe guests of inter-layer substances. There havelong been reports of attempts to obtain inter-layercompounds with guest organic polymers by poly-merizing monomers between layers. Bentonite,montmorillonite, or other substances in which theinter-layer ions of layer substances have beenreplaced by ion exchange with cationic surfactantions are used to put nonpolar organic moleculesbetween layers. However, as illustrated in Fig. 4, lim-itless swelling is not observed at times like thisbecause, in response to the size of the hydrophobicportion of surfactant ions, the material does not sorb
an amount of guest molecules larger than that whichis held in the space formed between layers. [19]
In recent years there has been much research onthe synthesis of intercalation compounds that aregood at bringing various substances between layers,as happens in this swelling. In particular there ismuch research of great interest on providing variousfunctions through surface modification between lay-
88 KONA No.20 (2002)
Fig. 4 Swelling model of toluene to montmorillonite intercalatedby trimetyldodecylammonium cations. (modified fromFukushima [19]).
Molar ratio
Product Si source Al sourceCrystallizing
SiO2 Al2O3 Na2O H2OCrystallizing
Time Temp. Ref.
agentagent
(Day) (K)
MFI SiO2 Al(NO3)3 (C3H7)3HNBr 1 0.01 0.05 40-100 0.1 2-17 403-473 10)
MFI SiO2 Al(NO3)3 (C3H7)3HNBr 1 0.01 0.05 80 0.1 0.25-1 443 11)
SAPO-5 SiO2 Al(OCH(CH3)2 (C3H7)3HNBr 0.3 1.0 47 1.0 1-5.5 398-473 12)
H3PO4* γ-AlO(OH)
MFI SiO2 (C3H7)3HNBr 1 2.2 2832 5.22 9 453 13)
GME SiO2 NaAlO2 Dab-4-Br** 1 0.067 0.6 26 0.16 4.17 368 14)
water glass 1 0.033 0.6 44 0.24
MFI SiO2 Al(NO3)3 (C3H7)3HNBr 1 0-0.02 0.05 40-400 0.11 0.08-2 393-453 15)
FUA SiO2 NaAlO2 1 0.09 0.7 30 0 1.25 353 16)
Table 3 Hydrothermal conditions for Zeolite membrane Synthesis
* As P souse** Polymer from 1,4-diazabicyclo[2.2.2]octane and 1,4-dibromobenzene
ers for the purpose of achieving molecular recogni-tion and reactions that select certain substances. [23,24] And in view of aim of this paper, our interest is inmethods of synthesizing porous materials throughinter-layer bridging, which have been researched forthe purpose of molecular sieves. We have alreadynoted that various organic and inorganic moleculesare adsorbed between the layers of layered clay min-erals, where they push the layers apart, but moleculesadsorbed between layers are easily desorbed bywashing or heating and exhausting. This makes ithard to use inter-layer adsorption compounds as sta-ble molecular sieves. In that regard, ion-exchanginginter-layer compounds whose intercalated cationsmaintain a balance with the negative charge of layerswill exist stably between the layers unless inter-layerions undergo exchange or separation reactions withother ions. Shabtai et al. [25] and Mortland et al. [26]reported on inter-layer compounds that made possi-ble a molecular sieve effect by making pillars of ethyl-enediammonium ions between montmorillonite layers(Fig. 5). This inter-layer compound, whose distancebetween layers is 0.53 nm, will not break down even ifheated to 350°C in air. But in consideration of theusual catalytic reaction or catalyst preparation condi-tions, organic cation pillars are actually not stableenough as catalysts or carriers. For that reason cre-ative efforts are being made to build sturdy pillars ofmetal oxides between layers by intercalating inor-ganic cations. Representative methods include inter-layer bridging by polynuclear inorganic ions, and bysol particles. Using the former method, dropping analkali into an aqueous solution of a metallic salt willoften result in the precipitation of a metal hydroxide.Under conditions in which hydrolysis is insufficient,
and just before a precipitate is formed, a number ofmetal ions gather by using OH group and are presentin water as a polynuclear hydroxide ion. [27] Al3
forms a variety of hydroxide ions, sometimes evenbulky ions like Al13(OH)32
7. And when ZrOCl2·8H2Ois dissolved in water, hydroxide ions of Zr4(OH)8
8
form. A method has been proposed to obtain bridgesusing metal oxide pillars by intercalating these largemetal hydroxide ions between the layers of clay min-erals using ion exchange, then firing the compoundsbetween clay layers at high temperature. Brindley etal. [28] and Lahav et al. [29] used this method to pre-pare a montmorillonite bridge using alumina as pil-lars. The distance between layers is about 0.75 nm.The specific surface area of this pillared material isabout 400 m2/g, which is far larger than the 20 to 30m2/g of montmorillonite before pillaring. It is alsoreported that inter-layer distance is almost perfectlymaintained even at 500°C, showing that thermal sta-bility is also good. Yamanaka et al. [30] created zir-conia pillars between montmorillonite layers andobtained an inter-layer compound with an inter-layerdistance of 0.84 nm and a specific surface area ofabout 500 m2/g. Also reported is a bridge formationmethod that selectively deposits metal hydroxidesonly between clay mineral layers, without using ionexchange. Yamanaka et al. [30] prepared nickel oxidepillars between layers and inter-layer distances of 0.52nm by causing the deposition of nickel hydroxidesbetween montmorillonite layers. Several methodshave been devised to intercalate unstable metalliccations in water. For example, ions are introducedbetween layers in the form of complexes, or firstorganic materials are inserted between layers, andthen the desired ions are introduced. [32]
Synthesis of Aggregate Molecules Pore
From physico-chemical point of view, gas adsorp-tion has a boundary region in which the microporefilling phenomenon and the capillary condensationphenomenon occur. Attention has focused on theunique structure and synthesis method, making thisone of the hottest research fields at present. Theinter-layer compounds discussed above become poresin this boundary region, depending on the pillar syn-thesis method. Here we shall discuss a group of syn-thesis methods for what are known as mesoporousmolecular sieves.
Pioneering mesoporous molecular sieves are FSM-16 [33-35] and MCM-41 (M41S) [36, 37], which weresynthesized by an American group and a Japanese
KONA No.20 (2002) 89
Fig. 5 Schematic model of montmorillonite pillared by ethylene-diammonium ions (modified from Montland [37]).
group, respectively. It is very interesting that thesenew substances were independently synthesized atabout the same time, and it would seem this is closelyrelated to these factors: technical levels had maturedto the point making synthesis possible, and there wasa strong need for the synthesis of large-pore zeolite.
Fig. 6 is a block diagram illustrating the synthesisprocesses and conditions of these large-pore zeolite.Basically they are synthesized in a series of opera-tions in which layered silicate, tetraethyl orthosili-cate, silica, or other Si feedstocks are heated forseveral hours to several days at 70 to 150°C in a sur-factant aqueous solution, after which the solid prod-ucts are filtered out and fired at 550°C or higher.When making FSM-16 the process of synthesizinglayered silicate comes in the first half. At first glancethis appears to be a useless process, but its advantageis that one can obtain a highly crystalline product
with processing at lower temperature and shortertime than MCM-41. Fig. 7 schematically models thesynthesis mechanism of FSM-16. [38] Kanemite is aclay mineral consisting of single-layer silicate sheetshaving Na ions between layers. [39] Ion exchange in-troduces alkyltrimethylammonium (ATMA) betweenkanemite layers, whereupon the silicate sheets bendand form composites with ATMA. Next, dehydrationand condensation of silanol radicals bridge the layers,resulting in a three-dimensional framework. This isa new inorganic synthesis method that demolishesthe traditional concept of crystal synthesis methodsby crystal growth. By contrast, the MCM-41 synthe-sis method is a process which, like the traditionalmethod of synthesizing zeolite, basically puts the rawmaterials into a sealed reactor and heats them at atemperature and for a time that are appropriate. Thismethod is illustrated in Fig. 8. [37] Varying the
90 KONA No.20 (2002)
Micelle Micellar Rod
Silicate
Silicate Calcination
MCM-41Hexagonal Array MCM precursor (Micelle/Silicate composites)
Fig. 8 Schematic model of MCM-41 synthesis (modified from Beck [37]).
FSM-16 process
Water glass
Calcination973K, 6hr.
343K 6hr.,in surfactant and water
Calcination833K
FSM-16
Layered silicate
FSM precursor
MCM-41 process
TEOS etc.
373-423K, 6hr.,in surfactant and water
Calcination833K
MCM-41
MCM precursor
Fig. 6 Comparison of synthesis methods for mesoporous molecu-lar sieve (modified from Beck [37] and Inagaki [38]).
FSM precursor(ATMA/Silicate composites)
Layered silicate(Kanemaite)
FSM -16
remove ATMA
add ATMA
Fig. 7 Schematic model of FMS-16 synthesis (modified fromInagaki [38]).
ratios of ATMA, Si, and NaOH in the ingredientsmakes it possible to control the structure into hexa-gonal, cubic, sheet, and mesostructures. [40, 41]Micelles form when the surfactant exceeds the criti-cal micelle concentration (CMC) in an aqueous solu-tion. It is known that further raising the concentrationover the CMC forms self-organizing molecular aggre-gates (liquid crystals) such as hexagonal, cubic, andsheet forms. [42] This is probably the reason thatthe mesopore family M41S synthesis mechanism, ofwhich MCM-41 is representative, is known as the “liq-uid crystal templating (LCT)” mechanism, becausethe liquid crystal structure of surfactant become as amold. [37] Like FSM-16, when synthesizing MCM-41the pore size is controlled by changing the length ofthe ATMA alkyl chains. [37] And instead of usingATMA, the addition of mesitylene will further enlargepore size to a maximum diameter of 10 nm. [37]
Little time has passed since these substances werefirst synthesized, but despite the many reports ofapplied research, they have yet to see practical use.We hope to see the industrial implementation of theseunique structures.
Synthesis of Liquid Phase Pore
Pores discussed in this section are those of the sizerange in which capillary condensation occurs, and themolecules trapped inside the pores generally behaveas liquid. Typical of the porous material manufactur-ing methods in this area are those which use theunique phenomenon called glass spinodal decomposi-tion, developed by Dow Corning Corp. The typicalsynthesis process is as follows. [43] SiO2, H3BO3, andNaCO3 are used as the main ingredients to makeNa2O-B2O3-SiO2-based borosilicate glass, which is
made into forms such as tubes and plates. In theseforms it is the borosilicate glass shown in Fig. 9a. Toseparate the phases, the product is then heat-treatedat several hundred degrees, which yields a B2O3-Na2O-rich glass phase and a SiO2-rich glass phasewhose sizes are on the order of several nm (Fig. 9b).The B2O3-Na2O phase is dissolved in an acid solutionor hot water, where dissolution is performed to yieldporous glass with a high SiO2 content (Fig. 9c). Theresult is a porous material whose molded shape isretained and which has countless perforations.
There is also a method of making porous silicamaterials by inducing phase separation with a chemi-cal trigger. Nakanishi et al. [43] report on a methodthat uses water-soluble polymers to induce phase sep-aration in a sol-gel silica system. Water-soluble poly-mers can be classified into two groups. First, as istypical of polyacrylic acid, polymers having compara-tively weak attractive interaction with silica are mainlypartitioned into a different phase from silica whenphase separation occurs, and the polymer-rich phaseforms pores. Second, surfactants, and polymers thatinclude polyoxyethylene units are partitioned into thesame phase as silica owing to the formation of hydro-gen bonds with silanol radicals. Therefore it is mainlythe phase comprising the solvent phase that becomespores. There are also reports that various poresizes and structures can be obtained by adjustinghydrolysis conditions and solvent polarity. [45] Fig.10 shows the steps in the synthesis method. Sili-con alkoxide (tetramethoxysilane, TMOS or tetra-ethoxysilane (TEOS)) is blended into a mixture of anacid catalyst and a solution in which an organic poly-mer is uniformly dissolved, and a hydrolysis reactionyields a product which is then gelated and maturedunder sealed conditions. After performing solvent
KONA No.20 (2002) 91
Heattreating
Acidleaching
Dark gray:Na2O-B2O3-SiO2
Black: Na2O-B2O3light gray: SiO2
(b) Phase separation (c) Porous glass(a) Alkali-borosilicate glass
light gray: SiO2
Fig. 9 Production process for porous glass (modified from Makishima [43]).
exchange if necessary, it is dried to obtain a porousmaterial. The porous silica produced by this methodfinds increasing use as monolithic HPLC columnsand in biology-related fields.
Synthesis of Spatial Pore
This is a group of porous materials with so calledmacropores, a range of pore sizes in which the capil-lary condensation phenomenon is no longer observedphysico-chemically. For that reason pore characteris-tics are assessed mainly with the mercury porosime-try. Additionally, such materials have been made for along time, and applied in many ways. There are manyindustrially important materials. Diatomaceous earth,which is the skeletons of diatoms, is well known as anatural mineral of this group having uniform pores ofabout 1 µm. The diatomaceous earth, after havingbeen fired organic contents, is applied to filteringauxiliary for brewer’s yeast, and moisture-adjustingbuilding materials. [47] Various methods of mak-ing artificial macroporous materials include primitivemethods that simply use the interstices between parti-cles, methods that maintain the pores in a formedmaterial by low-temperature sintering, and methodsthat impregnate organic objects having reticulatestructures with ceramic slurry, then firing to elimi-nate the organic material and leave pores (replicamethod). [48] Another method entails embedding aceramic or polymer matrix in the interstices of apacked particle structure, then removing the particlesby either firing or using a solvent to dissolve themout. [49-51] With this method, pore size and structureare determined by the particle size and coordinationnumber. When a structure is uniformly packed with
particles of a uniform size, uniform macropores willbe formed. This method is spotlighted also as amethod of making gas sensors and bioceramics. [52]A similar method is proposed that uses fibers in placeof particles. Here we shall discuss methods using newand old forming agents, and the synthesis of porousmaterials using an in situ solidifying method, which ispromising as a new porous material manufacturingprocess.
Autoclaved lightweight concrete (ALC) is oneporous material made with blowing agents. ALC is amaterial derived from the sand-lime bricks that werelong manufactured in Europe. It is made from aboutthe same raw materials as the bricks, and is impreg-nated with bubbles for lightness. ALC was first madein 1929 by the Swede Ytong, and similar techniquesthen spread to other regions, primarily in Europe. In1963 it came to Japan and its use widened. Commonto these manufacturing methods is autoclave process-ing that uses siliceous and calciferous materials, butraw materials vary from one company to another.
We shall describe A manufacturing process. [53]The raw materials silica (50 to 70%), quicklime (5 to20%), portland cement (10 to 40%), gypsum dihydrate(2 to 10%), and metallic aluminum (under 0.1%) aremade into a slurry, which is put into molds afterkneading well. The quicklime slurry is digested andbecomes slaked lime, and the cement begins hydra-tion. As this time, the metallic aluminum serving asthe blowing agent evolves hydrogen gas, resulting ingreen body that are lightweight owing to the bubblesproduced by forming. After demolding, the greenbody are cut to the prescribed thickness and treatedfor 5 to 10 h in an autoclave at about 180°C and undersaturation vapor pressure, yielding finished ALCproducts. In terms of chemical reactions, at the greenbody formation stage the ALC manufacturing processinvolves mainly the hydration of cement that formshigh-calcium-content calcium silicate hydrates andCa(OH)2. High-calcium-content calcium silicate hy-drates are also formed at the autoclaving stage. It isthought that hydrothermal reactions finish when theCaO supply is completely consumed, which meansthat some of the silicate in the SiO2 supply is left unre-acted. Usually the silica reaction rate is thought to be40 to 60%. A major drawback of ALC is its waterabsorptivity. Its water retention has adverse effectssuch as freezing damage. Recently innovative stepsare taken, such as making the product water-repel-lent.
Of particular interest in recent years as a formingmetal manufacturing method is the slurry forming
92 KONA No.20 (2002)
Starting Sol (Si(OR)4, H2O, water soluble polymer, Acid Catalyst )
Phase Separation and Gelation
Leaching and Solvent Exchange
Drying (Evaporation of Solvent)
Decomposition of Organics (873K)
Sintering (1273K)
Porous Silica Glass with Micropore and Interconected Macropores
Fig. 10 Synthesis of porous glass by chemical phase separation(modified from Nakanishi [45]).
method. [53] In this method, a surfactant and anevaporating forming agent (a hydrophobic volatileorganic solvent) are added to a water-based slurrycontaining metal powder. After formation, the formingagent is volatilized and its vapor pressure directlyforms bubbles in the slurry. This is dried, degreased,and sintered to yield the final product. The pore sizeis controlled in the slurry forming process, whosemechanism is pictured in Fig. 11. A slurry is createdwith a water-based binder, and a surfactant and form-ing agent are added in amounts sufficient to formbubbles in the entire slurry. The surfactant makesthe forming agent dissolve into the slurry, and theparticles disperse (Fig. 11a). Raising the tempera-ture causes the forming agent to gradually volatilizeand form bubbles (Fig. 11b). The aqueous surfactantsolution membrane makes the bubbles into isolatedbubble aggregates, and the metal powder agglomer-ates in the spaces between bubbles. In the subse-quent drying process the bubble aggregates arrangethemselves in a three-dimensional reticulate configu-ration, and the solid components form a spongelikestructure (Fig. 11c). Exercising strict control overslurry viscosity, surfactant types, forming agentamount, forming time, drying time, and other factorsmakes it possible to create various pore sizes andpore structures.
There is also a unique method known as solid-gaseutectic solidification that uses gas solubility to makemetallic porous materials called gasars. This methodtakes advantage of the fact that when the solubility ofgas atoms in a molten metal is high, but their solubil-ity in the same solid metal is low, the gas atoms thatcould not completely dissolve when the metal solidi-fied become bubbles. [55] Just as with the hydrogengas solubility in Mg, Ni, Fe, Cu, Al, Co, W, Mn, Cr,
Be, and Ti, or alloys of these, metals which have largegas solubility differences between their solid and liq-uid phases readily form bubbles and yield porousproducts. It is also possible to control the orientationin which pores are formed by making a certain part ofthe mold cool, which cools the molten metal in a cer-tain direction after it is put into the mold. Fig. 12schematically illustrates a mold constructed so thatthe bottom is partially cooled, and the product ob-tained with that mold. Making porous products withthis method allows one to freely control pore orienta-tion, pore size, and porosity by controlling a variety ofparameters including melting temperature, coolingrate, pressure of ambient gas while being dissolvedinto metal, mixing volumetric ratio and pressure ofinert gas, and gas pressure when solidifying. [56]
We shall now discuss methods of synthesizing po-rous materials by using in-situ solidification, devel-oped as a gel casting method by Oak Ridge NationalLaboratory in the US. [57, 58] This method entailspreparing a ceramic slurry into which monomers
KONA No.20 (2002) 93
(a) before forming(Particles are dispersed in the surfactant solution with a blowing agent.)
(b) after forming(The blowing agent generates the bubbles in slurry.)
(c) after drying(Bubbles connect and pore is generated.)
Fig. 11 Generation mechanism of pore by using blowing agent (modified from Wada [56]).
heat sink
molten metalwith hydrogen
mould
unidirectional poreinsulation
Fig. 12 Apparatus for solid-gas eutectic solidification and porousmaterial (modified from Nakajima [56]).
have been dissolved, putting the slurry into non-porous molds, and then polymerizing the monomers,resulting in the formation of a polymer network in thedispersed medium, and yielding a molded wet prod-uct. This method offers the following advantages.[59] (1) Because slurry production is basically thesame as casting, the method can be used if a high-concentration slurry is made; (2) molds of complexforms can be used, and near-net shaping is possible;(3) because the f luid and solidification processes canbe kept separate, and because the ceramic particlesare fixed in situ, unevenness and f laws occur inmolded products only with difficulty; and (4) thesmall amount of organic binder in the molded productmakes degreasing easy.
The in situ solidifying method makes it possibleto obtain porous products because its series ofprocesses introduces bubbles into the pre-polymeriza-tion slurry and then begins polymerization. [60] Weexplored the use of this method in creating porousceramic materials which have high porosity andwhose pore structure is controllable, and we suc-ceeded in raising porosity to 80% or more eventhough it was limited to 50% with traditional methods.
We further reported that it is possible to controlporosity, pore size, and other properties by takinginto consideration the type of frother and the poly-merization time. [61] In terms of strength as well, thismethod is superior to low-temperature firing and thereplica method because in low-temperature firing thematrix does not completely assume a minute struc-ture, and because with the replica method smallcracks form in the matrix when the large amount oforganic material decomposes. Innocentini et al. [62]report that porous materials made by gel casting havehigher strength than those made by the replicamethod.
Fig. 13 shows the basic process of a porous mater-ial synthesis method that employs in situ solidifica-tion. First, a slurry of ceramic powder, distilled water,monomers, and other ingredients is prepared. A sur-factant is added as a frother, and foaming is inducedby mechanical stirring. A polymerization initiator anda catalyst are then added to the bubble-impregnatedslurry, after which it is poured into molds. After hard-ening, the molded wet product is demolded, dried,degreased, and fired to yield a sintered porous prod-uct.
94 KONA No.20 (2002)
Forming
Surly
Casting
Gelation
Demoulding
DryingR.H95%~60%
Burning-out700°C 8h
Sintering1550°C 2h
InitiatorCatalystSurfactant
Holding of foam by three-dimensional framework of polymer gel
Introducing foam bymechanical stir and surfactant
2h
Powder DisperserWater Monomer, Crosslinking agent
Fig. 13 Fabrication route of porous solid material by applying in situ solidifying method (modified from Sepulveda [60]).
Fig. 14 shows a porous item made with thismethod. Research and development are underway forapplications of these porous materials as high-temper-ature filters and various ultra-light building materials.It is also thought possible to create processes whichtake into consideration resource-cycling systems thatinclude the productive use of wastes as raw materials,and reduced energy use. We hope that in the nearfuture readers will find in their midst porous materi-als made with this method.
Conclusion
Porous materials can be conceived as compositeswhose first component is their solid portions, andwhose second component is the air phase in theirpores. Hence it is perhaps beneficial to incorporatecomposite characteristics and function expressionmechanisms as guidelines for designing porous mate-rials. While dispersed composites assume variousstructures depending on the properties, state, andform of their materials, two-phase composites areclassified by the structural models in Fig. 15. [63] Asthis shows, the spatial connection state of each com-ponent, which can assume the zero, first, second, orthird dimension, determines the type (m-n) of com-posite by the connection order of each component.Usually m is assigned to the functional componentand n to the inactive component. For example, in a (0-3) type composite the functional component is iso-lated and dispersed, and the matrix component isconnected in three dimensions. In other words, thisporous material can be seen as having closed pores.Here we have shown only the structures, but readerscan see that many other findings on composite mate-rials can be turned to use as shared concepts for thedevelopment and manufacture of porous materials.
The functions of porous materials are affected notonly by pore size, but also by pore structure andother attributes. Incorporating methods of analyzingcomposites’ physical properties should bring aboutprogress in the assessment and analysis of porousmaterials. While our insufficient efforts are partlyto blame for not being able to include these here,another reason is that often a number of factors under-lie the function expression mechanisms of porousmaterials, and they have yet to be sufficiently ana-lyzed. From another perspective this suggests thepossibility of discovering many as yet unknown po-rous material properties.
This has been a review of porous materials thatinterest the authors. We hope this explanation willhelp people who are working on the design of newporous materials.
Acknowledgment
The study of super-light porous construction mate-rials prepared by an in situ solidification formingtechnique was financed under a contract from theMinistry of Economy, Trade and Industry as a partof Industrial Science and Technology Research andDevelopment.
KONA No.20 (2002) 95
Fig. 14 Porous ceramics prepared by in situ solidification form-ing technique.
(0-0) (1-0) (2-0) (3-0)
(1-1) (2-1) (3-1) (2-2)
(3-2) (3-2) (3-3) (3-3)
Fig. 15 Classification of two-phase composite. (From Newnham,Skinner and Cross [63])
200 µm
96 KONA No.20 (2002)
References
1) Shibazaki, Y. Ceramics, 37, 317 (2002).2) Ishida, K. Inorg. Mater., 4, 507 (1997).3) Toray Research Center, Japan. “New Development of
Porous Ceramics,” p. 5 (1998).4) Matsukata, M. Surface, 15, 385 (1996).5) Rice, R. W. Porosity of Ceramics, Dekker, p. 44 (1998).6) Sing, K. S. W., D. H. Everett, R. A. W. Haul, L. Moscou,
and R. A. Pierotti. Pure Appl. Chem., 57, 603 (1985).7) “Colloidal science I,” Chem. Soc. Jpn, Japan, p. 275
(1995).8) Kaneko, K. J. Mem. Sci., 96, 59 (1994).9) McBain, J. W. The Sorption of Gases and Vapors by
Solids, Rutlege, London (1932).10) Sano, T., Y. Kiyozumi, M. Kawamura, F. Mizumaki, H.
Haraya, T. Mouri, W. Inaoka, Y. Toida, M. Watanabe andK. Toyoda. Zeolites, 11, 842 (1991).
11) Sano, T., F. Mizukami, H. Takaya, T. Mouri and M.Watanabe. Bull. Chem. Soc. Jpn., 65, 146 (1992).
12) Kiyozumi, Y., I. Mukoyoshi, Y. Sano, and F. Mizukami.Bull. Chem. Soc. Jpn., 65, 877 (1992).
13) Tsikoyiannis, J. G. and W. O. Haag. Zeolites, 12, 126(1992).
14) Anderson, M. W., K. S. Pachis, J. Shi, and S. W. Carr. J.Mater, Chem., 2, 255 (1992).
15) Kiyozumi, Y., K. Maeda and F. Mizukami. Stud. Surf.Sci. Catal., 98, 278 (1995).
16) Seike, T., M. Matsuda, and M. Miyake. J. Mater. Chem.2, 366 (2002).
17) Kuznichi, C. T., et al. Nature, 412, 720 (2001).18) Norrish, K. Disc. Faraday Soc., 18, 120 (1954).19) Fukushima, Y. Surface, 7, 233 (1994).20) Watanabe, T. and T. Sato. Clay Sci., 7, 129 (1988).21) Fukushima Y. Clays Clay Miner., 32, 320 (1984).22) Viani, B. E., P. F. Low and C. B. Roth. J. Colloid Inter.
Sci., 96, 229 (1983).23) Kijima, T. Inorg. Mater., 3, 147 (1996).24) Segawa, K. and Y. Ban. J. Surf. Sci. Soc. Jpn., 16, 680
(1995).25) Shabtai, J., N. Frydman, and R. Lazar. “Proc. 6th Intern.
Congr. Catal.,” Chem. Soc., London, p. 660 (1976).26) Mortland, M. M. and V. Berkheiser. Clays Clay Miner.,
24, 60 (1976).27) Baes, C. F., Jr. and R. E. Mesmer. The Hydrolysis of
Cations, John Wiley, New York, p. 419 (1976).28) Brindly, G. W. and R. E. Semples. Clay Miner., 12, 229
(1977).29) Lahav, N., U. Shani, and J. Shabtai. Clays Clay Miner.,
26, 107 (1978).30) Yamanaka, S. and G. W. Brindley. Clays Clay Miner., 27,
119 (1979).31) Yamanaka, S. and G. W. Brindley. Clays Clay Miner., 26,
21 (1978).32) Endo, T., M. M. Mortland and T. J. Pinnavaia. Clays Clay
Miner., 29, 153 (1981).33) Yanagisawa, T., et al. Bull. Chem. Soc. Jpn., 63, 988
(1990).34) Inagaki, S., et al. J Chem. Soc., Chem. Commun., 680
(1993).35) Inagaki, S. and Y. Fukushima. J. Soc. Powder Technol.,
Jpn, 33, 868 (1996).36) Kresge, C. T., et al. Nature, 359, 710 (1992).37) Beck, J. S., et al. J. Am. Chem. Soc., 114, 10834 (1992).38) Inagaki, S., et al. Bull. Chem. Soc. Jpn., 69, 1449 (1996).39) Beneke, K., et al. Am. Mineral., 62, 763 (1977).40) Vartuli, J. C., et al. Chem. Mater., 6, 2317 (1994).41) Firouzi, A., et al. Science, 267, 1138 (1995).42) Luzzati, V., et al. Nature, 215, 701 (1967).43) Makishima, A. Surface, 21, 105-104 (1983).44) Nakanishi, K. and N. Soda. J. Am. Ceram. Soc., 74, 2518
(1991).45) Nakanishi, K. Surface, 8, 671 (1992).46) Nakanishi, K. and H. Mizuguchi. Chem. Chem. Ind. 55,
653 (2002).47) Kamigasa, S. “Diatomite and Its Applications in Indus-
try,” J. Soc. Powder Tech., Jpn., 39, 114 (2002).48) Saggio-Woyansky, J., C. E. Scott, and W. P. Minnear.
“Processing of Porous Ceramics,” Am. Ceram. Soc.Bull, 71, 1674 (1992).
49) Holland, B. T., et al. Chem. Mater., 11, 795 (1999).50) Carreon, M. A., et al. Chem. Commun., 2001, 1438.51) Soten, I., et al. Adv. Funct. Mater., 13, 1468 (2002).52) Scott, R. W. J., et al. Adv. Mater., 13, 1468 (2001).53) Soc. Inorg. Mater., Jpn., Hand Book of Cement, Gypsum
and Lime, Gihodo, Japan.54) Wasa, M. Chem. Chem. Ind., 54, 811 (2001).55) Shapovalov, V. I. US Patent 5, 181, 549 (1993).56) Nakajima, H. Ferrum, 6, 33 (2001).57) Omatete, O. O., M. A. Janney, and R. A. Strehlow.
“Gelcasting A New Ceramic Forming Process,”Ceram. Bull, 70, 1641 (1991).
58) Young, A. C., O. O. Omatete, M. A. Janney, and P. A.Menchhofer. “Gelcasting of Alumina,” J. Am. Ceram.Soc., 74, 612 (1991).
59) Jono, K., T. Hotta, H. Abe, M. Naito, and M. Takahashi.Ceramic Processing Science VI, 112, 459 (2001).
60) Sepulveda, P. “Gelcasting Foams of Porous Ceramics,”Am. Ceram. Soc. Bull., 76, 61 (1997).
61) Takahashi, M., M. Mizuno, Y. Shiroki, T. Yokoyama, H.Abe, and M. Naito. Ceramic Processing Science VI, 112,559 (2001).
62) Innocentini, M. D. M., P. Supulveda, V. R. Salvini, V. C.Pandolfulli, and J. R. Coury. “Permeability and Struc-ture of Cellular Ceramics: A Comparison Between TwoPreparation Techniques,” J. Am. Ceram. Soc., 81, 3349(1998).
63) Newnham, R. E., D. P. Skinner and L. E. Cross. Mater.Res. Bull., 13, 525 (1978).
KONA No.20 (2002) 97
Author’s short biography
Minoru Takahashi
Minoru Takahashi is Professor at the Ceramics Research Laboratory, NagoyaInstitute of Technology, Gifu. A graduate of the University of Tokyo, he receivedhis B.S. from the Dept. of Mineral Resources Development in 1973, his M.S. fromthe Faculty of Engineering in 1975, and his D. Eng. from the Faculty of Engineer-ing in 1984. With the Nagoya Institute of Technology since 1975, he has been con-cerned with ceramic processing and powder technology.
Masayoshi Fuji
Masayoshi Fuji is Associate Professor of Ceramics Research Laboratory, NagoyaInstitute of Technology, Gifu. A graduate of Tokyo Metropolitan University, hereceived his B.S. from the Dept. of Industrial Chemistry in 1989, his M.S. from theFaculty of Engineering in 1991, and his D. Eng. from the Faculty of Engineering in1999. He joined the Department of Industrial Chemistry, Tokyo Metropolitan Uni-versity, as a Research Associate in 1991. From 2000 to 2001 he was a VisitingResearcher at the University of Florida Engineering Research Center. He has beenwith the Nagoya Institute of Technology since 2002. His research interests are sur-face chemistry, ceramic processing, and powder technology.
98 KONA No.20 (2002)
Introduction
The development of a number of batch and continu-ous centrifugal separators over the past twenty yearshas resulted in the widespread use of these instru-ments in the gold mining industry [1]. Formerly, theindustry was faced with the problem of removing freegold particles that entered the circuit of a typical goldplant, causing increased gold hold-up, spiking and ageneral drop-off in efficient recovery. There are manyexamples of gold plants that have solved this problemby the introduction of a centrifugal separator in ableed stream of the mill product circuit, effectivelyscalping the free gold particles before they enter theleach train. Base metal plants that use f lotation torecover copper, zinc and lead concentrate tend to losetrace amounts of gold that may enter the circuit if pre-sent in the mine ore body. The heavier gold particlestend to migrate to the tailings of the f lotation cellsand are lost, thus eliminating a potential source of rev-enue for the mining company. There are a number ofexamples where the use of centrifugal technologyeffectively improved gold recovery [2]. In one case,the improvement was so marked that the status of theplant changed from that of a base metal to that of azinc/gold plant [3].
More recent publications have suggested that cen-trifugal technology could also be used in the recoveryof less valuable synthesised minerals [4], i.e. ferro-
chrome from crushed slag dump material. The pro-duction of ferro-chrome by reduction in a smeltertends to generate a mixed stratum of matt and slag atthe interface. The amount of ferro-chrome present inthis stratum is sufficient to warrant processing andrecovery. This challenge is common in the ferro-alloyindustry and is topical at present. As comminution ofthis stratum results in total ferro-chrome particle lib-eration, the removal from the slag particles, whichare approximately half the density, should be achiev-able by gravity/hindered settling techniques. Recentsuccesses in this regard have shown that by gravityseparation, most of the ferro-chrome particles largerthan 200 microns are easily removed [5]. The samecannot be said for the fully liberated, sub-200-micron,ferro-chrome particles, which is where the bulk of thepost-comminution ferro-chrome particles are found.Figure 1 gives the mass percentage per size fractionof ferro-chrome in a typical 750-g grab sample takenfrom the tailings of a Titaco (slag dump material) pro-cessing plant. We observe that some 60% of the ferro-chrome particles are in the sub-200-micron range andhave not been removed by conventional gravity sepa-ration, i.e. jigs. It is also apparent that approximatelytwo percent of the entire sample is ferro-chrome. Atan approximate market value of 1000 USD per tonneof ferro-chrome, this represents a calculable loss tothe plant. It is reported that a similar loss occurs withother ferro-alloy producing plants.
In this paper it is assumed that the hindered set-tling zone found in a centrifugal separator is compara-ble to a f luidised bed approaching steady state. Ourintention is to simulate the behaviour of such a bed
A. B. NesbittCape Technikon*S. Wanliss, and F. W. PetersenMintek**
The Feasibility of Ferro-alloy fines Recovery by using Centrifugal Separator Technology†
Abstract
The effect of an increase in gravitational force on the separation of a binary (dif ferent densities)mixture of particles in a centrifugal separator is investigated. An algorithm calculates the ef fect anincrease in gravity has on improving separation using established particulately f luidised bed models.These results are compared to separation data generated by a continuous centrifugal separator.
* P. O. Box 652, Cape Town 8000, South Africa** Mintek, Private Bag X3015, Randburg, 2125, South Africa† Accepted: June 5, 2002
using typical f luidised bed mathematical models,accommodating the increase in gravity that wouldbe the norm in a centrifugal separator. The densityand general physical properties of chromium oxide(Cr2O3), with an RD of approximately 7.0, wasdeemed to be very similar to that of the majority offerro-alloys and therefore, in the theoretical study andtest work, this material was considered to be the valu-able/recoverable material. Metal/silica oxides withRDs of approximately 3.0 were considered to be thegangue material. An algorithm was employed to simu-late the f luidised mixed bed of these two species thatdemonstrably showed the presence of three zones: anupper zone, where only the lower density species ispresent (metal/silica oxides); a middle zone compris-ing a mixture of both species; and a lower zone con-taining only the higher density species (ferro-alloy).Having established this simulation in the form of asoftware package, the effect of an alteration in gravitycould be observed. These results were then com-pared to those achieved by a centrifugal separator inchromium-oxide recovery duty.
Theory
The failure of gravity equipment to efficientlyrecover the sub-200-micron ferro-chrome particles byhindered settling can be attributed to two phenom-ena. The first is that the system is clearly in Stokes-laminar-settling regime. Calculation of the terminalvelocity Reynolds numbers in water of the sub-200-micron ferro-chrome particles proves this. These canbe estimated using a simple terminal velocity relation-ship proposed by Hartman et al [6], and are all less
than 14 for the sub-200-micron range. Classificationunder normal gravity will therefore be inefficient.The second challenge is the blinding effect of the freesettling ratio of the ferro-chrome to slag particles.The presence of a skew distribution of particlesresults in the probability that the hydrodynamic char-acteristics of the sub-200-micron ferro-chrome parti-cles are likely to be emulated by larger less denseslag particles. Assuming Stokes regime and that theferro-chrome/slag particles are spherical, it may becalculated that a slag particle in the 16 to 320-micronrange will emulate the terminal velocity of a ferro-chrome particle in the 10 to 200-micron range.
Common knowledge holds that by increasing thegravity forces (increasing terminal velocity of the par-ticles) on a hindered settling system, the first chal-lenge, i.e. the presence of Stokes settling regime, canbe overcome. This can be achieved by a centrifugal-gravity separator. The blinding effect, as understoodfrom the perspective of Stokes’ or Newton’s hinderedsettling equations, clearly shows that a sufficientincrease in gravitational force will cause the hydrody-namics of a hindered settling system to change fromthe laminar settling regime to the turbulent, effec-tively altering the blinding ratio. It can be calculatedthat in the case of a switch from Stokes’ to Newton’sregime, the average ferro-chrome particle would nowbe blinded by a larger slag particle than was the casein the Stokes’ regime. The removal of larger slag par-ticles by means of screening after the application ofconventional gravity separation ( jigs) should lead toimproved recoveries by subsequent treatment withhigh-gravity centrifugal separation. Examination of acentrifugal separator would indicate that the hinderedsettling zone is comparable to a f luidised bed ap-proaching steady state, under severe gravity. Figure2 clearly shows how a mixture of particles of different
KONA No.20 (2002) 99
Fig. 1 Mass of Ferro-Chrome in the tailings of a Titaco process-ing plant
0 1 2 3 4 5 6 7 8mass of FC found in sample (g), total mass of sample 750g
53
92-53
106-92
180-106
212-180
250-212
355-250
500-355
850-500
1000-850
1700-1000si
ze fr
actio
n (r
ange
in m
icro
ns)
Fluidisedzone
Fluidising
FeedLight
Heavy
Fig. 2 Typical centrifugal separator mechanism
densities moves through a centrifugal separator, withthe denser particles tending to move closer to therotating wall while the less dense tend to migrate overthe top of these particles under the inf luence of cen-trifugal forces. Fluidising water enters the separatorthrough the rotating wall, effectively causing a f lu-idised bed at higher gravity.
Traditional f luidisation expansion models for partic-ulate f luidisation correlate the voidage (e) of a systemto the superficial f luid velocity (U ) and the GalileoNumber of the particles, which itself is closely relatedto terminal velocity (Ut).
These correlations are summed up in the Richard-son and Zaki equation [7]:
UUten Eq. 1
where n is a function of the Galileo Numbers of theparticles present.
The application of this model has traditionally beenby means of the averaging [8], serial [9], or cellmodel [10] techniques. The model of Nesbitt andPetersen [11] has been shown to effectively predictthe expansion of a f luidised bed of polysized sphericalparticles, and relies entirely on the serial model phi-losophy and an original technique for application.
The model of Nesbitt and Petersen [11]:
Et1 dpl
dps
G(dp) 1d(dp) Eq. 2
where F(dp) is the terminal velocity function forthe particle size range
G(dp) is the function correlating particlesize to bed mass fraction, and
s,l refer to the smallest and largest par-ticle present, respectively (m).
In application, this model validates the assumptionthat a f luidised bed in an expanded state is a serialcombination of the expansion of each particle sizeclass. Each size class contributes to the overall extentof expansion to the same degree as it would demon-strate if isolated, with all other physical aspectsremaining unchanged. The cell model was proposedby Patwardhan and Tien [10], where they show howeach particle demands a certain volume around itselfdepending on its own physical properties and those ofthe f luid. This combination of the mass of particleand required void is said to act as a discrete finite ele-ment with a volume and density. An element locatedat the bottom will have the highest cell density of allelements in the bed. Cell density decreases withincreased height in the bed, and the cell with the low-est density is found at the top. The stratification of
1efws
1[U/F(dp)1/n]
particles on the basis of size for a large particle sizedistribution was observed by Al-Dibouni and Garside[12]. No reference could be found in the literatureeffectively testing traditional f luidisation/bed expan-sion mathematical models in a gravity field other thanthat of g9.81 m.s2. However, for the purposes ofthis study, the simulation of a change in gravity forcewas deemed to be achievable by altering the g term inthe Galileo Number, for the purpose of determiningthe n value in Eq. 1 and the terminal velocity of eachparticle present. Assuming the models of Nesbitt andPetersen [11] and of Patwardhan and Tien [10] to beeffective, it now becomes possible to define the verti-cal position of a discrete cell relative to the totalheight of the bed on the basis of its density. It hasalready been stated that the discrete element densitydecreases with bed height, and assuming perfectstratification, which is reasonable for a large particlesize distribution [12], the density of a discrete ele-ment is a function of particle size distribution and par-ticle density, both of which are well defined.
An algorithm was produced in the form of a com-puter program that simulated the separation of thebinary mixture of particles with each species possess-ing two distinct particle size distributions. A sche-matic diagram of the algorithm is given in Figure 3.To calculate the mass of particles that would be pre-sent in the mixed (central) zone, it is necessary toestablish its vertical boundaries. The steady-stateposition of the largest of the less dense particles(dp1L) would make up the lower boundary, while thesmallest of the more dense particles (dp2S) wouldform the upper boundary of this mixed zone. At agiven f low rate the voidage for the largest particles ofthe less dense species (dp1L) is calculated and conse-quently the bulk density of the associated discretefinite element is attained. The same calculation isachieved for the smallest particle of the denserspecies (dp2S). The density of the discrete finite ele-ment in each case was thus judged to be the bound-ary density for the lower and upper boundaries,respectively. Once these boundaries were set, thebulk density of the discrete finite element associatedwith every particle class of both species present wascalculated. If it fell between the boundary limits, theassociated particle was judged to be part of the mixedzone. The particle size distribution of each specieshad to be defined and this was achieved by examiningtypical raw data. The particle size distributions of thetwo species were considered to be of a continuousnature and hence spline routines were used to repre-sent each. The spline routines developed were impor-
100 KONA No.20 (2002)
tant for determining functions F(dp) and G(dp) foreach species.
The calculation of the bulk density of each discretefinite element was achieved by using Eq. 3. Initiallythe voidage (e) is calculated by applying Eq. 1 dis-cretely to every particle size class.
rc(1e)rserf Eq. 3
where rc is the relative density of the discretefinite element
rs is the intrinsic relative density of thesolid particle
rf is the relative density of the f luid.
Results and discussion
Figure 4a diagrammatically represents particles ofboth species on a mass basis that will migrate to themixed zone area between dotted lines under agravity force of one. The vertical component in thediagram refers to successive cell densities with thehighest density cell being at the bottom and the low-est at the top. The simulation was then repeated athigher gravity forces, primarily to observe the inf lu-ence this had on the mass of particles migrating tothe mixed zone. Figure 4b shows the characteristicreduction in the mass of particles migrating to themixed zone, observed for any increase in gravity. Forall simulated gravity forces in excess of normal grav-
KONA No.20 (2002) 101
Fig. 3 The algorithm used to determine the mass of particles in the mixed (central) zone
G01 m.s1
Calculated Ga, n, Ut, e and rc for dp1L and dp2S
i, MTi0
MTj, j0
Input: PSD of bothspecies and
system variables
PSD of both species splined and particlesize increment (inc) calculated G(dp).
Calculate mass of associated particles G(dp)
ii1MTiMTiMidp2Sidp
Calculated Ga, n, Ut, e and rc for dp
rc(dp)rc(dp1L)
MTMTiMTj
Calculate mass of associated particles G(dp)
jj1MTjMTjMjdp1Ljdp
Calculated Ga, n, Ut, e and rc for dpjj1MTjMTjMj
StopOutput
rc(dp)rc(dp2S)
MT0Yes
Yes
Yes
No
No
GG9.81 m.s1
ity, less mass migrated to the mixed zone. The f luidis-ing medium used in the simulation was given thephysical characteristics of water.
Certain parameters that would be present duringcentrifugal separation could not be brought into thesimulation. An example is the mass pull of densermaterial that is an independent setting likely to havean inf luence on the efficiency of separation. Anincrease in this setting is likely to move the systemaway from steady-state f luidisation. The setting is nor-mally presented as a “time duration” within a fixedtime cycle for which the concentrate valve remainsopen, allowing denser material to leave the centrifugalseparator. This oscillation effectively controls thechanging ratio, at which the two species migratethrough the centrifugal separator, relative to eachother. In addition, the violent nature of the centrifugalphenomenon could well cause a greater degree ofmixing than would be present in a steady-state f lu-idised bed experiencing a mild increase in gravity
force. Figure 5 is a typical result developed by thesimulator. It assumes the mass of particles present inthe mixed zone at a gravity of one to be 100%, andeffectively shows how a mixed f luidised bed experi-encing an increase in gravitational forces results in adecrease in the mass of particles present in the mixedzone. It is notable that perfect separation is achievedrelatively quickly at a gravitational force equivalent toan acceleration of 24.81 m.s2, and is an indication ofthe level of efficiency that could be achieved by a cen-trifugal separator.
From the results of test work carried out on achromium oxide/silica oxide mix passed through acentrifugal separator, an improvement in separationwith increase in gravity was clearly observed.
Table 1 gives the percentage of chromium oxide inthe feed to migrate to the concentrate versus gravity.The gravity acceleration was calculated from the rev-olutions per minute of the centrifugal separator.
Conclusion
The simulation proves that existing f luidisationmodels can be used to show the improvement in sepa-ration under artificially increased gravity. However,the lack of direct experimentation proving the effec-
102 KONA No.20 (2002)
Fig. 4a shows the mixed bed under normal gravity
Mixed particles (M 1)
ρspecies
ρspecies
dp2S
dp1L
Mixed particles (M 2)
ρspecies
ρspecies
dp2S
dp1L
Fig. 5 % Mass of mixed particles
Table 1 Percentage chrome oxide fed to a Knelson concentrator(CVD) reporting to concentrate
0
20
40
60
80
100
9.81 14.81 19.81 24.81 29.81
Acceleration (m.s-2)
% M
ass
of m
ixed
par
ticle
s
Generated increased Total chrome oxide in feed gravity as acceleration reporting to concentrate
(m.s2) %
392.4 50.4
588.6 67.5
882.9 87.6
Acceleration (m.s2)
Fig. 4b is the identical system to 4a, experiencing increased grav-ity.
KONA No.20 (2002) 103
tiveness of f luidisation models under these circum-stances is notable and can form part of a new study.
The test work categorically shows that an increasein gravity ultimately causes an improvement in clas-sification efficiency for the process challenge pre-sented in this paper. A process that consists ofapplying conventional-pulse f luidised bed separators( jigs) followed by a screening-off of the larger parti-cles, almost all of which will be slag particles, andfinally recovery of the sub-200-micron ferro-alloy in acentrifugal separator is suggested. Unlike gold parti-cles, the low returns that are offered by ferro-alloyson the open market will mean that optimisation ofsuch a process would be required. In addition, thetask will be made more complicated by the realitythat the mass pulls of the concentrate are muchhigher than in gold recovery service.
Nomenclature
dp particle diameter (m)dp1L particle diameter of the largest particle
of the less dense species (m)dp2L particle diameter of the largest particle
of the more dense species (m)dp1S particle diameter of the smallest particle
of the less dense species (m)dp2S particle diameter of the smallest particle
of the more dense species (m)e voidageefws free wet-settled voidageEt total bed expansion factorF(dp) is the terminal velocity function for the
particle size rangeg is gravitational constant (9.81 m.s2) G increased particle acceleration due
to centrifugal forces (m.s2)G(dp) is the function correlating particle size
to bed mass fractioni particle size increment of one micron
for the denser species (m)j particle size increment of one micron
for the less dense species (m)l refers to the largest particle present (m)MT is the total mass in the mixed zone for a
particular gravityMTi is the mass fraction of the less dense
species in a mixed zoneMTj is the mass fraction of the more dense
species in a mixed zone n empirical parameter of the Richardson
and Zaki equations refers to the smallest particle present (m)U empty tube linear f luid velocity (e1) (m.s1)Ut is the terminal velocity of the particle
derived from F(dp) (m.s1)rf is the relative density of the discrete f luidrc is the relative density of the discrete finite
elementrs is the relative density of the solid particle
References
1) Knelson B.: The Knelson Concentrator: Metamorphosisfrom crude beginning to sophisticated world wide ac-ceptance Byron Knelson, Minerals Engineering, Van-couver, Canada, 1992
2) Ounpuu M.: Gravity concentration of gold from BaseMetal Flotation mills. 24th Annual Canadian MineralProcessor Conf., Ontario, Canada, 1992
3) Poulter S., Fitzmaurice C., Steward G.: The Knelsonconcentrator: Application and Operation at Rosebery. 5th
Mill Operators Conf., Roxby Downs, Australia, 19944) Bogdanovich A., Baxilevsky A., Yermakov V., Pugachev
V., Samosy A., Moshninov V.: Theroretical aspects ofFine Particle Separation. XXI IMPC, Rome, 2000
5) Vorster H.: Titaco/Mintek in ferro-alloys recovery pro-ject from slag dump material. Mining Mirror February,1999
6) Hartman, M.; Trnka, O.; Svoboda, K.: Free Settling ofNonspherical Particles. Ind. Eng. Chem. Res., 33, 1994,pp. 1979-1983
7) Richardson, J. F.; Zaki W. N.: Sedimentation and f luidis-ation: Vol. 1. Trans. Instn chem. Engrs., 32, 1954, pp. 35-52
8) Wen C. Y., Yu Y. H.: Mechanics of f luidisation. Chem.Eng. Prog. Symp. Ser. Chem, 62, 1966, pp. 100
9) Lewis E. W., Bowerman E. W.: Fluidisation of solid par-ticles in liquids. Chem. Eng Prog., 48, 1952, pp. 603
10) Patwardhan V. S., Chi Tien: Sedimentation and liquidf luidisation of solid particles of different sizes and den-sities. Chem. Eng. Science, 40, 1983, pp. 1051
11) Nesbitt, A. B., Petersen, F. W.: A model for the predic-tion of the expansion of a f luidised bed of poly-sizedresin. Powder Technology, 98, 1998, pp. 258-264
12) Al-Dibouni, M. R., Garside J.: Particle mixing and classi-fication in liquid f luidised beds. Trans IchemE., 1979,57, pp. 94
104 KONA No.20 (2002)
Author’s short biography
Allan Nesbitt
Allan Nesbitt is presently a lecturer at the Cape Technikon. He has formally heldpositions at the University of Stellenbosch, Mintek (South African National Insti-tute of Metallurgy), Caltex South Africa and South African Breweries. He receiveda Masters Degree in Chemical Engineering from the Cape Technikon in 1996.Allan’s research interests lie in the fields of mineral processing, the application ofartificial-intelligence systems and the mathematical modelling of particulate f luidi-sation and ion-exchange systems. The latter has already earned him a SouthAfrican patent. He has published in accredited journals and presented scientificpapers, both internationally and locally. In 2001, he received the Cape Technikonaward for Most Promising Researcher of the Year, and recently started with a pro-ject towards his Doctorate.
Francis Petersen
Francis Petersen is a former head of the Department of Chemical Engineering atthe Cape Technikon from 1998 to 2001. Currently, he is a visting-Professor in theDepartment. He holds a BEng (Chem), MEng (Chem) and a PhD (Eng) from theUniversity of Stellenbosch. He has published widely in accredited journals. Otheracademic achievements include being recipient of the Ernest Oppenheimer Memo-rial Trust Award for research excellence, a study-visit to Singapore on technologytransfer and Researcher of the Year at the Cape Technikon. He serves on the SouthAfrican Government Commission, addressing the problem of toxic waste disposal.Although he presently holds the position of General Manager (Research andDevelopment) at Mintek (South African National Institute of Metallurgy), he is stillactively involved in the Chemical Engineering Department in research relating tohydrometallurgy, biotechnology, water treatment and mathematical modelling.
Stephen Wanliss
Stephen Wanliss is currently completing his Masters Degree in the department ofChemical Engineering at the Cape Technikon. He graduated with a bachelor’sDegree in Chemical Engineering Technology in 1997. His thesis is on the math-ematical modelling of the characteristics of particulately f luidised non-sphericalparticles in a liquid medium.
KONA No.20 (2002) 105
1. Introduction
Interest in granular materials behaviour has stead-ily grown over the last few decades as the impor-tance of powder technology has been increasinglyrealised. The challenges to understanding the under-lying fundamental mechanisms of granular f low areconsiderable. Whether the granular materials havebeen f luidised or are being stored, one finds new phe-nomena that are not observable in the usual states ofmatter. For example, in vibro-f luidised granular beds,one finds that the kinetic theory approach is broadlyapplicable under a range of situations [1], but thatimportant differences arise, principally due to the dis-sipation and friction during particle collisions [2]. Inaddition, it cannot be assumed a priori that a contin-uum approach will be appropriate [3]. Much progresshas been made in predicting granular f low behaviourusing the kinetic theory approach, but until recentlyhowever, there has been little experimental validationof these studies at the single particle level. Neverthe-less, in the past few years significant research hasbeen undertaken to investigate granular dynamics intwo dimensions, and more recently in three dimen-sions.
Much of the progress in understanding granularf lows has been through theoretical and numericalapproaches (e.g. see Ref. [4]). Recently though, anumber of experimental techniques have been devel-oped to investigate two- and three-dimensional vibro-f luidised granular beds. In two dimensions, a series ofexperiments by Warr et al using high-speed digitalphotography, demonstrated that highly vibro-f lu-idised two-dimensional granular beds can operatenear to equilibrium, e.g., the granular velocitiesbroadly follow Maxwell distributions [5, 6], and thelocal structure of the granular bed is similar to thatseen in a thermal f luid [7]. Later, a novel method ofcalculating granular temperature was developed [8]based upon the short-time behaviour of the meansquared displacement, which does not require detec-tion of the collision events. This method was usedto measure granular temperature concurrently withdetermination of the self-diffusion coefficient [1], andsubsequently allowed simple kinetic theory ap-proaches to granular beds to be validated [1].
The visualisation of the internal dynamics of three-dimensional granular f lows is more challenging thanviewing two-dimensional arrays of grains. A numberof techniques have recently been developed to probef lows in three-dimensional geometries, including dif-fusive wave spectroscopy (DWS) [9], magnetic reso-nance imaging (MRI) [10, 11] and positron emissionparticle tracking (PEPT) [12]. The authors haverecently demonstrated the suitability of PEPT for
R. Wildman and J. M. HuntleyWolfson School of Mechanical and Manufacturing EngineeringLoughborough University*
Stochastic Aspects of Granular Flow in Vibrated Beds†
Abstract
A stochastic approach has been taken to examine the f low behaviour of particles in a vibratedgranular bed. The coordinates of a single grain were determined as a function of time using the tech-nique of positron emission particle tracking. Following a particle for extended periods allowed adetailed representation of the displacement probability density to be built up. This showed that, ini-tially, particles dispersed according to a Gaussian law, but that the variation in the solid fraction ofgrains, their granular temperature and the presence of walls meant that significant distortions wereobserved over longer timescales. The determination of the displacement probability density allowedthe spatial distribution of the granular temperature and the dif fusion coefficient to be measured inboth mono- and bi-disperse granular systems.
* Loughborough, Leicestershire LE11 3TU, United KingdomE-mail: [email protected]
† Accepted: June 28, 2002
studies of highly f luidised granular beds [13]. In thatarticle, it was shown that variables such as the meansquared displacement and self-diffusion coefficientcould be measured, and that for very dilute systems(packing fractions 0.05) the granular temperaturecould be measured.
In this paper, we demonstrate that stochasticapproaches developed for near-equilibrium systemsmay be employed to develop an improved understand-ing of granular behaviour. We show that the displace-ment probability density is a useful measurand andleads naturally to the determination of variables suchas packing fraction, granular temperature and the dif-fusion coefficient.
2. Stochastic Motion in Fluids
If we consider a gas of similar particles undergoingrapid motion and successive collisions, and withinthat gas we “tag” a small number of the particles, thenif the concentration of the tagged particles is negligi-ble, the motion of the tagged particles is equivalent tothat of a single particle. In this case, the conditionaldisplacement probability density P(r,t) and the cur-rent j(r,t) satisfy the continuity equation [14]
P•
(r,t)∇ .j(r,t)0 (1)
and the Fickian constitutive relation
j(r,t)D∇ P(r,t) (2)
where r is the position vector of a tagged particle, Dis the self-diffusion coefficient and t is the time. Solu-tion of (1) and (2) in the low frequency limit, i.e. t >>tE, where tE is the mean time between collisions,leads to the result
P(r,t) exp( ). (3)
The mean squared displacement can be calculatedfrom this probability density function in the usual way(see e.g. Ref. [14]) and leads to the well-known Ein-stein relation
Dlimt→ r(t)r(0)2. (4)
However, this analysis is only true for unbounded,homogeneous systems such as an unconstrainedthermal gas or f luid. In a granular system, the pres-ence of gravity, as well as causing accelerationbetween collisions, results in a varying packing frac-tion profile in the vertical (y) direction, and so D isactually a position-dependent quantity. In this situa-
16t
r2
4Dt1
(4pDt)3/2
tion, the constitutive relation (2) is modified to
j(r,t)D(r)∇ P(r,t)u(r)P(r,t) (5)
and the combination of (5) with (1) results in theSmoluchowski equation
P•
(r,t)∇ .D(r)∇ P(r,t)u(r)P(r,t) (6)
where u(r) is the terminal velocity of a particle in aresisting medium, when an external potential field isapplied.
In the case of a vibro-f luidised granular bed, u(r)u( y) only, as gravitational forces act only in the ver-tical direction. Similarly D(r)D( y), since the granu-lar temperature and packing fraction distributions onwhich D depends are only weak functions of x and z[15]. Knowledge of the displacement probability den-sity P(r,t) can lead to determination of D from inverseanalysis of (6), and as we shall see, a measure of thepacking fraction and the granular temperature. A sin-gle particle tracking technique such as positron emis-sion particle tracking is ideal for the determination ofP(r,t), and developments in this area will be dis-cussed in the following section.
3. Experimental Procedure
In this paper we present results using the recentlyupgraded Birmingham PEPT facility. Although PEPTtracks only a single particle, the automated facilityallows experimental data to be logged for a consider-able length of time (up to 6 hours), resulting inpseudo whole-field data for steady state systems. Thetechnique has recently been used to investigate anumber of experimental situations, e.g., rotating beds[12] and paste f low [16], and more recently it hasbeen used to successfully analyse three-dimensionalvibro-f luidised granular beds [17-21]. The techniqueuses a radionuclide that decays by positron emission,and relies on detecting the pairs of back-to-backgamma rays produced when positrons annihilate withelectrons. These gamma rays are very penetratingand an accurate location can be determined fromdetection of a small number of back-to-back pairs.Coincident detection of two gamma rays in a pair ofposition-sensitive detectors defines a line passingclose to the point of emission without the need for col-limation. The University of Birmingham PositronCamera is a Forte dual-headed gamma camera (AdacLaboratories, Ca., USA). Each head contains a singlecrystal of NaI scintillator, 500400 mm2, 16 mmthick, optically coupled to an array of photo-multipliertubes. The current maximum count rate of 4104 s1
106 KONA No.20 (2002)
enables an ideal temporal resolution of 2 ms with aspatial accuracy of 1 mm. In the following experi-ments, a tracer particle was created by irradiating aglass ballotini sphere with a beam of 3He, which leadsto a bead that is physically indistinguishable from theremaining beads within the experimental cell. Thisradiolabelling process converts the available O nucleito a radioisotope of F, which decays resulting in theemission of positrons. In a dense medium such as bal-lotini, a positron quickly annihilates with an electron,producing two back-to-back 511-keV gamma rays.These are detected in the pair of diametrically placedcamera heads (Fig. 1). Through triangulation of suc-cessive location events, the position of the tracer par-ticle can be located in three dimensions.
A three-dimensional granular gas was generatedusing a Ling Dynamic Systems (LDS) vibration sys-tem. A sinusoidal signal was fed through a field powersupply [LDS FPS 1] and power amplifier [LDS PA1000] into a wide frequency band electro-dynamictransducer [LDS V651]. This system has a frequencyrange of 55000 Hz, a maximum acceleration of 100gand maximum amplitude of 12.5 mm. A cell of dimen-sions 145 mm in diameter and 300 mm in height wasplaced on the upper surface of the vibrating piston,itself placed between the photon detectors (Fig. 1).The cell was constructed of polymethyl methacrylate(PMMA) to limit the attenuation of the gamma raysas they travelled through the experimental apparatus,and the walls were coated with conducting coppertape to reduce electrostatic charging of the grains.The cell was vibrated at a frequency of 50 Hz. The
amplitude of vibration A O was 1.74 mm. Initially, glassballotini balls of diameter d5.00.2 mm (with aninter-grain restitution coefficient, ε, measured usinghigh-speed photography, of 0.91 and mass m1.875104 kg) were used as the granular medium(the number of grains, N700), though later 4 mmgrains were also employed (m0.96104 kg) inexperiments on binary mixtures.
At grain speeds of about –c 1 m s1, the PEPT cam-era has an accuracy in the x-y plane of about 1 mm.However, the accuracy in the z direction is substan-tially worse as the grain needs to be located in a direc-tion normal to the faces of the detectors. Whencalculating the granular temperature (Section 6), theaverage behaviour in the z direction was thereforeassumed to be equivalent to that in the x direction,due to cylindrical symmetry. During each experiment,the motion of a grain was followed for about one hour,resulting in up to twenty million location events. Eachlocation event was ascribed a coordinate in space andtime (x,y,z,t).
4. Displacement Probability Density
One expects that granular particles placed into ahighly agitated granular system will act very muchlike a Brownian particle; the buffeting of the grain bythe external particles will result in a random walk,causing diffusion of the displacement probability den-sity according to Eq. (6). The displacement probabil-ity density (DPD) is calculated experimentally byapportioning location events to discrete height inter-vals. The displacements of the grain at times afterthese location events are then binned to create theDPD. One then follows the development of the DPDas a function of time. Figure 2 shows one example ofthe evolution of the density function P(x,t) and P( y,t)over 100 ms at steps of 10 ms, with the grain startingat 22.5 mm above the base. Initially, P is a delta func-tion (not shown), as the particle is considered to havestarted at the same point every time it is located inthat region, but as time progresses, the particles dif-fuse outward from this location. One can see thisbehaviour when examining the function at times t0.At short times, the density function resembles theGaussian function expected from Eq. (3), but in the ydirection, as the particles move throughout the bedthe inf luence of the variations in density and the basebecomes apparent and distortions appear. The finalpositions of particles starting from different altitudesare shown overlaid onto Figure 3. This shows clearlythat the long-time probability density of the grains is
KONA No.20 (2002) 107
Fig. 1 A schematic of the positron emission particle trackingfacility showing the placement of the vibration systembetween the gamma ray detectors.
Position-sensitive g-ray detectors
Tracer particleBack-to-back 511 keV photons from positron-electron annihilation
Electrodynamicshaker system
y x
z
108 KONA No.20 (2002)
Fig. 2 Evolution of the displacement probability density as a function of time for the mono-disperse case, up to 100 ms, (upper figure) in the xdirection and (lower figure) as a function of y.
0
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the same regardless of their initial position, lendingfurther credence to the assumption of ergodiciditypreviously used [13]. Using such an assumption canlead to a more accurate measure of the packing frac-tion, h, and can be obtained by examining the resi-dence time distribution of the grain. The assumedergodicity means that a temporal average is equiva-lent to a spatial average leading to the following ex-
pression:
h (7)
where Vi is the volume of the ith segment and Fi( y)is the fraction of time spent by the particle in thisvolume element. The packing fraction distributiondetermined using this method is overlaid onto oneobtained from the DPD (Fig. 4) because at extremelylong times, the displacement density function is pro-portional to the packing fraction density. It shows theequivalence of the two methods but highlights thegreater accuracy obtained by calculating the packingfraction from the residence time distribution.
5. Mean Squared Displacement
The mean squared displacement of the grains overtime may be expressed as an integral equation interms of P(r,t):
r(t)r(0)2
(r(t)r(0))2P(r,t)dr (8)
or in the discretised form
r(t)r(0) 2∑nr
i=1(ri(t)r(0))2P(ri,t)∆r. (9)
where i is the ith interval of displacement, nr is thenumber of displacement bins and ∆r is the DPD binwidth. A typical result for the mean squared displace-ment is shown in Figure 5. Here we can observe anumber of important features. The evolution of themean squared displacement is clearly partitioned intoa number of regions. At the shortest times (∆t20ms), we can see the quadratic toe characteristic ofballistic motion [1, 8, 20]. At longer times, the systembecomes diffusive and the mean squared displace-ment is linear with time. At the longest times, how-ever, we see that the gradient of the mean squareddisplacement reduces. This is the effect of the cagingof the particles in the cell. The walls confine the parti-cles in the cell limiting the maximum mean squareddisplacement that is possible.
The behaviour of the grain in the x and y directionsis somewhat similar. Nevertheless the density doesnot vary significantly in the radial direction, and theDPD in the x direction remains broadly Gaussian atshort times. As the boundary regions are reached,clipping of the density function occurs, and this isref lected in the reduction of the gradient of the meansquared displacement. In the y direction, the pres-ence of gravity has a profound effect, but nonetheless
NFi( y)pd 3
6Vi
KONA No.20 (2002) 109
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y / mm
Time ResidenceDisplacement PDF
Fig. 3 A comparison of the long-time displacement probabilitycurves for a range of grain start heights (y2.5, 7.5, 12.5,17.5 and 22.5 mm). This indicates that the long-timesteady state behaviour of the system is broadly indepen-dent of the start location and suggests that an assumptionof ergodicity is likely to be appropriate.
Fig. 4 Comparison of the packing fraction profile determinedfrom the displacement probability density (start height22.5 mm) and one produced from the time residence dis-tribution of the particles. The two curves should in princi-ple be equivalent, though the time residence distributiongives a more accurate picture of the solids distribution.
the saturation effect is similar; once the base isreached or the particles reach the apex of their freetrajectories at the top of the cell, the DPD and themean squared displacement are constrained.
6. Granular Temperature
The granular temperature EO, or mean kinetic f luc-tuation energy, is defined in the usual manner,
EO (EXEYEZ) (m—v2
Xm—v2
Ym—v2
Z ) (10)
where m is the mass of the grain and vX, vY and vZ arethe f luctuating particle velocity components aboutthe mean, resolved in the x, y or z directions and EX,EY, and EZ are the granular temperatures for each ofthe respective directions. It is well known that due todissipation, the granular temperature in a vibro-f lu-idised bed is anisotropic [1, 5, 8, 19, 20, 22], and that,unlike the case of elastic spheres, equipartition ofenergy does not hold. In most cases EYEX EZ
[20]. This is an important consideration when prob-ing the spatial development of a system as it causes acorresponding anisotropy in the self-diffusion coeffi-cients [1, 23]. For simplicity, however, we treat D as ascalar throughout this investigation.
We measure the granular temperature by analysingthe short-time behaviour of the mean squared dis-
13
13
placement curves [24]. At times of the order of or lessthan the mean collision time, the random walk behav-iour embodied in Eq. (4) no longer holds, and in thelimit t→0, one can deduce from the equation ofmotion for a free particle that
r(t)r(0) 2c2t 2. (11)
By utilising the short-time mean squared displace-ment one can extract the mean squared speed, andthence the granular temperature. Bulk convectioncurrents in the granular bed are small and areneglected in this procedure [21]. This method can beapplied here for extracting the granular temperaturefrom the particle DPDs. Figure 6 shows an exampleof the granular temperature profile measured in thisway as a function of altitude. This is quite typical;high kinetic energy is apparent at the base of the cellthat is dissipated as grains collide with those posi-tioned above them. Boundary effects are visible closeto the bottom surface as the grain-base collisions leadto deviations from the expected form of the meansquared displacement versus time curve (Eq. (11))[20].
The relationships between D, EO and packing frac-tion h have been investigated in two dimensions [1].The Enskog kinetic theory equation in two dimen-sions was shown to be obeyed to within 10% for pack-ing fractions up to about 0.6 and for the restitution
110 KONA No.20 (2002)
Fig. 5 A typical mean squared displacement plot for grains with astarting location of y22.5 mm. This shows the three mainregimes in which the grain exists: (1) short time, thegrains are in free motion and the mean squared displace-ment is quadratic with time; (2) intermediate times, thegrain undergoes random walk-type behaviour (at whichpoint the grains obey the unbounded diffusion and Smolu-chowski equations); and (3) long times, boundary effectsbecome apparent.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Mea
n Sq
uare
d D
ispl
acem
ent /
m2
103
XY
t / secs
Fig. 6 Granular temperature profile for the system, showing thehigh f luctuation energy near to the base, which is dissi-pated at higher altitudes.
0 10 20 30 40 50 60 70 80 90 100Height / mm
10
9
8
7
6
5
4
3
2
1
Gra
nula
r Te
mpe
ratu
re /
J
105
XY
coefficient ε0.92. In three dimensions, the corre-sponding Enskog relation reads [14]
D ( ) . (12)
where n is the number density and gO(d), the radialdistribution function at contact is given by
gO(d) . (13)
At least two alternative expressions for D have beenderived in which the Enskog theory is modified totake account of inelasticity [23, 25]. However, for thecase of reasonably elastic collisions (ε0.91 in theexperiments described here), both modified expres-sions for D agree with Eq. (12) to within about 10%.The convective term in (6) can also be derived usingkinetic theory and Brownian motion methods [14]:
u( y) ( ) (14)
where g is the acceleration due to gravity.
7. Self-dif fusion
It can be seen from Eq. (6) that the dispersion ofthe grains in the system is effectively controlled bythe diffusion coefficient. Provided with experimentalvalues for the DPDs at given times, there are suffi-cient equations to calculate D as the system is overde-termined. This method will be presented in detailelsewhere, but will be brief ly described here.
Equation (6) can be expanded into a form that is apolynomial in the operator ∂/∂y. The coefficients ofthese terms are functions of D and u, each of whichcan be extracted by taking the experimental data andestimating the 1st and 2nd derivatives of the DPDsusing a finite difference approach. There are as manyDPDs as there are time steps, and as a result the ran-dom errors in using this method are reduced throughthe long timescale over which experiments are per-formed. This results in an overdetermined set ofequations that then allows the coefficients, andthence D, to be extracted using non-linear regressionmethods.
Figure 7 shows the values of the self-diffusioncoefficient extracted in this way. This compares rea-sonably with an estimate of D which can be obtainedfrom the gradient of the mean squared displacementin Figure 5 and predictions of D from Eq. (12), whichsuggests that D 0.0050.01 m2/s. However, thismethod tends to seriously underestimate D at high
12EO( y)
pmgd
16h( y)gO(d)
(2h)2(1h)3
12EO
pm3
8nd 2gO(d)
altitudes and Eq. (12) shows that D is expected toscale as 1/h which it clearly does not. This is mostlikely an artefact of the boundaries of applicability ofthe Smoluchowski equation. In rarefied systems,such as those near or in the Knudsen regime, thegrains tend to move as if in free f light rather than asin a random walk. Therefore, at large heights, onesees a diffusion coefficient broadly independent ofpacking fraction and dominated by wall collisionsrather than by grain-grain interactions.
One can attempt to quantify the conditions neces-sary to be able to extract the self-diffusion coefficientin this way as follows: Supposing that at least threegrain-grain collisions must have occurred in theperiod it takes for a grain to return to its originalheight under the inf luence of gravity (i.e., if less thanthree occur then we assume that the grains are nolonger in the random walk regime), then using simplekinetic theory predictions, one can estimate for amean speed of 0.43 m.s1 and particle diameter of 5mm that a packing fraction of 0.045 must exist forthe extraction of D from Eq. (6) to be successful, indi-cating that the above method is only applicable atheights of less than about 30 mm.
8. Binary systems
In reality, most granular systems do not consist ofmono-sized particles; but rather contain a distributionof particle sizes. Therefore, in order to understandtrue powder f low behaviour, one must go beyondmonodispersity and study systems containing more
KONA No.20 (2002) 111
Fig. 7 Self-diffusion coefficient as a function of altitude, extractedfrom the displacement probability functions using equa-tion (6). Error bars, representing the standard deviation ofthe mean, are shown for a sample of data points.
0 10 20 30 40 50 60 70 80 90 100y / mm
0.015
0.01
0.005
0
D /
m2 .s
1
than one particle size.In the following experiments two grain sizes were
used, 5 mm and 4 mm. The number of 5 mm particlesN1 was 525, and the number of 4 mm particles, N2 was270. The displacement probability density was mea-sured for each phase by first using a 5 mm tracer par-ticle, and then repeating the experiment using a 4 mm tracer. This allowed the particle coordinates foreach phase in the shaker system to be determinedindependently. Subsequently, the methods describedabove for calculation of the granular temperature andthe DPDs (Fig. 8) were used to determine thesefunctions for each size phase. One can see systematicdeviations in the development of the DPDs as thephases move towards their steady state distributions.The packing fraction profiles are shown in Figure 9and highlight the differences in the phase’s steadystate distributions of the two phases.
The granular temperature profiles for each phaseare shown in Figure 10. As previously observed[17], the system does not normally relax towards asingle temperature [26, 27]. The balance betweenenergy introduced into the system by the vibrating
base and that lost during inter-particle collisions andwall-particle collisions determines the granular tem-perature in a vibrated system. Because of differencesin the mass and size of the particles, there are dif-
112 KONA No.20 (2002)
Fig. 8 Evolution of the displacement probability density as a function of time for the bi-disperse case, up to 100 ms, showing the behaviour ofeach phase as a function of y. Solid line is the 4 mm displacement probability density, dashed is that for the 5 mm grains.
0
20
40
60
80
0 50
P /
m
1
10 ms
100 0 50
20 ms
100 0 50
30 ms
100 0 50
40 ms
100 0 50
50 ms
100
0
10
5
15
20
25
30
0 50
P /
m
1
60 ms
100 0 50
70 ms
100 0 50
80 ms
100 0 50
90 ms
100 0 50
100 ms
100y / mm
h
0 50 100 150y (mm)
0.06
0.05
0.04
0.03
0.02
0.01
0
5 mm4 mm
Fig. 9 Packing fraction profiles of the two phases in the binary-size vibrated granular bed.
ferent solids distribution profiles for each phase,resulting in significantly different collision rates anddissipation rates. This has the effect that the particlesrelax towards different granular temperatures, whichare coupled through the inter-phase particle colli-sions. The differences in the granular temperatureand packing fraction propagate in turn due to differ-ences in the diffusion coefficients.
The diffusion coefficients for each phase calculatedby the method described in Section 7 are shown inFigure 11. Though the diffusion coefficient of a par-ticle through particles of a different phase is usuallyreferred to as the mutual diffusion coefficient, in thiscase it is a composite of both the mutual and self-dif-fusion coefficients, since the particle collides withother particles of both phases. The fact that the frac-tion of each phase varies as a function of heightmeans that the relative dominance of the self-diffu-sion and mutual diffusion components also varies. Asexpected, the fact that each phase has its own packingfraction and granular temperature profile results indiffering diffusion coefficients for the two phases.
Knowledge of the granular temperature and thepacking fraction, as well as enabling the determina-tion of the self-diffusion coefficient, is vital for investi-gating granular f low behaviour at the single particlelevel, and provides a powerful route to validatingkinetic theory methods. The measurement of the par-ticle displacement probability density provides both aqualitative insight into the behaviour of grains in thesystem, and a means by which the above variables
may be extracted, providing much required data forthe understanding of granular f low mechanisms.
Conclusions
Particles in a granular gas are often observed to fol-low a random walk path. By investigating the motionof a single tracer particle in a vibrated granular bed, itis possible to estimate the displacement probabilitydensity. This function provides us with information onthe system, both in a dynamic way, with the evolutionof the displacement density, and on the steady statevariables such as granular temperature and packingfraction and on the self-diffusion coefficient when thedensity is sufficiently high for the stochastic ap-proach to be appropriate. Similar investigations onbinary systems were used to quantitatively comparethe diffusion coefficient for particles of differentdiameters.
References
1) Wildman, R.D., Huntley, J.M. and Hansen, J.P.: Phys.Rev. E, 60 7066 (1999)
2) Jaeger, H.M., Nagel, S.R. and Behringer, R.P.: Phys.Today, 49 32 (1996)
3) Kadanoff, L.P.: Rev. Mod. Phys., 71 435 (1999)4) Campbell, C.S.: Annu. Rev. Fluid Mech., 22 57 (1990)5) Warr, S., Huntley, J.M. and Jacques, G.T.H.: Phys. Rev.
E, 52 5583 (1995)6) Warr, S., Jacques, G.T.H. and Huntley, J.M.: Powder
KONA No.20 (2002) 113
Fig. 11 Self-diffusion coefficient as a function of altitude, ex-tracted from the displacement probability functions usingequation (6), for the bi-disperse case. Errors bars areshown representing the standard deviation of the mean.
5 mm4 mm
5 mm4 mm
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Gra
nula
r Te
mpe
ratu
re /
J104
103
y / mm y / mm
D /
m2 .s
1
Fig. 10 Granular temperature profiles of each of the phases inthe binary system.
Technol., 81 41 (1994)7) Warr, S. and Hansen, J.P.: Europhys. Lett., 36 589 (1996)8) Wildman, R.D. and Huntley, J.M.: Powder Technol., 113
14 (2000)9) Menon, N. and Durian, D.J.: Science, 275 1920 (1997)10) Ehrichs, E.E., Jaeger, H.M., Karczmar, G.S., Knight,
J.B., Kuperman, V.Y. and Nagel, S.R.: Science, 267 1632(1995)
11) Knight, J.B., Jaeger, H.M. and Nagel, S.R.: Phys. Rev.Lett., 70 3728 (1993)
12) Parker, D.J., Dijkstra, A.E., Martin, T.W. and Seville,J.P.K.: Chem. Eng. Sci., 52 2011 (1997)
13) Wildman, R.D., Huntley, J.M., Hansen, J.P., Parker, D.J.and Allen, D.A.: Phys. Rev. E, 62 3826 (2000)
14) Hansen, J.-P. and McDonald, I.: “Theory of Simple Liq-uids”, 2nd Edition, Academic Press, London (1986)
15) Campbell, C.S.: J. Fluid Mech., 348 85 (1997)16) Wildman, R.D., Blackburn, S., Benton, D.M., McNeil,
P.A. and Parker, D.J.: Powder Technol., 103 220 (1999)17) Wildman, R.D. and Parker, D.J.: Physical Review Let-
ters, 88 064301 (2002)18) Wildman, R.D., Hansen, J.P. and Parker, D.J.: Physics of
Fluids, 14 232 (2002)19) Wildman, R.D., Huntley, J.M., Hansen, J.P. and Parker,
D.J.: Phys. Rev. E, 64 051304 (2001)20) Wildman, R.D., Huntley, J.M. and Parker, D.J.: Phys.
Rev. E, 63 061311 (2001)21) Wildman, R.D., Huntley, J.M. and Parker, D.J.: Phys.
Rev. Lett., 86 3304 (2001)22) Lan, Y.D. and Rosato, A.D.: Physics of Fluids, 7 1818
(1995)23) Brey, J.J., Ruiz-Montero, M.J., Cubero, D. and Garcia-
Rojo, R.: Phys. Fluids, 12 876 (2000)24) Chandrasekhar, S.: “Noise and Stochastic Processes”,
ed. Wax, N., Dover Publishing, New York (1954)25) Savage, S.B. and Dai, R.: Mech. Mater., 16 225 (1993)26) Jenkins, J.T. and Mancini, F.: Physics of Fluids A-Fluid
Dynamics, 1 2050 (1989)27) Lu, H.L., Liu, W.T., Bie, R.S., Yang, L.D. and Gidaspow,
D.: Physica A, 284 265 (2000)
114 KONA No.20 (2002)
Author’s short biography
R. D. Wildman
Ricky Wildman graduated in Physics from the University of Manchester in 1992subsequently completing a PhD in Chemical Engineering at the University ofBirmingham in 1997. Since this time he has been involved in a range of fundamen-tal studies of granular f lows, with interests in shear f lows, chute f lows, vibratedand f luidised granular beds and stress propagation in granular packs. He has beena lecturer in the School of Mechanical and Manufacturing Engineering sinceAugust 2000, and was awarded an EPSRC Advanced Research Fellowship in 2002.
J. M. Huntley
Jonathan Huntley received his BA and PhD degrees in Physics from the Universityof Cambridge in 1983 and 1987, respectively. He was a research fellow at theCavendish Laboratory, Cambridge, from 1987 until 1994, was appointed to a Read-ership at Loughborough University in 1994, became Professor of Applied Mechan-ics in July 1999 and is currently a Gatsby Fellow. His research interests includedynamic speckle pattern interferometry, shape measurement techniques and gran-ular f low mechanics.
KONA No.20 (2002) 115
INTRODUCTION
In filtration, vibration has been considered to be amethod to increase the rate of filtration. Ronningen-Petter Div.1 introduced vibration as a means to pro-duce slurry agitation to cut premature blinding of thefilter medium, and Russel Finex2 use vibration in theirsieves and filters to prevent blinding of the separatormedium. Sawyer3 suggested the use of vibration tobreak up the cake deposited on the filter medium,and Snowball4 has more recently patented a vibratoryfiltration technique. Notwithstanding these applica-tions, there has been very little published work thatset out to investigate how vibration affects the filtra-tion process. The motion of particles settling towardsa vibrating filter medium has been analysed byWakeman et al 5. It was shown that the vibration of thefilter medium directly affects the motion of the parti-cles in the suspension as they approach the medium,and that critical vibration conditions exist when theparticle makes infrequent contact with the medium,leaving a liquid layer above the medium and hence ahigher liquid f low rate through it.
In order to investigate the effect of vibration on thefiltration velocity, Bakker et al6 studied the inf luenceof vibrations on the resistance of a polystyrene filtercake. They found that vibrations caused an increaseof the cake resistance, which seems contradictory
with the known practical applications in filtration.This suggests that if vibration is not applied properlyit may reduce the filtration rate rather than improveit. Podkovyrin et al7 found that the use of vibration ofthe filter medium improves the filtration rate with anincrease of the vibration amplitude, and Mellowes8
developed a filtration model for candle-type filters.Further work on applications of vibration to separa-tion problems has been reported by Metodiev et al9.
To start to understand the effects of vibration onfiltration rates, vibration filtration and permeationexperiments were carried out under different vibra-tion conditions. The experimental data were pro-cessed and analysed to determine the effects ofvibration on the filtration of coarse particles. Thispaper reports the results from these experiments.
EXPERIMENTAL TECHNIQUES
The apparatus used for the measurements is shownin Figure 1. The suspension to be filtered was pre-pared and stored in vessel A. The suspension waspumped into the filter B. The overf low on filter vesselB ensured that the height of the suspension (andhence also the static pressure) remained constantduring an experiment. The filter consisted of a filtermedium (with an area of 0.002 m2) attached to a rigidsupport. The vibration was applied to the rigid sup-port by a vibration generator (Model V406) driven bya vibration control system (Model DVC 48) and apower amplifier (Model PA500L), all supplied by Ling
R.J. Wakeman and P. WuAdvanced Separation Technologies Group,Department of Chemical Engineering Loughborough University*
Low-Frequency Vibration Effects on Coarse Particle Filtration†
Abstract
Results from an experimental investigation of the development of cake resistance during filtrationassisted by vibration are presented and the vibration conditions that lead to improved filtration ratesare identified. It is shown that vibration is a possible technique to increase the rate of filtration.However, a critical acceleration that is dependent on the vibration frequency and solids mass in thecake must be exceeded for filtration to be enhanced, otherwise the rate of f iltration is slowed.Changes in the visual structure of the “cake” with vibration acceleration are described and related tochanges in the “cake” resistance.
* Loughborough, LE11 3TU, UK.† Accepted: June 13, 2002
Dynamic Systems. The accelerometer (Endevco Mod-el 7201-560) located between the filter medium andthe shaker measured the vibration acceleration of thefilter medium and provided the control signal toensure that the shaker outputted a constant accelera-tion during vibration. The weighing scales and thetimer measured the cumulative mass of filtrate andthe filtration time.
In order to investigate the effect of vibration on fil-tration, three groups of experiments were carried out.The first was to investigate the effect of vibration onthe f low rate of liquid through the filter medium. Thesecond set of experiments investigated the effect ofvibration on the cake formation process and on theresistance of the cake during its development. Thethird set of experiments investigated the effects ofvibration on permeation after a cake had beenformed, to elucidate the relationship between cakeresistance and the dynamic characteristics of the fil-tration system. In each experiment, vibration with afixed frequency and acceleration was exerted on thefilter medium.
A primary purpose of this initial investigation wasto establish that a vibratory force could assist filtra-tion, before further investigations were carried out toestablish the mechanisms and interacting parametersbetween feed properties and operating parameters. Inorder to do this, PVC particles with the same size dis-tribution were used in both filtration and permeationexperiments. The average diameter of the particleswas 126 µm and the size range (measured using aMalvern MasterSizer) was 108 to 153 µm (105 to 125µm by sieving).
EXPERIMENTAL RESULTS
To measure the resistance of the filter medium,clean liquid was pumped into the filter vessel. Afterthe vessel began to overf low, the cumulative mass ofpermeate and the time were measured to give the liq-uid f low rate. This procedure was repeated using dif-ferent vibration characteristics. Some typical resultsare shown in Figure 2. These show the linearitybetween the permeate volume collected and the col-lection time (the offset is a result of some liquid beingin the permeate receiver at the start of the test).Changes in the gradients of the lines through the datapoints are very small, indicating correspondinglysmall variations in the medium resistance at differentvibration frequencies.
In the cake filtration experiments, vibration wasapplied to the filter medium throughout. The PVCsuspension, with a concentration of 6.1 kg m3, wasfed into the filter. When the suspension began to over-f low the filter vessel, the cumulative mass of filtrateand the corresponding filtration time were measured.The experiment was repeated under different condi-tions of vibration frequency and acceleration to give aseries of filtration curves. Figure 3 shows a typicalset of filtration curves measured at different vibrationaccelerations when the vibration frequency was 500Hz. The best achievable filtration rate is given by theline measured when there is no vibration and no parti-cles in the feed, that is, water is permeating throughthe filter medium. Adding particles into the feedreduces the filtration rate, and low accelerationsfurther reduce the filtration rate. Increasing the ac-celeration leads to higher filtration rates, and at anacceleration of 294 m s2, the filtration rate is almost
116 KONA No.20 (2002)
Timer
The
rmom
eter
Weight scale
Charge amplifier
A/D
Signal processing
and analyzer
Signal generator
Power amplifier
Shaker
A
BB
Fig. 1 Vibration filtration experimental system.
Fig. 2 The filtrate volume collected when passing a clean liquidthrough the filter medium.
No vibrationVibration of 200 Hz and 98 m/s2 accelerationVibration of 400 Hz and 98 m/s2 accelerationVibration of 600 Hz and 98 m/s2 acceleration
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
Cum
ulat
ive
filtr
ate
volu
me
(m3 )
0 20 40 60 80 100Time (s)
as great as when only water was permeating throughthe filter medium, which is a substantial increase overthe rate of filtration when no vibration is used.
In the cake permeation experiments, clean liquidwas passed through the filter cake after it hadformed. After the filter vessel started to overf low, thepermeation f low rate was measured. Then vibrationwas applied to the filter medium. After about 30 min-utes vibration, the f low of particles in the filter vesselapproached a quasi-steady state and the permeationf low rate was measured. Figure 4 shows a typicalpermeation f low rate curve under different conditionsof vibration acceleration. From this it is seen thatacceleration had little effect on the permeate f low rateuntil a threshold value was reached, when the f lowrate was increased substantially. There is an accelera-
tion at which a peak f low rate is reached, and beyondthat the f low decreases gradually.
DISCUSSION
A method to analyse the data and enable compar-isons to be drawn is outlined below, based on theform of Darcy’s law that is usually used in filtrationanalysis. Observations made during the experimentsare then described and the data is discussed with ref-erence to these observations and the analysis of thedata.
Vibration filtration theoryIn the analysis of constant pressure cake filtration,
the data is conventionally plotted as t/V versus V andthe straight line relation is used to estimate the av-erage specific resistance of the cake and the medi-um resistance, in which t is the filtration time andV is the cumulative filtrate volume (Wakeman andTarleton10). The filtration experiments using vibrationshow that it is very different from cake filtration. Ata fixed vibration frequency, when the accelerationis below a particular value, the straight line relationbetween t/V and V exists. Otherwise, the relationbreaks down as shown in Figure 5. This means thatthe cake filtration theory cannot be used directly forthe analysis of vibration filtration data.
During the vibration filtration process, the vibrationaffects the movement of particles above the filtermedium and may change the f lowing state of the liq-uid as it passes through the filter medium, when com-pared with filtration without vibration. This suggests
KONA No.20 (2002) 117
Fig. 3 The filtrate volume collected with 500 Hz vibration appliedto the filter medium during cake filtration experiments.
Fig. 4 Filtrate permeation rate under conditions of different vi-bration acceleration during cake filtration experiments.
0 50 100 150 200 250 300
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025
Fig. 5 Filtrate volume collected and the corresponding filtrationcurve obtained during a vibration filtration experiment.
No vibration and no particleNo vibration with particleVibration at 500 Hz 49 m/s2
Vibration at 500 Hz 68.6 m/s2
Vibration at 500 Hz 176.4 m/s2
Vibration at 500 Hz 196 m/s2
Vibration at 500 Hz 294 m/s2
Vibration with 500 Hz frequencyand 196 m/s2 acceleration No vibration
Vibration with 500 Hz frequencyand 196 m/s2 acceleration No vibration
0 100 200 300 400Filtration time (s)
PVC particle105 to 125 micrometer (sieve)31 gram dry cake
0.005
0.004
0.003
0.002
0.001
0.000
Cum
ulat
ive
filtr
ate
volu
me
(m3 )
0 49 98 147 196 245 294 343 392 441 490Vibration acceleration (m/s2)
1.8e5
1.6e5
1.4e5
1.2e5
1.0e5
8.0e6
6.0e6
4.0e6
2.0e6
Filtr
ate
flow
rat
e (m
3 /s)
300 Hz vibrationPVC particle105 to 125 microns (sieve)20 gram dry cake
1.3e51.2e51.1e51.0e59.0e48.0e47.0e46.0e45.0e4
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
Cumulative filtrate volume (m3)
Filtration time (s)
Cum
ulat
ive
filtr
ate
volu
me
(m3 )
Filt
rate
tim
e/C
umul
ativ
efil
trat
e vo
lum
e (s
/m3 )
that there needs to be an additional resistance term inthe conventional filtration equation. As a preliminaryapproach, it is assumed that the resistance can bebroken down into the following terms:
Resistance to liquid f low caused by the medium:Rm (constant)
Resistance to unidirectional liquid f low through thecake: Rc
Resistance to liquid f low arising from vibration of themedium and cake: Rv
According to Darcy’s law, the relation between thefiltrate f low rate Q and the resistances can be writtenas:
Q (1)
where m is the viscosity of the filtrate, A is the area ofthe filter medium, ∆p is the filtration pressure, V isthe cumulative volume of filtrate and t is the filtrationtime.
The resistance Rv can be separated into two parts.One part, Rvf, is caused by the change of the f lowingstate of liquid passing through the filter medium dueto the vibration. The other part, Rvp, is caused by thechange of particle movement in the filter vessel imme-diately above the filter medium, which is defined asthe vibrating particle movement resistance. When noparticles are in the liquid, RvpRc0. Under these cir-cumstances, the resistance RRmRvf is defined asthe vibrating medium resistance. When the vibrationis zero, Rv0, and the equation represents normalcake filtration.
It is difficult to estimate the Rc and Rv individually.Here it is investigated how the vibration affectsRcvRcRv, defined as the combined cake resistance.Rcv can be obtained from equation (1) as:
Rcv Rm( / )Rm (2)
Rm can be estimated from the experimental perme-ation data obtained without vibration and when onlyliquid was being fed to the filter. If the filtrate f lowrate Q at time t is known, the relationship of Rcv withfiltration time t can be obtained if the pressure differ-ence ∆p across the filter is assumed to be constantduring the vibration filtration process.
For the normal cake filtration, the resistance of thecake is directly proportional to the mass of dry solidsdeposited per unit area of filter w, and the proportion-ality constant a is defined as the specific cake resis-
dVdt
A∆pm
A∆pmQ
A∆pm(RmRcRv)
dVdt
tance (Wakeman and Tarleton10). For the vibrationfiltration, like normal cake filtration, the combinedcake resistance is related to the mass of dry solidsdeposited per unit area of filter w. But the ratio be-tween the combined cake resistance and the mass ofdry solids deposited per unit area of filter is not a con-stant during the vibration filtration process, whichchanges with the filtration time. It is defined as thevibrating specific cake resistance av(t). During vibra-tion-assisted filtration, suppose that the concentration,c, of the feed suspension is a constant and ignorethe liquid in the cake. The combined cake resistancehas the relation with the vibrating specific cake resist-ance and the cumulative filtrate as in equation (3)(Wakeman and Tarleton6):
Rcv av(t) (3)
Therefore, the average vibrating specific cake resis-tance, aavv, can be obtained during the filtration timeT as in equation (4):
aavv T
0
dt (4)
where Rcv and V were related to the vibration fre-quency and acceleration and the filtration time.Therefore, aavv is a function of the vibration charac-teristic (intensity) and the filtration time. When novibration is exerted on the filter medium, aavv is equalto the average specific cake resistance in conven-tional cake filtration.
Vibration effects on medium resistanceThe vibrating medium resistance was estimated
using the experimental data obtained from the me-dium resistance measurements, using equation (1).Some results are shown in Figures 6 and 7. Whenno vibration exists, Rvf 0 and the medium resistanceis equal to that found for a normal filtration process.
Figures 6 and 7 show that vibration changes toonly a small extent the f lowing state of liquid passingthrough the filter medium, indicated by the vibratingmedium resistance being different from the mediumresistance (the medium resistance is the value atzero frequency and zero vibration acceleration). Thechange (RRm) is very small compared with Rm. Infurther analyses of the data, Rvf is neglected andconsidered to be zero in vibration filtration.
Vibration effects on cake formation The cake formation process (slurry thickening
above the filter medium is included in this context)
Rcv
VATc
cVA
118 KONA No.20 (2002)
depends on the vibration characteristics. Differentvibration accelerations lead to different cake forma-tion processes. The qualitative state of the cake orsuspension in the filter chamber was observed visu-ally through the perspex walls of the filter. When thevibration acceleration was low at a particular fre-quency, for example 49 m s2 at 200 Hz, the cake for-mation process was similar to that without vibration;the particles progressed in a uniform directionthrough the filter vessel in an orderly manner to formthe cake, as shown in Figure 8(b). The cake forma-tion process changed with an increase of the vibrationacceleration. At the beginning of filtration, the state ofthe particles was as shown in Figure 8(a), that is, theparticles were uniformly distributed above the filtermedium. Once the filtration had started, cake formedon the filter medium but the morphology of the cakewas dependent on the vibration acceleration. For
lower vibration accelerations, the shape of cake wasas shown in Figure 8(b), whilst at higher vibrationaccelerations, the form of the cake was as shown inFigure 8(c). The “cake” in Figure 8(c) does notcover the filter medium, but exists as a dense “cloud”of particles lying just above the medium. There arezones around the “cloud” through which liquid is ableto f low freely and which appear to have particle con-centrations similar to the feed suspension. At 500 Hz,for example, the formation characteristics of the cakechanged from that depicted in Figure 8(b) at 196 ms2 to that shown in Figure 8(c) at 294 m s2.
Combined cake resistance (Rcv) during filtrationAfter filtration a typical thickness of cake was 27
mm. The pressure exerted on the cake was about1638 Pa for a suspension with a depth of 196 mm inthe filter vessel, and the pressure change on the cakefrom the beginning to the end of the filtration wasabout 262 Pa. Therefore, the pressure difference ex-erted on the cake was assumed to be constant in thefollowing analysis, and a value of 1800 Pa was used.
The combined cake resistance was estimated usingthe data obtained in the filtration experiments, and isshown in Figures 9, 10 and 11. These figures showthat the vibration characteristics strongly affect thefiltration velocity because the combined cake resis-tance approaches zero when the vibration accelera-tion exceeds a particular value, which we define asthe critical vibration acceleration (CVA). The CVAdepends on the vibration frequency. For example, at200 Hz, an acceleration greater than 98 m s2 causedthe combined cake resistance to reduce to zero (Fig-ure 9), whereas an acceleration of 294 m s2 at 300and 500 Hz was required to produce a similar effect(Figures 10 and 11, respectively).
The rate of increase of the combined cake resis-tance depends on the vibration acceleration exertedon the filter medium during the filtration process.
KONA No.20 (2002) 119
0 200 400 600 800 1000 1200 1400 1600
Fig. 6 The variation of the medium resistance with vibration fre-quency with clean liquid f lowing through the medium (nofiltration).
Filtrate
Feed
(b) Filtrate
Feed
(c)Filtrate
Feed
(a)
Fig. 8 State of the cake and particles during vibration-assisted fil-tration: the effect of increasing acceleration.
0 49 98 147 196 245 294
Fig. 7 The variation of the medium resistance with vibrationacceleration with clean liquid flowing through the medium(no filtration).
98 m/s2 vibration acceleration
400 Hz vibration frequency
Vibration frequency (Hz)
Vibration acceleration (m/s2)
1.78e8
1.76e8
1.74e8
1.72e8
1.70e8
1.68e8
1.76e8
1.75e8
1.74e8
1.73e8
1.72e8
1.71e8
1.70e8
Vib
ratin
g m
ediu
m r
esis
tanc
e (m
1 )
Vib
ratin
g m
ediu
m r
esis
tanc
e (m
1 )
Figures 9, 10, and 11 show that from the start of thefiltration a weak vibration acceleration, for example,49 m s2 at 200 Hz and 98 m s2 at 300 Hz, increasesthe combined cake resistance as compared with filtra-tion without vibration. A stronger vibration accelera-tion decreases the resistance at the beginning offiltration, but as the filtration proceeds, all vibrationsbelow the CVA allow the combined cake resistance toincrease quickly compared with the filtration withoutvibration. For example, use of 88.2 m s2 at 200 Hz or196 m s2 at 500 Hz leads to a resistance during theearlier stages of filtration that is lower than is the casewithout vibration, but the resistance later increasessharply to become greater. Higher accelerations de-lay the time before the resistance starts to increasequickly, as is shown in Figure 11 by comparison ofthe curves for accelerations of 176.4 and 196 m s2 at500 Hz. When the vibration acceleration is greaterthan the CVA, the resistance remains lower than isthe case in a normal filtration. There is some evi-dence that the CVA may depend on the weight of cakedeposited on the filter medium; for example, the 196m s2 at 300 Hz curve lies below that measured for anormal filtration but after some time starts to risetowards it.
Average vibration specific cake resistance (aaavv)during filtration
The average vibrating specific cake resistancechanges with the vibration characteristic. The aver-age vibrating specific cake resistance was estimatedfor vibration-assisted filtration at a filtration time of150 seconds, using the experimental data and equa-tion (4). The results are shown in Figure 12. Theresistance increases at low vibration accelerations andreaches a peak value at a specific vibration accelera-tion dependent on the vibration frequency. The peakvalues are reached at 49, 98 and 68.6 m s2 at 200, 300and 500 Hz respectively. After the peak, the averagevibrating specific cake resistance reduces with theincrease of the vibration acceleration. The magnitudeof these peak values are expected to depend on thesize and density of the particles, a factor that will beinvestigated in later experiments.
Beyond the acceleration corresponding to the peakresistance values, the cake resistance falls sharply at200 Hz and slowly at 500 Hz compared with that at300 Hz. When the vibration acceleration at differentvibration frequency exceeds a certain value, the aver-age vibrating specific cake resistance approacheszero and remains fairly constant. In this region, thevibration-assisted filtration behaves similarly to the
120 KONA No.20 (2002)
200 Hz vibration frequency
Fig. 9 Variation of the combined cake resistance with time dur-ing the vibration-assisted filtration process with the medi-um vibrating at 200 Hz.
300 Hz vibration frequency
Fig. 10 Variation of the combined cake resistance with time dur-ing the vibration-assisted filtration process with the medi-um vibrating at 300 Hz.
500 Hz vibration frequency
Fig. 11 Variation of the combined cake resistance with time dur-ing the vibration-assisted filtration process with the medi-um vibrating at 500 Hz.
0 100 200 300 400
0 100 200 300 400
0 100 200 300 400
9e11
8e11
7e11
6e11
5e11
4e11
3e11
2e11
1e11
0
8e11
7e11
6e11
5e11
4e11
3e11
2e11
1e11
0
8e11
6e11
4e11
2e11
0
Filtration time (s)
Filtration time (s)
Filtration time (s)
No vibration49 m/s2 vibration acceleration68.6 m/s2 vibration acceleration78.4 m/s2 vibration acceleration88.2 m/s2 vibration acceleration98 m/s2 vibration acceleration196 m/s2 vibration acceleration294 m/s2 vibration acceleration
No vibration49 m/s2 vibration acceleration98 m/s2 vibration acceleration147 m/s2 vibration acceleration176.4 m/s2 vibration acceleration196 m/s2 vibration acceleration294 m/s2 vibration acceleration
Com
bine
d ca
ke r
esis
tanc
e (m
1 /
m2 )
Com
bine
d ca
ke r
esis
tanc
e (m
1 /
m2 )
Com
bine
d ca
ke r
esis
tanc
e (m
1 /
m2 )
No vibration49 m/s2 vibration acceleration68.6 m/s2 vibration acceleration98 m/s2 vibration acceleration176.4 m/s2 vibration acceleration196 m/s2 vibration acceleration294 m/s2 vibration acceleration
permeation of a clean liquid (that is, filtration ratesare similar to permeation rates through the filtermedium). The filtration efficiency is then at a maxi-mum, in the sense that a maximum filtrate f low rate isbeing reached even though filtration is still beingachieved. The value of this vibration accelerationcorresponds with the CVA.
Vibration effects on permeationAfter a cake has formed, the vibration characteris-
tics strongly affect the state of the cake. Whereasweak vibration compacted the cake, intense vibrationloosened or broke up the cake and dispersed the par-
ticles in the liquid. When the vibration accelerationwas low at a particular frequency, for example 98 ms2 at 600 Hz, the cake compacted as shown in Fig-ure 13(b) compared with filtration without vibrationshown in Figure 13(a). There was a tendency, also,for more intense vibration to densify the cake to agreater extent. For example, the thickness of the cakeafter vibration at 98 m s2 and 300 Hz was 15 mm,while at 49 m s2 and 300 Hz it was 16.5 mm.
With a small increase in acceleration, the thicknessof “cake” in the centre zone of the filter just abovethe medium increased and the thickness around theboundaries of the cake reduced, as shown in Fig-ure 13(c) (such a result was obtained at, for ex-ample, 147 m s2 at 300 Hz). When the vibrationacceleration was further increased, for example tobetween 196 and 274 m s2 at 300 Hz, a channellingphenomenon occurred and some particles in the“cake” started to f low as shown in Figure 13(d). Thechange from the compaction to the channellingphenomena was gradual, caused by the increasingvibration acceleration. Increasing the vibration accel-eration still further caused the particles to dispersefurther into the liquid just above the filter medium, asshown in Figure 13(e). At higher accelerations, forexample using 490 m s2 at 300 Hz, the “cake” brokeup completely and the particles dispersed into theliquid as shown in Figure 13(f ). The acceleration atwhich each of the phenomena was prevalent dependedon the mass of solids in the cake (in the above, the
KONA No.20 (2002) 121
200 Hz300 Hz500 Hz
2.0e9
1.8e9
1.6e9
1.4e9
1.2e9
1.0e9
8.0e8
6.0e8
4.0e8
2.0e8
0.00 49 98 147 196 245 294
Fig. 12 Average vibrating specific cake resistance under differentvibration characteristics.
(c)
Permeateflow
Feed clean liquid
(b)
Feed clean liquid
Permeateflow
(a)
Feed clean liquid
Permeateflow
(e)
Feed clean liquid
Permeateflow
Permeateflow
(d)
Feed clean liquid
(f)
Permeateflow
Feed clean liquid
Fig. 13 State of the cake and particles during vibration permeation through a formed cake: the effect of increasing acceleration.
Vibration acceleration amplitude (m/s2)
Ave
rage
vib
rati
ng s
peci
fic c
ake
resi
stan
ce(m
/kg.
m2 )
mass of dry solids in the cake was 20 grams).
Combined cake resistance during permeation The critical vibration acceleration during perme-
ation (CVAP) depended not only on the vibration fre-quency but also on the mass of cake, as shown inFigure 14 obtained from the permeation experimen-tal data. When the vibration frequency was 600 Hz,the combined cake resistance increased with thevibration acceleration applied to a 56.77-gram drycake. In comparison, a frequency of 200 Hz causedthe resistance to increase with acceleration until 98 ms2 was reached, beyond which the cake resistancefell to almost zero at 196 m s2.
When the cake contained 20 grams of dry solids,vibration with 200 Hz and 147 m s2 showed a similareffect (that is, the combined cake resistance ap-proached zero). Compared with the result for thecake of 20 grams, resistances of cakes with masses of30.06 and 56.77 grams increased to greater extents.Beyond the CVAP, the cake resistance rose again withthe vibration acceleration for the 30.06- and 56.77-gram cakes. The greater the mass of the cake, thebigger the increase of resistance caused by the vibra-tion.
The combined cake resistance was related to thedynamic characteristics of the filtration system, asshown in Figure 15 from the permeation experimen-tal data. For a vibration with a fixed acceleration, ahigher frequency was associated with a lower vibra-tion energy. Therefore, if the vibration accelerationwas unable to break up the cake, the resistanceshould reduce with the increase of the vibration fre-quency. Figure 15 further shows that the resistance
increases with an increase of the vibration frequencyat frequencies above 1600 Hz.
Comparing the filtration and permeation experi-mental results, the conclusion can be obtained thatcritical vibration accelerations for filtration and per-meation are different. The critical vibration accelera-tion during permeation is larger than that duringfiltration (CVACVAP). For example, when a 200-Hzvibration was applied, CVAP for a 20-gram cake was147 m s2 as shown in Figure 14, while CVA for a 31-gram cake was 98 m s2 as shown in Figure 9.
CONCLUSIONS
Vibration of the filter medium caused only a smallchange to the resistance experienced by filtrate pass-ing through it, which itself was small compared withthe resistances of the cakes formed. However, theresistance of the cake could be reduced substantiallyunder the correct conditions of vibration.
Vibration can increase the rate of filtration, but itsintensity has to be greater than the critical vibrationacceleration. In turn, the critical vibration accelerationis related to the vibration frequency, the weight of drysolids in the cake and the dynamic characteristics ofthe filtration system. Also, the critical vibration accel-eration obtained during filtration is different from thatobtained during f luid permeation through an alreadyformed cake. If the vibration acceleration is smallerthan the critical vibration acceleration, the vibrationcannot improve the rate of filtration but will in factslow it.
122 KONA No.20 (2002)
Fig. 14 Combined cake resistance for various masses of cakesunder different vibration acceleration and frequency con-ditions during permeation experiments.
Fig. 15 Combined cake resistance under different vibration fre-quency and acceleration conditions during permeationexperiments.
0 49 98 147 196 245 294 343 392 441 490
0 500 1000 1500 2000
Vibration acceleration (m/s2)
Vibration frequency (Hz)
600 Hz vibration frequency 56.77 gram dry cake200 Hz vibration frequency 56.77 gram dry cake200 Hz vibration frequency 30.06 gram dry cake200 Hz vibration frequency 20 gram dry cake300 Hz vibration frequency 20 gram dry cake
49 m/s2 vibration acceleration98 m/s2 vibration acceleration
56.77 gram dry cake
2.5e11
2.0e11
1.5e11
1.0e11
5.0e10
0.0
1.4e11
1.3e11
1.2e11
1.1e11
1.0e11
9.0e10
8.0e10
7.0e10
6.0e10
Com
bine
d ca
ke r
esis
tanc
e (m
1 /
m2 )
Com
bine
d ca
ke r
esis
tanc
e (m
1 /
m2 )
NOMENCLATURE
A Filter area (m2)p Pressure (Pa)Q Filtrate f low rate (m3 s1)Rc Resistance of the filter cake (m1)Rm Resistance of the filter medium (m1)Rv Resistance arising from the applied vibrations
(m1)Rvf Resistance of the vibrating filter medium (m1)Rvp Vibration particle movement resistance (m1)T Total filtration time (s)V Filtrate volume (m3)c Concentration of suspension (kg m3)t Time (s)w Mass of dry solid unit area deposited
on the filter (kg m2)av(t) Vibration specific cake resistance (m kg1)aavv Average vibration specific cake resistance
(m kg1)m Filtrate viscosity (Pa s)
ACKNOWLEDGEMENT
The authors wish to record their gratitude forreceipt of an Engineering and Physical SciencesResearch Council grant in support of this work.
REFERENCES
1) Ronning-Petter Div., Dover Corp.: Chemical Engineer-ing, 80(6), March 19, 1973.
2) Russell Finex, Company Brochures.3) Sawyer, J.: Dynamic self-cleaning filter for liquids, US
patent No. 4158629, June 19, 1979.4) Snowball, M.R.: Fluid treatment by filtration and vibra-
tion, European patent No. EP1094036, April, 2001.5) Wakeman R.J., Wu P. and Koenders M.A.K.: Simulation
of the motion of particles settling towards a vibrating fil-ter medium, Transactions of The Filtration Society, 2(1),2001, 13-19.
6) Bakker P.J., Heertjes, P.M. and Hibou, J.L.: The inf lu-ence of the initial filtration velocity and of vibrations onthe resistance of a polystyrene filter cake, ChemicalEngineering Science, 10, 1950, 130-140.
7) Podkovyrin A.I., Korol’kov V.V. and Isakov A.P.: Filter-ing a fibrous suspension through a vibrating grid,Khimicheskoe I Neftyanoe Mashinostroenie, 1, 1973, 13-14.
8) Mellowes, W.A.: A vibratory filtration model for candle-type filters, Powder Technology, 43, 1985, 203-212.
9) Metodiev M., Stoev S. and Hall S.T.: Vibration spiral fil-tration, Mining and Geology, Sofia, Bulgaria, No. 5,1996, 28-31 (in Bulragian).
10) Wakeman R.J. and Tarleton E.S.: Filtration: Equipmentselection modelling and process simulation, Elsevier,1999.
KONA No.20 (2002) 123
124 KONA No.20 (2002)
Author’s short biography
Richard J. Wakeman
Richard Wakeman is Professor and Head of the Department of Chemical Engineer-ing at Loughborough University. He has worked extensively on most aspects ofsolid/liquid separation, including pre- and post-treatment processes, membrane fil-tration and the development of filter media. These works now also include fieldassisted separation techniques the concentration and filtration of particulatesusing electrical, ultrasonic or vibrating force fields. He has been the recipient ofMoulton Medals from the Institution of Chemical Engineers in 1978, 1991 and 1995and the Gold Medal of The Filtration Society in 1993. He was elected a Fellow ofThe Royal Academy of Engineering in 1996.
Pihong Wu
Pihong Wu was born in China in 1964. He received his Bachelor degree in TaiyuanHeavy Machine Institute in 1984, Master degree in Shanxi Mining Institute in 1987,and PhD in Southampton Institute in 2001.He worked as a Scientist in Mining Science and Technology Research Instituteduring 1987 to 1997. Currently he is a postdoctoral research associate at Lough-borough University. His research interests include multivariate data analysis,neural networks, fuzzy logic, digital signal processing, system modelling and simu-lation, and vibration analysis and control.
KONA No.20 (2002) 125
1. Introduction
Experiments with bulk solids during silo f low showa large effect of the wall inclination and wall imperfec-tions on wall stresses [1]-[7]. In general, wall stressesincrease when silo walls become convergent, andthey decrease when silo walls are divergent. A signifi-cant growth of wall stresses is usually observed atthe transition between bin and hopper (the so-called“switch”). A wall imperfection directed to the inside ofthe bulk solid causes an increase of wall stresses. Inturn, a wall imperfection directed to the outside of thebulk solid diminishes wall stresses.
The wall inclinations and wall imperfections inf lu-ence wall stresses due to the fact that bulk solids arevery sensitive to every change in the direction ofshear deformation [8]-[11]. Thus, a realistic calcula-tion of wall pressures due to the change of the wallinclination and the occurrence of imperfections in asilo is possible using a constitutive law taking intoaccount this important granular property.
The intention of the paper is to analyse numericallythe effect of the wall inclination and wall imperfec-tions on the evolution of wall stresses in granularmaterials at the beginning of confined granular f lowin a plane strain model silo with very rough walls.The calculations were carried out for quasi-static
mass f low in a silo with a constant outlet velocityalong the entire bottom (inertial forces were neg-lected). In a theoretical study, a finite element methodon the basis of a polar hypoplastic constitutive lawwas used. The constitutive law can describe thesalient properties of granular bodies during deforma-tion with allowances made for shear localisation [12]-[15]. The effect of density, pressure, deformationdirection, mean particle diameter and particle rough-ness is also captured. The FE calculations were carriedout within a silo research study aimed at determin-ing an optimal shape and roughness of silo walls toreduce an increase of wall stresses after outlet open-ing. In the paper, compressive stresses were consid-ered negative (as in soil mechanics).
2. Constitutive law for granular bodies
A polar hypoplastic law [12]-[15] is an alternative toa polar elasto-plastic formulation [16]-[17] for contin-uum modelling of granular materials. It was formu-lated within a polar (Cosserat) continuum [18]. Apolar (Cosserat) continuum differs from a non-polarone by additional rotations. For plane strain or axialsymmetry, each material point has three degrees offreedom: two translations u1 and u2, and one rotationωc. The polar rotation ωc is related with the micro-rotation and is not determined by displacements as ina non-polar continuum
wij0.5(ui, juj, i). (1)
J. TejchmanCivil Engineering Department, Gdansk University of Technology*
Effects of Wall Inclinations and Wall Imperfections on Pressures during Granular Flow in Silos†
Abstract
The effects of wall inclinations and wall imperfections at the onset of granular f low in a silo arenumerically studied. The calculations were carried out for the onset of quasi-static mass f low in asilo with a controlled outlet velocity along the entire bottom. In the analysis, a finite element methodand a polar hypoplastic constitutive law were used. A polar hypoplastic law describes the salientproperties of granular bodies. FE calculations were performed with a plane strain silo with parallelwalls, slightly convergent walls, slightly divergent walls, and parallel and convergent walls. Theinf luence of a wall imperfection directed inwards and a wall imperfection directed outwards in asilo with parallel walls was also analysed. The FE results showed a large sensitivity of stresses inbulk solids due to the change of the direction of shear deformation along the silo wall.
* 80-952 Gdansk-Wrzeszcz, Narutowicza 11/12, Poland† Accepted: June 17, 2002
The gradients of the polar rotation are connectedwith curvatures which are associated with couplestresses. The deformation and stress tensor becomenon-symmetric. As a consequence of the presenceof rotations and couple stresses, the constitutiveequation is endowed with a characteristic lengthcorresponding to the mean particle diameter. Thus,numerical results are independent of the spatial dis-cretisation, and boundary value problems remainmathematically well posed. Due to the presence of acharacteristic length, a polar approach can model thethickness of shear zones (which are inherent charac-teristics of granular f low in silos) and related particlesize effects. The polar hypoplastic law can reproduceessential features of granular bodies. It takes intoaccount such important properties as: dependence onpressure level, on density, and on the direction ofdeformation rate, dilatancy and contractancy duringshearing with constant pressure, and increase andrelease of pressure during shearing with constant vol-ume. The constitutive law is characterised by simplic-ity and a wide range of applications. The materialconstants can be found by means of standard elementtests and simple index tests. They are simply corre-lated with particle properties. Thus, they can be esti-mated from granulometric properties (encompassingparticle size distribution curve, shape, angularity andhardness of particles) [11], [19]-[21]. The capabilityof this law has been already demonstrated in solvingboundary value problems involving localisation suchas biaxial tests, monotonous and cyclic shearing of anarrow granular layer, trap door, silo filling, silo f low,furnace f low, footings, retaining walls and sandanchors. A close agreement between calculations andexperiments was achieved. The FE calculationsshowed also that the thickness of shear zones did notdepend upon the mesh discretisation if the size offinite elements in the shear zone was not more thanfive times the mean particle diameter when using tri-angular finite elements with linear shape functions fordisplacements and a Cosserat rotation [22].
Stress changes and couple stress changes duringthe plane strain deformation of granular bodies areexpressed by
soijF(e, d50, skl, mk, dc
kl, kk), (2)
mo
if(e, d50, skl, mk, dckl, kk), (3)
wherein σij and mi are the Cauchy stress tensor andthe Cauchy couple stress vector, respectively, edenotes the void ratio, the Jaumann stress rate tensor,and the Jaumann couple stress rate vector, dkl
c the
polar rate of deformation, kk the rate-of-curvaturesvector and d50 the mean particle diameter. The follow-ing representations of the general constitutive equa-tions (Eqs. 2 and 3) are used:
so
ijf s[Lij(skl,mk,dckl,kkd50)fdNij(sij)BNdc
kldNcklkNkkkdN250],(4)
mo
i/d50f s[Lci(skl,mk,dc
kl,kkd50)fdNci(mi)BNdc
kldNcklkNkkkdN250],(5)
wherein the normalised stress tensor sij and the nor-malised couple stress vector mi are defined by
sij , mi . (6)
The scalar factors fsfs(e, σkk) and fdfd(e, σkk) takeinto account the inf luence of the density and pressurelevel on the stress and the couple stress rates. Thestiffness factor fs is proportional to the granulatehardness hs and depends on the mean stress and voidratio:
fs ( )( )1n, (7)
with
hi ( )a . (8)
The constant c1 is defined by Eq. 16. The granulatehardness hs represents a density-independent refer-ence pressure and is related to the entire skeleton. Itshould not be confused with the particle hardnesswhich refers to single particles. The density factor fd,a kind of a pressure-dependent relative density index,is represented by
fd( )a. (9)
Here e is the current void ratio, ec is the criticalvoid ratio, ed denotes the void ratio at maximum den-sification due to cyclic shearing, ei is the maximumvoid ratio, and α and n are constants. The void ratio eis thus bounded by ei and ed. The values of ei, ed andec are assumed to decrease with pressure σkk
according to the equations [21]:
eiei0exp[(skk/hs)n], (10)
eded0exp[(skk/hs)n], (11)
ecec0exp[(skk/hs)n], (12)
wherein ei0, ed0 and ec0 are the values of ei, ed and ec
for σkk0, respectively. For the tensor and vector
eed
eced
1c1M3
ei0ed0
ec0ed0
13
1c1
2
skk
hs
1ei
ehs
nhi
mi
skkd50
sij
skk
126 KONA No.20 (2002)
functions L ij, L ic, Nij and Ni
c, the following representa-tions are used
Lija12d c
ijsij(skldcklmikkd50),
Lcia1
2kid50a12mi(skldc
klmikkd50), (13)
Nija1(sijs*ij), Ncia1
2acmi, (14)
where
a11c1c2
d's*kls*lk[1cos(3q)],
cos(3q) (s*kls*lms*mk), (15)
c1 , c2 . (16)
φc is the critical (residual) angle of internal friction, θdenotes the Lode angle, i.e. the angle on the devia-toric plane σ1σ2σ30 between the stress vectorand the axis σ3 (σi is a principal stress component).The coefficient a1
1 determining the shape of the sta-tionary stress surface lies empirically in the range 3to 4.5. The dimensionless polar constant ac controlsthe inf luence of the Cosserat quantities on the mater-ial behaviour. It lies in the range of 1.0-5.0 and is cor-related with the particle roughness; the higher theconstant ac, the smaller are the polar effects. σij
*
denotes the deviatoric part of σij. For an isotropicstress state with σij
*0, the expressions in Eq. 15become cos(3θ)0 and a1
1c1. The first terms arelinear and the second terms in Eqs. 4 and 5 are non-linear in dkl
c and kd50, respectively. The second termsin Eqs. 4 and 5 describe the modulus of the deforma-tion. Thus, a polar hypoplastic law depends on thedirection of deformation.
The FE analyses of silo f low for the case of planestrain were carried out with the following nine mater-ial constants (for so-called cohesionless Karlsruhesand [21]): ei01.3, ed00.51, ec00.82, φc30°,hs190 MPa, α0.3, n0.5, d500.5 mm and aca1
1.The parameters hs and n are determined from a sin-gle oedometric compression test with an initiallyloose specimen, hs ref lects the slope of the curve in asemi-logarithmic representation, and n its curvature.The constant α is found from a triaxial test with adense specimen. It ref lects the height and position ofthe peak value of the stress-strain curve. The angle φc
is estimated from the angle of repose or measured ina triaxial test with a loose specimen. The values of ei0,ed0, ec0 and d50 can be obtained with index tests(ec0emax, ed0emin, ei0(1.1-1.5)emax).
(3sinfc)sinfc
38
(3sinfc)sinfc
38
M6[s*kls*lk]1.5
3. Finite element data
The plane strain calculations of granular f low wereperformed with a bin with a height of h0.50 m and awidth of b0.20 m (h/b2.5, b/d50400) [23]. TheFE mesh with quadrilateral finite elements composedof four diagonally crossed triangles was applied toavoid volumetric locking and spurious element be-haviour. A total of 3000 triangular elements with lin-ear shape functions for the displacements and theCosserat rotation were used. Symmetry with respectto the centre line was taken into account. In order torealistically describe the interface behaviour alongthe wall, the FE mesh was strongly refined at thewall. The width of three quadrilateral elements closeto the wall was equal to 0.5 mm, 1.5 mm, 3 mm andthe width of the next five elements was 5 mm, respec-tively. The height of all quadrilateral elements was 10mm. Quasi-static f low (without inertial forces) wasinitiated through constant vertical displacement incre-ments prescribed to all nodes along a smooth bottom.Thus, mass f low was obtained in the silo.
The FE calculations were carried out mainly withan initially dense solid (low initial void ratio) betweenvery rough walls (rwd50). In this case, the largeststress increments occur during silo f low after bottomdisplacement [22]-[24]. The wall roughness rw is de-picted as a relative height between the highest andthe lowest point along the surface at a length of (2-3)d50 [22]. For modelling of very rough walls insilos, full shearing of the material along a wall wasassumed [22]:
u10, u20, wc0. (17)
As a result of the assumed polar boundary condi-tions along the wall (Eq. 17), the wall friction anglecan be derived and no special interface elements areneeded [22]. The remaining boundary conditions inthe silo fill were along the top traction and moment-free, and in the symmetry axis: u10, ωc0 andσ210 (σ21 vertical shear stress).
To investigate the inf luence of the wall inclinationand wall imperfection, the analyses were carried outwith the same initial stress state, namely with the so-called Ko state (frequently used in soil mechanics):σ22γx2, σ11σ33K 0γx2, σ12σ21m1m20 (σ11 horizontal normal stress, σ22 vertical normal stress,σ33 normal stress perpendicular to the plane ofdeformation, σ12 horizontal shear stress, σ21 ver-tical shear stress, m1 horizontal couple stress, m2 vertical couple stress, γ initial unit weight of sand,x2 vertical coordinate measured from the top of the
KONA No.20 (2002) 127
solid, K00.40 pressure coefficient at rest). Tostudy the effect of the initial stress state on wallstresses, a comparative calculation was also per-formed with initial stresses after filling according to aslice method by Janssen [6]:
s22 [1exp( )], (18)
s11NKs22, (19)
s12s21s11tanjw(12x1/b), (20)
s33s11, (21)
where NK is the mean pressure coefficient, ϕw denotesthe mean wall friction angle, x1 is the horizontal co-ordinate measured from the wall, b denotes the silowidth, and σ33 is the normal stress perpendicular tothe plane of deformation. Both model experiments[22] and numerical calculations [12] show thatstresses in silos during filling can be approximatedwith a slice method provided that NK and ϕw are empiri-cally estimated. The choice was made on the basis ofmodel tests [22]: NK0.29 and ϕw43° (initially densesand between parallel and very rough walls).
Four different wall inclinations in a silo wereassumed: parallel walls (Fig. 1a), slightly convergentwalls with a wall inclination from the bottom equal to
2NKtanjwx2
bgb
2NKtanjw
α88° (Fig. 1b), slightly divergent walls with a wallinclination from the bottom equal to α88° (Fig. 1c),and parallel walls (h0.25 m) and slightly convergentwalls (h0.25 m) with a wall inclination from the bot-tom equal to α88° (Fig. 1d).
Two different wall imperfections at the mid-heightof the wall (h0.25 m) were taken into account: asmall imperfection directed to the inside of the bulksolid (Fig. 1e) and a small imperfection directed tothe outside of the bulk solid (Fig. 1f ). The height ofboth imperfections was h140 mm (h1/b0.2) andthe width b12.5 mm (b1/b0.0125).
The calculations were carried out with large defor-mations and curvatures. In this case, an UpdatedLagrangian formulation was applied using both theJaumann stress rate and the Jaumann couple stressrate [22]. At the same time, the changes of the ele-ment configuration and the element volume weretaken into account.
The integration was performed in 3 sample pointsplaced in the middle of each triangular element side.The density of the silo fill was kept constant. For thesolution of the non-linear equation system, a modifiedNewton-Raphson scheme with line search was appliedusing an initial global stiffness matrix calculated withonly two first terms of the constitutive equations(Eqs. 4 and 5). To accelerate the calculations in the
128 KONA No.20 (2002)
Fig. 1 Different wall inclinations and wall imperfections assumed for FE calculations
a)
e)
b1 b1
0,1 m
0,5
m
0,25
m0,
25 m
0,25
m
h1 h1
0,25
m0,
25 m
0,25
m
0,1 m 0,1 m 0,1 m
ααα
f )
b) c) d)
softening regime, the initial increments of displace-ments and the Cosserat rotation in each calculationstep were assumed to be equal to the convergedincrements from the previous step. In addition, to pre-vent possible inadmissible stress states (in particularin the corner of the wall at the bottom), a sub-step-ping algorithm was used (deformation and curvatureincrements were divided into smaller parts withineach step). The iteration steps were performed usingtranslational and rotational convergence criteria(found by means of preliminary FE calculations). Forthe time integration of stresses and couple stresses infinite elements, a one-step Euler forward scheme wasapplied.
4. Numerical results
Influence of initial void ratio and initial stressstate
Figure 2 shows the evolution of normalised hori-
zontal normal stresses σ11/(γb) at the mid-height ofthe wall (h0.20-0.30 m) during the normalised verti-cal bottom displacement u2/h in a model silo with par-allel walls of Figure 1a at the onset of quasi-staticgranular f low. The onset of silo f low is crucial withregard to maximum wall stresses [22]-[24]. Later,wall stresses have a tendency to oscillate with wan-dering small peaks due to the appearance of shearzones along a wall and inside of the f lowing material[22]-[24]. The presented range of u2/h for dense sand(eo0.60) and loose sand (eo0.90) in Figure 2 is dif-ferent.
The shear stresses were not taken into account dur-ing filling (Ko initial stress state), thus wall stressesdecreased at the beginning of f low (Fig. 2). The wallelement ‘21’ is located at a height of 0.20 m and the wallelement ‘30’ at a height of 0.30 m above the bottom(Fig. 2). Other wall elements are located between ‘21’and ‘30’ at a distance of 10 mm. The wall stresses indense sand decrease first, then they increase andreach an asymptote or they reach an asymptote. Thewall stresses in loose sand decrease and very quicklyreach a residual state (u2/h0.0005). The maximumnormalised horizontal stresses σ11/(γb) in the mid-dle of the wall are about 0.70 (dense sand) and 0.55(loose sand). The stresses in loose sand increase withincreasing depth. However, the stresses in densesand are not distributed proportionally with a silodepth due to interior shear zones inside the f lowingsolid [22]-[24]. The maximum horizontal wall stressesfor dense sand are higher by about 30% than thosecalculated by the German Silo Code (plane strain,dense sand, very rough walls): σ11/(γb) 0.55 kPa(with γ17.0 kN/m3, NK0.70, tanϕw0.60, b0.20 m,h0.25 m). In large silos, the normalised wallstresses become smaller due to a decrease of d50/band an increase of pressure (reduction of the internalfriction angle, dilatancy angle and stiffness) [23],[24].
The effect of the initial stress state on the evolutionof stresses σ11/(γb) in a silo of Figure 1a is demon-strated in Figure 3. The calculations were performedwith dense sand and initial stresses according to aslice method by Janssen (Eqs. 18-21). The resultsshow that the initial stress state inf luences the hori-zontal wall stresses only up to u2/h0.0005. Later, theevolution of stresses is the same, independent of theinitial stress state. The maximum normalised stressincrement after outlet opening is about ∆σ11/(γb)0.40 (dense sand). The stresses during f lowincrease more than twice when compared to silo fill-ing.
KONA No.20 (2002) 129
Fig. 2 Evolution of normalised horizontal normal stresses σ11/(γb) during normalised vertical bottom displacement u2/halong the wall at height h0.20-0.30 m in a silo with paral-lel walls:
a) dense sand (eo0.60), b) loose sand (eo0.90)
0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1.00 0.00025 0.00050 0.00075 0.00100 0.00125
302621
302621
0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1.00 0.004 0.008 0.012
21
26
30
σ 11/
(γb)
σ 11/
(γb)
u2/h
u2/h
Influence of wall inclinationThe effect of the wall inclination on horizontal wall
stresses during f low (at different scales of u2/h) isshown in Figures 4 and 5 (Ko initial stress state).Even a small change of the wall inclination influencesthe stresses. The maximum normalised horizontalnormal stresses on the wall σ11/(γb) (Fig. 4) in themiddle region are 8% higher in a silo with slightly con-vergent walls of Figure 1b, and by 2% lower in a silowith slightly divergent walls of Figure 1c comparedto the silo with parallel walls (Fig. 2a). The increaseof horizontal normal stresses (Fig. 5) below the tran-sition between a parallel and convergent part of thesilo of Figure 1d is similar to that in the silo with con-vergent walls at mid-height (Fig. 4a).
Influence of wall imperfectionsThe evolution of normalised horizontal normal
stresses σ11/(γb) during vertical bottom displacementin the middle region of the wall in a model silo withparallel imperfect walls (dense sand with eo0.60, Ko
initial stress state) is depicted in Figure 6.The FE results demonstrate that a small imperfec-
tion in the wall increases (by about 40%) or decreases(by about 30-50%) the maximum horizontal wallstresses compared to a perfect wall (Fig. 2a). Thestresses increase significantly on the convergent partof the imperfection (α75°) and decrease signifi-cantly on the divergent part of the imperfection(α75°). They also increase directly above the diver-gent part. Other stresses at imperfections are approx-imately in the range of stresses for a silo with perfectwalls.
130 KONA No.20 (2002)
Fig. 4 Evolution of normalised horizontal normal stresses σ11/(γb) in dense sand (eo0.60) during normalised verticalbottom displacement u2/h along the wall at height h0.20-0.30 m:
a) silo with slightly convergent walls, b) silo with slightlydivergent walls
0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1.00 0.002 0.004 0.006
21
2629
21
2629
Fig. 5 Evolution of normalised horizontal normal stresses σ11/(γb) in dense sand (eo0.60) during normalised verticalbottom displacement u2/h along the wall at height h0.20-0.30 m (silo with parallel and slightly convergent walls ofFig. 1d)
0
0.3
0.6
0.9
1.20 0.006 0.012 0.018
212430
25
0
0.3
0.6
0.9
1.20 0.004 0.008 0.012 0.016
21
2630
21
2630σ 1
1/(γ
b)σ 1
1/(γ
b)
u2/h
u2/hFig. 3 Evolution of normalised horizontal normal stresses σ11/(γb) during normalised vertical bottom displacement u2/halong the wall at height h0.20-0.30 m in a silo with par-allel walls (dense sand, eo0.60, initial stress state byJanssen)
0
0.3
0.6
0.9
1.20 0.002 0.004 0.006 0.008 0.010
21
26
30
21
26
30
σ11/(γb)
σ11/(γb)
a)
b)
5. Conclusions
The following conclusions can be drawn from FEcalculations at the onset of granular f low in a silo withvery rough walls using a polar hypoplastic law:
Bulk solids during silo f low are sensitive to everychange in the direction of shear deformation.
The effect of the initial void ratio has a large inf lu-ence on horizontal normal stresses on the wall. Thewall stresses in a dense solid are larger during f lowthan in a loose one.
The initial stress state has an insignificant effect onmaximum wall stresses.
Horizontal wall stresses decrease along divergentwalls and increase along convergent ones.
Even small imperfections in a silo wall can cause asignificant increase of local horizontal stresses.
The wall stresses during f low of dense solids insilos with very rough walls can be larger during f lowthan standard values.
The FE calculations will be continued. The inf lu-ence of the wall roughness, the initial void ratio in thesolid, and the magnitude and shape of wall imperfec-tions will be analysed. To realistically describe thelocalisation of shear zones inside a f lowing solid, thecalculations will be performed for the entire silo. Theinitial void ratio will be stochastically distributed inthe solid with a random generator.
Literature
[1] Schwedes, J.: Fließverhalten von Schüttgütern inBunkern, Verlag Chemie, Weinheim, 1968.
[2] Jenike, A. W., Johanson, J. R., Carson, J. W.: Bin loads part 2, 3 and 4, Journal of Engineering for Industry,ASME, pp. 1-6, 1973.
[3] van Zanten, D. C., Mooij, A.: Bunker Design, part 2:Wall pressures in mass f low, Journal of Engineeringfor Industry, ASME, pp. 814-818, 1977.
[4] Stashevskii, S. B.: Stresses in the neighbourhoods ofdefects in bunker walls, Fiziko-Tekhnicheskie Prob-lemy Razrabotki Poleznykh Iskopaemykh, 5, pp. 29-37,1982.
[5] Stashevskii, S. B.: Neue Silo-Konzepte, Lecture at theInstitute for Soil Mechanics, University Karlsruhe,1992.
[6] Schwedes, J., Schulze, D., Kwade, R.: Lagern undFliessen von Schüttgütern, Script of the Institut fürMechanische Verfahrenstechnik, Technische Univer-sität Braunschweig, 1999.
[7] Tejchman, J., Ummenhofer, T.: Bedding effects in bulksolids in silos experiments and a polar hypoplasticapproach, Thin-Walled Structures, 37, 4, pp. 333-361,2000.
[8] Lo, S. C. R., Lee, I. K.: Response of granular soil alongconstant stress ratio path, ASCE Eng. Mech., SM6, pp.117-141, 1990.
[9] Wu, W.: Hypoplastizität als mathematisches Modellzum mechanischen Verhalten granularer Stoffe, Publi-cation Series of the Institute of Soil and Rock Mechan-ics, University Karlsruhe, 129, 1992.
[10] Tatsuoka, F., Siddiquee, M. S. A., Yoshida, T.: Testingmethods and results of element tests and testing con-ditions of plane strain model bearing capacity testsusing air-dried dense Silver Leighton Buzzard Sand,Internal Report, University of Tokyo, 1994, pp. 1-120,1994.
[11] Herle, I.: Hypoplastizität und Granulometrie einfacherKorngerüste, Publication Series of the Institute of Soiland Rock Mechanics, University Karlsruhe, 142, 1997.
[12] Tejchman, J.: Numerical simulation of filling in siloswith a polar hypoplastic constitutive law, Powder Tech-nology, 96, pp. 227-239, 1998.
[13] Tejchman, J., Herle, I., Wehr: FE-studies on the inf lu-ence of initial void ratio, pressure level and mean graindiameter on shear localisation, Int. J. Num. Anal.Meth. Geomech., 23, pp. 2045-2074, 1999.
KONA No.20 (2002) 131
Fig. 6 Evolution of normalised horizontal normal stresses σ11/(γb) in dense sand (eo0.60) during normalised verticalbottom displacement u2/h along the wall (h0.25 m) in asilo with:
a) inward wall imperfection, b) outward wall imperfection
0 0.002 0.004 0.006 0.008
27
0.010
0
0.5
1.0
1.5
0
0.5
1.0
1.5
2221232925
262428
27
2221232925
262428
30
29
28
23
22
27
24
26
25
0 0.002 0.004 0.006 0.008 0.010
0
0.5
1.0
1.5
0
0.5
1.0
1.5
27
2523
222826
24
27
2523
222826
242928
2322
27
24
26
25
σ 11/
(γb)
σ 11/
(γb)
u2/h
u2/h
a)
b)
[14] Tejchman, J., Gudehus, G.: Shearing of a narrow gran-ular strip with polar quantities. J. Num. and Anal.Methods in Geomechanics, 25, pp. 1-28, 2001.
[15] Tejchman, J.: Patterns of shear zones in granular ma-terials within a polar hypoplastic continuum, ActaMechanica, 155, 71-94, 2002.
[16] Gudehus, G., Tejchman, J.: Silo music and silo quake experiments and a numerical Cosserat approach,Powder Technology, 76, pp. 201-212, 1993.
[17] Tejchman, J.: Silo-quake measurements, a numericalpolar approach and a way for its suppression, Thin-Walled Structures, 31/1-3, pp. 137-158, 1998.
[18] Schäfer, H.: Versuch einer Elastizitätstheorie deszweidimensionalen ebenen Cosserat-Kontinuums,Miszellaneen der Angewandten Mechanik, FestschriftTolmien, W., Berlin, Akademie-Verlag, 1962.
[19] Gudehus, G.: A comprehensive constitutive equationfor granular materials, Soils and Foundations, 36, 1, pp.1-12, 1996.
[20] Herle, I., Gudehus, G.: Determination of parameters
of a hypoplastic constitutive model from propertiesof grain assemblies. Mechanics of Cohesive-FrictionalMaterials, 4, 5, pp. 461-486, 1999.
[21] Bauer, E.: Conditions of embedding Casagrande’s criti-cal states into hypoplasticity, Mechanics of Cohesive-Frictional Materials, 5, pp. 125-148, 2000.
[22] Tejchman, J.: Shear localisation and autogeneousdynamic effects in granular bodies, Publication Seriesof the Institute for Rock and Soil Mechanics, Karls-ruhe University, 140, 1997.
[23] Tejchman, J.: Scale effects in bulk solids during silof low. The International Journal of Storing, Handlingand Processing Powder (Powder Handling and Pro-cessing), Vol.13, No.2, pp. 165-173, 2001.
[24] Tejchman, J., Gudehus, G.: Verspannung, Scherfugen-bildung und Selbsterregung bei der Siloentleerung.“Silobauwerke und ihre spezifischen Beanspru-chungen”, eds.: J. Eibl and G. Gudehus, DeutscheForschungsgemeinschaft, Wiley-VCH, pp. 245-284,2000.
132 KONA No.20 (2002)
Author’s short biography
Jacek Tejchman
Prof. Dr.-Ing. habil. Jacek Tejchman was born in Poland. He received his MScdegree from the Civil Engineering Department at the Gdansk University of Tech-nology (speciality: reinforced concrete structures). He received his PhD degreefrom the Technical University of Karlsruhe in Germany in 1989 (Institute of Rockand Soil Mechanics) with a thesis on scale and dilatancy effects during granularf low. Afterwards, he made his habilitation thesis in 1996 again at the TechnicalUniversity of Karlsruhe (Institute of Rock and Soil Mechanics) on shear localisa-tion and autogeneous dynamic effects in granular bodies. He has worked at theTechnical University of Karlsruhe for 10 years (1986-1996). He became professorin 1998 and head of the Institute for Building and Material Engineering at theGdansk University of Technology in Poland (Faculty of Civil Engineering). Hismain research interests concern numerical modelling of the behaviour of granularmaterials, concrete and reinforced concrete elements and structures taking intoaccount the localisation of deformations (shear zones and cracks). He is a memberof the Deutsche Gesellschaft für Erd- und Grundbau and the International WorkingParty on the Mechanics of Particulate Solids.
KONA No.20 (2002) 133
1. Introduction
Non-invasive experimental techniques are invalu-able for providing a detailed insight into the f low pat-terns and general hydrodynamic characteristics ofmultiphase systems. One such technique involves theuse of X-rays and is based on the same principles asare used in diagnostic medicine to record the struc-tures of body parts that are opaque to visible light.The first recorded use of X-rays to study gas-solid f lu-idized beds dates from the mid-1950s, and over thesubsequent fifty or so years, the technique has beenapplied to a wide range of two- and three-phase f lu-idized systems. The technique has enabled gas andsolids f low patterns to be observed and quantifiedand has led to the improved design of internal struc-tures such as gas distributors and heat transfer sur-faces in industrial units.
2. Bubbling fluidized beds
Grohse [1] first reported the use of X-rays to deter-mine the instantaneous and time-averaged bulk den-sity of a finely divided powder f luidized at a range ofgas velocities and with three different designs of gasdistributor, namely a perforated plate, a mesh screenand a porous plate. The X-ray source consisted of
standard components of an X-ray diffraction unit witha tungsten target X-ray tube. The detection equip-ment consisted of a modification of the rate meter in astandard X-ray detector fed by a scintillation probe.The rate meter response was logarithmic over mostof its range of sensitivity and in accordance with Eq.(1) below, the reading varied approximately linearlywith the local bed density being measured. The f lu-idized bed material was silicon powder with a meanparticle size of about 50 µm and was contained in acylindrical borosilicate glass column of diameter 8.5cm. The results were analysed in terms of the Beer-Lambert law which for the attenuation of essentiallyparallel, monochromatic X-rays may be written:
II0 exp(mmrl) (1)
where mm is the mass attenuation coefficient of thebed material, r is its density and l is the bed thick-ness. In practice, polychromatic radiation is normal-ly employed but Eq. (1) is generally considered anadequate approximation. The term mmrl is called theoptical density of the absorbing material and for twodifferent materials A and B producing identical X-rayattenuation, the two optical densities are equal:
mmArAlAmm
BrBlB (2)
then the bulk density of A may be written:
rAKlB (3)
Grohse [1] determined the value of K, which hasunits of kg m3m1, by expanding the f luidized bed of
J.G. Yates, D.J. Cheesman and P. LettieriUniversity College London*D. NewtonBP Chemicals**
X-Ray Analysis of Fluidized Beds and Other Multiphase Systems†
Abstract
The attenuation of a beam of X-rays as it passes through a body has been used for over 100 yearsin diagnostic medicine. A more recent application of the technique has been in the study of indus-trial-type units such as gas-solid f luidized beds, and this paper reviews this application in the analy-sis of the hydrodynamic features of bubbling and circulating f luidized beds. The measurement of jetpenetration into bubbling beds and the study of bubble slurry columns are also considered. Theequipment used and its methods of operation are described and the salient results of the more reveal-ing investigations are summarised both from a qualitative and a quantitative viewpoint.
* Torrington Place, London WC1E 7JE, UK** Chertsey Toad, Sunbury-on-Thames, Middlesex TW16
7LL, UK† Accepted: June 17, 2002
powder at gas velocities between zero and the mini-mum bubbling point and accurately measuring theexpanded bed height; then under knowledge of themass of powder in the bed, an average bed densitycould be found for each gas velocity. The value of lBwas the thickness of pure aluminium that gave thesame beam attenuation as a bed of solids of densityrA. The work clearly demonstrated the two-phasenature of f luidized beds but gave little in the way ofdetailed structure. It did, however, make the firstmention of the “bed collapse” technique which hasbeen applied more recently to investigate the effect ofoperating parameters on dense-phase voidage (seebelow).
Romero and Smith [2] used f lash X-ray radiographyto study the internal structure of f luidized beds andobtained data not only on bed density distribution butalso on the shape, size and velocity of gas bubbles inan air-f luidized bed of sand. Their unit consisted oftwo f lash tubes, one operating at 300 kV and the otherat 600 kV, each producing a square pulse of energy at1,000 amps for a duration of about 0.2 µs. The tubeswere mounted on opposite walls of a lead-lined roomwhich housed a 7.6-cm square plexiglass column con-taining a f luidized bed of sand. After passing throughthe bed, the X-ray beam was recorded on 2025-cmsheets of film, the 300-kV tube illuminating the lowerpart of the bed and the 600-kV tube the upper part. Tomeasure bubble velocity, the two units were fired insequence a few tenths of a second apart.
To determine bed density, Romero and Smith mea-sured the darkness of their films using an optical den-sitometer, but in order to compensate for variations inX-ray operating voltages and variations in the qualityand processing of the films, each photograph wascompared with a standard consisting of sand-filledwedges made from plexiglass. These were mountedon the side of the f luidization column so that an X-rayphotograph of them was obtained each time the X-raywas fired. The wedge gave a film darkness gradationthat could be related to sand thickness, and by com-paring film darkness in the wedge with darkness inthe bed, the local bed density could be obtained.
Rowe and Everett [3,4,5] described the design andoperation of a f luidized bed X-ray system in whichthe attenuated beam on passing through the bed wasregistered on a 0.22-m diameter Mullard image in-tensifier. The X-ray tube used was a Machlett SuperDynamax 125 with a rotating anode and a fine orbroad focal spot of 1 mm or 2 mm diameter. It had arating of 200 mA at 120 kVp for 102 s on fine focus or500 mA at the same voltage and duration on broad
focus. The image intensifier augmented the beamintensity by a factor of 3103 and was filmed by a 70-mm cine camera at a rate of 6 or 8 frames/s, the X-raybeam being synchronised with the camera and pulsedfor 2.5 ms. A series of rectangular section f luidizedbeds were studied with thicknesses from 1.4 cm to29.5 cm. Bubble sizes, their number and velocitywere measured at various heights up to 70 cm inbeds of alumina, carbon, quartz, glass ballotini andcrushed glass powder f luidized by ambient air; Fig. 1shows a typical image. Fig. 2 shows a sketch of theX-ray imaging technique.
134 KONA No.20 (2002)
Fig. 1 X-ray image of a freely bubbling f luidized bed [3]
Fig. 2 X-ray imaging technique
Image intensifierfield of view
Internal f low patternsGas bubbles
Image intensifier
CCDvideocamera
HTGenerator
X-raysource
One result to come from these three seminal papersrelated to the effect of the bed thickness on the mini-mum f luidization velocity, Umf. It was found that Umf
remained constant for beds thicker than 15 cm butdecreased by up to 50% as the bed size decreased tothe smallest dimension of 1.4 cm.
A similar system to that of Rowe and Everett [3,4,5]was used by Rowe et al. [6] to make detailed measure-ments of the emulsion-phase voidage in f luidizedbeds and its variation with the particle size distribu-tion of the bed material. In this study the cine camerawas operated at 50 frames/s. As described above forRomero and Smith [4], a calibrating wedge filled withbed material was used to quantify the observations.By comparing the optical density of a region on thefilm with that at a given level of the wedge of knowndimensions, the powder voidage in that region couldbe determined from:
ee1(1ew)(DW/DB) (4)
where ee and ew are the powder voidages in the emul-sion phase and the wedge, respectively, DW is thewedge thickness with the same optical density as thebed, and DB is the bed thickness. An example of sucha measurement is shown in Fig. 3.
A series of powders with different contents of“fines” was studied, fines being defined as the weightpercentage of particles with sieve sizes less than 45µm. The experimental results are summarised inFigs. 4 and 5 and consisted of measurements of thedense-phase voidage in bubble-free regions of the bedand measurements of the bed height. No variation
with height of the dense-phase voidage was observed.Settled-bed voidages refer to the tapped, unf luidizedbed.
Theoretical considerations by Rowe et al. [6] led tothe following expression for the emulsion-phase gas
KONA No.20 (2002) 135
Fig. 4 Variation of f luidized bed height with superficial gas veloc-ity [6]
4.cm
Vertical distance
Marker wires
Scan of calibrationwedge
Ligh
t int
ensi
ty(
void
age)
ε0.365
Scan off luidised bed
27.6%
27.6%
20%
20%
2.7% ‘Fines’
2.7% ‘Fines’
0
0
0.30
0.35
0.40
0.45
5 10 15
30
32
34
36
38
40
5B
ed h
eigh
t, H
cmGas velocity, U cm/s
Gas velocity, U cm/s
Settled bed values
Den
se p
hase
voi
dage
, εi
10 15
Increasingfines content
Increasingfines content
Fig. 3 Microdensitometer scan of an X-ray film and a calibratingwedge [6]
Fig. 5 Variation of emulsion-phase voidage with superficial gasvelocity [6]
f low rate:
Qe/AUge(34fb)ee/3 (5)
where all the quantities on the right-hand side of theequation could be calculated from the experimentalresults. Figure 6 shows the results of plotting Eq.(5), and it is clear that the emulsion gas f low rate isvery much greater than the f low corresponding tothat at minimum f luidization of the powder containing27.6% fines, 0.207 cm/s, and that it increases withoverall gas velocity and fines content.
This is favourable from the point of view of f lu-idized bed reactor operation, a conclusion that wasverified in a subsequent study by Yates and Newton[7].
The X-ray technique was used by Hoffmann andYates [8] to study the effect of pressure on f luidizedbeds of powders in Groups A and B of the Geldart [9]classification. They found in the case of Group A pow-ders that while the minimum fluidization velocity,Umf, was unaffected, the region of bubble-free expan-sion between Umf and Umb, the minimum bubblingvelocity, increased with increasing pressure. Thisobservation is in accordance with the theory of f luid-bed stability developed by Foscolo and Gibilaro andrecently reviewed by Gibilaro [10]. For Group B pow-ders, Hoffmann and Yates found that mean bubblediameters increased slightly up to 16 bar and de-creased thereafter up to 60 bar pressure. In addition,
the bubble velocity coefficient k in:
ubk(gdb/2)1/2 (6)
was found to decrease up to 20 bar pressure but thento increase quite markedly above 20 bar up to thehighest pressures at which observations were made.This latter increase coupled with the observed de-crease in bubble size meant that although bubbleswere becoming smaller, their rise velocities wereincreasing, the reverse of the tendency observed atambient pressure. These results were subsequentlycorroborated by Olowson and Almstedt [11] using acombined capacitance and pressure probe to measurebubble characteristics in a bed of Group B powder.
Other X-ray studies of the effects of system pres-sure on f luidization were reported by Rowe et al. [12]and Barreto et al. [13].
X-ray images of f luidized beds may be enhanced soas to investigate solids volume fractions in the regionsclose to the boundaries of bubbles. In one such study[14], the X-ray source was pulsed for a period of 1 msand the pulses synchronised with a video recorder atan equivalent speed of 25 frames/s. Both the radia-tion source and the detector could be moved verti-cally relative to the f luidized bed, thus allowingdifferent positions to be examined. The recordedimages were transferred off-line for processing andanalysis using a PC. The video signal was relayed to aframestore board (Imaging Technology VP 1100) viaa timebase corrector, and the images processed usingBioscan Optimas software operating in Windows 3.0.
As discussed above, when X-rays pass through asolid material they are attenuated by processes ofabsorption, ref lection and scattering, and the extentof the attenuation is a function of the chemical natureof the solid and of the quantity of material in the pathof the beam. The Beer-Lambert law (Eq. 1) may bewritten:
II0I0(mmrl)… (7)
In many cases, the second order and higher termsin the exponential may be neglected and Eq. (7) maybe used to an acceptable degree of accuracy.
The attenuation of X-rays by ambient air is negligi-ble and so for an air-f luidized bed we can express thebulk density r in terms of the solids fraction of thebed through which the beam passes:
II0I0(mmrs)(1e)l (8)
where rs is the solids density and e is the voidage ofthe bed material.
In order to relate the measured intensity of the
136 KONA No.20 (2002)
Gas velocity, U cm/s0
0
5
10
15
105 15
Inte
rstit
ial f
low
, Qe/
Acm
/s
2.7% ‘Fines’
Qe/AUge(34fb)εe/3
27.6%
20%
Fig. 6 Variation of emulsion-phase gas f low with superficial gasvelocity [6]
transmitted beam to the voidage of the materialthrough which it passes, it is necessary to calibratethe system according to Eq. (8) and this may be doneas before using a wedge filled with the powder to bestudied. The wedge is set up vertically in the X-raybeam and the transmitted intensity measured on arange of grey scales from 0 to 225 as a function of thewedge thickness lw. The calibration for the Group Balumina powder used in this study [14] gave anexplicit relationship between bed voidage, transmittedintensity and path length l of:
e1(655.2I)/(55.47 l) (9)
The recorded X-ray images of single bubbles werecomputer-enhanced to show coloured zones of vary-ing voidage; such an image is shown in Fig. 7, wherethe regions of expanded voidage surrounding thebubble, the so-called “shell” region, are clearly visible.The black area is the emulsion phase with an averagevoidage of 0.445, the green with 0.495, the blue with0.526, the cyan with 0.627 and the red area is the bub-ble itself with a voidage of 1.0.
Two points must be emphasised about this image.Firstly, the computer is programmed to calculate aver-age values of voidage between any predeterminedrange of intensity values and to colour-code thatrange; there is in fact a continuous gradation invoidage between one zone and the next. Secondly, theimage is a representation in two dimensions of a trulythree-dimensional object, in other words a silhouette.This means that the voidage indicated is an averagevalue across a chord of the more or less sphericalregion of the bed around the bubble. The deconvolu-
tion of these averages to give point values of porositywill now be considered.
The X-ray intensity measured in the x-directionacross a section of such a sphere may be expressedas:
I(x)b
[ε(x, z)εmf]dz (10)
where b is a calibration factor, ε(x,z) is the space-aver-aged voidage across a chord within the shell, and εmf
is the voidage of the background emulsion phase.
Now: z(r 2x2)1/2 (11)
and hence: dz (12)
I(x) may be expressed in terms of the variation ofvoidage in the radial direction, ε(r):
I(x)2b
x (13)
This is the Abel transform of [ε(r)εmf] [15], and asolution for the inverse transform of the function I(x)will enable the radial variation in voidage to be found.The Abel transform is useful for converting three-dimensional images into two dimensions and viceversa, and is based on the assumption that the three-dimensional object being considered is axially sym-metrical, e.g., a perfect sphere. Clearly, bubbles inf luidized beds are not perfect spheres but they can beconsidered as having to a first approximation a suffi-cient degree of axial symmetry for the transform tobe applicable, i.e. it can be assumed that the voidagearound a bubble is a function of the radius of thesphere centred on the bubble. The transform may bereduced to a convolution integral and solved numeri-cally to obtain ε(r) [15]. The method was applied to asingle bubble in the Group B powder observed 30 cmabove the distributor with the results as shown inFig. 8, and it is clear that no very sharply definedboundary exists between the shell and the emulsionphase.
Lettieri et al. [16] used the X-ray technique to studychanges in the behaviour of the dense phase of f lu-idized beds with increasing temperature. The bedcontainer was constructed from Inconel with a wallthickness of 3 mm, and was capable of being heatedto 650°C. Fluidized beds of a range of materials weresubjected to the “bed collapse test” in which the f lu-idizing gas supply was abruptly cut off and the result-ing collapse of the bed surface observed using X-rays.Two solenoid valves were fitted to the equipment, oneto cut the gas supply to the bed, the other to vent the
[ε(r)εmf]rdr(r 2x2)1/2
rdr(r 2x2)1/2
KONA No.20 (2002) 137
Fig. 7 X-ray image of a bubble in a f luidized bed of a Group Bpowder [14]
gas trapped in the windbox below the gas distributor.From these observations, a number of quantities maybe derived for Group A powders, including the emul-sion-phase voidage, εe, and the “standardised collapsetime” (SCT s/m) which gives a measure of the aera-tion capacity of the powder [17]. The SCT is definedas follows:
SCT(tct0)/Hs (14)
where t0 and tc are the initial cut-off time and the timefor the bed to reach total collapse, respectively, and Hs
is the settled bed height. The longer the SCT, thehigher the aeration capacity of the powder and hencethe larger the void fraction of the emulsion phase.Lettieri et al. [16] showed that for powders such asf luidized cracking catalyst (FCC) that are free frominter-particle forces, the SCT and hence the emulsion-phase voidage increase markedly with increasingtemperature, whereas powders that were coated so asto induce inter-particle adhesion showed the oppositeeffect. Table 1 summarises these results for threeFCC powders and one silica powder coated with 10 wt% of potassium acetate.
Bed collapse experiments using X-rays to follow theprocess were also described by Chen and Weinstein[18]. The X-ray image of the bed was projected onto a0.23-m diameter image intensifier screen, the visiblelight from which was focused onto another screenequipped with 48 phototransistors. These were posi-tioned such that three rows of 16 transistors scanned
the projected image of the bed across three elevationsat 1 cm intervals. The system is described in detail byFeindt [19]. In this work, which also employed crack-ing catalyst, a single solenoid valve was used to shutoff the gas supply to the bed. The bed collapse datawere used to calculate the solids stress modulus andthe drag coefficient for the catalyst powder in thesolid fraction range between minimum fluidizationand loose packing. The sedimentation wave velocityfor the bed material was 0.027 m/s, a figure in goodagreement with the SCT measurements of Lettieri etal. [16].
3. Jet penetration
When gas first enters a f luidized bed from a sub-merged orifice, it does so either in the form of dis-crete bubbles or as a f lame-like jet which decays atsome point above the grid into a bubble stream.Whether one or the other form seems to depend onthe properties of the bed material and the size of theinlet nozzle. Rowe et al. [20] observed the point ofentry of gas into a bed of a Group B powder using X-rays and saw only bubbles forming with a well-defined frequency.
Chen and Weinstein [21] carried out an X-ray studyof a horizontal jet into a 1538-cm cross-section f lu-idized bed of cracking catalyst. Instantaneous solidsvolume fractions averaged along 15-cm chords weremeasured for two jet diameters and three initial jetvelocities, and it was shown that there are three dis-cernible regions in the area of the bed inf luenced bythe jet: a coherent void; bubble trains; and a sur-rounding compaction zone. The jet penetration lengthwas found to agree well with the correlations devel-oped by a number of earlier workers. Weinstein et al.[22] have more recently studied the sudden injectionof a horizontal gas jet into a bed at just above the min-
138 KONA No.20 (2002)
Fig. 8 Scan of X-ray intensity across a horizontal plane throughthe equator of a single bubble in a Group B powder [14]
5 10 15 20
0
50
100
150
200
250
300
Distance / cm
Inte
nsity
SCT (s/m)T(°C)
FCC 1 FCC 2 FCC 3Silica powder
(10%wt KOAc)
018 27.3 38.2 32.6 16.7
100 36.1 44.4 39.6 24.7
200 42.9 54.4 43.3 16.0
300 47.4 59.8 48.1
400 50.1 66.0 52.2
500 51.7 67.5 55.1
640 52.7 72.8 57.5
Table 1 Experimental SCT for FCC powders and a silica powdercoated with KOAc
imum f luidization conditions, but no quantitative cor-relation from the observations was given.
Yates and Cheesman [23] and Yates [24] measuredjet penetrations, Lmax, in three-dimensional beds oftwo Group B powders at pressures of up to 20 bar atambient temperature, and at temperatures of up to800°C at ambient pressure. The results were corre-lated with:
9.77 0.38(15)
Rcf (16)
Ucf being the velocity of complete f luidization of thepowder.
Newton et al. [25] reported results from an X-raystudy of upshot, downshot, horizontal and 30°-angledupshot jet penetration lengths from multiple orificegrid plates and nozzle spargers. Bed materials wereGeldart Group A. The study concluded that none ofthe correlations for predicting vertical and horizontaljet penetrations adequately accounted for the mea-sured values, but that the correlation of Zenz [26] waswell suited for downshot jet penetrations over therange of conditions studied.
4. Circulating fluidized beds
Fluidized beds undergo a number of state transi-tions as the superficial gas f low rate increases. Thusa bubbling bed exists at gas velocities somewhat inexcess of the minimum fluidization f low rate but athigher f low rates, bubbles become unstable and thebed passes into the “turbulent” regime. At sufficientlyhigh f low rates, the bed particles become entrainedand carried out of the containing vessel, and in orderto maintain a constant solids inventory, the entrainedmaterial must be captured in a cyclone and returnedto the bed normally at a point near its base. Such asystem is called a “circulating” f luidized bed, andindustrial interest in this type of system goes backto the earliest days of f luidization when they wereemployed in the catalytic cracking process [27]. Seri-ous scientific study of the area dates from the work ofthe group at City College, New York, in the mid-1970s[28], although Kehoe and Davidson [29] had identi-fied the transition from bubbling to turbulent f luidiza-tion somewhat earlier. One of the earliest reports ofthe application of the X-ray technique to study gas andsolids f low in the riser section (the so-called “fast”bed) of a circulating bed was that of Weinstein et al.
(Ucf)pressure / temperature
(Ucf)ambient
Uo2
gdo
rf
rprf
1Rcf
Lmax
do
[30]. Their X-ray tubehead and the image recordingdevices (plate film and TV camera) were mounted onopposite sides of a carriage which could be moved upand down a 3-m long centre section of the f luidizedbed. Data were obtained on the radial distribution ofvoid fraction in the lower dense-phase region of thefast bed and demonstrated its dilute core-dense annu-lus structure. Variations in radial voidage were stud-ied in response to three types of f low variation, (i)increasing superficial gas velocity from 1.1 m/s (aturbulent bed) to 5 m/s with varying solids circula-tion f lux, (ii) increasing gas velocity with a constantsolids f lux, and (iii) holding the gas velocity constantat 3.1 m/s and varying the solids f lux between 50 and121 kgm2s1. The results are shown in Figs. 9-11,from which it was concluded that (a) at a constant gasvelocity changes in solids f lux have a small effect onradial voidage, (b) decreasing solids f lux moves thepoint of inf lection between the lower fast bed and theupper dilute-f low region in a downward direction untilat a sufficiently low value of the f lux, the dense-phaseregion disappears.
Subsequent X-ray studies by the City College grouphave investigated internal scales of turbulence inhigh-velocity beds [31], the effect of gas nozzle con-figuration on the acceleration of solids and the distrib-ution of solids and gases in a riser [32-34], and thef low characteristics of downflowing high-velocity f lu-idized beds [35,36].
KONA No.20 (2002) 139
1.0
0.8
0.6
0
Void
frac
tion
0.2 0.4
Ug1.1, Gs012.1 kg/m2sUg2.1, Gs057.5 kg/m2sUg3.1, Gs121.0 kg/m2sUg4.0, Gs143.0 kg/m2sUg5.0, Gs154.0 kg/m2s
0.6 0.8 1.0r/R
Radial position, Dimensionless
Fig. 9 Radial variation of void fraction at different velocities, openvalve [30]
5. Slurry bubble columns
By virtue of their excellent heat transfer character-istics, three-phase reactors in which a gas issparged into a solid-liquid slurry are favoured forprocesses involving highly exothermic reactions such
as the Fischer-Tropsch process [37,38]. Smith et al.[39] used an X-ray system to study the hydrodynam-ics of a system in which an inert gas (nitrogen orhelium) was passed into a slurry of zirconia particlesin water. The solids loading was varied in the range10-30%, and three 2-m long “reactors” with diametersof 50, 127 and 178 mm were used, each being fittedwith a grade C sintered brass distributor plate. Forcomparison, a holed plate distributor was designedfor the 127-mm column and consisted of 373-mmdiameter holes arranged on a triangular pitch. Systempressures were up to 8 bar and gas velocities up to0.09 m/s. Gas bubbles were generally small, of theorder of a few mm in diameter, and since the gasesused were insoluble, the mean bubble diameter couldbe estimated from the extent of expansion of theslurry column:
VglsVls(p/6)db3nb (13)
where nb is the number of bubbles of mean diameterdb, nb being obtained by direct counting from thevideo image. Figure 12 shows the effect of gas veloc-ity on mean bubble size, and it is clear that systempressure has a significant effect. Increasing the solidsloading was found to increase both the hold-up andthe mean size of bubbles, the latter increasing from 8mm to 12.5 mm on increasing the loading from 10% to
140 KONA No.20 (2002)
0 0.2 0.4 0.6 0.8 1.0r/R
Radial position, Dimensionless
0.6
0.8
1.0
Void
frac
tion
Solid rate
1.64 m0.00 m
Height abovebottom x-rayposition
121.0 kg/m2s85.9 kg/m2s74.9 kg/m2s62.5 kg/m2s49.7 kg/m2s
Gas velocity 3.1 m/s
Fig. 11 Radial variation of void fraction, constant gas velocity [30]
Fig. 12 Effect of gas velocity on bubble size [39]
18
161 bar
8 bar14
12
10
8
10% Loading/38µ/Holed grid127 mm diameter Reactor
6
4
2
00 1 2 3 4 5 6 7 8 9 10
Gas velocity / cm/s
Mea
n bu
bble
dia
met
er /
mm
0 0.2 0.4 0.6 0.8 1.0r/R
Radial position, Dimensionless
0.6
0.8
1.0Vo
id fr
actio
n
Solid rate 122 kg/m2s
1.64 m0.00 m
Height abovebottom x-rayposition
3.1 m/s4.1 m/s5.1 m/s
Gas velocity
Fig. 10 Radial variation of void fraction, constant solids rate [30]
20% in the 127-mm column at 8 bar and 0.04 m/s gasvelocity.
6. Conclusions
The X-ray technique is one of an increasing numberof non-invasive methods currently being employed tostudy multiphase systems of industrial interest [40].The above examples demonstrate the versatility ofthe technique for real-time observation and analysisof the many hydrodynamic features of f luidized beds,and it will continue to be used for this purpose. Animportant application which is currently at an earlystage is as a tool to validate theoretical models of f lu-idized systems based on computational f luid dynamiccodes such as Fluent and CFX [41]. The high degreeof discrimination possible with X-rays makes it idealfor this validation process, and much progress in thisdirection can be expected in the near future.
Nomenclature
A area m2
b calibration factor in Eq. (10) d diameter mfb bubble fraction g acceleration due to gravity ms2
Gs solids circulation f lux kgm2s1
Hs settled bed height mI, I(x) transmitted intensity I0 incident intensity K coefficient in Eq. (3) kgm3m1
l length mLmax maximum jet penetration length mn number Qe volumetric f low rate m3s1
r radial distance mR riser diameter mRcf defined in Eq. (16) STC standardised bed collapse time sm1
tc total collapse time st0 time at gas cut-off su velocity ms1
ug gas velocity ms1
U superficial velocity ms1
V volume m3
x,z Cartesian coordinates mD thickness me voidage k coefficient in Eq. (6) mm mass attenuation coefficient m1
r density kgm3
Subscriptsb bubbleB bedcf complete f luidizatione emulsion phasege emulsion gasgls gas-liquid-solidls liquid-solidmb minimum bubblingmf minimum f luidizationo orifices solidsw wedge
References
[1] Grohse, E.W., 1955, Analysis of gas f luidized solid sys-tems by X-ray absorption, AIChEJ, 1, 358-365
[2] Romero, J.B. and Smith, D.W., 1965, Flash X-ray analy-sis of f luidized beds, AIChEJ, 11, 595-600
[3] Rowe, P.N. and Everett, D.J., 1972, Fluidized bed bub-bles viewed by X-rays, Trans IChemE, 50, 42-48
[4] Rowe, P.N. and Everett, D.J., 1972, ibid 49-54[5] Rowe, P.N. and Everett, D.J., 1972, ibid 55-60[6] Rowe, P.N., Santoro, L. and Yates, J.G., 1978, The divi-
sion of gas between bubble and interstitial phases inf luidized beds of fine powders, Chem Eng Science, 33,133-140
[7] Yates, J.G. and Newton, D., 1986, Fine particle effectsin f luidized bed reactors, Chem Eng Science, 41, 801-806
[8] Hoffmann, A.C. and Yates, J.G., 1986, Experimentalobservations of f luidized beds at elevated pressures,Chem Eng Commun, 41, 133-149
[9] Geldart, D., 1973, Types of gas f luidization, PowderTechnol., 7, 285-292
[10] Gibilaro, L.G., 2001, Fluidization Dynamics, Butter-worth Heinemann, Oxford
[11] Olowson, P.A. and Almstedt, A.E., 1990, Inf luence ofpressure and f luidization velocity on the bubble behav-iour and gas f low distribution in a f luidized bed, ChemEng Science, 45, 1733-1741
[12] Rowe, P.N., Foscolo, P.U., Hoffmann, A.C. and Yates,J.G., 1982, Fine powders f luidized at low velocity atpressures up to 20 bar with gases of different viscosity,Chem Eng Science, 37, 167-174
[13] Barreto, G.F., Yates, J.G. and Rowe, P.N., 1983, Theeffect of pressure on the f low of gas in f luidized bedsof fine particles, Chem Eng Science, 38, 1935-1945
[14] Yates, J.G., Cheesman, D.J. and Sergeev, Y.A., 1994,Experimental observations of voidage distributionaround bubbles in a f luidized bed, Chem Eng Science,49, 1885-1895
[15] Bracewell, R.N., 1986, The Fourier Transform and itsApplications, McGraw-Hill, Singapore
[16] Lettieri, P., Newton, D. and Yates, J.G., 2001, high tem-
KONA No.20 (2002) 141
perature effects on the dense phase properties of gasf luidized beds, Powder Technology, 120, 34-40
[17] Geldart, D. and Wong, A.C.Y., 1985, Fluidization ofpowders showing degrees of cohesiveness II Experi-ments on rates of de-aeration, Chem Eng Science, 40,653-661
[18] Chen, L. and Weinstein, H., 1994, Measurement ofnormal stress and hindrance factor in a collapsingf luidized bed, Chem Eng Science, 49, 811-819
[19] Feindt, H.J., 1990, Radial and axial density f luctuationsin a high velocity f luidized bed. PhD Thesis, The CityUniversity of New York, New York
[20] Rowe, P.N., MacGillivray, H.J. and Cheesman, D.J.,1979, Gas discharge from an orifice into a gas f luidizedbed, Trans IChemE, 57, 194-199
[21] Chen, L. and Weinstein, H., 1993, Shape and extent ofthe void formed by a horizontal jet in a f luidized bed,AIChE Journal, 39, 1901-1909
[22] Weinstein, H., Cao, C., Mangado, K.B., Mohraz, A.,Graff, R.A. and Koelle, P., 2001, Time resolution of atransient event in a gas f luidized bed, “Fluidization X”,Kwauk, M., Li, J. and Yang, W-C. (Eds), United Engi-neering foundation, New York, 293-300
[23] Yates, J.G. and Cheesman, D.J. 1987, Unpublishedresults
[24] Yates, J.G., 1996, Effects of temperature and pressureon gas-solid f luidization, Chem Eng Science, 51, 167-205
[25] Newton, D., Smith, G.B. and Gamblin, B., 1997, Jetpenetrations and gas entry effects from large scalemultiple orifices into f luidized beds of fine powders,Proceedings 2nd European Conference on Fluidization,Bilbao, Spain, 83-90
[26] Zenz, F.A., 1968, Bubble formation and grid design,IChemE Symposium Series, 30, 136-139
[27] Yerushalmi, J. and Avidan, A., 1985, Chapter 7 “HighVelocity Fluidization” in “Fluidization”, Davidson, J.F.,Clift, R. and Harrison, D. (Eds), Academic Press, Lon-don
[28] Yerushalmi, J., Turner, D.H. and Squires, A.M., 1976,The fast f luidized bed, I&EC Proc Des Dev, 15, 47-52
[29] Kehoe, P.W.K. and Davidson, J.F., 1971, Continuouslyslugging f luidized beds, IChemE Symposium Series,33, 97-101
[30] Weinstein, H. Shao, M., Schnitzlein, M. and Graff,
R.A., 1986, Radial variation in void fraction in a fastf luidized bed, “Fluidization V”, Østergaard, K. andSørensen, A. (Eds), Engineering Foundation, NewYork, 329-336
[31] Weinstein, H., Feindt, H.J., Chen, L. and Graff, R.A.,1989, the measurement of turbulence quantities in ahigh velocity f luidized bed, “Fluidization VII”, Potter,O.E. and Nicklin, D.J. (Eds), Engineering Foundation,New York, 305-309
[32] Weinstein, H., Feindt, H.J., Chen, L. and Graff, R.A.,1995, Riser gas feed nozzle configuration effects on theacceleration and distribution of solids, “FluidizationVIII”, Large, J-F. and Laguerie, C. (Eds), EngineeringFoundation, New York, 263-270
[33] Kostazos, A.E., Weinstein, H. and Graff, R.A., 1998,The effect of the location of gas injection on the distri-bution of gas and catalyst in a riser, “Fluidization IX”,Fan, L-S. and Knowlton, T.M. (Eds), EngineeringFoundation, New York, 221-228
[34] Kostazos, A.E. and Weinstein, H. 1997, A detailedexperimental description of the f low in the entrancesection of a f luidized catalytic cracking unit, AIChESymposium Series, 93(317), 36-39
[35] Cao, C. and Weinstein, H., 2000, Characterization ofdownf lowing high velocity f luidized beds, AIChE Jour-nal, 46, 515-522
[36] Cao, C. and Weinstein, H., 2000, Gas dispersion indownf lowing high velocity f luidized beds, ibid 523-528
[37] Fan, L-S., 1989, “Gas-Liquid-Solid Fluidization Engi-neering”, Butterworths, London
[38] Deckwer, W-D., Louisi, Y., Zaidi, A. and Ralek, M.,1980, Hydrodynamic properties of the Fischer-Trop-sch slurry process, I&EC Proc Des Dev, 19, 699-708
[39] Smith, G.B., Gamblin, B.R. and Newton, D., 1995, X-rayimaging of slurry bubble column reactors, TransIChemE, 73(A), 632-636
[40] Yates, J.G. and Simons, S.J.R., 1994, Experimentalmethods in f luidization research, Int J MultiphaseFlow, 20(Suppl), 297-330
[41] Lettieri, P., Micale, G.D.M., Cammerata, L. and Cole-man, D., 2002, Computational Fluid dynamics simula-tions of gas-f luidized beds; a preliminary investigationof different modelling approaches, Proc 10th Workshopon Two-Phase Flow Predictions, Sommerfeld, M. (Ed),Mersberg, Germany, April 9-12, 300-309
142 KONA No.20 (2002)
KONA No.20 (2002) 143
Author’s short biography
John Yates
John Yates is Ramsay Memorial Professor and Head of the Department of Chemi-cal Engineering at University College London. He trained as a chemist andreceived a BSc as an external student of London University in 1959. He then didresearch in the Department of Chemical Engineering at Imperial College and wasawarded the PhD in 1963. Two years at BP research centre at Sunbury-on-Thameswere followed by a move to UCL in 1964 as a Lecturer. He became a Senior Lec-turer in 1976, a Reader in 1984 and a Professor in 1990. His research area is “f lu-idization” in which he has published a monograph and over 120 papers. He is aFellow of the Institution of Chemical Engineers and of the Royal Society of Chem-istry. He became a Fellow of the Royal Academy of Engineering in 1999.
David Cheesman
David Cheesman is an Experimental Officer in the Department of Chemical Engi-neering at University College London. He has been involved in f luidizationresearch for almost 30 years with a special interest in the X-ray analysis of f luidizedbed systems. He is co-author of over 35 publications in the area.
Paola Lettieri
Paola Lettieri is a Research Fellow of the Royal Academy of Engineering, the firstwoman Engineer to win one of The Academy’s Research Fellowships. She joinedthe Department of Chemical Engineering at UCL in January 2001, after 5 yearsemployment at BP Chemicals, Sunbury-on-Thames. She originally qualified inMechanical Engineering from the University of Rome, and then obtained a PhD in Chemical Engineering at UCL. Her research activities to date have covered a vari-ety of f luidization aspects including experimentation, theoretical modelling andcomputational f luid-dynamics (CFD) simulations, with emphasis on the effect ofprocess conditions on the operation of gas f luidized beds.
David Newton
David Newton is a Research Associate in Fluidization with BP Chemicals. He hasbeen involved since its inception in developing and applying X-ray imaging tech-niques to large-scale f luidized beds for both oil and chemicals applications. He haspublished over fifty papers on X-ray imaging of f luidized beds, f luid catalytic crack-ing (FCC) and other processes. The principle areas of research have included thestudy of commercial scale f luidized bed processes such as FCC, Gas-phase Poly-ethylene, Acrylonitrile, Polymer Cracking ,Vinyl Acetate and Gas-to-Liquids Tech-nology. He has been with BP for eighteen years. He is the current Chairman of thePICNAC Group.
144 KONA No.20 (2002)
Introduction
Mechanochemical synthesis and mechanical alloy-ing are in wide use as experimental methods forthe production of highly dispersed powders andnanocomposites. Using mechanical activation we havemanaged to prepare nanocomposites in immisciblesystems such as Cu-Bi, Fe-Bi, Fe-In. It is possible toget supersaturated solid solutions in many other inter-metallic systems (Cu-Ga, Cu-In, Cu-Sn, Ni-In, Ni-Bi,Ni-Sn, Ni-Ge, Ni-Al) [1, 2]. However, from a techno-logical point of view, mechanical activation poses alot of problems which cannot be easily solved. Thebiggest problem is the low productivity of the tech-niques currently available, as well as the contami-nation of the end products caused by abrasion ofthe grinding media. The energy consumption shouldalso be taken into consideration in some large-scaleprocesses.
One of the alternatives to mechanochemistrymay be self-propagating high-temperature synthesis(SHS), which is energy-saving and can be applied tothe large-scale production of many intermetallic com-pounds or complex oxides (nitrides, carbides) [3].Nevertheless, this method includes a combustionstage which requires very high temperatures. As a
result, final products can be obtained only in the formof dense sintered or solidified products when SHSexceeds the melting point of reagents and/or prod-ucts. To transform such products into commerciallyinteresting powders, one needs to use milling as anunavoidable step. The grinding leads to further con-tamination and to additional energy consumption,which may be comparable with that required for themechanochemical synthesis itself.
Another disadvantage of SHS is a relatively hightemperature gradient near the combustion surfacewhich leads to a non-uniform phase composition ofthe obtained products.
The shortcomings of these two methods can beovercome, and their advantages can be extended.This allows one to obtain the final products of re-quired phase composition and disperse state, thusenabling the development of a new energy-saving andwaste-free technology.
Experimental
The materials used in the investigation were: car-bonyl nickel and iron, powdered aluminum, silicon,germanium, tungsten, molybdenum, titanium, and zir-conium, pure gallium, barium peroxide, tungsten andmolybdenum oxides.
A ball planetary mill AGO-2 [4] was used for theinvestigations. The volume of the mill drums was
T. Grigorieva, M. Korchagin and N. LyakhovInstitute of Solid State Chemistry*
Combination of SHS and Mechanochemical Synthesis for Nanopowder Technologies†
Abstract
The combination of mechanochemical activation and self-propagating high-temperature synthesis(SHS) have widened the possibilities for both methods. For metallic systems, the investigationshowed that a short-term mechanochemical activation of heterophase SHS products leads to single-phase and ultrafine intermetallides obtained from the elements by mechanical alloying. It wasdemonstrated that metastable phases, usually obtained by mechanical alloying, can be obtained fromthe equilibrium intermetallic compounds synthesized by SHS. Besides this, the investigations showedthat preliminary mechanical activation, during which layered composites are formed from the ini-tial elements, allows one to extend the concentration limits of SHS processes up to a solid solutionregion.
The preliminary mechanical activation also allows production of single-phase ultrafine complexoxides.
* 18. Kytateladec Str., 630128 Novosibirsk, Russia† Accepted: June 28, 2002
250 cm3, the ball diameter was 5 mm, the ball loadwas 200 g and the weighed portion of powder treatedwas 10 g. In order to avoid oxidation of the metals, allthe experiments on mechanical alloying were carriedout in an argon atmosphere. The X-ray phase analysiswas performed with a DRON-3M diffractometer withCuKα radiation.
IR absorption spectra were recorded with aSPECORD 75 IR spectrometer.
Electron microscopic studies were carried outusing the JSM-T20 electron microscope and the high-resolution electron microscopes JEM-2010 and JEM-400.
The extent of aluminum recovery from intermetal-lic compounds was calculated as the ratio of theamount of hydrogen evolved in the reaction of sam-ples with a 20% κOH solution to the amount of hy-drogen that should be evolved in case of completedissolution of the aluminum present in the sample.The amount of the evolved hydrogen was recordedautomatically with a DAGV-70-2M volumeter.
1. Mechanochemical activation of SHS products in metal systems
1.1 Homogenizing effect of MAUltrafine single-phase intermetallic compounds are
widely used in powder metallurgy for making heat-resistant materials, materials with a high corrosionstability and special magnetic properties. Single-phase intermetallic compounds are usually obtainedby fusing or sintering followed by homogenizing andannealing for a long time [5]. The major disadvan-tages of these processes are deviations in the compo-sition of the mixture in the case of high melting pointsof the initial components because of evaporation ofthe lower melting point ingredients. As a result, along time interval is necessary for the process, andhigh energy consumption at the stage of homogeniz-ing and annealing. Besides this, most of the powderintermetallides are obtained by grinding for a ratherlong time, which usually leads to substantial contami-nation caused by abrasion of the grinding media. Insuch cases, additional purification is required.
For metal systems with high enthalpies of the inter-metallide formation, the SHS method can be applied;heterophase SHS products can be homogenized dur-ing mechanochemical activation at a simultaneoussubstantial decrease of the particle size, which shouldfinally lead to finely dispersed material with a highstructural defect content. This material is similar inits properties to that obtained by mechanical alloying
of the elements; however, the time for mechanicaltreatment in the former case is several decadesshorter.
Phase formation and morphological changes wereinvestigated for the mechanochemical synthesis ofintermetallides from elements and for the mechano-chemical activation of heterophase products of theSHS process. For comparison purposes, systemswere considered for which it is known that the SHSprocess can be performed, but the products of thissynthesis are substantially different in phase compo-sition: – Ni-Al within the concentration region of NiAl phase
existence. It is known that this phase can be ob-tained by SHS [3];
– Ni-Si, in which the SHS process is possible [6], butit is difficult to achieve single-phase compositionduring SHS synthesis;
– Ni-Ge in the NiGe intermetallide homogeneityregion. Due to the rather high melting point of Ni(1455°C) and the rather low temperature of NiGeintermetallide decomposition (850°C), the homo-geneity region is very narrow for this compound. The X-ray investigation of the mechanical alloying
of an NiAl intermetallide from a mixture of metal pow-ders of the composition Ni 32 wt.% Al demonstratedthat the synthesis started after mechanical activationfor about 2.53 minutes. First, the Ni2Al3 intermetal-lide forms. Some amounts of unreacted nickel andaluminum still remain (Fig. 1a). After activation for57 min., the amount of the formed Ni2Al3 phasestarts to decrease and the ref lections of the NiAlintermetallide increase (Fig. 1b). Then, the Ni2Al3
intermetallide disappears, the nickel and aluminumcontents decrease gradually and the intensities ofNiAl ref lections increase. After mechanochemical
KONA No.20 (2002) 145
Fig. 1 X-ray patterns of Ni 32 wt.% Al mixture after mechanicalactivation during 3 (a), 7 (b), 25 min. (c).
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c
b
a
Ni
NiAlNiAl
NiAl
Ni
Al
Al
Al
Ni2Al3
degree
Ni2Al3
activation for 2530 min., very broad ref lections onlyof the NiAl phase are present in the X-ray diffractionpatterns (Fig. 1c). The coherent scattering domainsfor this product are 810 nm.
The electron microscopic investigation of the prod-ucts of the mechanical alloying of NiAl-based solidsolutions in a ball mill demonstrated that after activa-tion for 30 s, the initial nickel and aluminum particlescould not be detected in the sample. The productsconsist of agglomerates of various shapes and sizes.An increase of the activation time to 1 min. leads to anincrease of the fraction of coarse agglomerates whichattain a plate-like shape as their density increases.Figure 2a shows a microphotograph of the cross sec-tion of the agglomerate, clearly exhibiting its layeredstructure. A further increase to the time of mechani-cal alloying causes a drastic change to the morphol-ogy of the product particles. The destruction of largelayered agglomerates starts after mechanical alloyingfor 3 min.; whereas they disappear completely after 5
min. of alloying. The major part of the samples by thistime is composed of rather dense agglomerates ofirregular shape with a size of 210 µm. Larger parti-cles (up to 50 µm) are also present. These agglomer-ates are composed of the layered particles 15 µm insize. It should be noted that according to XRD data, itis the mechanical alloying for 3 min. that causes theappearance of the Ni2Al3 intermetallide in the prod-ucts, which is likely to be the reason of the significantchange of the particle morphology. An increase inthe time of mechanical alloying brings insignificantchanges to the morphology of the formed products.The fine fraction (15 µm) content increases, thedensity of the formed particles increases (Fig. 2b).
The SHS of a metal powder mixture comprisingNi 32 wt.% Al results in the NiAl intermetallide withadmixture of the Ni2Al3 phase; judging from the widthof diffraction peaks, the formed products are wellcrystallized. Electron microscopic studies showedthat the intermetallides were most likely crystallized
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Fig. 2 Microphotograph of a cross section cleavage of the lay-ered composite of the system of Ni 32 wt.% Al aftermechanical activation for 30 s (a), 25 min. (b).
10 µm
10 µma
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Fig. 3 Microphotograph of the SHS product in the system Ni 32wt.% Al (a), the same product after mechanical activationfor 1.5 min.
10 µm
50 µm
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b
from the melt (Fig. 3a).Mechanochemical activation of SHS products for
1.5 min. results in a material similar in morphology,particle size and coherent scattering domain to thematerial obtained by the mechanical alloying of nickeland aluminum powders for 25 min. This means that ashort-time mechanochemical activation of a mixtureof phases obtained by the SHS process in this systemallows preparation of an ultra-fine single-phase inter-metallic product (Fig. 3b). Similar products wereobserved for the Ni-Si system (Fig. 4).
X-ray analysis showed that a significant amount ofthe Ni3Si2 phase can be found in the products of themechanical alloying of an NiSi mixture correspond-ing to an Ni5Si2 intermetallic compound.
The X-ray diffraction investigation of the mechani-cal alloying of nickel and germanium at the ratio of Ni55 wt.% Ge demonstrated that formation of the NiGeintermetallide starts within the first minute (Fig. 5a);a drastic increase in the intensity of the ref lectionsfrom this phase starts after mechanical activation for67 minutes (Fig. 5b); the maximum is achievedafter 25 minutes of mechanical treatment (Fig. 5c).However, an admixture of the second phase (Ni5Ge2)appears during mechanochemical synthesis of theNiGe intermetallide; at first, the content of the secondphase increases, then decreases and disappears com-pletely after 1213 minutes of mechanical alloying.By the end of the process (2530 minutes) there isonly one phase, which is the NiGe intermetallide,with a coherent scattering domain of 58 nm.
According to the data of the electron microscopicinvestigation, mechanical alloying in the mixture of astoichiometric composition NiGe for 40 s results inthe formation of rounded three-dimensional agglom-erates with a maximal size of up to 400 µm, originat-ing from particles of 0.21 µm in diameter. Besidesthis, separate particles of 0.21 µm in diameter arepresent; their number is rather large. An increase ofthe mechanical alloying time for this system to 57minutes leads to the formation of very dense agglom-erates; traces of a strong plastic deformation aresometimes observed on their surface. However, inthis case the amount of separate fine particles is alsorather large. A further increase of the mechanicalalloying time to 30 min. has practically no effect onthe morphology and size of the resulting particles; itis only the fraction of coarse agglomerates whichincreases. The final product of mechanochemical syn-thesis NiGe is composed of rather dense particleswith a size of 0.52 µm; they sometimes form larger
agglomerates. An SHS process was carried out in a mixture of this
composition. According to XRD data, it is mainly the
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Fig. 4 Microphotograph of the SHS product in the system of Ni16 wt.% Si (a), the product of mechanical alloying in thissystem for 10 min. (b).
100 µm
100 µm
a
b
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c
b
aGe
θ, degree
NiGe
NiGe
NiGeNiGe
NiGe
NiNi
Ge
Fig. 5 X-ray patterns of Ni 55 wt.% Ge mixture after mechanicalactivation during 1 (a), 7 (b), 25 min. (c).
equilibrium well-crystallized NiGe which forms, withan admixture of a second intermetallide (Ni5Ge2)(Fig. 6a). One can see from microphotographs thatthe final products are formed from the melt (Fig. 7a),which means that the SHS proceeds via the liquidphase.
The X-ray diffraction investigations of the mechano-chemical treatment of the SHS products demonstratethat a broadening of the diffraction patterns startsafter mechanical activation for 30 s. Phase homoge-nization of the system (NiGe) is achieved after 1.52minutes (Fig. 6b). After mechanical activation for3 min., the material exhibits a coherent scatteringdomain of 810 nm. Further mechanical activationleads to some narrowing of the peaks. According tothe electron microscopic data, after mechanical ac-tivation of the SHS products for 30 s, the major part ofthe sample is composed of fine particles of irregularshapes, their size being 0.23 µm (Fig. 7b). Largerparticles are still present, though they rarely occurin this case. A sintered agglomerate of fine particlesstarts to form. An increase of the treatment timecauses an intensive formation of such agglomerates.Their density increases gradually. Traces of substan-tial plastic deformation are observed on the surface ofsome of these agglomerates. After mechanical activa-tion for 3 min., the sample consists of agglomerates ofdifferent density and shape, their size being 1 to 400µm.
Similar results were obtained for the Ni-Si system(Fig. 4a, 4b).
The investigation of the metallic systems showedthat a short-term mechanochemical activation of het-erophase SHS products leads to single-phase andultrafine intermetallides obtained from the elementsby mechanical alloying.
1.2 Formation of non-equilibrium phases byactivation of SHS products
It is known that it is practically impossible to obtainnon-equilibrium intermetallic compounds by SHS;however, highly reactive intermetallic compounds(which is exactly what metastable phases usually are)are used in hydrogen energetics, in preparation ofRaney catalysts, metal cements, diffusion-hardeningsolder, metal dental materials, etc. Mechanochemicalsynthesis and mechanical activation are among themost efficient methods to obtain metastable phases inmetal systems; it is known that a series of equilibriumintermetallic compounds can be transferred into non-equilibrium concentration regions by means of me-chanical activation.
A comparative investigation of phase and micro-structural transformations during the mechanochemi-cal synthesis of non-equilibrium solid solutions fromthe elements and during mechanical activation of
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Fig. 7 Microphotograph of the SHS product in the system Ni 55wt.% Ge (a), the same product after mechanical activationfor 2 min.
50 µm
10 µm
a
b
Fig. 6 X-ray patterns of the SHS product in the system Ni 55 wt.%Ge (a), the same product after mechanical activation for 2min.
38 36 34 32 30 28 26 24 22 20 18 16 14θ, degree
NiGe NiGeNiGe
NiGeNiGe
NiGeNiGe
NiGe
Ni5Ge2
Ni5Ge2
Ni5Ge2
NiGe
equilibrium intermetallic compounds obtained bySHS was carried out.
The Ni-Al system was selected for investigation,because it is known that the SHS process in the Ni-Alsystem can be carried out within a broad concentra-tion range [3]. The limit solubility of aluminum innickel ranges from 3.85 wt.% at 500°C to 10.3 wt.% at1385°C. The structural similarity of the Ni3Al inter-metallide (cubic lattice of the Cu3Au type) and β-nickel makes it possible to mechanochemically passfrom the intermetallide to the non-equilibrium solidsolution [7]. The structure of the Ni2Al3 intermetal-lide (40.8 wt.% Al) is close to that of NiAl. Aluminumatoms form distorted cubes in the rhombohedral lat-tice of Ni2Al3. Two-thirds of the positions in the cen-tres of cubes are occupied by nickel atoms, the otherpositions are vacant. Disordering of these vacanciesshould lead to the formation of a supersaturated solidsolution with a non-equilibrium concentration of va-cancies.
The X-ray and electron microscopic studies of themechanical alloying in a mixture of nickel and alu-minum powders at a ratio of Ni 40.8 wt.% Al (calcu-lated for the formation of the Ni2Al3 intermetallide)showed that the process is largely similar to themechanical alloying of the Ni 32 wt.% Al mixture. Atfirst, the Ni2Al3 intermetallide is formed; during fur-ther activation it is transformed into the supersatu-rated solid solution with a non-equilibrium concentra-tion of vacancies based on the intermetallic compoundNiAl. After mechanical activation for 30 minutes, thesize of its coherent scattering domains is around 8to10 nm.
The X-ray diffraction patterns of the product of theSHS process in the Ni 40.8 wt.% Al mixture exhibit theformation of a well-crystallized Ni2Al3 intermetallide(Fig. 8a). Mechanochemical activation of this prod-uct for 2 min., under the same conditions as thoseunder which mechanical alloying was carried out,gives the diffraction patterns corresponding to thematerial obtained by mechanical alloying after 2530minutes (Fig. 8b), which has been mentioned aboveto be a supersaturated solid solution with a non-equi-librium concentration of vacancies based on the NiAlintermetallide. Further mechanical activation doesnot bring any substantial changes.
Electron microscopic investigations showed thatthe formed porous fused SHS product (Fig. 9a) canbe transformed mechanochemically within 2 min. intoa product which is morphologically very similar tothat formed at the final stage of mechanical alloying(Fig. 9b).
Metastable phases obtained by mechanical alloyingand by mechanical activation of the SHS productshave approximately equal reactivity.
For the example of a well-studied aluminum leach-
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Fig. 8 X-ray patterns of the SHS product in the system Ni 40.8wt.% Al (a), the same product after mechanical activationfor 3 min.
36 34 32 30 28 26 24 22 20 18 16 14
Fig. 9 Microphotograph of the SHS product in the system Ni40.8 wt.% Al (a), the product of mechanical alloying in thissystem for 25 min. (b).
10 µm
100 µm
a
b
NiAl
b
a Ni2Al3
Ni2Al3 Ni2Al3
NiAl
NiAl
NiAl
θ, degree
ing reaction, it was stated that non-equilibrium solidsolutions based on NiAl, which were synthesized bymechanical alloying from metal powders within theconcentration range of the Ni2Al3 intermetallide andactivated for 1 min., exhibit a very high reactivity(Fig. 10). These samples exhibit similar dynamicsto hydrogen evolution in leaching. This is one moreconfirmation of the fact that the formed metastablephases are identical. This means that the non-equilib-rium solid solutions based on the NiAl intermetallide,with largely similar structure, particle morphology,coherent scattering domains, and reactivity can beobtained both by the mechanical alloying of the initialpowders of the composition Ni 40.8 wt.% Al, and alsoby short-time mechanical activation of the Ni2Al3
intermetallide obtained by SHS. An important fact!The X-ray diffraction studies of the mechanical al-
loying of the Ni 13.5 wt.% Al composition (the concen-tration region of equilibrium Ni3Al intermetallide)showed that a broadening and a slight decrease of theintensity of diffraction peaks related to metals occurwithin the first two minutes of activation. Diffractionref lections of the Ni2Al3 intermetallide appear after2.5 minutes of mechanical treatment. The intensity ofaluminum peaks decreases drastically while the inten-sity of Ni ref lections decreases slowly. The Ni latticeparameter remains unchanged. Only after mechanicalactivation for 5 min. do the diffraction patterns ofaluminum disappear completely. The diffraction re-f lections of nickel broaden substantially (which isespecially noticeable in the large-angle region). Itslattice parameter increases (Fig. 11a), which is evi-dence of the incipient formation of a nickel-based
solid solution. After 15 minutes of activation, the lat-tice parameter of the solid solution reaches its maxi-mum a0.3590 nm. The coherent scattering domainof the resulting solid solution is 810 nm. Furthermechanical activation causes a narrowing of the dif-fraction peaks. The formation of the Ni3Al phase,which is characteristic in this concentration range,was not detected at any stage of activation.
Electron microscopic investigations of the productsof mechanical alloying in the mixture Ni 13.5 wt.% Alshowed that the dynamics of particle morphologychanges at the initial stages of the process is verysimilar to that observed for the composition Ni 32wt.% Al. The formation of layered composites wasobserved, too. However, in this case they start toform as early as after only 30 s of mechanical alloying,which is much earlier than for the Ni 32 wt.% Al com-position. The particles of the initial components areno longer detected at this moment. A substantial partof the resulting agglomerates look like plate-shapedparticles with traces of strong plastic deformation ontheir surface. Relatively sintered and round-shapedagglomerates are also present. The maximal size ofthe plate-like agglomerates is 12 mm, while therounded ones are between 12 and 4050 µm insize. An increase of the mechanical treatment time to15 min. leads to a decrease of the fraction of thesmallest and the largest particles; they become moredense and uniform in size, almost monolithic.
A product of SHS in the mixture Ni 13.5 wt.% Al isan Ni3Al intermetallide. Diffraction patterns are evi-dence of a high order in the structure of the formedphase (Fig. 11b). Mechanical activation of the SHSproduct for only 30 s results in a significant decrease
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Fig. 10 Curves of leaching of the SHS product in the system Ni40.8 wt.% Al (a), of the product of mechanical alloying inthis system for 25 min. (b), of the SHS product after 1min. activation (c).
0
5
10
15
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25
30
35A, %
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Time, min
abc
36 32 28 24 20 16
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b
c
Fig. 11 X-ray patterns of Ni 13 wt.% Al samples: obtained from ametal powder mixture by mechanical alloying for 15 min.(a), obtained by SHS (b), the SHS product after mechani-cal activation during 1 min. (c).
of the intensity of diffraction peaks and to their sub-stantial broadening. After 1.5 min., a non-equilibriumsolid solution of aluminum in nickel is formed. Its lat-tice parameters are identical to those of the productformed in a mixture of initial powders mechanicallyalloyed for 15 min. (Fig. 11c). Further activation ofthis SHS product causes no change in diffraction pat-terns.
It was stated in electron microscopic studies thatthe particle size decreases sharply at the very firststages of the mechanical treatment of SHS products.After mechanical activation for 1.5 min., the productparticles are practically identical in size and morphol-ogy to the products obtained from the initial Ni and Alpowders after mechanical alloying for 15 min.
The investigation demonstrated that metastablephases, usually produced by mechanical alloying, canbe obtained from the equilibrium intermetallic com-pounds synthesized by SHS.
Short-term activation following the SHS processtherefore allows one to homogenize intermetallicphases and to obtain metastable structures. The finalproducts are formed in the ultrafine state with mini-mal contamination caused by abrasion of millingtools.
This approach can also be used in the SHS synthe-sis of complex oxides, nitrides, borides, and carbides,etc. However, for this method of preparing ultrafinepowders, the range of compounds is limited by thepossibilities of the SHS method, i.e. involved are sys-tems with very high temperatures of the final productformation.
2. The effect of preliminary activation on SHSprocess
2.1 Metal systemsA high exothermal effect of reaction and a strong
Arrhenius-type temperature dependence of the reac-tion rate are of decisive importance for the feasibilityof SHS processes. For diffusion-controlled processes,to which SHS processes also belong, another impor-tant parameter is the disperse state of the initial com-ponents, including the uniformity of their mixing andthe surface area of contacts between the components.Mechanical alloying is known as a process whichleads to the formation of layered mechanocompositesformed at the initial stage of the mechanical activationof metal mixtures (see Fig. 2a). Most metals exhibitgood plasticity; under mechanical action in ball plane-tary mills where shock and shock-with-shear occur[8], the metal undergoes plastic deformation resulting
in a change to the shape of the metal particles. Theyf latten, adsorption films on their surface are de-stroyed; components come into contact with eachother by atomic-pure planes [9]. ‹‹Point›› contacts ofinitial particles transform into f lat ones, while the con-tact area increases considerably [10]. As a result, ashort-term preliminary activation can extend the pos-sibilities of reaction in a self-propagating regime evenfor systems where the SHS process cannot be carriedout without preliminary heating.
In order to establish the lower limit of the condi-tions for the SHS process to occur with mechanicalactivation involved, we investigated the Ni-Al, Ni-Si,Ni-Ge systems, which are SHS systems and for whichthe lower concentration limits for silicon and alu-minum in SHS without preliminary mechanical activa-tion are known [11]. In the Ni-Al system, the limitingsolid-phase solubility of aluminum in nickel is 10.3wt.% at 1385°C and decreases to 3.85 wt.% at 500°C,but SHS cannot be performed in this concentrationrange. The minimal aluminum concentration at whichSHS can be performed by the traditional method is 13wt.% Al [3].
Preliminary mechanical activation in the Ni-Al sys-tem allows one to decrease the minimal content of Alin the initial mixture for the SHS process. This mini-mal Al content is 7 wt.%. We succeeded in performingSHS in the sample compacted from the powder aftermechanochemical treatment. The Ni3Al, Ni2Al3 inter-metallides and unreacted nickel were detected in thesynthesis products. Subsequent mechanochemicalactivation homogenizes the product and leads to theformation of a solid solution only.
In the Ni-Si system, similarly to the Ni-Al system,the concentration range of the solid solution isstrongly dependent on temperature; at room tempera-ture, the solubility of silicon in nickel is 5 wt.%,while at 1150°C it is 9.3 wt.% [12, 13]. It is not pos-sible to realize an SHS process in the solid solutionrange without preliminary mechanical activation inthis system.
Our investigations showed that in the solid solutionrange, the layered composites of nickel and siliconcould be formed under activation within 1 min.,though they do not look so dense as in the Ni-Al sys-tem. The SHS process was also performed in thesemixtures containing 9 wt.% Si, the products being amixture of the Ni2Si, Ni5Si2 intermetallides and unre-acted nickel. Similarly to the case of the Ni-Al system,subsequent mechanical activation results in a single-phase product which is a supersaturated solid solu-tion.
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In the Ni-Ge system, in which the limiting solubilityof germanium in nickel is 13.8 wt.% [5, 14], we investi-gated the possibility of performing SHS also in thesolid solution concentration range. Composites areformed in a Ni 13 wt.% Ge mixture after mechanicalactivation for 1.5 min. The Ni5Ge2 and NiGe intermet-allides and unreacted nickel are the products of SHS.The formation of a single-phase solid solution is a-chieved by a subsequent short-term activation.
The investigations therefore showed that prelimi-nary mechanical activation, during which layeredcomposites are formed from the initial elements, al-lows one to broaden the concentration limits of SHSprocesses up to the solid solution region, perhaps dueto reagent dispersion and an increase of contact area.The products of this synthesis are mixtures of in-termetallides, the doping elements being completelyconsumed for their formation, and an excess of sol-vent metal. The conservation of the layered structurein SHS products allows us to assume that intermetal-lic compounds are formed locally inside the layeredstructure, its framework being built of solvent metal.
Using the discovered effect of preliminary mechani-cal activation on the possibility of performing SHSeven in the concentration range of solid solutions, wetested it in the systems in which SHS cannot be per-formed without preliminary heating of the reactionmixture even in the range of intermetallide existence[3]. As an example, Figure 12 shows the combustionrate and the maximum combustion temperature plot-ted versus time of the preliminary mechanical activa-tion for the Ni 45 wt.% Ti composition. The samplesstart burning at room temperature after 2.5 min. ofmechanical activation. Similarly to all the systemsconsidered above, an increase of the burning rate isconnected to the formation of dense layered compos-ites. A photograph of the sample after mechanicalactivation for 2.5 min. is shown in Figure 13. Increas-ing the time of mechanical activation also leads to afurther increase of the density of the composites, adecrease of the grain size to 0.1 µm, and to theappearance of particles with traces of strong plasticdeformation on the surface. The decrease of the com-bustion rate is connected to the start of destruction ofthe largest composites. Only NiTi (the main phase)and Ti2Ni lines are observed in the diffraction pat-terns of the SHS products at any time of mechanicalactivation. No titanium or nickel lines are observed!The relative content of these phases in the productsremains practically independent of the time of me-chanical activation.
2.2 Oxide systemsThe synthesis of nanocrystalline mixed oxides is
among the major problems of advanced ceramic tech-nology. Conventional processes for manufacturingmulti component mixed-oxide ceramics involve high-temperature reactions between metal oxides orbetween metal oxides and carbonates. These diffu-sion-controlled processes require the application ofhigh temperatures and the use of highly dispersedprecursor powders; mixed oxides are formed in parti-cles of 1 to 5 µm in size. Mechanochemical alloyingpartly removes the diffusion control. The consider-
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0
0,5
1
1,5
2
2,5
3
1,5 2 2,5 3 3,5 4 4,5Time of MA, min
Uc, mm/sec
400
500
600
700
800
900
1000
T, C
Fig. 13 Microphotograph of a Ni 45 wt.% Ti sample after mechani-cal activation for 2.5 min.
Fig. 12 Dependence of the combustion rate (Uc) and combustiontemperature of the Ni 45 wt.% Ti mixture on the time ofpreliminary mechanical activation.
10 µm
able heat of the chemical reaction provides the highrate of the mechanochemical reaction. For example,for most reactions of mechanochemically assistedmetal oxidation in a gaseous phase, the oxidation ratecorrelates with variations in Gibbs’ free energy [15].For the exothermal reactions, the mechanochemicalreaction rate of solid solution formation is a functionof the enthalpy of formation of intermetallic com-pounds in equilibrium [16]. Therefore, if reactionswith small decreases in Gibbs’ free energy are used inthermodynamically controlled mechanochemical syn-thesis, a large power supply and a long mechanicalactivation time would be necessary, by analogy withmechanochemical synthesis of mixed oxides frombinary oxides, either alone or mixed with carbonates[17]. Efficient mechanochemical synthesis is notfeasible unless in energy-intensive activators (steeldrums and steel balls), and contamination of the prod-uct is inevitable. Therefore, mechanochemistry isalmost useless for commercial ceramic processeswith their extremely high purity requirements. Themechanochemical approach becomes practicable onlywith high rates of promoted reactions, i.e., those thatare not only thermodynamically allowed, but that alsogive an energy gain. High rates of mechanochemicalprocesses result in final products which are highlydispersed, and this can significantly inf luence theproperties of the resultant ceramics.
The change of Gibbs’ energy in the synthesis ofcomplex oxides from simple ones shows that all thesereactions are thermodynamically allowed, while themajority of reactions with the participation of car-bonates are available only at high temperatures(Table 1).
Some of these reactions were performed mechano-chemically when a sufficient amount of energy wasapplied [17]. All the values obtained for the systemsunder consideration are approximately of the same
order of magnitude, so the conditions for these reac-tions to proceed should be rather similar.
The use of peroxide compounds and oxides as theinitial components of mixtures, as proposed by someauthors [17], does not bring substantial changes tothe ∆G of the reaction of complex oxide synthesis.
Among the methods to obtain oxides, the energeti-cally most profitable ones are the direct oxidation ofmetals (or metal mixtures) by oxygen (Table 2).However, in reality one can hardly perform this typeof synthesis mechanochemically due to the high plas-ticity of metals.
The most promising way seems to be the oxidationof metals by peroxide compounds, especially if wetake into account that there is a rather large class ofstable metal peroxides that can provide a couple fora proper metal to synthesize a complex oxide. In suchcases, one should keep in mind that the mechano-chemical interaction of metal peroxide with metalscan follow two routes: either with the formation ofcomplex oxides or with the formation of a mixture of
KONA No.20 (2002) 153
No. Reaction product ∆Go298 ∆Go
1273
Me′OMe′′CO3 kcal/mol
1 BaTiO3 16.3 17.7
2 BaZrO3 24.2 10.0
3 BaHfO3 21.9 13.2
4 BaMoO4 2.5 30.5
5 BaWO4 4.2 42.6
6 BaAl2O4 26.5 16.3
7 CaMoO4 9.3 44.7
8 SrMoO4 6.6 41.7
9 PbMoO4 1.6 35.6
Table 1 Changes of Gibbs’ energy in the reactions of the mixturesof metal oxides and the metal oxides with metal carbon-ates resulting in the formation of complex oxides.
Table 2 Changes of Gibbs’ energy in the oxidation of metals or metal mixtures by oxygen or barium peroxide resulting in the formation ofoxides and complex oxides.
No. Product of reaction ∆Go298 Product of reaction ∆Go
298 Product of Me ∆Go298
MeO2 kcal/mol Me′Me′′O2 kcal/mol BaO2 interaction kcal/mol
1 BaO 251.1 Ba2TiO4 231
2 TiO2 212.1 BaTiO3 373.9 BaTiO3 235
3 ZrO2 248.5 BaZrO3 402.0 BaZrO3 263
5 MoO3 159.7 BaMoO4 334.9 BaMoO4 196
6 WO3 182.6 BaWO4 364.5 BaWO4 225
7 Al2O3 378.0 BaAl2O4 556.3 BaAl2O4 390
simple ones, because both reactions are profitablefrom the thermodynamic viewpoint, and the changeof Gibbs’ energy is much higher than that for the syn-thesis from oxides and carbonates. The calculation of∆Go
298 for the BaO2 interaction with metals demon-strated that the decrease of Gibbs’ energy was largerby 3040 kcal/mol than when the products of thesame reaction would be a sum of simple oxides. Onecan assume that synthesis will proceed to the forma-tion of complex oxides.
According to X-ray diffraction data, the mechano-chemical interaction of barium peroxide with titaniumfor 5 min. results in the formation of a mixture of bar-ium titanates. The ref lections corresponding to BaO2
and Ti disappear and ref lections corresponding toBa2TiO4, BaTiO3 [18], etc. appear. No diffraction re-f lections from simple oxides of barium and titaniumare observed.
The complex oxides were obtained for the systemBaO2Me (MeZr, Al).
For the BaO2-Ti mixture, an antisymmetric absorp-tion band peaking at 700 cm1 and a very weak peakat 775 cm1 appear after 1 min. of activation. After 5min. of activation, a shoulder of the 700 cm1 bandappears at 550 cm1 (Fig. 14b). This band is assigna-ble [21-23] to ν (Ti-O) stretches in [Ti04] tetrahedraof barium titanates [23]. The positions of the peaksand the band shape do not correspond to ν (Ti-O)vibrations in various TiO2 polymorphs [22, 24].
The BaO2-Zr mixture mechanically activated for 5min. exhibits an absorption band with a peak at 550cm1 (Fig. 14c). This band can be assigned to bar-ium zirconate [21, 23].
A broad asymmetric band with a maximum at 530cm1 appears as a result of activation of a mixture ofBaO2 with aluminum (Fig. 14d). Magnesium alumi-nate exhibits a similar IR spectrum in this region [21,26, 27], and the formation of barium aluminate can beassumed in the BaO2-Al system under mechanicalactivation [28].
The electron microscopic investigation of the prod-uct of mechanochemical synthesis in a mixture ofBaO2 with Zr shows that activation for 1 min. resultsin the formation of particles of 0.31 µm in size. Theyare composed of small blocks of 612 nm in size(Fig. 15). The microdiffraction picture obtained froma separate particle also points to a developed micro-block structure. The diffraction spots are shaped asrings, which is characteristic of polydisperse materi-als, while microdiffraction from a separate block givesa point, which is evidence of the single crystal state ofthe substance. Diffraction ref lections in both electron
diffraction patterns, though somewhat broadened, arepoint ref lections, which is evidence of a rather highdegree of crystallinity of the substance formed inmechanochemical synthesis. A similar picture wasalso observed for other complex oxides, with only asmall difference in microblock size.
The investigations therefore demonstrate that themechanochemical interaction of barium peroxide with
154 KONA No.20 (2002)
Fig. 14 IR spectra of (a) an initial mixture of barium peroxidewith metals and after 1 min. mechanical activation: (b) -Ti, (c) - Zr, (d) - Al.
Fig. 15 Microphotograph of a BaZrO3 particle obtained bymechanochemical synthesis during 1 minute.
50 µm
a
b
c
d
10 9 8 7 6 5 4100 sm1
metals, which proceeds with a substantial decrease ofGibbs’ free energy, as it follows from thermodynamiccalculations, allows one to synthesize complex oxideswith nanocrystalline particles in a relatively shorttime.
The mechanochemical oxidation of metals by per-oxide compounds allows the preparation of single-phase particles of complex oxides with nanometer-sized microblocks [29-32]. However, in the case ofsome metals such as tungsten, molybdenum, and tan-talum, mechanochemical synthesis does not proceedto completion, whatever reagent ratio is taken, evenafter prolonged mechanical activation. Some part ofthe metal always remains unreacted. At the reagentsmolar ratio of BaO2:W1:1, the products are BaWO4
and Ba2WO5; unreacted W remains. At an increasedbarium peroxide content (up to 2:1), part of W alsoremains unreacted. A mixture of tungstates BaWO4,Ba2WO5 and Ba 3WO6 is formed. At the reagents ratioof 3:1, only the content of complex oxide Ba3WO6
increases. Mechanochemical activation of the mix-tures of BaO2 with Mo, the molybdates BaMoO4,Ba2Mo5 and Ba3MoO6 are formed. Similarly to thecase of tungsten, a part of molybdenum remains unre-acted.
The SHS process in these mixtures also results inthe formation of a mixture of complex oxide phases;unreacted metal remains. The preliminary mechani-cal activation of the mixture has practically no effecton the phase composition of the SHS products al-though it does increase the process rate.
For BaO2-Me (MeW, Mo, Ta) systems, it was notpossible to synthesize single-phase complex oxides,neither by mechanical activation nor by SHS.
IR spectroscopic investigations of the mechano-chemical interaction of BaO2 with WO2 showed thatthe formation of a complex oxide starts within thefirst seconds of activation. The IR spectra of the initialmixture BaO2WO2 contain one broad band at850550 cm1, without clearly exhibited maximums.It is assigned to the stretching vibrations ν (W-O)(Fig. 16a) [21]. The ν (Ba-O) band is below 400cm1. After activation for 10 s, a clear band with amaximum at 810 cm1 is observed instead of theabove-mentioned broad band; the intensity of thisnew band increases with increasing activation time(Fig. 16b, c). The similarity of the IR spectra of acti-vated mixtures to the spectra of stolzite [21] allows usto assume that the activation of the BaO2WO2 mix-ture results in the formation of BaWO4 with a spinelstructure. However, according to the IR spectroscopicdata, the mechanochemical reaction of BaO2WO2 →
BaWO4 does not proceed to completion, which is evi-denced by the presence of noticeable absorption inthe region 800500 cm1 as a shoulder of the bandwith a maximum at 810 cm1 related to ν (W-O) of thelower tungsten oxide.
According to the XRD data, a growth of the ref lec-tions from the BaWO4 phase starts at the secondminute of activation and reaches its maximum by 5minutes (Fig. 17 a, b). But, with increasing activa-tion time, the intensity of the diffraction peaks of thecomplex oxide does not increase, and the intensitiesof the peaks related to the initial tungsten oxidedo not decrease. This means that the result ofmechanochemical interaction between BaO2WO2 isa mixture of phases.
For the interaction of BaO2 with MoO2, the IR spec-tra and XRD also reveal a mixture of phases.
The relatively high temperatures of formation ofthe complex oxides in the system involving the oxida-tion of the lowest tungsten oxide with barium perox-ide allows one to perform these reactions by means ofSHS. However, pretreatment of the barium peroxideand sometimes heating of the initial mixture are nec-essary [33]. This is due to the fact that BaO2 particlesentrained in air become coated with a layer of bariumcarbonate and hydroxide. This layer prevents an SHSreaction. One can assume that a short-term prelimi-
KONA No.20 (2002) 155
a
b
c
d
14 10 6 ν102 sm1
Fig. 16 IR spectra of an initial mixture of barium peroxide withWO2 (a), after its mechanical activation for 10 s (b) and 2min. (c), of the SHS product in this mixture (d).
nary mechanochemical activation of the initial mix-ture leads to the destruction of these barrier layersand provides a substantial increase of the area of con-tact between the oxides and the barium peroxide.
An investigation of the effect of the preliminarymechanochemical activation of commercially avail-able BaO2 with WO2 showed that the maximal tem-perature and rate of SHS process are achieved afteractivation for 2 min., and the single-phase complexoxide BaWO4 is formed (Figs. 16d and 17c). A dis-advantage of the resulting substance was the largeparticle size (300500 nm) and in some places evenpartial agglomeration (Fig. 18a). Electron micro-scopic studies show that subsequent mechanicaltreatment of the product for 2 minutes in a high-energy activator of planetary type produces a materialwith a particle size of 2030 nm (Fig. 18b) withoutchanges of phase composition ( !).
Similar results were also obtained for the BaO2MoO2 system, in which the maximal rate of the SHSprocess with the formation of the complex oxideBaMoO4 is achieved after preliminary mechanicalactivation for 30 s.
The structural similarity of the higher oxide WO3
and barium tungstate BaWO4 and rather high temper-ature of the reaction BaO2WO3 → BaWO41/2 O2
(128 kJ/mol) allow us to assume that this reaction
156 KONA No.20 (2002)
Fig. 18 Microphotograph of the SHS product of a BaO2WO2 mixture (a), the same product after mechanical activation for 2 min. (b).
a b
a
b
c
28 24 20 16 12θ, degree
Fig. 17 X-ray patterns of an initial mixture of barium peroxidewith WO2 (a), after its mechanical activation for 5 s (b)and of the SHS product in this mixture (c).
can be conducted mechanochemically. It follows fromthe analysis of the IR spectra (Fig. 19). Similarly tothe case of the lower oxide, the reaction starts duringthe first seconds of activation. The shape of the ν (W-O) band of WO3 (1000500 cm1) and the ratio ofintensities of their maximums are changed. After acti-vation of the mixture for 1 min., the IR spectrum ofthe sample contains only one intensive band with amaximum at 810 cm1. This band relates to ν3 vibra-tions of WO4 tetrahedrons of the reaction productBaWO4.
X-ray phase analysis showed that the growth of theintensity of the BaWO4 phase ref lections was accom-panied by the decrease of the WO3 ref lections intensi-ties till their complete disappearance after activationfor 5 min. (Fig. 20). Microphotographs suggest thatthe initial stage of the process involves intensive dis-persion of the particles; their aggregation starts at thesecond minute of the process. After activation for 5min., complex oxide particles are formed; the size oftheir blocks is 2030 nm (Fig. 21).
The mechanochemcial activation of BaO2 withMoO3 results in the formation of the complex oxideBaMoO4. The complex oxide with the same composi-tion (BaMoO4) can be obtained via SHS between bar-ium peroxide and the higher molybdenum oxide,both reagents being activated preliminarily for 30 s.
Conclusion
Our investigations show that a combination of theSHS process with the mechanical activation both ofreagents and products could be rather attractive for
KONA No.20 (2002) 157
Fig. 19 IR spectra of an initial mixture of barium peroxide withWO3 (a), after its mechanical activation for 10 s (b) and1 min. (c).
Fig. 20 X-ray patterns of an initial mixture of barium peroxidewith WO3 (a), after its mechanical activation for 5 min.(b).
Fig. 21 Microphotograph of the product of mechanochemicalinteraction of BaO2WO3 (time of MA 5 min.).
a a
b
b
c
14 10 6 ν·102 sm1 28 24 20 16 12θ, degree
Russian).12) Nash A., Nash P. Bull. Alloy Phase Diagrams, Jun. 1987,
8(3).13) Samsonov G.V., Dvorina L.A., Rud’ B.M. Silicides.
Moscow, Metallurgia (1979) (in Russian).14) Vol A.E. Structure and properties of binary metal sys-
tems. V. 2. Moscow, Fizmatgiz (1962) (in Russian).15) Heinicke, R. Riedel, H. Harenz. Z. Phys. Chem., 227, 62
(1964).16) Grigorieva T.F., Barinova A.P., Boldyrev V.V., Ivanov
E.Yu. Materials Science Forum, 235-238, 577 (1997).17) Zyryanov V.V., in: ‹‹Mechanochemical synthesis in inor-
ganic chemistry››, ed. by E.G. Avvakumov, Novosibirsk,Nauka, 1991, p. 102-125 (in Russian).
18) Powder Diffraction File. Swarthmore: Joint Committeeon Powder Diffraction Standards. Card NoNo 8-277, 8-368, 8-372, 5-626.
19) ibid. Card No 6-0399.20) ibid. Card No 17-306.21) Plyusnina I.I. Infrared spectra of minerals, Moscow,
MSU Publishers, 1977 (in Russian).22) Lowson L., Infrared absorption spectra of inorganic sub-
stances, Moscow, Mir (1964).23) Barker M., Wood D.I. J. Chem. Soc. Dalton Trans., 22,
2448 (1972).24) Boldyrev A.I. Infrared spectra of minerals, Moscow,
Nedra, 1976 (in Russian).25) Last J.T., Phys. Rev., 105, No 6, 1740 (1957).26) Landolt-Bornstein H. Physikalisch-Chemische Tabellen,
1951, Teil 2.27) Henning O., Paselt G., Z. Phys. Chem., 233, No 3-4, 170
(1933).28) Audette R.J., Quail J.W. Inorganic Chemistry, 11, No 8,
1904 (1972).29) Grigorieva T.F., Barinova A.P., Ivanov E.Yu., Boldyrev
V.V. Doklady Akademii nauk (Reports of the RussianAcademy of Sciences). 354, No 4, 489 (1997) (in Rus-sian).
30) Grigorieva T.F., Barinova A.P., Kryukova G.N., BoldyrevV.V. Proceeding of EUROMAT ’97. (5th European Con-ference on Advanced Materials, Processes and Applica-tions, Maastricht, April, 1997). 2, 333 (1997).
31) Grigorieva T.F., Barinova A.P., Vorsina I.A., KryukovaG.N., Ivanov E.Yu., Boldyrev V.V. Chemistry for Sustain-able Development. 6, 115 (1998).
32) Grigorieva T.F., Barinova A.P., Vorsina I.A., KryukovaG.N., Boldyrev V.V. Zhurn. Neorg. Khimii. 43, No 10,1594 (1998).
33) Smirnov V.I., Aleksandrov V.V. Inzhenerno-fizicheskiyzhurnal. 65, No 5, 594 (1993) (in Russian).
158 KONA No.20 (2002)
technological applications. The preliminary activationfacilitates combustion, making it possible even in theconcentration region where conventional SHS isnever observed. In other cases, the very short me-chanical activation of SHS products allows us to pre-pare uniform single-phase products.
For complex oxides, the picture is very similar if wecan only provide the energetic conditions for SHS.There is usually quite a wide variety of precursorsavailable for ceramic synthesis, which makes it possi-ble to find an energetically efficient root.
The complex oxides can be obtained by mechano-chemical synthesis, by SHS, and by a combination ofmechanical activation and SHS.
The combination of mechanical activation and SHSbrings advantages to both methods. As a result, theshort-term mechanochemical activation of SHS prod-ucts becomes an extremely convenient method formanufacturing nanopowders.
References
1) Grigorieva T.F., Korchagin M.A., Barinova A.P., IvanovE.Yu., Boldyrev V.V. Inorg. Materials. Angl. Tr. 36(12),1467 (2000).
2) Grigorieva T.F., Barinova A.P., Lyakhov N.Z. RussianChem. Reviews, 70(1), 45 (2001).
3) Avvakumov E.G., Potkin A.R., Samarin O.I. A.C. USSRNo 975068. BI, 1982, No 43 (in Russian).
4) Samsonov G.V., Bondarev V.N. Germanides. Moscow,Metallurgia, (1968). (in Russian).
5) Itin V.I., Naiborodenko Yu.S. High-temperature synthe-sis of intermetallic compounds. Tomsk State UniversityPublishing House, Tomsk, (1989) (in Russian).
6) Munir Z.A., Anselmi-Tamburini U. Materials ScienceReports, 3, No 7-8, 277 (1989).
7) Grigorieva T.F., Barinova A.P., Boldyrev V.V., IvanovE.Yu. Solid State Ionics, 101-103, 17 (1997).
8) Avvakumov E.G., Mechanical methods of the activationof chemical processes. Nauka, Novosibirsk (1986) (inRussian).
9) Gilman P.S., Benjamin J.S. Ann. Rev. Mater. Sci., 13, 270(1983).
10) Charlot F., Gaffet E., Zeghmati B., Bernard F., NiepceJ.C., Mater. Sci. Eng., A262, 279 (1999).
11) Grigorieva T.F., Korchagin M.A., Barinova A.P.,Lyakhov N.Z. Doklady Akademii nauk (Reports of theRussian Academy of Sciences). 369, No 3, 345 (1999) (in
KONA No.20 (2002) 159
1. Introduction
Chemicals such as aluminum sulfate or ferric chlo-ride are traditionally added to water to reverse thesurface charge on microbes, promoting their coagula-tion and f locculation with other particulate matter inthe water. An alternate approach is to modify the sur-face properties of the filter media, e.g., by coatingwith an electropositive material. The first investiga-tors of this approach (Brown et al., 1974a, Brown etal., 1974b; Farrah et al., 1988; Farrah et al., 1991)found that iron aluminum hydroxide coating in-creased removal of viruses by diatomaceous earthfrom less than 30% to greater than 80%. Subsequently,Lukasik et al. (1996, 1999) tested removal of virusesby columns filled with fine sand (less than 0.3 mm)coated with iron aluminum hydroxide. They reported
that virus removal by uncoated sand was typicallyless than 30%, whereas coated sand gave removals ofgreater than 99%.
One objective of the present work was to extend theevaluation of the use of coated granular media forvirus removal. We chose a media size range (0.6-0.7mm) for sand that lies within that used in large-scale municipal and industrial water filters (J.M.Montgomery, Inc., 1985). We also evaluated granularactivated carbon as a filtration medium, because it is acommon component of point-of-use filtration systems,e.g., faucet filters. Such systems are becoming in-creasingly popular in households because of concernover microbiological quality of water delivered bymunicipal utilities.
A second objective was to evaluate a coating withantibacterial activity. This is desirable to limit bacter-ial growth in point-of-use water filters. The coatingchosen for this purpose (AEM 5700; Aegis, Midland,MI) consists of a positively-charged quaternary am-monium linked to a carbon chain. It is widely used asa bactericidal agent in consumer products.
T.M. Scott1, R.C. Sabo2, J. Lukasik1, C. Boice1, K. Shaw3, L. Barroso-Giachetti3, H. El-Shall4, S.R. Farrah1, C. Park2, B. Moudgil4 and B. Koopman3*1 Department of Microbiology and Cell Science2 Department of Chemical Engineering3 Department of Environmental Engineering Sciences4 Department of Materials Science & Engineering **
Performance and Cost-Effectiveness of Ferric and Aluminum HydrousMetal Oxide Coating on Filter Media to Enhance Virus Removal†
Abstract
Coating sand and granular activated carbon with iron aluminum hydroxides changed the zetapotential of these filtration media from negative to positive at pH 6-9, while also signif icantlyimproving removal of viruses (MS2, PRD1, Polio1). A quaternary ammonium based coating onsand also increased zeta potential, but led to limited improvement in virus removal. The coated acti-vated carbon was ef fective in both columns and faucet f ilters. Performance of faucet f ilters decreasedslightly (e.g., 98% removal initially vs. 89% removal after 1 month) with time. The chemical costs ofcoating would add approximately 10% to the cost of water delivered by large-scale municipal systems,whereas coating chemical costs would add less than 1% to the cost of water treated by point-of-usefaucet filters. The improvement in virus removal performance gained by use of coated filter mediaprovides a significant benefit to the consumer in terms of increased microbiological quality at amodest-to-negligible increase in cost.
* Corresponding author**University of Florida, Gainesville, Florida† Accepted: May 22, 2002
The final objective of this work was to determinethe costs of chemicals used in the coating processand compare them, expressed on a unit volume basis,to the typical costs of water from municipal supplysystems and point-of-use systems.
2. Materials And Methods
2.1 ChemicalsAluminum chloride (AlCl3·6H2O), ferric chloride
(FeCl3·6H2O), and ammonium hydroxide (28-30% asNH3) were obtained from Fisher Scientific. AEM5700 antimicrobial agent, consisting of 42% 3-(tri-methoxysilyl) propyldimethyl-octadecyl ammoniumchloride, with the balance of the solution consisting ofmethanol and inerts, was obtained from Aegis Envi-ronmental Management (Midland, MI).
2.2 Viruses and Viral AssaysThe following phages and their hosts were
used: MS-2 (ATCC 15597-B1) was assayed usingEscherichia coli C-3000 (ATCC 15597) as a host. Bac-teriophage PRD-1 was assayed using Salmonellatyphimurium (ATCC 19585) as a host. These phagesare commonly used models of enteric viruses (Gerba,1984). Phages were assayed as plaque-forming units(PFU) using agar overlay procedure (Snustead andDean, 1971). Poliovirus was proliferated and assayedas PFU on Buffalo Green Monkey (BGM) cells usingan agar overlay method (Smith and Gerba, 1982).
2.3 Coating Procedure2.3.1 Modification of Filter Media by In Situ
Precipitation of Metallic HydroxidesActivated carbon (2040 mesh) was obtained from
Aldrich Chemical Company. Ottawa sand (2530mesh after sieving) was obtained from Fisher Scien-tific. The media were first rinsed with deionizedwater, then soaked to saturation in a solution of 0.25Mferric chloride and 0.5M aluminum chloride, andfinally heated at 60°C until dry. The media was thenmixed to saturation with 3N ammonium hydroxideand heated at 60°C until dry. A second precipitationwith ammonium hydroxide was performed to precipi-tate any un-reacted chlorides.
2.3.2 Modification of Ottawa Sand withAEM5700
Ottawa sand (2530 mesh) was washed three timesin deionized water then soaked to saturation in a 1%aqueous solution of AEM 5700. The solution was agi-tated for ten minutes at room temperature. The media
was then filtered from the solution using Whatmanpaper, rinsed 5 times, and dried overnight.
2.3.3 Faucet Filter ModificationFaucet filters (Ameritech Co.) were cut open and
the activated carbon removed. The carbon was thencoated with iron aluminum hydroxide as describedpreviously. The modified carbon was placed backinto the shell and the shell was sealed with epoxy.Unmodified filters were also cut open and resealed toact as controls.
2.4 Characterization of Filter MediaThe zeta potential of the filtration media was deter-
mined using an Anton Paar Electro Kinetic Analyzer(EKA, Anton Paar, Graz, Austria). The cylindricalf low cell had an I.D. of 2.0 cm and a packed lengthof 4.0 cm. The electrolyte was 1.0103 M KCl.Zeta potential (ζ) was computed according to theFairbrother and Mastin (1924) equation:
ζ (1)
where η is the viscosity of water and k is conductivity.The parameter in SI units is found from:
r0 (2)
where εr78.54 at 25°C and 08.851012 C2/(J m).
2.5 Experimental Protocols2.5.1 Comparison of Coated and Uncoated
Media in ColumnsFour identical filtration columns, each 1.9 cm in
diameter and 50 cm long, were filled with eitherOttawa sand, AEM 5700 coated Ottawa sand, or metalhydroxide coated Ottawa sand. The filter media wasadded incrementally through the top of the columns,which were partially charged with water from the bot-tom. After the addition of sand, the column was thor-oughly tapped to pack the media and to remove anytrapped air bubbles. Wire mesh was placed at theends of the column to prevent loss of media. Acrylicplastic caps were secured to the columns to hold themesh and to provide connections for the PVC tubing(1/8 in. ID) used in the experiments. Once packedand assembled, water was passed through thecolumns to further rinse the media. The columnswere operated in parallel using two multi-head peri-staltic pumps, which were calibrated prior to theexperiments.
Viral suspensions were passed top-to-bottomthrough the columns at a superficial velocity of about
ηkε
∆U∆P
160 KONA No.20 (2002)
1 mm/s, which is typical of industrial and other watertreatment processes. The same suspension was fed toall four columns. Samples were taken for assay fromthe inlet and from the exit of each column periodicallyfor about two hours or about 70 pore volumes, ensur-ing steady-state conditions.
2.5.2 Comparison of Coated and UncoatedGranular Activated Carbon in Columns
Activated carbon (Aldrich Chemical Co.) was fresh-ly prepared and coated with iron aluminum hydroxideas previously described. Modified carbon was packedinto one column while unmodified carbon was packedinto another column (30 cm long, 5 cm diameter).Four liters of deionized water, containing bacterio-phage MS2, were then pumped through each of thecolumns at a rate of 40 mL/sec. After initial passageof the water through the columns, the eff luent wasrecirculated through the columns to assess second-pass removals. Triplicate samples of column inf luentand eff luent were collected and assayed for virusremoval.
2.5.3 Comparison of Point-of-Use Filters containing Coated and Uncoated Media
Faucet filters containing either coated or uncoatedgranular activated carbon were attached to a pressurevessel that contained dechlorinated tap water seededwith bacteriophage and poliovirus 1. The test solutionwas forced through the filters at a rate of 25 mL/susing nitrogen gas. Multiple inf luent and eff luentsamples were collected and assayed to determine per-cent removal of viruses. For long term coating stabil-ity and performance studies, the filters were rinseddaily with at least 8 L of tap water. Samples were col-lected and assayed weekly for a period of one month.
3. Results
3.1 Surface Characteristics of Filter MediaThe coating of Ottawa sand with iron aluminum
hydroxide increased the zeta potential from 406.6mV to 459.8 mV at pH 7.0. The zeta potential ofthe uncoated activated carbon used in the columnexperiments (Aldrich) was 2.63.0 mV. After coat-ing, the Aldrich carbon had a zeta potential of 24.88.2 mV. The activated carbon used in the faucet filterexperiments had a measured zeta potential of 1.25.1 mV before coating. After coating, the zeta poten-tial measured 27.210.2 mV (Table 1). Coatingsand with AEM5700 also resulted in a change in zetapotential from negative to positive (data not shown).
3.2 Effect of Coating on Virus Removal bySand in Columns
Filtration columns packed with Ottawa sand, ironand aluminum coated Ottawa sand, and AEM5700coated Ottawa sand were charged with suspensions ofMS-2 and PRD-1. Virus removals for each column andorganism are reported in Figure 1. Metal hydroxidecoated sand removed 527% and 469% of MS-2 andPRD-1, respectively, whereas viral reductions forunmodified sand were 169% and 34%, respec-tively. A two-factor analysis of variance revealed a sig-nificant difference (α0.05) in percent removalsbetween different sand columns. Tukey’s test wasperformed with α0.05 to directly compare the per-cent removals of pairs of columns. Metal hydroxidecoated Ottawa sand removed more MS-2 and PRD-1than uncoated Ottawa sand and more PRD-1 thanAEM5700 coated Ottawa sand. AEM5700 coated sandremoved significantly more MS-2 than unmodifiedsand but not significantly more PRD-1.
KONA No.20 (2002) 161
Filter media Zeta potential (mV)*
Sand (uncoated) 40.06.60
Sand (coated) 45.09.80
Faucet Filter carbon (uncoated) 1.25.10
Faucet Filter carbon (coated) 27.210.2
Aldrich carbon (uncoated) 2.63.00
Aldrich carbon (coated) 24.88.20
* Values represent the mean 1.0 S.D. (N10)
Table 1 Zeta potentials of sand and activated carbon with andwithout iron aluminum hydroxide coating
Uncoated Sand AEM5700Coated Sand
Metal HydroxideSand
Vir
us R
emov
al
MS-2 PRD-1
10.0
10.0
30.0
50.0
Fig. 1 Performance of coated and uncoated sand in columns[error bars give 1.0 S.D. (N3)]
3.3 Effect of Coating on Virus Removal byGranular Activated Carbon in Columns
Columns containing modified activated carbon out-performed columns containing unmodified activatedcarbon in the removal of viruses from aqueous solu-tions. The first pass of water seeded with bacterio-phage MS2 through the columns resulted in anaverage 92% reduction of MS2 by the coated carbon,compared to an average 32% reduction by unmodifiedcarbon (Table 2). Passage of column eff luents backthrough the respective columns resulted in a cumu-lative 99% reduction of bacteriophage MS2 by thecoated carbon and a cumulative 54% reduction by theunmodified carbon.
3.4 Effect of Coating on Virus Removal by Activated Carbon in Faucet Filters
Faucet filters containing activated carbon coatedwith ferric and aluminum hydroxide removed moremicroorganisms from water than all unmodified fil-ters. The modified filters removed 99% of MS2 and848% of poliovirus 1 while the unmodified filtersremoved 3411% of MS2 and 354% of poliovirus(Table 3). Long-term evaluation indicated that thecoatings are stable and capable of maintaining theireffectiveness for several weeks. Each filter testedremoved greater than 85% of all organisms used tochallenge the system after 30 days of use (Fig. 2).
3.5 Economic ComparisonThe chemical costs of coating filter media with iron
aluminum hydroxides were estimated based on ob-served chemical requirements for coating media inthe laboratory, together with costs of chemicals inbulk quantities (Table 4). The total coating cost forsand was 7.0 cents per kg, whereas the coating costfor activated carbon was 55 cents per kg. These costswere used in determining the added price to the con-sumer of water treated by coated filter media.
The lower of the mean percent removals (46%achieved with PRD1) was chosen to be representativeof virus removals obtained by coated sand. Given thislevel of performance in a 0.5 m deep column, a corre-sponding removal of 70% may be expected in a 1.0 mdeep column based on first-order removal (Tien,1989). The cost of coating filter media to achieve thisremoval can be based on a unit cross-sectional area of1.0 m2 (normal to the downward f low direction of thewater being treated). The chemical cost to coat themedia contained in this unit area would be $120.57(Table 5). The volume of water treated in 1 month bythis unit area, based on a superficial velocity of 1.4mm/s [2 gal/(ft2 min)] and a 5% loss for backwash-ing, would be 3498 m3. The unit chemical cost for
162 KONA No.20 (2002)
* Values are the means 1.0 S.D. (N3)** Significantly greater than control (uncoated) at α0.01
Table 2 Effect of Coating on Performance of Activated Carbon inColumns*
% Cumulative removalPass Coated Uncoated
1 925** 324
2 99.60.5** 547
* Values are the means 1.0 S.D. (N5)** Significantly greater than control (uncoated) at α0.01
Table 3 Effect of Coating on Granular Activated Carbon in FaucetFilters*
% RemovalVirus Coated Uncoated
MS2 99.70.4** 3411
Polio 1 848** 355..
0 5 10 15 20 25 30
Vir
us r
emov
al (
%)
MS2
0 5 10 15 20 25 30
Time (days)V
irus
rem
oval
(%)
PRD1
20
30
40
50
60
70
80
90
100
2030405060708090
100
Fig. 2 Long-term performance of faucet filter containing coatedactivated carbon [error bars give 1.0 S.D. (N3)]* Filters containing uncoated activated carbon removed
less than 35% of viruses
water treatment with coated media is thus computedto be 3.4 cents per cubic meter. This compares to atypical delivered water price in U.S. municipal sys-tems of 40 cents per cubic meter.
The cost of water treatment by a conventionalhousehold faucet filter as compared to the chemicalcost of coating the activated carbon in such a filter isdetermined in Table 6. Based on a retail cost of $10per filter, a lifetime of 1 month, and a daily throughputof 8 L, the unit cost of water treated by a faucet filterwas estimated to be 4.1 cents per liter. Coating theactivated carbon contained in one faucet filter wouldrequire 2.9 cents worth of chemicals, amounting to anadditional cost of 0.01 cents per liter.
4. Discussion
Coating of sand and granular activated carbon withiron aluminum hydroxide made the zeta potentialmore electropositive, while also significantly improv-ing virus removal. This effect on sand has beenobserved by several other investigators (Lukasik etal., 1999; Chen et al., 1998; Truesdail, 1999; Shaw etal., 2000), who attributed increased removals of vi-ruses, bacteria and protozoa to the change in filtermedia potential from negative to near-zero or positive.A similar effect on zeta potential of sand was achievedby the AEM5700. Although AEM 5700 is a popularantimicrobial agent for consumer products, use of thismaterial for coating water filter media is novel. How-ever, the AEM 5700-coated sand showed a limitedcapacity to remove viruses.
Use of iron aluminum hydroxide coating to increasethe zeta potential of granular activated carbon fromnegative to positive values was reported for the firsttime in this work. Uncoated granular activated car-bon, which is a standard component in point-of-use fil-
KONA No.20 (2002) 163
a 28-30% as NH3 with a specific gravity of approximately 0.9b Chemical Market Reporter (2001)
Table 4 Chemical costs of coating sand and activated carbon
Table 5 Cost of using coated sand for municipal/industrial filtra-tion
FeCl3·6H2O AlCl3·6H2O NH4OHa Total
Bulk chemical cost b $0.33/kg $1.76/kg $0.25/kg
Amount used to coat 1 kg mediaSand 16.9 g 30.2 g 45 g
Activated carbon 135 g 231 g 346 g
Cost in cents per kg mediaSand 0.5 5.3 1.2 7.0
Activated carbon 4.4 41 9.5 55
* Specific gravity of sand2.65
Filter coefficient 1.2 m1
Bed depth 1.0 m
Initial virus removal 70%
Porosity 0.35
Bed cross-sectional area 1.0 m2
Bed depth 1.0 m
Bed volume 1.0 m3
Media weight* 1722.5 kg
Unit coating cost $0.07/kg
Coating cost for 1.0 m3 bed $120.57
Superficial velocity 1.4 mm/s
Volume treated in 1 month 3498 m3
Unit cost 3.4 cents/m3
Typical U.S. delivered municipal water cost (conventional filter media) 40 cents/m3
Table 6 Cost of using coated activated carbon in faucet filters
Media weight per filter 52 g
Initial virus removal 98%
Unit coating cost $0.55/kg
Coating cost for 1 filter 2.9 cents
Daily water consumption 8 L
Volume treated in 1 month 243.5 L
Typical retail cost of conventional faucet filter $10
Water cost for conventional faucet filter(assuming change-out after 1 month) 4.1 cents/L
Additional chemical cost for using coated media in faucet filter 0.01 cents/L
ters, was a moderate to poor collector of viruses. Aftercoating, the activated carbon achieved very highvirus removals in both columns and faucet filters.
An important issue in the application of coated filtermedia is the lifetime of the coating. The performanceof faucet filters decreased slightly (e.g., 98% removalof PRD1 initially vs. 89% removal after 1 month) withtime. Previous studies using coated sand in columnsindicated that little of the coating was lost over time.Chen et al. (1998), in a study of aluminum hydroxidecoated sand for bacterial removal from wastewater,found that three-fourths of the aluminum originallycoated on the sand was still present after 3 months ofcontinuous f lushing. Lukasik et al. (1999) reportedthat iron and aluminum concentrations in the eff lu-ents of filtration columns containing coated mediawere below the detection limit (0.1 ppm for Fe; 0.01ppm for Al) of ICP.
The estimated chemical costs for coating sand andactivated carbon, when expressed relative to the vol-ume of water treated, are low relative to typical con-sumer costs for water. The chemical costs of coatingwould add approximately 10% to the cost of waterdelivered by municipal systems, whereas coatingchemical costs would add less than 1% to the cost ofwater treated by faucet filters. Improvement in virusremoval performance gained by use of coated filtermedia thus provides a significant benefit to the con-sumer in terms of increased microbiological quality ata negligible-to-modest increase in cost.
Acknowledgments
The authors gratefully acknowledge the financialsupport of the Engineering Research Center (ERC)for Particle Science & Technology at the University ofFlorida, the National Science Foundation (NSF) grant#EEC-94-02989, and the Industrial Partners of theERC.
References
1) Brown, T.S., J.F. Malina, Jr., and B.D. Moore. Virusremoval by Diatomaceous earth filtration, part 1. J. Am.Water Works Assoc. 66: 98-102 (1974a).
2) Brown, T.S., J.F. Malina, Jr., and B.D. Moore. Virusremoval by diatomaceous earth filtration, part 2. J. Am.Water Works Assoc. 66: 735-738 (1974b).
3) Chemical Market Reporter. Inorganic chemicals. Vol.257, No. 1, pp 18-25 (2001).
4) Chen, J., Truesdail, S., Lu, F., Zhan, G., Belvin, C., Koopman, B., Farrah, S., and Shah, D. Long-term evalu-ation of aluminum hydroxide-coated sand for removal ofbacteria from wastewater. Water Research 32, 2171-2179(1998).
5) Farrah, S.R., M.A. Girard, G.A. Toranzos, and D.R.Preston. Adsorption of viruses to diatomaceous earthmodified by in situ precipitation of metallic salts. Z.Gesante Hyg. 34, 520-521 (1988).
6) Fairbrother, F. and Mastin, H. Studies in Electro-endos-mosis. Part I. J. Chem. Soc. 125, 2319-2330 (1924).
7) Farrah, S.R., D.R. Preston, G.A. Toranzos, M. Girard,G.A. Erdos, and V. Vasuhdivan. Use of ModifiedDiatomaceous Earth for Removal and Recovery ofViruses in Water. Appl. Environ. Microbiol. 57(9): 2502-2506 (1991).
8) Gerba, C.P. Applied and theoretical aspects of virusadsorption to surfaces. Advances in Applied Microbiol-ogy. 30: 133-167 (1984).
9) J.M. Montgomery, Inc. Water Treatment Principles &Design. John Wiley & Sons, New York (1985).
10) Lukasik, J., Y.F. Cheng, F. Lu, M. Tamplin, and S.R.Farrah. Removal of microorganisms from water bycolumns containing sand coated with ferric and alu-minum hydroxide. Wat. Res. 33(3): 769-777 (1999).
11) Lukasik, J., S. Truesdail, D.O. Shah, and S.R. Farrah.Adsorption of microorganisms to sand and diatoma-ceous earth particles coated with metallic hydroxides.Kona Particle and Powder. 14: 87-91 (1996).
12) Shaw, K., Walker, S., and Koopman, B. Effect ofHydrous Iron Aluminum Oxide Coating on Sand in theFiltration of Cryptosporidum Oocysts. Journal AmericanWater Works Association. 92, 103-111 (2000).
13) Smith, E.M. and C.P. Gerba. Laboratory methods forthe growth and detection of animal viruses. In C.P.Gerba and S.M. Goyal, ed. Methods in environmentalvirology. Marcel Dekker, Inc. New York (1982).
14) Snustad, S.A. and D.S. Dean. Genetic experiments withbacterial viruses. W.H. Freeman and Co., San Francisco(1971).
15) Tien, C. Granular filtration of aerosols and hydrosols.Butterworths, Boston (1989).
16) Truesdail, S. Fundamental forces important to theenhancement of biological colloid removal. Ph.D. Dis-sertation, University of Florida, Gainesville, FL USA(1999).
164 KONA No.20 (2002)
KONA No.20 (2002) 165
Author’s short biography
T.M. Scott
Dr. T.M. Scott received his B.S., M.S., and Ph.D. degrees in Environmental andMolecular Microbiology from the University of Florida and was a graduate studentmember of the National Science Foundation Engineering Research Center forParticle Science and Technology at the University of Florida (ERC) when thisresearch was carried out. He is currently a Visiting Scientist in the EnvironmentalMicrobiology Laboratory at the University of South Florida’s College of MarineScience. His areas of research interest include the development of novel microbialsource tracking methodologies as well as development and improvement of meth-ods used for the concentration and detection of pathogenic viruses and protozoa inthe environment.
R.C. Sabo
Dr. R.C. Sabo, Jr. graduated magna cum laude from Vanderbilt University with aBaccalaureate of Engineering in chemical engineering and mathematics in 1997.He then moved to Gainesville, Florida, where he obtained a Doctor of Philosophyin chemical engineering from the University of Florida. He was a graduate studentmember of the ERC at the time of this research and is currently an ERC post-doc-toral fellow.
J. Lukasik
Dr. J. Lukasik was a post-doctoral fellow at the ERC when this research was carriedout. He is currently Senior Research Scientist for Biological Consulting Services,Inc., Gainesville, Florida.
C. Boice
C. Boice received her B.S. (1998) and M.S. (2000) degrees in Microbiology andCell Science from the University of Florida. She is currently pursuing a doctoraldegree in Microbiology and Cell Science and is a graduate student member of theERC. Her research interests include f lotation, filtration, adsorption, and surfacemodification.
K. Shaw
Dr. K. Shaw was a graduate student member of the ERC when this research wascarried out. She received her Ph.D. in Environmental Engineering Sciences fromthe University of Florida and is currently Project Manager for CH2M-Hill.
166 KONA No.20 (2002)
Author’s short biography
L. Barroso-Giachetti
L. Barroso-Giachetti received his B.S. in environmental engineering sciences fromthe University of Florida and was an ERC undergraduate scholar when thisresearch was carried out.
H. El-Shall
Dr. H. El-Shall is an Associate Professor of Materials Science and Engineering atthe University of Florida and Associate Director of the ERC. His research interestsare applied surface and colloid chemistry and mineral, chemical, and metallurgicalengineering.
S.R. Farrah
Dr. S.R. Farrah is a Professor in the Department of Microbiology and Cell Scienceat the University of Florida. He received his B.A. in Science in 1965 and his Ph.D.in Microbiology in 1974 from the Pennsylvania State University. His research inter-ests include detecting viruses in environmental samples and adsorption of microor-ganisms to solids.
C. Park
Dr. C. Park received his BS in Chemical Engineering from Seoul National Univer-sity in Korea in 1980, and his MS and PhD in Chemical Engineering from StanfordUniversity in 1982 and 1985, respectively. He worked for Union Carbide Corpora-tion as a project scientist for 4 years since 1984. Subsequently he joined the facultyof Chemical Engineering at the University of Florida where he is currently a pro-fessor of Chemical Engineering. His research interest includes interfacial phenom-ena in multiphase f lows, filtration of colloidal particles, and polymer rheology andprocessing.
B. Moudgil
Dr. B. Moudgil is a Professor of Materials Science and Engineering and Director ofthe ERC. His research interests are particulate processing, solid-solid/solid-liquidseparations, fine particle packing, sol-gel processing, crystal modification, disper-sion & aggregation of fine particles, polymer & surfactant adsorption, orientationof particles in slurries, and rheology of concentrated suspensions.
KONA No.20 (2002) 167
Author’s short biography
B. Koopman
Dr. B. Koopman is a Professor of Environmental Engineering Sciences and Co-Leader of Goal I Advanced Separations in the ERC. His research interest is biologi-cal wastewater treatment.
168 KONA No.20 (2002)
1. Introduction
Consolidation of granular materials is a complexprocess operated by several mechanisms includingparticle rearrangement, elastic and plastic deforma-tion, fracture and pulverization [1]. The particlerearrangement is a void-filled-in process which ischaracterized by minute driving or applied forces andby large non-affine particle motion. In contrast, thepost-rearrangement stage or compaction stage isidentified by the inability of the particles to reducethe volume by relative motion, requiring larger driv-ing forces to deform or fracture the particles for fur-ther consolidation [2, 3]. While for brittle particlesfracture is the dominant mechanism of consolidation after the initial and localized elastic deformationstage , for ductile particles inelastic or plastic defor-mation provides a source for reducing the interparti-cle porosity, and consequently the total volume.
For systems dominated by frictional forces, re-arrangement and compaction tend to operate simulta-neously at different spatial locations of the specimen.In those cases, molecular dynamics methods [4] ordiscrete element methods (DEM) [5] provide a toolto simulate these conditions. However, due to the
intrinsic nature of these formulations, which traceeach individual particle, only relatively small samplescan be effectively simulated. Often the permissiblesizes are too small to characterize the macroscopicproperties of the material. In the present work, werestrict our attention to thoroughly lubricated sys-tems where interparticle friction is weak. For thiscase, the compaction may be uncoupled from the par-ticle rearrangement as a follow-up process. In thisscenario, the rearrangement is simulated first, fol-lowed by the subsequent compaction. A description ofthe particle rearrangement methodology is brief lydescribed in Section 2. This method is a modifiedDEM version (see for example [6, 7] for traditionalDEM formulations) which can simulate large sampleswith keeping an excellent agreement with the experi-mental data. The compaction regime is simulated bythe application of a mixed discrete-continuum or gran-ular quasi-continuum (GQC) formulation. The mainaspects of the model are presented in Section 3 andthe details are available elsewhere [8].
The present GQC, which can simulate granularbeds of nonlinear spherical (3D) or cylindrical (2D)particles with an arbitrary size distribution, is utilizedto investigate the inf luence of the composition ofgranular structure and material properties on themacroscopic compaction behavior. To that effect, twogroups of particles with a given size distribution aregenerated and later mixed with different ratios to con-form the samples, as described in Section 4. A para-
S. Zheng and A. M. CuitiñoDepartment of Mechanical and Aerospace Engineering Rutgers University*
Consolidation Behavior of Inhomogeneous Granular Beds of Ductile Particles using a Mixed Discrete-Continuum Approach†
Abstract
In this paper we study the consolidation behavior of inhomogeneous granular beds of elasto-plasticparticles by means of a discrete-continuum formulation, which systematically bridges the micro andmeso scales. The methodology is particularly suitable for describing the post-rearrangement regimewhere consolidation proceeds mostly by elastic and inelastic deformation. This formulation is able toprovide the quantitative estimates of the evolution of macroscopic variables, such as pressure anddensity, while following microlevel processes, such as local coordination number and loading paths.This methodology is used to simulate binary mixtures composed by particles with dif ferent nonlinearproperties. The predictions are in general agreement with the experimental data during both loadingand unloading cycle.
* Piscataway, NJ 08854, USA† Accepted: September 12, 2002
metric study of the effect of particle size, Young’smodulus, yield stress and initial microstructure isthen presented in Section 4 along with a detailed dis-cussion.
2. Die Filling and Particle rearrangement
The initial particle bed structure is generated by aballistic deposition technique, which simulates the diefilling process. The algorithm proceeds by droppingindividual particles from the container top until theyreach a stable position. The condition of stability isdictated by the cohesivity of the powder. Cohesivepowders result in open structures, as shown inFig. 1(a) for a container of 5060 mm2 filled with 0.4mm-radius monosized particles. Due to the openstructure of this powder bed, particle rearrangementoperates in the early stages of densification. Thisprocess is simulated by forcing the particles residingat the top surface to move down at a specified rate. Ateach step, the punch is displaced 0.15 mm and theparticles are allowed to accommodate until a newequilibrium configuration is attained. Due to the factthat the rearrangement is an evolution process ofposition change, an iterative scheme is required toestablish the updated equilibrium configuration.Fig. 1(b) shows an intermediate stage during therearrangement process, where the punch has beendisplaced by ∆5.1 mm. Three clear regions areobserved: an unperturbed region near the bottom, apacked region near the punch, and a narrow gap inbetween or rearrangement front. Massive non-affinemotion is only observed on rearrangement front inclose agreement with the experiment record [9].
Fig. 1(c) depicts the final stages of rearrangement,where the front is reaching the bottom of the sample.
3. Compaction
Due to the inability of the particles to modifiedtheir current structure, further punch motion inducesparticle deformation as a mechanism of volume re-duction. During this stage both relative roll and slipare drastically reduced and play a negligible role onthe macroscopic response of the granular bed [2,3]. Under these conditions a discrete/continuumapproach can be effectively exploited to accountexplicitly for the interparticle interactions within aconstrained kinematic field, as described succinctly inthe next section and in [8].
3.1 Mixed Discrete/Continuum ApproachThe central idea of this approach hinges on the abil-
ity of constraining particle motion by a coarse grid ofdimensions commensurable with the sample size. Inaddition, the constrained displacement field can berealized by utilizing standard Finite Element tech-niques. Within this framework, a mesh is generated,in either 2D or 3D, and the motion of each particle isdescribed by the element that contains the particle’scenter. Interaction with particles in the same andneighboring elements are allowed via an interparticleor local constitutive relation. It should be noted thatthis approach is equally applicable to both dynamicand quasi-static conditions, offering similar advan-tages. In the present case of analysis, we are inter-ested in the evolution of the powder bed underrelatively slow loading conditions compared with
KONA No.20 (2002) 169
(a) ∆0 (b) ∆5.1 mm (c) ∆9.6 mm
Fig. 1 Rearrangement processes of monosized particle bed. (a) Initial open structure; (b) intermediate structure; (c) closely packed structure.
characteristic wave speed in these materials , andthus, we concentrate on a quasi-static formulation.Details of the formulation are presented in [8].
3.2 Local Constitutive EquationsThe response between spherical particles can be
divided into five regimes: i ) tension, ii) local elasticcontact, iii ) local elastic-plastic contact, iv) fully plas-tic, and v) finite particle deformation. Although thepresent approach can be extended to describe thewhole range, the present study is restricted to thefirst four. The tension regime (cohesion) is describedby a potential law with Lennard Jones’ functionaldependence and a cut-off. The cohesivity is then mod-ulated by the value of the only adjustable coefficient.While the elastic response is governed by a Hertizanlaw,
, (1)
where F is the contact force, α is the relativelyapproaching displacement of the particle centers aftercontact, R and E are the equivalent radius and theequivalent modulus of the contact which are definedby
, . (2)
where E1, E2 and ν1, ν2 are Young’s moduli andPoisson’s ratios respectively of two particles in-con-tact with radius R1 and R2. The elastic regime onlydominates the initial stages of compaction where par-ticle deformation is minimal, and the plastic deforma-tion quickly eclipses the elastic part. If the elastic/plastic response of the solid materials of particles isdescribed by assuming a linear elastic regime fol-lowed by a power-law plastic regime characterized byhardening exponent m (which is set equal to 3 in thepresent study)
i ssyi,, (3)
m ssyi
where the label i1, 2 refers to the particles in con-tact, the interaction law for these particles is thengiven by the similarity solution [3]
B(m)2c2(m)1k(m)· 1
, (4)
and no interaction of the contacts need be considereddue to the localized nature [3]. The reference yield
12mα
R
12mF
πR2Γ
ssi
sEi
1ν22
E2
1ν12
E1
1E
1R2
1R1
1R
32
αR
4E3π
FπR2
stress si relates with yield stress syi in
sisyi1 Ei , (5)
and the equivalent reference stress Γ
, (6)
is given in terms of the yield stress si of each particlei. The values of c, k and B for a given exponent arenumerically estimated by [3] resulting in the follow-ing expressions
c2(m)1.5 , k(m)3.070.16 ,
B(m)0.740.26 m3,
0.640.57 m3.(7)
The two limiting regimes of the local constitutiveequation, elastic (m1) and elastic/perfectly plastic(m→), agree well with experimental data. For m 1the Hertzian regime is recovered for which existsample experimental validation. For m→, a lineardependency is predicted by (4) which is in a goodagreement with the recent experiments of [10] fornearly ideal plastic materials.
To account for the irreversibility of the plasticdeformation, a Hertizan unloading branch is intro-duced, which allow us to trace elastic recovery duringejection as well as heterogeneous fields where load-ing and unloading are concurrent. The unloadingregime is described by
(8)
where αres is the residual indentation depth that left inthe particle and might be obtained from both (4) and(1). Another indication of the irreversibility of theprocess is observed on the evolution of αres, whichsatisfies α· res0.
4. Results and discussions
4.1 Sample GenerationIn order to investigate the inf luence of particle size
and material on the compaction behavior, differentparticle beds are generated by mixing two sets of par-ticles, each one with a different size distribution andmaterial properties. The Group I with a relativelysmall mean diameter and the Group II with a largerone. The size distribution follows a normal distribu-tion characterized by an average radius –r and a vari-
32
ααres
R4E3π
FπR2
1m
1m
1m
121
m
1s2
m1
s1m
1Γm
1m
1m
170 KONA No.20 (2002)
ance s which are listed in Table 1 (units are mm).Lower and upper limits cut-off are introduced to simu-late particle populations within two given thresholds.The details of the selection of the size distributionand material properties are provided in the followingsections.
For the purpose of this analysis, two cohesive gran-ular beds are generated by mixing Group I withGroup II. The mixture A has 30% in volume of parti-cles from Group I and 70% from Group II, conversely,mixture B has 70% of group I and 30% of group II.With these simulated mixtures we fill a frictionlesscontainer of 5060 mm2 utilizing the ballistic deposi-tion method described in Sec. 2. The resulting struc-tures are shown in Fig. 2, which share commonfeatures, such as voids, with the monosized distribu-tion shown in Fig. 1(a).
The samples are then subjected to consolidationby rearrangement using the simulation approachdescribed in Sec. 2, which provides the initial samples
for consolidation by compaction. The post-rearrange-ment structures are shown in Fig. 3, where the over-imposed mesh shows the resolution of the coarsegrain simulation using our discrete-continuum ap-proach. It is interesting to notice that the structuresformed after the rearrangement of both inhomoge-neous and monosized beds show some qualitative andquantitative differences, such as the appearance ofgrain-like structure, which is only observed in themonosized case. The inhomogeneous cases consis-tently exhibit a lower post-rearrangement averagedensity, as indicated in Table 2 (compare to the valueof 0.867 for the monosized case), indicating a betterpacking for the monosized case. During the processof rearrangement both the average density, ρ, andthe average coordinate number,
Nc, increase as
shown in Table 2. Also, there is a tendency to reducethe inhomogeneity on the initial or pre-rearrange-ment density distribution resulting from the die fillingprocess. This effect is clearly indicated in Fig. 3. Aninteresting observation is that the post-rearrange-ment density of mixture B is not a direct function ofthe fraction of fines, in contrast, the average coordina-tion number of the sample shows a direct correlation.This observation is in good agreement with theproposition that only when the size of the fine fractionis small enough to reside at the interparticle spaces ofthe coarse fraction (no perturbation of the packing),
KONA No.20 (2002) 171
Fig. 2 The initial open structure of polydispersed granular material of (a) mixture A; (b) mixture B.
(a) Mixture A (b) Mixture B
Radius limits Average radius Specified/actual variance
Group II 0.050.35 0.20 0.10/0.075
Group II 0.400.80 0.60 0.15/0.101
Table 1 Characteristic distribution values of particle sets.
the densification is improved [16]. Although ρ for theinhomogeneous samples are lower than the mono-sized ones,
Nc is higher. This is consistent with the
observation that in monosized beds the low numberof contacts along the disorder regions (grain bound-aries) significantly reduces the average coordinationnumber of the entire region (maximum coordinationnumber is 6 for a perfect hexagonal arrangement). Incontrast, in inhomogeneous beds large particles maybe surrounded by more than 6 smaller particles, in-creasing the average coordination number.
4.2 Size DistributionIn order to focus on the effect of post-rearrange-
ment structure, the Group I and II are assumed tohave the same solid material behavior which is char-acterized by a Young’s modulus of 10 GPa, a Poisson’sratio of 0.33 and yield stress of 100 MPa. The globalpressure-deformation responses and unloading pathsare plotted in Fig. 4, where the curve corresponding
172 KONA No.20 (2002)
Fig. 3 The closely packed structure of polydispersed granular material of (a) mixture A; (b) mixture B.
(a) Mixture A (b) Mixture B
Particles Before rearrangement After rearrangement
fine/coarse ρNc Bed region ρ
Nc Bed region
Mixture A 4609/1318 0.725 5.13 5060 0.851 5.53 5051.11
Mixture B 10643/549 0.716 5.19 5060 0.845 5.65 5050.86
Table 2 Average density, coordinate number and particle bed region before and after particle rearrangement.
Mixture A
Mixture B
Monosized
350
300
250
200
150
100
50
0
p (M
Pa)
0 0.1 0.2 0.3 0.4∆/H
Fig. 4 The global pressure-deformation responses of mixture A,B and monosized particle bed.
to monosized bed is also included for comparison pur-poses. The pressure p is computed as the applied ver-tical force per unit of effective area. The effective areais estimated as the multiplication of the width of thecontainer (50 mm) by the weighted average thicknessof each particle in the bed, where the particle diame-ter is used as the weighting factor. The deformation ischaracterized by the ratio of the punch displacementover the initial height of particle bed (60 mm). Anevident conclusion from the figure is that size dis-tribution has small effects on the macroscopic re-sponse as indicated by the parallelism among thethree curves. The only observed difference (horizon-tal shift) is due to the disparity of structures inducedduring the rearrangement process. This observationcan be understood with the aid of (1) for the elasticregime and (4) for the plastic one. The average localor particle pressure may be equated to F/πR2, whichis a function (nonlinear) of the average particle defor-mation α /R. Thus, the average pressure vs. averagedeformation is then independent of the particle ra-dius, in accordance with the simulation results. Thepresent approach provides, in addition of the macro-scopic pressure-deformation response, the local dis-tribution of the average stresses and their temporalevolution. These distributions are of key importancein tracking regions with potential defects and imper-fections. In Fig. 5 shows the spatial distribution ofsyy (normal stress in the direction of the compac-tion) for mixtures A and B, and the monosizedrecorded for the same applied displacement of thepunch. The samples show different distributions withmore uniformity for the mixture B where a largenumber of fine particles present. The non-uniformityin the monosized particle bed agrees with the exis-
tence of the heterogeneous structure as grains andboundaries.
4.3 Elastic BehaviorThe elastic properties affect not only the local
stress distribution but also the global pressure-defor-mation response. In order to investigate the inf luenceof Young’s modulus on the compaction behavior, weconduct a parametric study by adopting hEEI/EII[0.1,1,10], where EI and EII are the modulus of thetwo groups. The global pressure-deformation curvesare plotted in Fig. 6. The Young’s modulus of the par-ticle group with higher volume percentage controlsthe average responses, even in the plastic regime. Inthat regime, (4) shows that the interparticle pressureis proportional to the effective stress Γ which inturns relates to the Young’s modulus by (5). In theelastic regime (initial loading or unloading), (1) and(8) provide a direct connection between pressure andYoung’s modulus.
The local stress distributions are highly dependentof the elastic properties as shown in Fig. 7, wherethe contour of syy is plotted for both mixture A and B.The stress may have different limits due to the vari-ety of Young’s modulus, but the f lood contours aredrawn by setting the difference of the limits the sameas it is done in Fig. 5, which is 50 MPa. At the samepunch displacement as in Fig. 5, as expected, thestress distribution is more heterogeneous than thecase of uniform material.
4.4 Plastic BehaviorTo quantify the effect of the interparticle plastic
behavior on compaction response, we vary, at con-stant Young’s modulus, the parameter hsysyI/syII
KONA No.20 (2002) 173
Fig. 5 The local stress contours of (a) mixture A; (b) mixture B; (c) monosized particle bed.
(a) Mixture A (b) Mixture B (c) Monosized bed
174 KONA No.20 (2002)
Fig. 6 The global pressure-deformation responses of both mixtures at a various of combinations of Young’s moduli.
Fig. 7 The local stress contours of both mixtures at uniform yield stress but various combinations of Young’s moduli.
(a) Mixture A∆/H
(b) Mixture B∆/H
500
400
300
200
100
0
σyIσyII100 MPa
M1: EI 10M1: EII10
M2: EI 100M2: EII10
M3: EI 10M3: EII100
(E in GPa)
σyIσyII100 MPa
M1: EI 10M1: EII10
M2: EI 100M2: EII10
M3: EI 10M3: EII100
(E in GPa)
M3
M3
M1
M2
M2
M1
0 0.1 0.2 0.3 0.4
p (M
Pa)
500
400
300
200
100
00 0.1 0.2 0.3 0.4
p (M
Pa)
(a) Mixture A: EI100, EII10 (b) Mixture A: EI10, EII100
(c) Mixture B: EI100, EII10 (d) Mixture B: EI10, EII100
KONA No.20 (2002) 175
Fig. 8 The global pressure-deformation responses of both mixtures at a various of combinations of yield stresses.
(a) Mixture A∆/H
(b) Mixture B∆/H
500
400
300
200
100
0
EIEII10 GPa
Y1: σYI 100Y1: σYII100
Y2: σYI 10Y2: σYII100
Y3: σYI 100Y3: σYII10
(σY in MPa)
EIEII10 GPa
Y1: σYI 100Y1: σYII100
Y2: σYI 10Y2: σYII100
Y3: σYI 100Y3: σYII10
(σY in MPa)
Y3
Y3
Y1
Y2
Y2
Y1
0 0.1 0.2 0.3 0.4
p (M
Pa)
500
400
300
200
100
00 0.1 0.2 0.3 0.4
p (M
Pa)
Fig. 9 The local stress contours of both mixtures at uniform Young’s modulus but various combinations of yield stresses.
(a) Mixture A: σYI10, σyII100 (b) Mixture A: σYI100, σyII10
(c) Mixture B: σYI10, σyII100 (d) Mixture B: σYI100, σyII10
176 KONA No.20 (2002)
[0.1,1,10], where syI and syII are yield stress foreach group. Changes in hsy introduces not only quan-titative effects but also qualitative ones, as observedin Fig. 8, where there is no crossing between theload and unload path on graphs of the load-displace-ment curves. The local stress distribution is alsoshown in Fig. 9 for both mixtures and for hsy0.1and 10. Compared with Fig. 5, it may be found thatdecrease of yield stress in either of the particlegroups will lead to more uniform of stress distribu-tion.
5. Conclusions
The present mixed discrete-continuum approachprovides a methodology to effectively link differentlength and time scales for nonlinear heterogeneousparticle systems. This technique resolves the kineticsat interparticle level while constraining the kinemat-ics by a grid with suprapartcle resolution. This formu-lation is utilized to study the consolidation behavior ofa series of samples after the pre-consolidation bymeans of particle rearrangement. The process ofrearrangement, which consolidates the highly openstructures resulting from simulation of die filling ofcohesive powders, is simulated using a modifiedDEM approach. Model systems are studied to quan-tify the role of the size distribution as well as the elas-tic and plastic properties. In these studies, differentcomposition of binary mixtures of two particle setsare consolidated to relatively high pressures. Eachparticle set is endowed with a particle size distribu-tion (characterized by the mean and variance) and theparticle’s elastic module (E), yield stress (sy) andhardening exponent (m). The results clearly indicatethe significant effect of each of these characteristicsnot only on the overall behavior of powder bed butalso on the development of local stress states. It isinteresting to notice that the post-rearrangement pre-consolidation structures are significantly affected bythe disparity on the size distribution between the 2particle sets. These structures prevail during the sub-sequent consolidation giving rise to dissimilar localstates even when the overall applied force againstpunch displacement remains mostly unchanged. Thisobservation shows some noteworthy features of thecurrent methodology: 1) the ability to follow the his-tory of the material before consolidation, which isindicated by the heterogeneity of the local fields and2) the ability of computing consistent averages ofthese local states, which is indicated by the similar
force-displacement response. Finally, due to the intro-duction of non-elastic effects the different paths dur-ing loading and unloading can be readily traced inaccordance with the experimental observations.
References
[1] Huffine C.L., “A Study of the bonding and cohesionachieved in the compaction of particulate materials,”Ph.D. Dissertation, Columbia University (NY) (1954).
[2] N.A. Fleck, L.T. Kuhn and R.M. McMeeking, “Yieldingof metal powder bonded by isolated contacts,” J. Mech.Phys. Solids, 40 1139-62 (1992).
[3] B. Storakers, N.A. Fleck and R.M. McMeeking, “Theviscoplastic compaction of composite powders,” J.Mech. Phys. Solids, 47 785-815 (1999).
[4] R.L. Williamson, “Parametric studies of dynamic pow-der consolidation using a particle-level numericalmodel,” J. Appl. Phys., 68 1287-96 (1990).
[5] P.A. Cundall and O.D.L. Stack, “A discrete numericalmodel for granular assemblies,” Grotechnique, 29 47-65 (1979).
[6] Chu-Wan Hong, “New concept for simulating particlepacking in colloidal forming processes,” J. Am. Ceram.Soc., 80 2517-24 (1997).
[7] Y.F. Cheng, S.J. Guo and H.Y. Lai, “Dynamic simulationof random packing of spherical particles,” Powder Tech-nol. 107 123-30 (2000).
[8] A.M. Cuitiño, S.F. Zheng and G. Gioia, “A Quasi-contin-uum approach for particle systems,” to be submitted forpublication.
[9] G. Gioia, A.M. Cuitiño, S. Zheng, and T. Uribe “Two-phase densification of cohesive granular aggregates,”Phys. Rev. Lett. 88 204302 (2002).
[10] M. Naito, K. Nakahira, T. Hotta, A. Ito, T. Yokoyamaand H. Kamiya, “Microscopic analysis on the consolida-tion process of granule beds,” Powder Tech., 95 214-19(2000).
[11] J.L. Finney, “Fine structure in randomly packed, denseclusters of hard spheres,” Mater. Sci. Eng., 23 199-205(1976).
[12] G.T. Nolan and P.E. Kavanagh, “Computer simulationof random packing of hard spheres,” Powder Technol.,72 149-55 (1992).
[13] G.T. Nolan and P.E. Kavanagh, “Computer simulationof random packings of spheres with log-normal distri-butions,” Powder Technol., 76 309-16 (1993).
[14] Yasuhiro Konakawa and Kozo Ishizaki, “The particlesize distribution for the highest relative density in acompacted body,” Powder Technol., 63 241-6 (1990).
[15] S.Dj. Mesarovic, N.A. Fleck, “Frictionless indentationof dissimilar elastic-plastic spheres,” Int. J. SolidsStruct., 37 7071-91 (2000).
[16] A.B. Yu and N. Standish, “Analytical-parametric theoryof the random packing of Particles,” Powder Technol.,55 171-86 (1988).
KONA No.20 (2002) 177
Author’s short biography
Shanfu Zheng
Shanfu Zheng is a research associate at Rutgers, the State University of NewJersey. He received his Ph.D. degree in Mechanical & Aerospace Engineering atRutgers University in 2000. He can be reached by email at [email protected]
Alberto M. Cuitiño
Alberto M. Cuitiño is an associate professor in the Department of Mechanical andAerospace Engineering at Rutgers University since 1993. Cuitiño received a CivilEngineering Diploma from the University of Buenos Aires, Argentina, in 1986, anda MS degree in Applied Mathematics and a Ph.D. degree in Solid Mechanics fromBrown University in 1992 and 1994 respectively. His research interests includemulti-scale modeling, dislocation mechanics, fracture in metal single crystals, gran-ular materials, mechanical behavior of solid foams and folding patterns in thinfilms. Cuitiño is subject editor for Applied Mechanics of the Latin AmericanApplied Research. He can be reached by email at [email protected]
178 KONA No.20 (2002)
1. Introduction
The traditional method for producing active drugparticles within the respirable range involves solventbased crystallisation followed by filtering, drying andhigh energy micronisation. This processing sequenceonly provides limited opportunity for control over par-ticle characteristics such as size, shape and morphol-ogy and introduces uncontrolled structural variations(decreased crystallinity, polymorphism) and surfacemodifications (increased surface free energy, adhe-sion, cohesiveness and charge). These uncontrolledvariations have an adverse effect on dry-powder for-mulation and may even render the formulation inef-fective. Salmeterol xinafoate (SX), selected as a modeldrug compound in this work, exhibits similar prob-
lems. SX is a long-acting β2 adrenoreceptor agonist,widely used in the management of moderate andsevere chronic asthma. This compound has been for-mulated for both metered-dose suspension (MDI)and dry powder inhalers (DPI). It is reported that SXmaterials are generated by a conventional crystalliza-tion process using dissolution in 2-propanol at ele-vated temperatures and natural cooling to inducesupersaturation [1]. These products were highlycohesive and showed very poor powder f low proper-ties making it unsuitable for f luid energy milling. Amore advanced crystallization process therefore wasdeveloped in which a hot SX solution in 2-propanol isadded to a chilled quench solvent inducing large (inthe range between 100-250 µm) spherical aggregates.These granular SX powders have improved f low andhandling properties and are used for micronisation[1].
Supercritical f luid (SCF) technology offers a morebenign and commercially viable process capable ofdirect production of respirable drug particles. Theadvantages of this technology are related to the abil-
Boris Y. Shekunov1,2, Jane C. Feeley2, Albert H. L. Chow3, Henry H. Y. Tong3
and Peter York1,2
1 School of Pharmacy, University of Bradford2 Bradford Particle Design Ltd3 School of Pharmacy, The Chinese University of
Hong Kong
Physical Properties of Supercritically-Processed and Micronised Powdersfor Respiratory Drug Delivery†
Abstract
Comparative analysis between salmeterol xinafoate (SX) powders was carried out to define quan-titatively the solid-state and surface particle properties relevant to formulation of these materialsinto dry powder respiratory drug delivery systems. SX powders were prepared in supercritical CO2
using a single-step crystallization process (Solution Enhanced Dispersion by Supercritical f luids,SEDS™), the volume mean diameter and deagglomeration behaviour of pure drug compound wereoptimised for respiratory applications. This compound together with reference samples of startinggranulated material and micronised powder were used in analytical studies which involved assess-ment of polymorphic purity and crystallinity (domain size and strain) using high-resolution X-raypowder dif fraction, determination of powder surface energetics using inverse gas chromatography(IGC), electrostatic charge and adhesion measurements. The supercritically-processed powdersshowed low surface energy, low strain, higher crystallinity and higher polymorphic purity than bothgranulated and micronised powders and resulted in reduced agglomeration, electrostatic charge andadhesion of this powder.
1 Bradford BD7 1DP, United Kingdom2 69 Listerhills Science Park, Campus Road, Bradford BD7
1HR, United Kingdom3 Shatin, N.T., Hong Kong SAR, China† Accepted: September 20, 2002
ity of supercritical solvents, the most important ofwhich is supercritical carbon dioxide (scCO2), to beefficiently separated, by decompression, from bothorganic co-solvents and solid powders, facilitatingone-step, clean and recyclable process engineering.Particle formation using SCF is a crystallisationprocess [2], with sufficient f lexibility to produce sin-gle crystal, uniform particles with low surface energy.The benefits of SCF-processed particles in both DPIand MDI formulations have been demonstrated. Forexample, particles of several steroid drugs were pro-duced by direct spraying of drug solutions into themedium of scCO2 [3] and an increase of fine particlefraction (FPF) for steroid formulations prepared withlecithin for an MDI was observed [3,4]. Protein pow-ders were also prepared and tested using this methodfor DPI applications [5]. The SEDS™ method (Solu-tion Enhanced Dispersion By Supercritical Fluids) [6]has an added advantage of very fast, homogeneousnozzle mixing between supercritical antisolvent anddrug solution leading to consistent production ofmicron sized particulate products [7]. By changingthe working conditions of pressure, temperature,solution concentration and f low rates, it is possible tocontrol the size, shape, morphology and crystal formof the micron sized particles [2,7-9]. In studies withDPI formulations of salbutamol sulphate, increasedFPF and targeted in vitro delivery have been demon-strated for SEDS-prepared powders when comparedwith micronised material [10,11]. For salmeterolxinafoate, aerosols of both polymorphs have been pro-duced [12,13] and a detailed thermal analysis hasshown a high degree of chemical and crystallo-graphic purity of these compounds [13]. The presentwork represents a comparative study of the micro-nised and supercritically-processed powders with theaim to distinguish the solid-state properties importantfor successful formulation of dry-powder aerosols.
2. Materials and methods
2.1 Chemicals and reagentsSalmeterol xinafoate (SX) in the form of granulated
material (G-SX) used for micronisation and micro-nised powder (M-SX) were generously supplied byGlaxoWellcome, Ware, UK. HPLC grade solvent forSEDS were purchased from BDH Chemicals, Leices-ter, UK. All analytical grade liquid probes used in IGCstudies were purchased from Labscan, Dublin, Ire-land. Industrial grade (99.95% pure) CO2 was sup-plied by Air Products (Manchester, UK).
2.2 Production of SX powdersThe SEDS™ method was employed to prepare pow-
ders of SX, form I (S-SX). This technique (Fig. 1) isbased on mixing between supercritical CO2 antisol-vent and a drug solution using a twin-f luid nozzle.Methanol, acetone and tetrahydrofurane were testedin this work, after which methanol was selected forfurther studies because of high yield (95%) and suit-able particle size distribution (PSD) (x9010 µm) ofthe SX products. The particle formation vessel (500ml volume) with the nozzle was placed in an air-heated oven. The temperature in the vessel was moni-tored by a thermocouple with accuracy 0.1°C andwas kept constant at 40°C. Pressure in the vessel wascontrolled by an air-actuated back-pressure regulator(26-1761 with ER3000 electronic controller, Tescom,Elk River, MN, USA) and kept constant at 2501 bar.The difference in the inlet and outlet pressure wastypically within 1% of its absolute value. The CO2 f lowrate, supplied by a water-cooled diaphragm pumpMilton Roy B (Dosapro Milton Roy, Pont-Saint-Pierre,France) was typically between 25 and 50 NL/minas monitored after expansion using a gas f lowmeter (SHO-Meter 1355, Brooks Instruments B.V.,Veenendal, Holland) and also controlled before expan-sion using high-pressure liquid f low meter (DK34,Krohme Messtechnik GmbH, Duisburg, Germany).Solution concentration of SX varied between 1 and10% w/v. Solution f low rate was provided by a meter-ing pump PU-980 (Jasco Co, Tokyo, Japan) and variedfrom 0.5 to 10 ml/min.
Prior to crystallization experiments, an on-line dy-namic solubility method [14] was used to determinethe equilibrium solubility profile of SX in methanol/
KONA No.20 (2002) 179
CO2 pump thermostat
nozzle
filter
HPvessel
cooler solutionmetering pump
flow meter and pressure regulator
Fig. 1 Experimental system for particle formation using super-critical CO2 as an antisolvent.
CO2 mixtures at different mole fractions of methanol.On this basis, the solution f low rate and the solutionconcentration were optimised to achieve maximumsupersaturation and maximum yield according to adeveloped method [15]. Several batches were pre-pared with batch quantities between 1 and 10 g. Theobtained cumulative PSD for all batches had x9010µm and volume-moment mean particle diameter,d4,35 µm, as determined using the laser diffraction(LD) method. Further improvement in nozzle geome-try (the diameter, length and volume of the mixingzone) allowed the mean particle diameter to decreasedown to d4,33.5 µm with cumulative x9910 µm.
2.3 High resolution X-ray powder dif fractionThis technique was used to determine the charac-
teristic diffraction peaks of SX forms I and II and todistinguish crystallographic changes (peak shift andpeak broadening) of G-SX, M-SX and S-SX com-pounds. The experiments were carried out at theSynchrotron Radiation Source (SRS) Daresbury Lab-oratory, station 2.3 (Warrington, UK). The X-raywavelength was λ1.4016 Å. The diffractometer hada f lat-plate/parallel foils Hart-Parrish geometry andwas calibrated using the diffraction peaks of crys-talline silicon with accuracy 104 degrees. The instru-mental broadening (shape of diffraction peaks relatedto the instrument geometry) was obtained using lan-thanum hexaboride standard (NIST, Denver, USA).All samples were placed in rotating plate holders andscanned between 2θ140° with resolution 0.01°(0.005° for the standard) and typical signal integra-tion time 1 s.
The diffraction data of SX were corrected for thebeam decay and indexed using program CHEKCELL[16] in order to find the crystal cell parameters. Theexact position of a minimum of five characteristic dif-fraction peaks, 2θ, the Full Width at Half Maximum,FWHM, and the mixing parameter, η, of pseudo-Voigtfunction were determined using peak fitting option ofprogram ORIGIN. The instrument broadening wasassessed using program SHADOW [16]. The ob-tained parameters were then input into programBREATH [16] to analyse the physical diffraction linebroadening caused by distribution of domain size andstrain in particles [17]. Alternatively, the diffractiondata were examined using program POWDER CELL[16] applying the whole profile Le Bail fitting optionof this software. In this case, the instrument broaden-ing FWHM was assumed to be 0.025° which is typicalfor an SRS diffractometer [18]. This procedure wasless accurate then that using calibration line broad-
ening and therefore only relative trends on the size/strain were interpreted from these results.
2.4 Time-resolved small-angle X-ray powderdiffraction
Dynamic analysis of polymorphic transition of SXwas carried out at the SRS Daresbury Laboratoryusing temperature-controlled small-angle X-ray scat-tering (SAXS) arrangement at station 8.2. The experi-mental method [19] involved time-resolved detectionof the SX polymorphic transition with characteristicpeaks at diffraction angles 2θ5°. Measurementswere carried out at wavelength λ1.54 Å. The quad-rant SAXS detector was placed at a distance 1 m fromthe sample. Samples were placed in a modified alu-minium DSC pan. The pan top and bottom wereremoved with a punch and replaced with thin micadiscs. Sealed pans were placed in a spring-loadedholder in a modified Linkam TMH600 (Linkam Scien-tific Instruments, Tadworth, UK) hot stage mountedon the optical bench in the center of X-ray beam.Heating rates between 5°C/min and 40°C/min wereused. Prior to X-ray measurements, the Linkam tem-perature range was calibrated using potassium ni-trate (melting onset 128°C), indium (154°C) and tin(230°C). The diffraction pattern of silver behenatewas used to calibrate the SAXS detector. Incident andtransmitted beam intensity monitored by ionizationdetectors were used to correct for X-ray beam decay,detector sensitivity and background scattering. Thesignal integration time was 6 s.
2.5 Inverse gas chromatography (IGC)IGC was performed on a Hewlett Packard Series
II 5890 Gas Chromatograph (Hewlett Packard,Wilmington, DE, USA) equipped with an integratorand f lame ionization detector. Injector and detectortemperatures were maintained at 100 and 150°Crespectively. Glass columns (60 cm long and 3.5 mmi.d.) were deactivated with 5% solution of dimethyl-dichlorosilane in toluene before being packed with SXpowder. The columns were plugged with silanisedglass wool at both ends and maintained at 40°C. Datawere obtained for a known weight and surface area ofthe sample using a nitrogen gas (purity99.995%)f low at 20.0 ml/min. The column was weighed beforeand after the experiment to ensure no loss of materi-als during the run. A trace amount of vapour fromnon-polar and polar probes was injected. The reten-tion times and volumes of the injected probes weremeasured at infinite dilution and thus were indepen-dent of the quantity of probes injected. The non-polar
180 KONA No.20 (2002)
probes employed were pentane, hexane, heptane,octane and nonane; the polar probes were di-chloromethane, chloroform, acetone, ethyl acetate,tetrahydrofuran and diethyl ether. Triplicate measure-ments in separate columns were made for G-SX, M-SXand S-SX powders. Differences in surface energeticswere ref lected in the calculated dispersive componentof the surface free energy, γs
D; specific component ofsurface free energies of adsorption, ∆GA
sp; and theacid-base parameters, KA and KD. A more detailed the-ory of these measurements is discussed elsewhere[13,20-22].
Data on specific surface areas required for IGCstudies were determined by BET nitrogen adsorptionusing a Surface Area Analyzer Coulter SA 3100 (Coul-ter Corp., Miami, FL, USA). Samples were placed inglass sample holders and out-gassed with helium(purity99.999%) at 40°C for 16 hours before analy-sis. Nitrogen (purity99.999%) was used as adsorbateand BET surface area was recorded as specific sur-face area of the samples. All measurements were per-formed in triplicate using the same batch of eachmaterial.
2.6 Electric charge and adhesion measurementsTriboelectrification was undertaken against a stain-
less steel contact surface using either a turbula mixeror a cyclone separator. Triboelectrification in a tur-bula mixer (Glen Creston, UK) was carried out byagitating a powder sample for 5 minutes at 30 rpm in a100 ml stainless steel vessel at ambient temperatureand relative humidity. A sample was poured in areproducible manner into a Faraday well connected toan electrometer (Keithley 610, Keithley Instruments,Reading, UK). Charge and mass of sample was thenrecorded to give specific charge before and after tri-boelectrofication. % w/w adhesion to the inner sur-face of the mixing vessel was calculated from theoriginal mass of sample and the mass of samplepoured into the Faraday well. During triboelectrifica-tion in a cyclone separator, a powder was fed from asteel vibratory table into a venturi funnel. Com-pressed air (velocity 8 m/s, relative humidity below10%, ambient temperature) was used to convey thepowder from the venturi along a horizontal pipe intothe cyclone separator. The Faraday well and forcecompensation load cell was fitted at the base of thecyclone and used to collect charged particles. Finalspecific charge was recorded for non-adhered powderresiding in the Faraday well and, where possible, pow-der adhering to the cyclone wall was dislodged by astream of air and its charge and mass recorded. In
both cases, the results were obtained from triplicatemeasurements.
2.7 Particle size analysisThe instrument consisted of a laser diffraction sen-
sor HELOS and dry-powder air-dispersion systemRODOS (Sympatec GmbH, Germany) with WINDOXOS computer interface. The dispersion process wascontrolled by means of adjusting pressure of the com-pressed air f low between 0.5 and 5 bar. The pressureof 2 bar was found to be sufficient to disperse most ofthe agglomerates avoiding, at the same time, attritionof the primary particles. All measurements were per-formed in triplicate. The particle shape factor, f, wascalculated as fSv/Sv* where Sv is the experimentalspecific surface area and Sv* is the specific surfacearea determined using the LD instrument assumingthe particle sphericity.
3. Results and discussion
3.1 CrystallinityAnalysis of diffraction patterns (Fig. 2) showed that
peak-fitting, background determination and indexingwere performed more consistently and with higheraccuracy using the S-SX sample than with the M-SXand G-SX samples. This fact is related to the smallerdiffraction line-broadening and higher signal-to-noiseratio for the S-SX sample (see Fig. 2). The strongestcharacteristic peaks of SX were identified as (001),(1
—13) and (
—1
—34). The crystal cell calculated from
this diffraction pattern is of triclinic P-1 (or P1) formwith parameters: a9.487; b16.242; c21.372 Å;α93.16; β97.73; γ90.94°, calculated cell volumeV3257.3 Å3 and theoretical crystal density ρ1.256g/cm3.
Physical broadening of diffraction peaks is a cumu-lative measure of crystal lattice imperfections. This isgrouped into size effects (grains, small-angle bound-aries, stacking faults) or as strain defects (point de-fects and dislocations). The basis for discriminationbetween these effects lies in the fundamental princi-ple that the size term does not depend on the diffrac-tion angle whereas the strain does [17]. Comparisonof the diffraction peaks (Fig. 2) indicates that thepeak broadening is much smaller for S-SX samplethan for both G-SX and M-SX samples. Quantitatively,these differences can be expressed through the shiftin the peak position, 2θ, the peak width, FWHM, andthe integral breadth, β* (all expressed in the degreeunits). The latter parameter is defined as the width ofrectangle having the same area, A, and height, I, as
KONA No.20 (2002) 181
182 KONA No.20 (2002)
the observed line profile:
β*A/I (1)
Table I shows these parameters for two character-istic diffraction peaks. S -SX sample shows highercrystallinity (smaller FWHM and β*) than the othertwo compounds. In addition, there is a small but sig-nificant shift of the diffraction peaks produced by M-SX and G-SX compounds towards smaller 2θ, relativeto the same peaks of S-SX compound. Such shift isbetween 0.001-0.003° for different lines which corre-sponds to a relative increase of d-spacing, d/dbetween 1 and 2% and to correspondent increase ofcrystal volume, V/V between 1 to 2% for both M-SX and G-SX samples.
More fundamental analysis of line broadening con-
sists of the “double-Voigt” method [17] which approxi-mates the physically broadened line profile as aconvolution of Cauchy (C) and Gauss (G) integralbreaths, containing size (S) and strain (distortion, D)contributions according to the equations:
βCβCSβCDs2/s02 (2)
βG2βG
2SβG
2Ds2/s0
2 (3)
The integral breaths, β, are given in the units (Å1) ofthe wave-vector, s:
s2sinθ/λ (4)ββ*cosθ/λ (5)
Here, βCD/s02 and βGD/s0
2 are constant for the wholepattern (taken at zero-value of the wave-vector, s0, ofthe first peak). The integral breaths found from the
0
40000
80000
120000
160000
0 5 10 15 20 25 30
2θ°
Inte
nsity
0
10000
20000
30000
15.4 15.6 15.8 16 16.2
G-SX
M-SX
S-SX
Fig. 2 X-ray diffraction patterns of salmeterol xinafoate samples: granulated (G-SX), micronised (M-SX) and SEDS-produced (S-SX) obtainedat the wavelength 1.4 Å. The inserted diagram allows a comparison between characteristic (1
—13) diffraction peaks for these samples.
S -SX M-SX G-SX
2θ 15.74200.0003 15.73960.0003 15.73950.0003
(1—13) FWHM 0.0840.001 0.1220.001 0.1710.001
β* 0.0930.001 0.1320.001 0.1780.001
2θ 22.36130.0005 22.35950.0005 22.36050.0005
(—1
—34) FWHM 0.0800.002 0.1100.002 0.1410.002
β* 0.0880.002 0.1190.002 0.1500.002
Table I The position (2θ), width (FWHM ) and integral breadth (β*) of characteristic diffractionpeaks of the salmeterol xinafoate samples.
experimental diffraction profiles allow calculation ofthe surface-weighted, DS, and volume-weighted, DV,domain size and a mean-square (Gaussian) strain, ε,which is the total strain averaged over infinite dis-tance:
DS1/(2βCS) (6)DV(EF)exp(βC
2S/βG
2S)/βG
2S (7)
εβGD/(s0BN2π) (8)
Here EF denotes a complementary error functionrelated to the background determination [17].
The results of computation using eqs. [2-8] aregiven in Table II. Clearly, S -SX compound consists oflarger crystalline domains (by about 20%) and smallerstrain (by about 60%) than both M-SX and G-SX com-pounds. The granulated batch under investigation, G-SX, was shown to be the least crystalline material.Table II also presents the data obtained using thealternative computation method with Le Bail diffrac-tion profile fitting. Both methods gave consistentresults in terms of domain size and strain.
It should be emphasized that S-SX shows highercrystallinity compared to both M-SX and G-SX com-pounds. In the first instance, this fact seems to becontradictory. It is widely believed that micronisationprocedure is the major factor responsible for the crys-tallinity decrease, and in general, for transition into ahigher free energy solid state. The analytical resultsobtained in this work indicate that “aggressive” crys-tallisation procedures [1] may also lead to crystal dis-ordering which is comparable to or greater than thosedefects induced by micronisation. It is unlikely thatmicronisation can improve the crystallinity. The factthat G-SX sample has a higher crystal strain and spe-
cific surface free energy is likely to indicate that M-SX compound was obtained from a different batch ofgranular SX than that available for the present study.Low consistency of batch solution crystallisation hasbeen acknowledged in the pharmaceutical industry.
3.2 Polymorphic puritySX has two polymorphs which are related enan-
tiotropically [1,12,13]. The estimated transition tem-perature is between 90 and 110°C [13]. Although theX-ray analysis shows that there is no significant pres-ence of form II in form I substances produced usingboth SEDS and micronisation, the polymorphic purityof these compounds was under question because theyshowed different melting-recrystallization behaviouraccording to differential scanning calorimetry (DSC).This problem was addressed in the present workusing time-resolved X-ray diffraction combined with athermal analysis.
The strongest characteristic diffraction peaks (001)of both SX polymorphs are located at low angles2θ4.13° (form I) and 2θ2.87° (form II) at λ1.54 Å.These high intensity peaks enable presence of form IIto be detected above 0.5% w/w in samples preparedby mixing the two polymorphs. Fig. 2 shows that,within this sensitivity, the S-SX, M-SX and G-SX arethe form I compounds. However, the dynamic X-raystudies of melting behaviour (Fig. 3) indicated that atrelatively fast heating rates equal or above 10°/min, asingle diffraction profile of form I, without recrystal-lization into form II was obtained for S -SX samples. Atthe same heating rate, M-SX samples showed meltingof form I and immediate recrystallization into form II.The characteristic (001) peak of form II appeared
KONA No.20 (2002) 183
S-SX M-SX G-SX
βCS, Å1 0.11102 0.13102 0.15102
βCD, Å1 0.30105 0.13104 0.21104
βGS, Å1 0.39103 0.40103 0.38103
βGD, Å1 0.63104 0.97104 0.12103
DS, Å 45344 38260 32650
DV, Å 78560 68286 60674
ε (0.530.02)103 (0.830.03)103 (0.1010.006)102
DV*, Å 1320 670 640
ε* 0.70103 0.17102 0.22102
Table II The integral breaths of Voigt-approximated diffraction profile, β, and calculated values ofthe surface-weighted, DS, and volume-weighted, DV, domain size and the Gaussian strain,ε. The corresponding size and strain parameters, DV* and ε*, were calculated on the basisof the diffraction profile Le Bail fitting and the instrument broadening FWHM0.025°.
simultaneously with the corresponding (001) peak ofform I and coincided with the exothermic DSC peakat this temperature. When the heating rates weredecreased below 10°/min, both S-SX and M-SX mate-rials showed recrystallization into form II at about130°C. These data indicate that S-SX compound has ahigher activation energy barrier to recrystallizationinto form II than M-SX compound. Assuming that S-SX consists of pure polymorph I, the characteristictime required for formation of polymorph II nucleiin the melt is estimated to be ∆T/10°C90 s where∆T(°C) is the difference of melting temperatures ofthe polymorphs I and II. In the case of M-SX, this timeis significantly smaller, possibly indicating a presenceof seeds of the high-melting polymorph II in themicronised sample.
The crystallinity and polymorphic purity are di-rectly related to the physical stability of SX powders.The present study demonstrates that while the M-SXmaterial possesses the crystal structure of form I, it ismore prone to polymorphic conversion than the S-SXcompound, as evidenced by time-resolved diffractionanalysis. It is likely that the micronization and solu-tion crystallisation processes employed for produc-tion of these particles created nuclei of form II whichaccelerate the polymorphic transition at high temper-
ature. It is also possible that supercritical f luid pro-cessing removes some impurities (soluble in thesupercritical phase) from the starting salmeterol com-pound also lowering the activation energy of nucleiformation.
3.3 Surface free energy and specific surfacearea
The fundamental quantity of inverse gas chro-matography is the net retention volume, VN, deter-mined from the retention time of a given solvent [20].Adsorption of the probe molecules on solid surfacescan be considered in terms of both dispersive andspecific components of surface free energy, corre-sponding to non-polar and polar properties of the sur-face. By virtue of their chemical nature, non-polarprobes of the alkane series only have dispersive com-ponent of surface free energy, which can be deter-mined from the slope of the plot based on the follow-ing equation:
RT lnVN2aNA(γSD)1/2(γL
D)1/2const (9)
where R is the gas constant, T is the absolute temper-ature of the column, a is the probe’s surface area, NA
is the Avogadro’s number, γSD is the dispersive com-
ponent of surface free energy of a SX powder and γLD
is the dispersive component of surface free energy ofthe solvent probes.
Polar probes have both dispersive and specific com-ponents of surface free energy of adsorption. The spe-cific component of surface free energy of adsorption(∆GA
SP ) can be estimated from the vertical distancebetween the alkane reference line and the polarprobes of interest. This free energy term can berelated to the donor number (DN ) and acceptor num-ber (AN *) of the polar solvent by the following equa-tion:
∆GASP KADNKDAN * (10)
DN describes the basicity or electron donor abilityof a probe whilst AN * defines the acidity or electronacceptor ability. Here AN * denotes a correction forthe contribution of the dispersive component andthe entropy contribution into the surface energy isassumed negligible [22]. Thus plotting ∆GA
SP/AN *versus DN/AN * yields a straight line where KA andKD correspond to the slope and intercept respectively.The IGC data for the various SX samples analysed bythe above approach are summarized in Tables IIIand IV. Comparison between different materialsshows that the magnitude of γS
D is 15% smaller for S-SX compounds than for both M-SX and G-SX com-
184 KONA No.20 (2002)
138T
empe
ratu
re, °
C
136
134
132M-SX
130
128
126
124
1222θ2.87° 4.13°
138
136
Tem
pera
ture
, °C 134
132S-SX 130
128
126
124
122
Fig. 3 Kinetics of melting and recrystallization of M-SX and S-SXcompounds as shown by time-resolved small-angle X-raydiffraction. Heating rate is 10°/min. The characteristic dif-fraction peaks correspond to the (001) ref lections with d-spacing: d00121.348 Å (form I) and d00130.708 Å (formII).
pounds. In addition, ∆GASP for all polar probes used
reduced by at least half for S-SX compound comparedto the other two materials. Comparison between M-SX and G-SX materials indicates that, although the γS
D
are almost equal within the experimental error, ∆GASP
for all the polar probes is larger for the granulatedmaterial.
The reduced magnitude of γSD for S -SX compound
implies that the surfaces of these particles are lessenergetic for non-polar, dispersive surface interac-tions than the other two compounds. The overallstrength of the polar interactions (∆GA
SP ) is also thesmallest for S-SX compound. Comparison betweenthe KA and KD values of the three samples indicatethat the acidity constant has the following trend:KA(S-SX)KA(M-SX)KA(G-SX). The basicity con-stants follows the reverse order with KD(S-SX) beingthe largest. Thus S-SX sample which has the weakestacidic property exhibits the strongest basic interac-tions with respect to its exposed polar groups at theinterface. This suggests that S -SX crystal surfaceshave, in relative terms, more exposed basic groupsbut fewer exposed acidic groups than both G-SX andM-SX compounds. Particles of all three samples havea similar platelet shape with the dominant 001 crys-tal faces. However, S -SX particles have the largestshape factor, f (see Table III), which means that
platelets of G-SX and M-SX are thicker. The othermaterials have more energetic lateral crystal surfacesas a result of the solution crystallisation procedure(G-SX) and particle breakage on micronisation (M-SX). Therefore the observed differences in KA andKD, combined with the smallest value of ∆GA
SP and γSD
for S -SX compound, suggest a combination of threedifferent factors affecting the specific surface energy:(a) difference in the crystal habit, i.e. the 001 crys-tal faces have stronger basic and weaker acidic in-teractions than the lateral crystal faces, (b) smalleroverall specific surface energy of the 001 crystalplanes as compared to any other crystallographicplanes and (c) disturbances of the crystal structurewhich also contribute to the higher surface energy ofG-SX and M-SX compounds.
It is clear that solvent adsorption progresses morerapidly with the M-SX and G-SX samples than with S-SX material. This fact indicates that supercritical f luidprocess is capable of producing particles with lowersurface activity (and greater surface stability) thanpowders produced by solution crystallisation andmicronisation.
3.4 Electrostatic charge and adhesionTable V presents results on the charge, Q, and frac-
tion of adhered material, AD. S -SX particles exhibitedsignificantly less (between one and two orders ofmagnitude) accumulated charge than the micronisedpowder before and after turbula mixing and also forthe non-adhered drug in cyclone separator. Corre-spondingly, the fraction of adhered material is severaltimes smaller for S-SX powder than for M-SX powderin both the turbula mixing and cyclone separatortests.
These results are consistent with the superior pow-der f low properties of S -SX material. Although thebulk powder density of S -SX material is very low(about 0.1 g/cm3 vs. 0.5 g/cm3 for M-SX) it f lows welland does not adhere to the container walls.
KONA No.20 (2002) 185
S-SX M-SX G-SX
γSD(s.d.), mJ/m2 32.476 38.285 36.972
(0.254) (0.907) (0.520)
KA (s.d.) 0.110 0.172 0.233(0.013) (0.001) (0.003)
KD (s.d.) 0.356 0.298 0.157(0.120) (0.021) (0.018)
SV (s.d.), m2/g 7.040 9.243 10.699(0.029) (0.002) (0.016)
f 3.78 2.80
Table III The dispersive component of the surface free energy,γS
D , the acidic, KA, and basic, KD, surface parameters,surface area, SV and calculated particle shape factor, f.
∆GASP , kJ/mol
Dichloromethane Chloroform Acetone Ethyl acetate Diethyl ether Tetrahydrofuran
S-SX 2.808 (0.147) 0.153 (0.080) 3.797 (1.173) 2.705 (0.613) 1.488 (0.390) 2.446 (0.279)
M-SX 0.810 (0.053) 4.560 (0.096) 3.995 (0.013) 2.774 (0.041) 3.609 (0.027)
G-SX 1.885 (0.047) 5.454 (0.154) 4.739 (0.015) 2.958 (0.038) 4.854 (0.069)
Table IV The specific component of surface free energies of adsorption, ∆GASP .
186 KONA No.20 (2002)
contact area and average distance between non-spher-ical particles. These problems will be addressed inour following study.
Acknowledgements
We would like to thank Prof. G. Rowley, Mr. A.Brennan and Dr. P. Carter (the University of Sunder-land) for performing the electrostatic tests and Mr. S.Bristow and Ms. D. Huddleston for obtaining the solu-bility data of salmeterol xinafoate in modified super-critical CO2. We gratefully acknowledge a continuoussupport from the SRS Daresbury Laboratory, in par-ticular, Dr. L. Cranswick (CCP-14 computation), Dr. J.G. Grossmann (SAXS studies) and Dr. C. Tang (HighResolution Powder Diffraction). G-SX and M-SX com-pounds were generously supplied by GlaxoWellcome.This work was also supported by the UK Engineeringand Physical Sciences Research Council (EPSRC).
References
1) S. Beach, D. Latham, C. Sidgwick, M. Hanna and P.York. Control of the physical form of salmeterolxinafoate. Organic Process Research & Development. 3:370-376 (1999).
2) B. Y. Shekunov, M. Hanna and P. York. Crystallizationprocess in turbulent supercritical f lows. J. CrystalGrowth, 198/199: 1345-1351 (1999).
3) H. Steckel, J. Thies and B. W. Müller. Micronizing ofsteroids for pulmonary delivery by supercritical carbondioxide. Int. J. Pharm., 152: 99-110 (1997).
4) H. Steckel and B. W. Müller. Metered-dose inhaler for-mulation of f luticasone-17-propionate micronized ithsupercritical carbon dioxide using the alternative pro-pellent HFA-227. Int. J. Pharm., 173: 25-33 (1998).
5) R. T. Bustami and H.-K. Chan and N. R. Foster. Aerosoldelivery of protein powders processed by supercriticalf luid technology. Proceedings of the Conference on Respi-ratory Drug Delivery, Palm Harbor, Florida, VII: 611-613(2000).
6) P. York and M. Hanna. Particle engineering by super-critical f luid technologies for powder inhalation drugdelivery. Proceedings of the Conference on Respiratory
3.5 Particle size and powder dispersabilityThe difference in particle size distribution (PSD) of
S-SX and M-SX powders is ref lected in the magnitudeof the mean particle sizes d4,33.5 µm (S-SX) and 1.8µm (M-SX) as measured using the LD technique. Forboth materials the cumulative PSD 98% is withinrespirable particle size range 0.5x10 µm. How-ever, a significant difference was observed betweenthe dispersion behaviour of micronised and supercrit-ically-processed powders. At high dispersing pres-sures above 2 bar, d4,3 is smaller for M-SX powder,as indicated by the primary PSD for this compound.This situation changes dramatically at dispersingpressures below 2 bar. At low pressures, S -SX pow-ders consistently produce a large fraction of primaryparticles in the respiratory size range, whereas M-SXpowders form stable agglomerates outside the 5 µmrange which are not be dispersed at such pressures.
The enhanced dispersability of S -SX powdersmeans a decrease of the inter-particulate contact areaand/or reduction of the cohesive forces leading tobetter performance of S -SX compound in the inhala-tion devices as shown in our work [23]. Despite alarger geometric (and volume) diameter for S-SX par-ticles, the Andersen cascade impactor measurementsindicated a greater than two-fold increase (from 25.15to 57.80%) of FPF for S -SX powder compared withFPF of M-SX powder.
4. Conclusion
The physical properties of micronised and super-critically-processed powders for respiratory drugdelivery have been quantitatively defined in terms ofspecific surface energy, polymorphic purity, acquiredcharge and crystallinity. The enhanced physical prop-erties for S -SX powders correlate well with theenhanced dispersion and f low behaviour of this pow-der. However, new analytical approaches are requiredto discriminate between the specific contributionssuch as aerodynamic forces and powder cohesive-ness, nature and statistics of inter-particulate forces,
Turbula Mixer Cyclone Separator
Q, nCg1 Q, nCg1 AD, Q, nCg1 Q, nCg1 AD,(before mixing) (after mixing) % w/w (for non-adhered drug) (for adhered drug) % w/w
S-SX 0.52 (51) 0.17 (431) 1.5 (1.4) 4.9 (6.8) 34.6 (42)... 05.5 (1.6)
M-SX 12.1 (7.3) 42.6 (53) . 27 (58). 48.4 (17.5) 49.7 (14.8) 16.7 (9.7)
Table V Summary of the mean specific charge, Q, and mean adhesion fraction, AD, of supercritically-processed (S-SX) and micronised (M-SX)powders. The data represent the mean of three determinations with coefficient of variation (% CV).
KONA No.20 (2002) 187
Drug Delivery, Phoenix, Arizona, V: 231-239 (1996).7) B. Y. Shekunov, J. Baldyga. and P. York. Particle forma-
tion by mixing with supercritical antisolvent at highReynolds numbers. Chem. Eng. Sci. 56: 1-13 (2001).
8) R. Sloan, M. E. Hollowood, G. O. Humphreys, W. Ashafand P. York. Supercritical f luid processing: preparationof stable protein particles. Proceedings of the 5th Meetingon Supercritical Fluids, Nice, France. 1: 301-306 (1998).
9) S. Moshashaee, M. Bistrat, R. T. Forbes, H. Nyqvist, P. York. Supercritical f luid processing of proteins I:Lysozyme precipitation from organic solution. Eur. J.Pharm. Sci., 11: 239-245 (2000).
10) P. York. Strategies for particle design using supercriticalf luid technologies. PSTT, 2: 430-440 (1999).
11) J. C. Feeley, P. York, B. S. Sumby, H. Dicks and M.Hanna. In vitro assessment of salbutamol sulphate pre-pared by micronisation and a novel supercritical f luidtechnique. Drug Delivery to the Lungs, IX: 196-199(1998).
12) M. Hanna, P. York and B. Yu. Shekunov. Control of poly-morphic forms of a drug substance by SEDS technique.Proceedings of the 5th Meeting on Supercritical Fluids,Nice, France. 1: 325-330 (1998).
13) H. H. Y. Tong, B. Y. Shekunov, P. York, A. H. L. Chow.Characterisation of two polymorphs of salmeterolxinafoate crystallized from supercritical f luids. Pharm.Res. 18: 1-7 (2001).
14) S. C. Bristow, B. Y. Shekunov and P. York. Solubilityanalysis of drug compounds in supercritical carbondioxide using static and dynamic extraction systems.Ind. Eng. Chem. Res. 40: 1732-1739 (2001).
15) S. C. Bristow, T. Shekunov, B. Y. Shekunov and P. York.Analysis of the supersaturation and precipitation pro-cess with supercritical CO2. To be published in the J.
Supercritical Fluids (2001).16) J. J. Laugier and B. Bochu. “Chekcell”; G. Nolze and
W. Kraus. “Powder Cell 2.3”, S. A. Howard and R. L.Snyder. “Shadow”; D. Balzar and H. Ledbetter. “Breath”.CCP14 Suite for Windows (www.ccp14.ac.uk);
17) D. Balzar and H. Ledbetter. Software for comparativeanalysis of diffraction line broadening. Advances in X-ray Analysis, 39: 457-464 (1997).
18) J. I. Langford and D. Louër. Powder diffraction. Rep.Prog. Phys. 59: 131-234 (1996).
19) A. D. Edwards, B. Yu. Shekunov, R. T. Forbes, J. G.Grossmann and P. York. Polymorphic transition of car-bamazepine studied using simultaneous small- andwide-angle x-ray scattering. In print. J. Pharm. Sci.(2001).
20) J. Schultz and L. Lavielle. Interfacial properties of car-bon fiber-epoxy matrix composites. In D. R. Lloyd, T. C.Ward, H. P. Schreiber and C. C. Pizana (eds.), InverseGas Chromatography Characterization of Polymers andOther Materials, American Chemical Society, Washing-ton, 185-202 (1989).
21) M. D. Ticehurst, R. C. Rowe and P. York. Determinationof surface properties of salbutamol sulphate by inversegas chromatography. Int. J. Pharm. 111: 241-249 (1994).
22) J. C. Feeley, P. York, B. S. Sumby and H. Dicks. Deter-mination of surface properties and f low characteristicsof salbutamol sulphate, before and after micronisation.Int. J. Pharm. 172: 89-96 (1998).
23) B. Y. Shekunov, J. C. Feeley, A. H. L. Chow, H. H. Y.Tong, S. E. Walker and P. York. Aerosol performance ofsalmeterol xinafoate powders prepared by micronisa-tion and by direct supercritical f luid crystallisation. Pro-ceedings of the AAPS Annual Conference, Denver, AAPSPharmSci. 3: 96 (2001).
188 KONA No.20 (2002)
Introduction
The importance of particle shape has gained in-creasing recognition in recent years. It is clear thatshape can play a significant role in the use of particlesas abrasives and in applications involving packing inpowder compacts, slurry rheology, etc. For particlesproduced by comminution, shape may be determinedby material characteristics such as crystal cleavageand by the nature of the breakage process involved.While it is generally recognized that comminution canlead to changes in particle shape, relatively few at-tempts to quantify these effects have been reported.Furthermore, largely due to the lack of widely ac-cepted measures of shape, there is some disagree-ment on the evolution of particle shape in grindingprocesses. For example, Bond [1] considered that thecharacter of the material being broken has moreinf luence on the shape of the product than the type ofsize reduction machine used. Similarly, Heywood [2]stated that the shape of particles produced on initial
fracture is dependent upon the characteristics of thematerial. On the other hand, Rose [3] suggested thatthe type of the mill has the major effect on the parti-cle shape although the properties of the material arealso a factor. Similarly, Charles [4] observed that theshape of glass particles produced by a single fracturedepended on the rate of application of stress.
The particular mode of breakage is likely to affectthe shape of product particles. Massive fracture canbe expected to produce highly irregular particles withsharp edges formed by the intersection of propagat-ing cracks. Attrition of particles, by surface erosion orchipping at edges or corners, is more likely to causerounding of particles although the small fragmentsremoved may be quite irregular in shape. It followsthat grinding conditions that favor one breakagemode over another may be critical in determiningproduct particle shape. For any system, the prevailingconditions will generally depend on the type ofmachine and the properties and size of the particlesbeing broken. Since there are normally distributionsof particle sizes and applied stresses, it is reasonableto expect a distribution of product shapes. Gaudin [5]observed that large particles were often subject pri-marily to attrition, tending to become more roundedin shape, while finer material typically underwent
E. KayaProcess Technology Center, Phelps Dodge Mining Company*R. HoggDepartment of Energy and Geo-Environmental Engineering, The Pennsylvania State University**S. R. KumarSeisint, Inc***
Particle Shape Modification in Comminution†
Abstract
The evolution of particle shape during the course of comminution processes has been investigated.Shape is characterized using a variety of quantitative shape descriptors determined from particleprofiles obtained by image analysis. Descriptors related to particle elongation, roundness and angu-larity are emphasized. Distributions of the descriptors have been determined for a range of particlesizes, for dif ferent extents of grinding for various equipment types. For a given descriptor, the distrib-utions of measured values generally follow a consistent pattern (often roughly log normal). Typi-cally, the means and standard deviations show progressive changes as grinding time increases. Forthe most part, prolonged exposure to the grinding environment leads to rounding of the particles.
* Safford, AZ** University Park, PA*** Boca Raton, FL† Accepted: September 20, 2002
massive fracture leading to more angular product par-ticles. Based on examination of crushed glass parti-cles, Tsubaki and Jimbo [6] concluded that particleshape varies with size.
Holt [7] reviewed the effect of comminution deviceson particle shape and concluded that single-passdevices such as roll crushers generally produce angu-lar particles while retention systems such as ball millsproduce more rounded particles. Dumm and Hogg[8] showed that the rounding effect in ball millsbecomes more pronounced with increased grindingtime. Durney and Meloy [9] investigated the shape ofparticles produced by jaw crushers using Fourieranalysis to provide a quantitative description of theshape characteristics. In particular, they comparedthe results of crushing under single-particle andchoke-feeding conditions. They observed that whenthe particles were fed into the mill one at a time theproducts were highly angular, while choke feedingproduced more “blocky” or rounded particles. In eachcase, the finer particles had more angular and irregu-lar shapes.
In the present paper, populations of crushed parti-cles from different comminution devices were evalu-ated using a computerized image analysis techniqueto quantify particle shape in terms of physically recog-nizable shape descriptors.
Shape Analysis
Several different approaches to the analysis of par-ticle shape have been described in the literature.Fourier analysis of the vector of polar coordinates thatrepresent the particle profile yields a set of Fouriercoefficients that, in principle, define the shape of theparticle [10,11]. Meloy [12] observed simple correla-tions among the coefficients for a variety of differentshapes and defined a two-parameter particle “signa-ture” as an overall characteristic of the particle shape.Durney and Meloy [9] used statistical procedures todetect significant differences in the Fourier coeffi-cients obtained from different populations. Fractalanalysis [13,14] has been widely applied to particleshape characterization and is especially attractive forhighly complex shapes such as those of agglomer-ates. The approach adopted in the present work isbased on an attempt to define shape in terms of physi-cally recognizable features such as elongation andangularity.
An image processing system was used to providedigitized particle profiles from optical microscopy (orfrom scanning electron micrographs) by means of a
procedure developed by Dumm and Hogg [8] andmodified by Kumar [15] and Kaya [16]. A series ofstraight-line segments was fitted to the set of N pointsrepresenting the complete profile as illustrated in Fig-ure 1. The intersections of these linear segmentsdefine a reduced set of n perimeter points (nN)and describe an n-sided polygon that represents theessential features of the original profile.
In order to minimize the errors associated with theuse of the fitted polygon, the projected area and cen-troid of the image were first obtained from the origi-nal digitized profile. Designating the x-y coordinatesof the original perimeter points as (xi, yi), the cross-sectional area of the particle was determined from:
A ∑N
i1(xi1xi)(yi1yi) (1)
where the point at (xN1, yN1) represents the returnto the initial starting point (i1). The coordinates x–, y–
of the centroid of the image can be obtained from:
x– (2)
and
∑N
i1(x2
i1xi2)(yi1yi)
2∑N
i1(xi1xi)(yi1yi)
12
KONA No.20 (2002) 189
Fig. 1 Representation of a particle profile consisting of N perime-ter points (N40 in this example) by a fitted polygondefined by a set of n reduced perimeter points (n7 in thiscase).
R i1
(xi, yi)
(–x, –y)
(xi1, yi1)
(df)i(dF)min
(dF)π/2
R i
Original Perimeter Point
Reduced Perimeter Point
βi
α i
φi1
L i
y– (3)
The equivalent-circle mean radius of the particle canbe calculated using:
R0BA/πN (4)
The radial vectors Ri from the centroid to each ofthe n perimeter points on the reduced profile aregiven by:
R iBN(xiNx–)2N(yiNy–)2 (5)
The angles φi between adjacent edges of the fittedpolygon were evaluated by applying the cosine rule tothe triangles defined by the edge and the adjacentradial vectors as shown in Figure 1. Thus, for theedges intersecting at the perimeter point (xi, yi) theangle α i is given by:
cosα i (6)
where Li is the length of the edge connecting points(xi, yi) and (xi1, yi1) (see Figure 1). Similarly, βi canbe obtained from:
cosβi (7)
The angle φi is simply the sum: α iβi.Feret’s diameters are defined as the distance be-
tween two parallel lines tangent to opposite sides ofa particle, in some particular orientation. For anyperimeter point, the corresponding Feret’s diameter,(df)i can be obtained by projecting the other perime-ter points on to the vector Ri and determining themaximum distance from the original point (see Fig-ure 1).
The following shape descriptors were defined torepresent specific geometric features of the profile.1) The elongation E was defined using the ratio ofthe minimum Feret’s diameter to that at right anglesto it. Thus,
E[(dF)π/2/(dF)min]1 (8)
where (dF)min is the minimum of the set of measuredFeret’s diameters and (dF)π/2 is the Feret’s diametermeasured perpendicular to (dF)min. As defined, theelongation is zero for a circular profile.2) The angular variability Vφ was defined to repre-sent the variation in the angles φi between adjacent
R2i1L i
2R2i
2R i1L i
Ri2L i
2R2i1
2R iL i
∑N
i1(y2
i1yi2)(xi1xi)
2∑N
i1(yi1yi)(xi1xi)
edges on the reduced profile. Specifically, for φi ex-pressed in radians,
Vφ∑n
i11
3(9)
The third power was used in order to emphasize therole of the smaller angles, which are considered tocontribute the most to the “angularity” of a particle[15]. A many-sided polygon fitted to a circle gives aset of angles close to π with a corresponding angularvariability close to zero.3) The radial variability VR was used to describe thedeparture of the profile from a circle. The particulardefinition used was
VR∑n
i1 1 (10)
where R0 is the equivalent spherical diameter asdefined by Equation 4 and the Ri are the lengths ofthe radial vectors from the centroid to each of the nperimeter points (Equation 5). Since each Ri would beequal to R0 for a circle, the radial variability would bezero.
Calculated values of the various parameters aregiven in Table 1 for the schematic profile shown inFigure 1.
Experimental Systems
Shape descriptors were measured for a range ofparticle sizes produced by crushing and grindingunder a variety of conditions. Approximately 600 par-ticles were analyzed from each population and thedistribution of each descriptor was evaluated. The
R i
R0
φi
π
190 KONA No.20 (2002)
Reduced Perimeter Relative Distance Angle betweenPoint, i from Centroid, Adjacent Faces,
(clockwise from top) Ri/R0 φi
Radians Degrees
1 1.409 1.479 084.7
2 1.070 2.336 133.8
3 0.885 2.549 146.0
4 1.454 1.227 070.3
5 0.878 2.656 152.2
6 1.111 1.855 106.3
7 0.915 3.607 206.7
Table 1 Relative dimensions and calculated shape descriptors forthe schematic particle profile shown in Figure 1.
Shape Parameters:Elongation, E: 0.41Radial Variability, VR: 1.37Angular Variability, Vφ: 0.47
materials used were a high-volatile bituminous coalfrom a continuous mining operation in the PittsburghCoal Seam (Green Country, PA) and quartz fromNorth Carolina. The following crushing and grindingdevices were used to produce particles in differentsize ranges:
• Jaw Crusher used to reduce feed materialsabout 1 cm in size to less than about 5 mm
• Hammer Mill (Holmes pulverizer) used tocrush coal particles in the 5 mm to 1 cm sizerange to less than 1 mm
• Disk Mill (Quaker City) used to pulverize 1mm feed particles
• Ring and Puck Mill (Bleuler Pulverizer) usedfor fine grinding of disk mill product to micronsizes
• Planetary Ball Mill (Retsch) also used for finegrinding of disk mill product.
The jaw crusher, hammer mill and disk mill areessentially single-pass devices, although some, lim-
ited retention of broken material may occur. The ring-and-puck and planetary mills are retention devicesthat can subject particles to repeated breakage. In thecase of the latter two devices, different grinding timeswere used to vary the exposure of particles to thegrinding environment.
Experimental Results
Analysis of Shape for Different Materials
In order to evaluate particle shape effects for differ-ent materials, samples of the coal and quartz wereprepared as 9.512.7 mm size fractions and fed to ajaw crusher with a gap setting of 6.4 mm. Products indifferent size classes (3040, 5070, 70100, 140200 and 200270 US mesh) were analyzed using digi-tized images obtained by optical microscopy.
Examples of the distributions of angular variabilityfor coal and quartz particles of different sizes are pre-sented in Figures 2 and 3. In each case, the distribu-
KONA No.20 (2002) 191
Fig. 3 Graphical and visual representations of the number distri-butions of angular variability for quartz particles producedin a jaw crusher (feed size 9.512.7 mm; gap setting 6.4mm).
99.9
99
90
705030
10
1
0.10.1 0.2 0.3 0.5 0.7 1 2
Angular Variability, Vφ
Angular Variability
Size, US mesh
Perc
ent L
ess
Tha
n V
φ
3040507070100140200200270
3040 Mesh
0.10 0.19 0.25 0.32 0.42 1.00
Angular Variability
200270 Mesh
0.10 0.19 0.25 0.32 0.42 1.00
Fig. 2 Graphical and visual representations of the number distri-butions of angular variability for coal particles produced ina jaw crusher (feed size 9.512.7 mm; gap setting 6.4 mm).
99.9
99
90
70
50
30
10
1
0.10.1 0.2 0.3 0.5 0.7 1.0 2.0
Angular Variability, Vφ
Angular Variability
Size, US mesh
Perc
ent L
ess
Tha
n V
φ
3040507070100140200200270
3040 Mesh
0.10 0.19 0.25 0.32 0.42 1.00
Angular Variability
200270 Mesh
0.10 0.19 0.25 0.32 0.42 1.00
tions are shown graphically as cumulative plots and avisual representation to illustrate the significance ofthe variations is included. The particles in each col-umn are typical of that range of angular variabilitywhile the number of particles in each column repre-sents the number fraction in that range. The resultsindicate that, for coal particles, the distributions gen-erally become somewhat narrower and shift to lowervalues as size decreases, implying a size dependencyof the shape. On the other hand, the distributions ofangular variability for the quartz particles show noclear systematic variation with size. Very similartrends were observed for the other shape descriptors:elongation and radial variability. It is interesting tonote that the distributions appear to conform quiteclosely to the log-normal distribution.
Effect of Grinding Procedure
The particle shape is expected to be affected by thetype of machine, by the specific breakage mechanismin a grinding device and by the time spent in thegrinding environment. The effect of grinding deviceon shape was analyzed for coal particles using theBleuler ring-and-puck pulverizer and the planetaryball mill. The grinding times were set so as to give asimilar extent of grinding for each mill. The quantityof feed (10 mesh) was 20 g for the Bleuler and 9.5 gfor the planetary mill. The distributions of elongationare presented in Figure 4. The graph indicates thatdifferent grinding devices affect shape differently.Shape does not change substantially with grindingtime in a high-energy mill (Bleuler). On the otherhand, the shape distributions of the particles pro-duced in the planetary mill shifted towards lower val-ues, indicating that particles become more roundedwith increased grinding time. Similar trends havebeen observed for particle sizes in the size rangefrom 3 to 5 µm.
Examples of the distributions of angular variabilityfor 70100 US mesh coal obtained from a single passthrough different crushing and grinding devices areshown in Figure 5. It appears that the jaw crusher,for which massive fracture is the dominant breakagemechanism, produces the most irregular particles.The Quaker City mill, for which most of the breakageis probably by massive fracture of coarse feed par-ticles, also produces quite irregular particles. TheHolmes pulverizer, which allows some retention ofmaterial and may include contributions from the attri-tion-type mechanisms, and the Bleuler mill (30 sec-ond grinding time), generally produce particles ofmore regular shape. Similar trends have been ob-
served for 200270 US mesh fractions. Changes infeed size to the devices did not lead to significant dif-ferences in product particle shape.
The effects of mill type on the average particleshape for different coal product sizes are illustrated inFigure 6. While the variations are generally small,
192 KONA No.20 (2002)
Fig. 4 Number distributions of elongation for coal particles(200270 US mesh) produced in both the Bleuler andplanetary mills using different grinding times.
99
90
70
50
30
10
1
Elongation, E
Bleuler Mill4 seconds30 seconds
Planetary Mill12 minutes46 minutes
Perc
ent L
ess
Tha
n E
0.07 0.1 0.2 0.3 0.5 0.7 1 2 3
Fig. 5 Number distributions of angular variability for coal parti-cles (70100 US mesh) produced by different comminu-tion devices.
99
90
70
50
30
10
1
0.1
Angular Variability, Vφ
Holmes PulverizerQuaker City millJaw Crusher(1/4˝ gap)Bleuler mill
816 mesh1/2˝1/4˝1/2˝3/8˝
3040 mesh
Perc
ent L
ess
Tha
n V
φ
0.1 0.2 0.3 0.5 0.7 1 2 3
Mill Feed Size
the trends are consistent and similar for each of thethree descriptors. Large particles produced by singlebreakage events tend to be quite irregular in shapewhile particles subject to repeated breakage or longexposure to the grinding environment are usuallymore rounded.
Conclusions
The results of this investigation indicate that, forthe materials studied (quartz and coal), the shape ofparticles produced by size reduction is controlled by
a) the nature of the material being reducedb) the type of comminution device used and the
predominant breakage mechanisms involvedc) the time spent in the grinding environment.
In particular, it is concluded that the products of in-dividual breakage events are typically angular andirregular in shape. Continued exposure to the grind-ing environment leads to rounding of the particles.For a given product size distribution, devices thatemploy high energy input yield products containinga high proportion of newly-created particles. Suchdevices, therefore, favor the production of irregularparticles. Grinding machines for which the energyinput is relatively low, on the other hand, rely onrepeated breakage action for size reduction and tendto produce more rounded product particles.
KONA No.20 (2002) 193
Fig. 6 Variation in shape with particle size for coal ground in different mill types.
JawHolmesQuaker CityBleuler, 30 sec
0.3
0.4
0.5
0.6
0.7
101 100 1000
Mea
n E
long
atio
n
JawHolmesQuaker CityBleuler, 30 sec
0.3
0.4
0.5
101 100 1000
Mea
n A
ngul
ar V
aria
bilit
y, V
φ
JawHolmesQuaker CityBleuler, 30 sec
3
2
4
101 100 1000
Mea
n R
adia
l Var
iabi
lity,
VR
Size, µm
The differences in the size dependence of product-particle shape for coal and quartz suggest that theexistence of structural features such as cleats in coalor cleavage planes in crystals may lead to more angu-lar and irregular products of comminution. Further-more, since the effect appears to be more pronouncedfor low-energy devices, it may be possible to achievesome degree of control over shape through appropri-ate equipment selection. However, considerable addi-tional work would be needed to establish the basis forsuch control.
Acknowledgements
The work described in this paper was supported inpart under the Mineral Institutes Program by GrantNos. G1105142, G1115142 and G1125142 from theBureau of Mines, US Department of the Interior, aspart of the Generic Mineral Technology Center forRespirable Dust.
Nomenclature
A : Cross-sectional area [m2](df)i : Feret’s diameter corresponding to
perimeter point i [m](df)min : Minimum Feret’s diameter of a particle [m] (df)π/2 : Feret’s diameter perpendicular to (df)min [m]E : Elongation of a particle []L i : Edge-length on a particle profile [m]n : Number of reduced perimeter points
on a fitted particle profile []N : Number of measured perimeter points
on a particle profile []R0 : Equivalent-circle mean particle radius [m]Ri : Length of radial vector from particle
centroid to the ith perimeter point [m]VR : Radial variability []Vφ : Angular variability []xi, yi : Cartesian coordinates of the ith
perimeter point [m]x–, y– : Cartesian coordinates of a particle
centroid [m]α i : Angle defined in Figure 1 [radians]βi : Angle defined in Figure 1 [radians]φi : Angle between adjacent edges on
a particle profile [radians]
References
1) Bond, F. C., “Control Particle Shape and Size,” Chemi-cal Engineering, pp. 195-198 (Aug. 1954).
2) Heywood, H., “Powder Production by Fine Milling,” inPowders in Industry, Society of Chemical Industry, pp.25-26 (1962).
3) Rose, H. E., “Particle Shape, Size and Surface Area,” inPowders in Industry, Soc. Chem. Ind., pp. 130-149 (1961).
4) Charles, R. J., “High Velocity Impact in Comminution,”Mining Engineering, pp. 1028-1032 (1956).
5) Gaudin, A. M., “An Investigation of Crushing Phenom-ena,” Trans AIME, 73. pp. 253-317 (1926).
6) Tsubaki, J. and Jimbo, G., “Identification of ParticlesUsing Diagrams and Distributions of Shape Indices,”Powder Technology, 22. pp. 171-178 (1979).
7) Holt, C. B., “The Shape of Particles Produced by Com-minution A Review,” Powder Technology, 28. pp. 59-63 (1981).
8) Dumm, T. F. and Hogg, R., “Characterization of ParticleShape,” Proceedings of International Symposium on Res-pirable Dust in the Mineral Industries, SME, Littleton,CO, pp. 283-288, (1990).
9) Durney, T. E. and Meloy, T. P., “Particle Shape Effectsdue to Crushing Method and Size,” Intl. J. Miner.Process, 16. pp. 109-123 (1986).
10) Beddow, J. K. and Meloy, T. P., Advanced ParticulateMorphology, CRC Press, Boca Raton FL (1977).
11) Meloy, T. P., “Particulate Characterization: FutureApproaches,” Chapter 3 in Handbook of Powder Scienceand Technology, M. E. Fayed and L. Otten, editors, vanNostrand Rheinhold, New York, pp. 69-98 (1984).
12) Meloy, T. P., “Fast Fourier Transforms Applied to ShapeAnalysis of Particle Silhouettes to Obtain MorphologicalData,” Powder Technology, 17. pp. 27-35 (1977).
13) Mandelbrot, B. P., Fractals: Form, Chance and Dimen-sion, W. H. Freeman, San Francisco (1977).
14) Kaye, B. H., “The description of Two-Dimensional Rug-ged boundaries in Fineparticle Science by Means ofFractal Dimensions’,” Powder Technology, 46. pp. 245-254 (1986).
15) Kumar, S. R., “Characterization of Particle Shape,” M. S.Thesis, The Pennsylvania State University (1996).
16) Kaya, E., “Control of Particle Characteristics in the Pro-duction of Fine Powder By Grinding,” Ph.D. Thesis,The Pennsylvania State University (1996).
194 KONA No.20 (2002)
KONA No.20 (2002) 195
Author’s short biography
Erol Kaya
Erol Kaya is currently a Senior Research Engineer at the Process Technology Cen-ter, Phelps Dodge Mining Company. He received a B. Sc. degree in mining engi-neering from the Istanbul Technical University, the M.S. and Ph.D. degrees inmineral processing and M. Eng. in environmental pollution control from the Penn-sylvania State University. His research interests include particulate technology,grinding and copper f lotation.
Richard Hogg
Richard Hogg is Professor of Mineral Processing and GeoEnvironmental Engi-neering at the Pennsylvania State University. He received a B.Sc. from the Univer-sity of Leeds and the M.S. and Ph.D. degrees from the University of California atBerkeley. Dr Hogg’s research interests include fine particle processing, particlecharacterization, and colloid and surface chemistry.
Senthil Kumar
Senthil Kumar graduated from the Pennsylvania State University with an M.S. inMineral Processing and an MEng. in Computer Science and Engineering. Hereceived his BTech. in Metallurgical engineering from the Indian Institute of Tech-nology, Bombay. He is presently a technical architect at Seisint Inc., a softwarecompany in Boca Raton, Florida.
196 KONA No.20 (2002)
1. Introduction
The handling, storage, f low, and mixing of particu-late materials are important processing steps in manyindustries. During all of these processing steps, prod-uct quality may be lowered by a phenomenon knownas segregation. Segregation is defined as a demixingprocess in which components of a mixture separate aslong as one component of the mixture is differentthan another. Size-segregation is the most common inwhich finer particles gather in the center and larger
particles tend towards the walls of storage container.However, other types of segregation caused by den-sity, shape and composition have been observed. Seg-regation is a serious problem in the processing andmanufacturing of particulate materials. Several stud-ies have investigated segregation for a particularprocess and reported a segregation coefficient inorder to quantify the severity of segregation. Some ofthe processes that have been studied include dis-charge from a hopper, vibrated channels, vibratedcolumns, heap formation, and die filling. Anotherapproach in solving segregation problems was iden-tifying fundamental segregation mechanisms for agiven process and determining the dominant mech-anism. By identifying the dominant mechanism ofa particular process, segregation can be predicted
S. P. Duffy and V. M. PuriDepartment of Agricultural and Biological EngineeringThe Pennsylvania State University*
Primary Segregation Shear Cell for Size-Segregation Analysis of Binary Mixtures†
Abstract
Segregation is important in many bulk handling industries due to its impact on product qualityand mixing. Previous studies have focused on quantifying segregation as a coef ficient for a particu-lar process. Although this has provided insights into the ef fect of segregation during particularprocesses, it has not provided a rational approach to understanding the phenomena of segregation.Toward this end, a vertically oriented segregation shear cell was designed, fabricated and used to testthe response of binary mixtures of spherical glass beads. Three size ratios of 10.9:1, 8.7:1, and 5.1:1were used in this study. Variables such as strain, strain rate (i.e., cycle speed) and bed depth wereused to quantify size-segregation characteristics under dif ferent input energies. Size ratio was themost dominant variable that af fected the percolation rate of f ines through a bed of coarse particles.Based on the dif ferences in percolation between the smaller ratio of 5.1:1 and larger ratios of 8.7:1and 10.9:1, there are indications of a critical size ratio that determines the mechanism of percola-tion. Two mechanisms were observed. First, the larger size ratios exhibited an initial free-fall dis-charge of fines at the beginning of the test. This initial discharge was followed by a dif fusivebehavior, i.e., monotonically increasing trend that approaches an asymptotic value. The smallerratio did not exhibit the initial discharge and the responses were described adequately by the dif fu-sive behavior. Strain also had an ef fect. Input energy, as related to strain, was found to be critical inthe type of percolation exhibited, i.e., the presence or absence of an initial rapid discharge. For thesize ratio of 10.9:1, the amount of input energy was critical because the size of the fine particles wasnear the size of the coarse bed pore space. When the input energy was below a critical limit, mechan-ical arching was occurring. Although, the input energy is a function of bed depth and strain rate,these parameters did not inf luence the results outside random behavior.
* 229 AG Engineering BuildingUniversity Park, PA 16802
† Accepted: October 17, 2002
based on previously observed and simplified experi-ments. For example, heap formation is the process inwhich a stream of powder is deposited onto a f latplate. The powder forms a conical heap as powder iscontinuously deposited onto itself. It has been shownduring this process that fines tend to the center of theconical heap and coarse particles concentrate on theouter boundaries of the cone. The dominant mecha-nism for this example of size-segregation was identi-fied to be a rolling mechanism. Coarse particles moreeasily roll down the conical plane formed duringdeposition. Therefore, fines concentrate at the centerdue to the inability to roll down the conical plane andcoarse particles concentrate at the outer surfaces.
A particulate material will f low as long as theprocess induces enough internal shear to overcomethe shear strength of the powder. This is the funda-mental approach to hopper design using the Mohr-Coulomb theory and Jenike’s Flow/No-Flow hy-pothesis. Previous observations have shown thatsegregation is occurring in a hopper during f low/dis-charge. Based on these observations, researchersdeveloped a simple shear test apparatus to measuresize-segregation during shear. When the shear mech-anism was isolated, size-segregation was quantifiedby measuring the drainage of fine particles through abed of coarse particles. This type of segregation isknown as percolation. In this study, percolation wasdefined as a demixing process perpendicular to theshear deformation and parallel to gravity where thefines traveled through the bed of coarse particles dur-ing a shear disturbance. The size of the particles thatwere studied had mean diameters ranging from 2.4mm to 37.2 mm. The mean sizes selected were lim-ited by the construction of the simple shear cell andapplicable fines to coarse ratios. The bed of coarseparticles was fixed similar to a roller assembly so thatpure shear could be obtained and the fines could eas-ily escape at the bottom of the tester. Therefore, a pri-mary shear apparatus that would overcome the meandiameter limitations of the previous work by measur-ing the discharge of fine particles through a bed ofcoarse particles will be an invaluable experimentaldevice to quantify size-segregation induced by perco-lation. Therefore, a vertically oriented the primarysegregation shear tester was designed, fabricated,and tested to evaluate its feasibility for quantifyingpercolation segregation.
2. Literature Review
Segregation, while important in every aspect of
powder technology, has limited understanding. Mostresearchers define a segregation coefficient andexplore segregation for a particular process. The fol-lowing subsections summarize the key segregation-related findings relevant to this study.
2.1 Mechanisms of SegregationTen unranked main mechanisms of segregation
have been identified (Mosby et al., 1996): 1) Rolling,2) Sieving, 3) Push-away, 4) Angle of repose, 5) Perco-lation, 6) Displacement, 7) Trajectory, 8) Air current,9) Fluidization, and 10) Impact. Rolling ef fects aredominant in heap formation, because segregation in aheap has been described as a surface phenomenonwhere the heap surface remains constant. Rollingeffects are also important, because friction varies as afunction of size and stumbling effects, the ability oflarger particles to roll over obstacles. Sieving ef fectsoccur in conjunction with rolling effects during heapformation. The larger particles rolling along the sur-face create a non-blinding screen. This type of segre-gation continues as long as the large particles are inmotion. Sieving effects are also present in die filling.Different densities cause push-away effects. A top layerwith a higher density will push the bottom layers withlower densities to the side. Therefore, the center coreof the powder sample will have a higher density thanthe wall area of the sample. Johanson (1988) gave thefirst indication of angle of repose ef fects in a binarysample of mung beans and fine salt. A high percent-age of salt prohibited sieving effects, however highcontents of mung beans were near the wall. Percola-tion has been studied as a function of vibration andinduced by gravity. Vibration can cause a small indi-vidual particle to travel downward through the pow-der mass. Bridgwater et al. (1978) developed a simpleshear apparatus that induced percolation. Percolationis similar to sieving during shear, however a movinglayer is absent.
Displacement segregation describes the phenomenain which a single large particle placed at the bottomof a pile of smaller particles travels to the top duringvibration. A critical frequency of vibration was found.Trajectory ef fects encompass larger particles travelingfurther off a chute than do smaller particles. Studieshave shown that a large amount of fines were foundon the side of a heap closest to the chute. Particulatematerial filled centrally into a tall bin or hopper thatcontains a significant amount of fines (defined as50 µm) creates an air f low channel. This air f lowcauses fines to travel to the sides of the silo or hopperand leaves the core filled with coarse particles. Flu-
KONA No.20 (2002) 197
idization ef fects are similar to air current effects. Dur-ing the filling of a hopper, fines become f luidized, oraerated, which enables the coarse particles to fallthrough the aerated fines. The two mechanisms ofimpact ef fects are interparticle collisions and particle-boundary collisions. As a small particle collides with alarger particle, the small particle can either stop orincrease in velocity. This results in a wider distri-bution among the fine particles. Impact effects areincreased with an increase in f low rate.
2.2 Segregation TestersThis section has been divided into two major cate-
gories. First, testers that were specifically designed tomeasure segregation are reviewed. Second, test tech-niques used to measure segregation for existing han-dling equipment are examined.
2.2.1 Specific test designsThe following test designs were developed to quan-
tify segregation during a specific operation. Flow outof a hopper, filling a hopper, and free-surface f lowwere operations that were targeted for this reviewbecause of their relevance to the present study.
Mosby et al. (1996) detailed two testers that weredeveloped at Telemark. The first was a two-dimen-sional, rectangular box, tester that has an interior,inclined channel. The angle of the channel and ninesampling holes can be adjusted simultaneously sothat the sampling holes are parallel to the channel.Various channel lengths were tested and it was foundthat a channel length of 630 mm gave reproducibleresults. Five types of tests were completed to showthe different segregation mechanisms in a heap. Vari-ables that were changed between the tests were mix-ing ratios, feed rates, and length of channel. Themixing ratio was not defined, but it appears to be thepercent of fines (alumina). Sand and alumina werethe two components of the mixture. It was concludedfrom this work that f luidization, rolling, and sievingare predominant mechanisms in heap segregation.
Bagster (1996) built a tester similar to that of Tele-mark. It consists of a Perspex box with three feederguides and several sampling holes. The feed tube isadjusted during the test so that no impact velocityoccurs at the feed point. This also minimizes the lat-eral velocity of the particles. Sand was used as thetest material and several concentrations of fines wereused. Segregation was measured by determining anon-dimensional parameter of coarse concentration.No correlation between the non-dimensional parame-ter and degree of segregation was found.
Harwood (1977) used radioactive tracer sand tomeasure segregation in a powder bed during vibra-tion. The tracer technique did not disturb the powderbed and enabled time measurements of segregation.The following conclusions were made: 1) migration oflarger particles tends to be upwards when the vibra-tion is at the base of the powder sample; 2) in a binarysystem (similar density and size) of free-f lowing parti-cles, very slow migration takes place in both upwardand downward directions; 3) in a binary system (onefree f lowing, one slightly cohesive), limited migra-tion takes place; 4) there exists a level of vibrationalenergy that maximizes segregation; and 5) particlesize is the main effect that controls segregation.
Williams and Shields (1967) introduced vibration tofree f lowing particles on an inclined channel. Equalweights of feed of coarse and fine fertilizer granuleswere fed onto a fixed plate. The particles continueddown the chute into a vibrating channel. The testdevice was constructed so that the length of the bed,direction, and amplitude and frequency of the vibra-tion could be varied. Segregation was defined as acoefficient. It was concluded from the study that mostsegregation took place in the first 15 cm of the bedand segregation was maximum when direction ofincline was about 30° with a frequency of 1300 rpmand amplitude of 0.35 cm.
Hwang (1978) used a chute to create a two layerf low. The chute was 10.1 cm wide by 3.8 cm deep andthe length could be varied by raising and lowering thechute. The angle of the chute could also be changed.The stainless steel chute surface was roughened byapplying a thin layer of particles using contact paper.This roughness was used to enhance mixing duringf low. The twin hoppers were used to produce a twolayer f low stream. A sampling device was used at theend of the chute to collect particles at various loca-tions in the f low stream. Using experimental data,Hwang developed a mathematical model for diffusion-type segregation.
Stephens and Bridgwater (1978a) selected an annu-lar shear cell to study the mixture quality of cohesion-less powders in the failure zone. The annular shearcell was selected so that powder behavior after initialfailure could be maintained. This aspect is not avail-able in the linear direct shear cell of Jenike (1964).Two particle sizes (1.91 and 4.00 mm) were used inthe shear cell. Velocity distributions for the two sizeswere similar in the failure zone. However, the depthof failure zone could not be characterized by eitherdimensional or dimensionless values. It was deter-mined that increasing the normal load decreased the
198 KONA No.20 (2002)
failure zone depth. Stephens and Bridgwater (1978b)in a second part presented the significance of theannular shear cell in determining percolation veloci-ties and diffusion coefficients. Using an annular shearcell, they found that for spherical particles large con-centration gradients or zones of constant concentra-tion can arise in failure zones. It was concluded thatpercolation, migration and diffusion are the control-ling factors of segregation in concentration profile.The steady-state profile was inf luenced by theamount of material in the failure zone.
2.3 Tester TechniquesSleppy and Puri (1996) examined size-segregation
of granulated sugar discharging from mass f low andfunnel f low bins. Two particle size ratios were used ineach of the bins, 2:1 and 5.7:1, and mixed by equalweight. It was concluded that funnel f low leads to pre-dominant fines in the first half of discharge and a pre-dominant coarse f low in the second half of discharge.No specific segregation pattern was observed duringmass f low. There was no difference in segregationbetween the two size ratios in mass f low, but segrega-tion patterns in funnel f low had a minimal differencebetween the two size ratios. Segregation coefficientwas defined as a fines to coarse ratio in this study.Markley and Puri (1998) continued the work ofSleppy and Puri by examining the effect of hoppersize on segregation of granulated sugar. Two hoppersizes (small and large) were used for both funnel f lowand mass f low conditions. The same trends wereobserved, i.e., during funnel f low a predominant finemixture at the beginning and coarse mixture at theend. In addition, more segregation was found in thelarge bins for both mass and funnel f lows.
Ahmad and Smalley (1973) investigated particlesegregation of a coarse particle and fine mixture dur-ing vibration. At a given frequency, segregation in-creased with an increase in acceleration. However, anincreasing frequency reduced segregation in a rangeof accelerations. Segregation was found to increasewith an increase in the particle size of the large par-ticle and lighter particles were found to segregatemore quickly than heavier particles under the sameoperating conditions. Shape did not seem to have aneffect on segregation.
Lawrence and Beddow (1968) examined segrega-tion of lead (Pb) particles during deposition into a die.It was found that the fines filtered down through mov-ing mass and resulted in a collection of fines at thebottom. This filtering of fines caused the larger parti-cles to drift outwards toward the die wall. The size
ratio affected segregation by increasing segregationwith an increase in size ratio. It was also found in thisstudy that particle shape and density had little effecton segregation and increasing drop height minimizedsegregation.
Williams (1976) introduced a coefficient of segre-gation, which was later revised by Popplewell et al.(1989) based on their results. The difference betweenWilliams’ index and Popplewell et al.’s index is thatPopplewell et al. consider the fines weight fraction atthe very bottom of the cell. They found that thissegregation index was much more sensitive andproduced better results. A simple shear model wasproposed by Bridgwater et al. (1978).
In summary, segregation has been measured usinga coefficient, mechanism, and model. The coefficienttechnique is by far the most common. However, itonly describes the degree of segregation taking placefor a particular set of operating conditions. The mech-anism technique provides insight for processes thatexhibit a dominating segregation mechanism. How-ever, the most encompassing method is to model aparticular process. It is neither possible nor practicalto model every mechanism for a given process. How-ever, if a specific mechanism can be identified thatexplains the majority of segregation taking place, itwould provide a powerful tool in understanding andminimizing segregation. Therefore, the objectives ofthis paper were: 1) to conduct tests to demonstratethe feasibility of the primary segregation shear testerusing binary mixtures, and 2) to determine segrega-tion characteristics of these mixtures.
3. Experimental Methodology
This section describes the selection of test mate-rials, rationale for test technique, primary testerdesign, and test methodology.
3.1 Selection of Test MaterialsFor this study, three binary particulate material
mixtures of glass beads were selected. Glass beadswere used based on the availability of narrow cutsizes, sphericity, and non-hygroscopic properties un-der controlled ambient test conditions. All tests wereconducted in an environment-controlled laboratorywith average temperature of 21°C 3°C and relativehumidity less than 40% to minimize the effects ofmoisture on the test results. The glass spheres wereconsidered dry (i.e., moisture content was equal tozero). A dehumidifier, placed near the shear appara-tus, was used to reduce the ambient moisture in the
KONA No.20 (2002) 199
environment. Two size ranges of fines (106-125 µm and 180-212
µm) and two size ranges of coarse particles (800-1200µm and 1000-1500 µm) were used to obtain three sizeratios, 5.1:1 (1000:196), 8.7:1 (1000:115), and 10.9:1(1250:115), for size-segregation (Table 1). Size ratioof 6.4:1 (1250:196) was used to validate segregationconstitutive models. These results will be reported ina subsequent publication. The particle density andbulk density of the glass spheres were 2500 kg/m3
(Quantachrome Multipycnometer) and 1300 kg/m3,respectively.
Preliminary tests determined the applicable sizeranges used in this study. Smaller ratios (3:1 to 5:1)were attempted with different size ranges. However,due to the design of the tester, significant blinding(i.e., clogging of the screen) of the exit screen and/orinsignificant percolation occurred at the small sizeratios. The sizes of the coarse and fine particles werechanged until significant percolation was measuredand blinding was eliminated.
3.2 Tester DesignDue to its advantages, a vertically oriented shear
tester was designed (Duffy and Puri, 2000). The newtester the Primary Segregation Shear Cell (PSSC) is capable of applying strains from 5 to 25% bychanging the cam (Figure 1). The cam is connectedto a variable speed motor that can cycle the cambetween 0.25 revolutions per second and 1.67 revolu-tions per second. A confining pressure between 0 kPa(no confining pressure) and 10 kPa can be appliedusing the air inlets and the f lexible membrane. Amesh screen with an opening of 533 µm at the bottomof the tester prevents coarse particles from passingand allows fine particles to pass without blinding. Themesh screen is replaceable, based on the selected testparticle size ratio.
The tester is mounted on a frame that also housesthe load cell collection assembly and electric motorthat drives the cam. Nylon walls were used as side-walls to contain the particulate system and minimizethe friction between the moving walls and fixed walls.The load cell collection assembly is aligned below the
mesh screen of the tester (Figure 2). There are 18individual compartments in the collection assemblywith six of the compartments containing load cells.All compartments were square with dimension 16.9mm 16.9 mm including divider plates (2 mm thick-ness). Six load cells were selected to measure the per-colation of fines and minimize the cost of the tester.Each load cell had a capacity of 50 g 0.01% (0.005g). This was the smallest load cell that could be useddue to the handling involved with the collectionassembly during emptying after each test while pre-serving significant precision and accuracy. Each loadcell was preloaded with a 5 g plate to minimize driftand noise associated with an unloaded load cell. Thedata from the load cells was collected using a HewlettPackard 3852A data acquisition system connected to apersonal computer through the general purpose in-
200 KONA No.20 (2002)
Coarse Size, d50 1000 µm 1250 µm
Fine Size, d50 0115 µm 0196 µm
Size Ratios For 1250:115 1000:115 1000:196Segregation Data (10.9:1) (8.7:1) (5.1:1)
Table 1 Summary of size ratios used for this study
Motor
Cam
Nylon Walls
Collection Pan
Shear Box
Air Inlet
MovingPivot
MovingPivot
Motion
Support PivotFixed Location
Cam Riding Pin
Screen
10.16 cm
10.16 cm
5.08 cm
All components arestainless steelexcept flexible
(a)
(b)
Fig. 1 Vertically oriented primary segregation shear cell (a) over-all schematic, and (b) 3D schematic
formation bus (GPIB). LabVIEW software (NationalInstruments, Austin, TX) provided the translationfrom analog to digital so that the information could beprocessed using standard spreadsheets.
In order to facilitate the identification of cell loca-tion, a lettering system was developed. The threerows (left to right) were identified as Front Row (FR),Middle Row (MR), and Back Row (BR) as shown inFigure 2 (a). The collection assembly was dividedinto two halves Left (L) and Right (R) as shown in
Figure 2 (b). Furthermore, the left half was subdi-vided into Center (C), Middle (M), and Left (L), andthe right half into Center (C), Middle (M) and Right(R). To identify a cell by the lettering system, the firsttwo letters designate the row location, the subsequenttwo letters pinpoint the cell location. The first of thelast two letters identifies the half (L or R) and the sec-ond letter identifies the cell location (L or M or C). Asan example, cell #10 has letter identification of BR-RC.This refers to Back Row (BR) Right (R) half andCenter (C) cell as illustrated in Figure 2. The sixload cells were placed in BR-LM (Cell #4), FR-LM(Cell #6), MR-LC (Cell #8), MR-RC (Cell #11), BR-RM(Cell #13), and FR-RM (Cell #15). Theoretically, twoload cell locations (e.g., BR-LM and FR-RM) could beused to determine anisotropy. Therefore, the six se-lected locations can measure anisotropic behavior andgive an average (or overall) degree of anisotropy.
3.3 Design of Experiment and Test MethodologyBased on preliminary experimentation, 25% and 20%
strains provided excessive energy into the particulateassembly. At these strains, the fines f looded throughthe bed of coarse particles. Flooding is defined as avery rapid percolation rate that could not be consis-tently measured for meaningful comparisons by theload cell sensors. Strains of 25% and 20% are alsoextreme limits in shear cell testing (i.e., Jenike sheartests and conventional triaxial shear tests are com-pleted under 20% strain). Therefore, the design ofexperiments included 5%, 10%, and 15% strains. In thisstudy, strain is defined as 100 times the maximumvertical movement of the moving pivot (Figure 1(b))divided by the vertical wall dimension (10.16 cm).Two cycle speeds, 0.75 cycles/second and 1.33cycles/second, were selected in the operating rangeof the electric motor. Rates below 0.75 cycles/seconddid not provide enough energy to percolate the finesthrough the bed of coarse particles in an efficientmanner especially at the lower strains. Rates above1.33 cycles/second caused f looding. Both of thesestrains produce linear velocities in the powder samplelarger than standard shear testing techniques. Thestrain and cycle speeds selected for this study repre-sent the upper and lower operating limits for mean-ingful comparisons. Three bed depths were alsoincorporated into the study to determine the effect oftravel length on percolation velocity, i.e., determineif the dimensions of the cell inf luenced the results(Table 2).
KONA No.20 (2002) 201
#1BR-LL
#2MR-LL
#3FR-LL
#4BR-LM
#5MR-LM
#6FR-LM
#7BR-LC
#8MR-LC
#9FR-LC
#10BR-RC
#11MR-RC
#12FR-RC
#13BR-RM
#14MR-RM
#15FR-RM
#16BR-RR
#17MR-RR
#18FR-RR
Left Right
Back Row
Middle Row
Front Row
Left Middle Center RightMiddleCenter
#10BR-RC
Cell Number
Row Identification:BR – Back RowMR – Middle RowFR – Front Row
Column Identification:LL – Left LeftLM – Left MiddleLC – Left CenterRC – Right CenterRM – Right MiddleRR – Right Right
(a)
(b)
Fig. 2 Schematic of load cell collection assembly (a) isometricview, (b) top view
FR
MR
BR
different load cell locations for the same treatment todetermine the degree of anisotropy. All treatmentswere analyzed. However, due to the large number oftreatments, typical data are presented to give anoverview. The second subsection compares (signifi-cance level, α0.05) the same load cell location fortwo different treatments. Again, typical data are pre-sented to give an overview of the statistical analysis.
4.2.1 Statistical analysis at dif ferent locationsand same treatment
Seven statistical comparisons were calculated foreach treatment to determine any anisotropic behaviorof percolation. The comparisons include Cells BR-RMvs. FR-RM, Cells BR-LM vs. FR-LM, Cells MR-LC vs.MR-RC, Cells BR-LM vs. BR-RM, Cells FR-LM vs. FR-RM, Cells BR-LM vs. FR-RM, and Cells BR-LM vs. FR-RM (Figure 2). Comparisons for Cells BR-RM vs.FR-LM and the 95% confidence interval are shown inFigure 3. Other comparisons being similar are notincluded. The comparison between Cell BR-RM andCell FR-RM had a small time zone of significant differ-ence (p0.05). This only occurred between 18 s and36 s with the final masses being statistically similar(p0.05). The remaining comparisons were not sig-nificantly different (p0.05) during the entire dura-tion of the test. Therefore, it was concluded that thepercolation of fines through the bed of coarse parti-cles was isotropic, i.e., directionally independent orcell location independent. The size of the 95% confi-dence intervals for the individual load cells is largerthan normal (COV10%). However, the 95% confi-dence intervals decrease considerably when com-puted in the effective percolation direction. This is
202 KONA No.20 (2002)
3.3.1 Test methodologyFor each test described above, the following proce-
dure was used:01. The nylon walls were screwed tightly towards
each other to secure the tester for deposition.02. Moving pivot at top of tester was removed and
top plate swung open.03. Flexible membranes were inf lated to 2 kPa us-
ing nitrogen gas.04. Collection pan assembly was aligned with the
mesh screen at the bottom of the tester usingalignment guides and visual alignment marks.
05. The coarse particles were deposited into thetester using a spoon to a specific bed height.
06. Fines deposition mould was aligned on the topof the bed of coarse particles.
07. Data collection was started.08. Fines were deposited into mould (40 grams)
and mould was removed.09. Top plate was closed and moving pivot replaced.10. The nylon walls were relaxed and the motor
was set at specified strain rate.
4. Results and Discussion
This section includes the statistical, qualitative, andquantitative comparisons of the mass versus timerelationships for the different treatments. The com-parisons have been grouped based on the treatmentof size ratio, which was found to be the dominatingtreatment. However, the effect of strain, cycle speed,and bed depth are included to highlight trends ofthese treatments.
4.2 Statistical AnalysisThe statistical analysis is divided into two subsec-
tions. The first subsection includes statistical com-parisons between mass versus time relationships at
Parameter Number (Values)
Size Ratios 3 (10.9:1, 8.7:1, 5.1:1)
Strains 3 (5%, 10% 15%)
Cycle Speed 2 (0.75 cycles/s, 1.33 cycles/s)
Bed Depths 3 (2.54, 5.08, 7.68)
Replications 4 per combination
Total Number of Tests 216
Table 2 Testing schedule for size-segregation analysis of binarymixtures
0 10 20 30 40 50 60
Time (s)
Mas
s (g
)
Mean Value BR-RM
Mean Value FR-LM ()
95% Confidence Interval Limits
0.000
0.500
1.000
1.500
2.000
2.500
Fig. 3 Mean measured mass versus time relationships for CellBR-RM and Cell FR-LM and the 95% confidence intervals
due to the fact that the fines percolate through thebed of coarse particles along a preferred direction,which may lead to high deviations when looking atone particular cell location. The size of the 95% confi-dence intervals in the effective percolation directionsupports the foundation of four replications in thedesign of experiment. An average coefficient of var-iation for all treatments was 9.7%, which is withinstandard error of other powder testing techniques(Kamath et al., 1993, Puri et al., 1995, Duffy and Puri,1999).
4.2.2 Statistical analysis at same location anddifferent treatments
Mass versus time relationships at specific load celllocations were statistically compared (α0.05) todetermine any significant differences between treat-ments. All treatment trends being similar, the graphi-cal statistical comparison at measurement locationFR-LM is given in Figure 4. In most treatment com-parisons, only one or two of the cell locations weresignificantly different. This was due to relatively large95% confidence intervals at certain locations. Most ofthe variation was attributed to the paths that the finestraveled. In other words, the mean path length variedfrom test to test. It is hard to determine the overalleffect by looking at the individual load cells sepa-rately. Therefore, a normalized mass versus timealong an effective percolation direction was created tobetter describe the percolation process utilizing thedata from all load cells. Normalized mass values werecalculated for each measurement location by dividingwith the maximum mass accumulated at that locationupon completion of the test.
KONA No.20 (2002) 203
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
Size Ratio5.1:1
Size Ratio8.7:1
No Significant Differences (p0.05)
95% Confidence Interval Limits
0 10 20 30 40 50 60
Time (s)
Mas
s (g
)
Fig. 4 Mean measured mass versus time relationships at FR-LMand 95% confidence intervals
4.3 Qualitative AnalysisNormalized mass versus time relationships were
used to qualitatively assess percolation data from theprimary segregation shear cell (PSSC). Extensiveanalysis of data clearly showed that size ratio was themost dominant treatment. Therefore, the qualitativeanalysis focuses on the effect of size ratio on the massversus time relationships. A similar effect has beenobserved and reported by Bridgwater et al. (1978).For a given strain and cycle speed, there are threecomparisons based on bed depths of 2.54 cm, 5.08cm, and 7.62 cm. The analysis groups the compar-isons based on strain and cycle speed and summa-rizes the results for the three bed depths. The 95%confidence intervals are also given and representedby labeled symbols.
4.3.1 Comparisons of 15% strain and 0.75 cpsA typical normalized mass versus time relationship
for bed depth of 2.54 cm is given in Figure 5. Typicalresults were collected at 15% strain and 0.75 cps cyclespeed. At any given time, the normalized mass forthe size ratios of 10.9:1 and 8.7:1 were significantly(p0.05) greater than the normalized mass for thesize ratio of 5.1:1. In addition, the normalized massrelationships for 10.9:1 and 8.7:1 were statisticallysimilar (p0.05). At the bed depth of 7.62 cm, the nor-malized relationship of 8.7:1 approached the normal-ized relationship of 10.9:1. For deeper coarse beds,the mean path lengths for fines about a certain sizeratio (such as 10.9:1 and 8.7:1) approach each other.This hypothesis explains the similar normalized massprofiles. The similarity of profiles for 10.9:1 and 8.7:1was observed for other treatments.
0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000
0 10 20 30 40 50 60
Time (s)
Nor
mal
ized
Mas
s
Size Ratio 10.9:1 (x)
Size Ratio 8.7:1 (o)
Size Ratio 5.1:1 ()
Fig. 5 Mean (solid lines) and 95% CI (symbols) for normalizedmass as a function of time Strain15%, Cycle Speed0.75 cycles/second and Bed Depth2.54 cm
4.3.2 Comparisons of 15% strain and 1.33 cpsThe normalized mass versus time relationships for
bed depth of 5.08 cm is given in Figure 6. Theincrease in cycle speed resulted in the normalizedrelationships of 10.9:1 and 8.7:1 to have similar re-sponses while maintaining a significantly (p0.05)faster percolation through the coarse bed than the5.1:1 size ratio. Generally, the increase in cycle speedprovided enough energy for the fines of the 8.7:1treatment to percolate through the bed of coarseparticles with minimal resistance, i.e., simulating the10.9:1 treatment. The relationships for the 10.9:1treatment and 8.7:1 treatment at a bed depth of 5.08cm are reversed. This trend, which is more pro-nounced at lower energy inputs, may be attributed tothe minimum pore size of the 10.9:1 ratio (1250 µm :115 µm). The pore size is large enough for two fineparticles to mechanically arch. However, the mini-mum pore size of the 8.7:1 ratio (1000 µm : 115 µm)prevents two fine particles from arching and allowsfine particles to freely travel through the bed ofcoarse particles. For the filling method used, thecoarse particle structure is expected to be betweenthat of cubic and orthorhombic arrangements. It isknown that the cubic arrangement is unstable;whereas, orthorhombic is stable but does require tap-ping or vibration to attain the theoretical porosity.The minimum pore sizes for the two arrangementsare given in Table 3. The mean pore size was calcu-lated by assuming that the orthorhombic arrange-ment is the dominant arrangement, i.e., 2/3 weightfactor was assigned to this arrangement, comparedwith the cubic arrangement which contributes only1/3. The mean pore sizes for 1250 µm and 1000 µm
204 KONA No.20 (2002)
assemblies were estimated to be 270 µm and 215 µm,respectively. For both size ratios, the size of fines was115 µm. The calculated pore sizes of 270 µm and 215µm lend credence to the mechanical arching hy-pothesis.
4.3.3 Comparisons of 10% strain and 0.75 cpsThe same trend as for 15% strain continues for
strain of 10% and cycle speed of 0.75 cps. For a beddepth of 2.54 cm, the normalized mass versus timerelationship for the 8.7:1 treatment has a faster perco-lation rate than the 10.9:1 treatment as shown in Fig-ure 7. At bed depths of 5.08 cm and 7.62 cm, thepercolation rates of 8.7:1 and 10.9:1 are very similar.For all three bed depths, the percolation was statis-tically similar (p0.05) between 10.9:1 and 8.7:1.Again, the reversal observed for 2.54 cm bed depthwas attributed to the pore size of coarse particles andthe ability of the fines in the 10.9:1 ratio to form amechanical arch in the pore spaces. In the precedingsection’s comparison the reversal occurred for beddepth of 5.08 cm, which had a higher strain (15%) andcycle speed (1.33 cps) compared with this case.Higher energy inputs impact deeper beds, thus a criti-
Minimum Pore Size (µm)
Coarse Particle Cubic Orthorhombic Weighted Mean Size (µm)
1250 µm 520 150 270
1000 µm 415 120 215
Table 3 Minimum pore sizes for cubic and orthorhombic arrange-ments
0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000
0 10 20 30 40 50 60
Time (s)
Nor
mal
ized
Mas
s
Size Ratio 10.9:1 (x)
Size Ratio 8.7:1 (o)
Size Ratio 5.1:1 ()
Fig. 6 Mean (solid lines) and 95% CI (symbols) for normalizedmass as a function of time Strain15%, Cycle Speed1.33 cycles/second and Bed Depth5.08 cm
Size Ratio 10.9:1(x)
Size Ratio 8.7:1 (o)
Size Ratio 5.1:1 ()
0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000
0 10 20 30 40 50 60
Time (s)
Nor
mal
ized
Mas
s
Fig. 7 Mean (solid lines) and 95% CI (symbols) for normalizedmass as a function of time Strain10%, Cycle Speed0.75 cycles/second and Bed Depth2.54 cm
cal energy exists that selectively inf luences the rever-sal, i.e., can not dislodge the mechanical arches. Aswas the case with the previous comparisons, the per-colation for 5.1:1 size ratio is significantly (p0.05)less than the other treatments. It was hypothesizedthat the fines in the 5.1:1 ratio are actually changingthe pore structure of the coarse bed. In other words,the size of the fine particle is nearer the size of thepore space of the coarse particles and does not freelyf low through the bed of coarse particles. Rearrange-ment of the coarse bed may be taking place. Gener-ally, the fines in the other treatments are f lowingfreely through the pore spaces of the coarse bed andmay alter the pore structure, but not to the extent toimpede the rapid f low of fines.
4.3.4 Comparison at 10% strain and 1.33 cpsA change in cycle speed from 0.75 cycles/second to
1.33 cycles/second at a strain of 10% did not changethe relationships found for 0.75 cycles/second. At thesmaller bed depths of 2.54 cm and 5.08 cm, it appearsa strain of 10% and cycle speed of 1.33 cycles/secondprovides enough energy to dislodge the fine particlesfor the 10.9:1 treatment because the percolation wasgreater than or equivalent to the 8.7:1 treatment (Fig-ure 8). However, when the bed depth was 7.62 cm, itappears there was mechanical arching at the 10.9:1treatment due to the lower percolation rate. However,for all three bed depths, the responses for 10.9:1 and8.7:1 are statistically similar (p0.05). From these ob-servations, it appears that the energy combination ofa strain of 10% and a cycle speed of 1.33 cycles/sec-ond is large enough to dislodge mechanical arches inthe 10.9:1 treatment at small bed depths. However,
this energy input is near its limiting value, because atthe largest bed depth, arching is occurring.
4.3.5 Comparison at 5% strainSeveral changes occur when the energy input is
decreased to a strain of 5%. For all cases at strain of5%, the percolation is greater for the 8.7:1 treatmentthan the 10.9:1 treatment and significantly greater(p0.05) at a cycle speed of 0.75 cycles/second. Infact at low input energy level corresponding to 0.75cycles/second, the 10.9:1 treatment behaves statis-tically similar (p0.05) to the 5.1:1 treatment. Anincrease in energy input, i.e., increase in cycle speedfrom 0.75 cycles/second to 1.33 cycles/second, af-fects the relative percolation of the 10.9:1 ratio. The10.9:1 percolation approaches the 8.7:1 percolation.This supports the hypothesis of mechanical archesforming in the pore spaces of the coarse particles.The relationships at strain of 5% also show the effectof strain on the percolation. The normalized massaccumulated after 60 seconds at a strain of 5% isappreciably lower than the mass accumulated athigher strains.
4.4 Other Treatment Variables and Their Effecton Percolation
The previous analyses qualitatively assessed theeffect of size ratio on the percolation. However, theeffects of three other parameters (strain, cycle speed,and bed depth) were also quantified. Strain, as dis-cussed above, has a significant (p0.05) effect on thepercolation rate. Higher strains resulted in a faster per-colation (Figure 9). In most cases, cycle speed hadminimal effect on the percolation rate (Figure 10).
KONA No.20 (2002) 205
Size Ratio 10.9:1 (x)
Size Ratio 8.7:1 (o)
Size Ratio 5.1:1 ()0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000
0 10 20 30 40 50 60
Time (s)
Nor
mal
ized
Mas
s
Fig. 8 Mean (solid lines) and 95% CI (symbols) for normalizedmass as a function of time Strain10%, Cycle Speed1.33 cycles/second and Bed Depth2.54 cm
15% Strain
10% Strain
5% Strain
0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000
0 10 20 30 40 50 60
Time (s)
Nor
mal
ized
Mas
s
Fig. 9 Typical mass versus time relationships as a function ofstrain Size Ratio10.9:1, Cycle Speed0.75 cycles/sec-ond, Bed Depth5.08 cm
206 KONA No.20 (2002)
10.9:1, the amount of input energy was criticalbecause the size of the fine particles was near thesize of the coarse bed pore space. When the inputenergy was below a critical limit, mechanical arch-ing was occurring. Although the input energy is afunction of bed depth and cycle speed, these para-meters did not inf luence the results outside ran-dom behavior.
3. The percolation of fines through a bed of coarseparticles was isotropic. There was no observedbias in the collection pan at the end of the tests.
4. Significant differences (p0.05) were measuredbetween individual load cells under different treat-ments in one out of six treatments. Many treat-ments were not significantly different (p0.05).However, when statistical comparisons were madein the effective percolation direction, differences(p0.05) were significant when comparing thesize ratios of 10.9:1 and 8.7:1 to the size ratio of5.1:1.
6. Acknowledgements
This study was partially funded by the U.S. Depart-ment of Agriculture and Pennsylvania AgriculturalExperiment Station.
7. References
1) Ahmad, K. and I. J. Smalley. 1973. Observation of parti-cle segregation in vibrated granular system. PowderTech. 8:69-75.
2) Bagster, D. F. 1996. Studies on the effect of moisturecontent and coarse and fine particle concentration onsegregation in bins. KONA 14:138-143.
3) Bridgwater, J., M. H. Cooke, and A. M. Scott. 1978.Inter-particle percolation: equipment development andmean percolation velocities. Trans IChemE, 56: 157-167.
4) Duffy, S. P. and V. M. Puri. 2000. Measurement of perco-lation velocity during shear. ASAE Paper No. 00-4008.ASAE, St. Joseph, MI.
5) Duffy, S. P. and V. M. Puri. 1999. Evaluation of the com-puter controlled dynamic yield locus tester. PowderTech. 101:257-265.
6) Harwood, C. F. 1977. Powder segregation due to vibra-tion. Powder Tech. 16:51-57.
7) Hwang, C. 1978. Mixing and segregation in f lowingpowders. Doctor of Philosophy Thesis. The Pennsylva-nia State University, University Park, PA.
8) Jenike, A. W. 1964. Bulletin No. 123 Storage and f lowof solids. Utah Engineering Experiment Station. SaltLake City, Utah.
9) Johanson, J. R. 1988. Solids segregation causes andsolutions. Powder and Bulk Eng. 13-19.
10) Kamath, S., V. M. Puri, H. B. Manbeck, and R. Hogg.
For 5.1:1 ratio, the bed depth also did not influencethe percolation as expected. In some cases bed depthof 2.54 cm had a lower percolation rate than beddepth of 7.62 cm. However, these differences are notsignificant (p0.05).
5. Conclusions
A primary segregation shear cell (PSSC) has beendesigned and fabricated to measure the size-segre-gation response of fines traveling through a bed ofcoarse particles. The effects of size ratio, strain, cyclespeed, and bed depth on the percolation of fine par-ticles in binary mixtures of glass spheres were evalu-ated. Based on the test results, the following conclu-sions were made.1. Size ratio was the most dominant variable that
affected the percolation rate of fines through abed of coarse particles. Based on the differencesin percolation between the smaller size ratio of6.4:1 and larger ratios of 8.7:1 and 10.9:1, thereexists a critical size ratio which determines themechanism of percolation. Two mechanisms wereobserved. First, the larger size ratios exhibited aninitial free-fall, i.e., convective, discharge of finesat the beginning of the test. This initial dischargewas followed by a diffusive behavior. The smallerratios did not exhibit the initial discharge andtheir response was observed to be diffusive be-havior.
2. Strain also had an effect. Input energy, as relatedto strain, was found to be critical in the type of per-colation exhibited, i.e., the presence or absence ofan initial rapid discharge. For the size ratio of
Cycle Speed 1.33 cycles/
secondCycle Speed0.75 cycles/second
0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000
0 10 20 30 40 50 60
Time (s)
Nor
mal
ized
Mas
s
Fig. 10 Typical mass versus time relationships as a function ofcycle speed Size Ratio10.9:1, Strain15%, Bed Depth7.62 cm
KONA No.20 (2002) 207
1993. Flow properties of powders using four testers measurement, comparison, and assessment. PowderTech. 76:277-289.
11) Lawrence, L. R. and J. K. Beddow. 1968. Powder segre-gation during die filling. Powder Tech. 2:253-259.
12) Markley, C. and V. M. Puri. 1998. Scale-up effect on size-segregation of sugar during f low. Transactions of theASAE, Vol. 41(5): 1469-1476.
13) Mosby, J., S. R. de Silva, and G. G. Enstad. 1996. Segre-gation of particulate materials mechanisms andtesters. KONA 14:31-42.
14) Popplewell, L. M., O. H. Campanella, V. Sapru, and M.Peleg. 1989. Theoretical comparison of two segregationindices for binary powder mixtures. Powder Tech. 58:55-61.
15) Puri, V. M., M. A. Tripodi, G. L. Messing, and H. B.Manbeck. 1995. Constitutive model for dry cohesive
powders with application to powder compaction. KONA13:135-150.
16) Sleppy, J. A. and V. M. Puri. 1996. Size-segregation ofgranulated sugar during f low. Trans. of the ASAE 39(4):1433-1439.
17) Stephens, D. J. and J. Bridgwater. 1978a. The mixingand segregation of cohesionless particulate materials Part I. Failure zone formation. Powder Tech. 21:17-28.
18) Stephens, D. J. and J. Bridgwater. 1978b. The mixingand segregation of cohesionless particulate materials Part II. Microscopic mechanisms for particles differingin size. Powder Tech. 21:29-44.
19) Williams, J. C. and G. Shields. 1967. The segregation ofgranules in a vibrated bed. Powder Tech. 1:134-142.
20) Williams, J. C. 1976. The segregation of particulatematerials a review. Powder Tech. 15:245-251.
Author’s short biography
Shawn P. Duffy
Dr. Shawn P. Duffy was a Graduate Research Fellow in the Department of Agricul-tural and Biological Engineering at the Pennsylvania State University. He receivedhis BS, MS and PhD from Penn State specializing in Powder Mechanics. Dr. Duffyreceived numerous recognitions including US Department of Agriculture NationalNeeds Fellowship and Particulate Materials Center’s Research Fellowship. Heserved on American Society of Agricultural Engineers Bulks Solids Storage andProperties of Cohesive Materials Committees. The work reported in this paper isbased on his PhD research. Currently, Dr. Duffy is employed by PPG Industries,Inc, as a Research Engineer.
Virendra M. Puri
Dr. Virendra M. Puri is Professor in the Department of Agricultural and BiologicalEngineering at the Pennsylvania State University. Professor Puri also served as theActing Director of the Particulate Materials Center, a National Science Founda-tion’s Industry/University Cooperative Research Center. He is also the researchthrust leader of Powder Mechanics group of the Particulate Materials Center. Dr.Puri received his B.S. from Indian Institute of Technology and M.S. and Ph.D. fromthe University of Delaware in Mechanical Engineering. Professor Puri’s researchinterests include: measurement of fundamental engineering properties of powders,development and validation of constitutive models, and use of numerical methodsto model f low, segregation, and compaction behavior of powders. He has served asthe chairperson of the Bulk Solids Storage Systems Committee of the AmericanSociety of Agricultural Engineers. Professor Puri is a Co-Editor-in-Chief of the Par-ticulate Science and Technology, An International Journal. Dr. Puri regularly offersa postgraduate course in the area of powder mechanics and several hands-onindustrial short courses. Professor Puri has received several teaching and researchawards.
208 KONA No.20 (2002)
1. Introduction
The word autogenous is derived from the Greekautogenes which means self (auto) generated, bornor produced (genes). In mineral processing however,autogenous grinding designates generically the actionof rocks grinding upon themselves, as occurring intumbling mills. For reasons that will be further ad-dressed in this work, grinding in autogenous (AG)mills is frequently assisted by steel balls, in whichcase it is called semi-autogenous (SAG) grinding.
Conceptually, any AG/SAG mill consists of a rotarycylindrical metallic chamber in which the feed is con-tinuously introduced through the hollow feed trun-nion at one end and discharged to another. Thedischarge mode does vary substantially between hol-low discharge trunnions to screen plates (grates) thatcan be either placed at the periphery of the cylinderor radially to the trunnion. The mill shell is internallyprotected by means of steel liners.
Today’s extensive use of AG/SAG mills is creditedto the combination of relative high throughput and
high reduction ratios allied with compactness of theirphysical installations. There is, consequently, an in-creasing demand for techniques, which enable theprediction of the performance of such equipment,under a wide range of conditions. Mathematical mod-elling and simulation have proven to be a reliabletechnique to assist the development of comminutioncircuits in conceptual design, scale-up from pilot planttest work and the optimisation of industrial opera-tions. Over the last 30 years JKMRC has been contin-uously developing mathematical models of AG/SAGmill performance. The current model is incorporatedin a computer program for process simulation JKSimMet, which has been used successfully to simu-late a number of closed and open circuit situations. Itis arguably the most popular and widely used modelin the world. There are, however, a number of areaswhere the model is still limited in its ability to predictthe effect of changes in operational variables. In par-ticular its limited inherent ability to relate the perfor-mance with charge composition and motion is seen asa major drawback. This has prompted the use ofempirical “corrections” to the model (Mutambo, 1992;Morrell and Morrison, 1996), which resulted in theformulation of equations that have been only partiallysuccessful. Significant progress has been recentlyachieved towards the modelling of mill charge
Homero Delboni Jr.Dept. of Mining and Petroleum Engineering University of São Paulo*Steve MorrellJulius Kruttschnitt Mineral Research CentreUniversity of Queensland**
A Load-Interactive Model for Predicting the Performance of Autogenous and Semi-Autogenous Mills†
Abstract
The Julius Kruttschnitt Mineral Research Centre (JKMRC) has been involved in the study andmodelling of industrial autogenous (AG) and semi-autogenous (SAG) mills for over 25 years.Recent research at the JKMRC has developed a new AG/SAG mill model which is based on chargedynamics. The model relates charge motion and composition to power draw and size reduction. Sizereduction is described by considering impact and attrition/abrasion as separate processes. These arelinked to energy available in the mill, the charge size distribution and the relative motion of thegrinding media. Ore specific energy-breakage are described using laboratory data which are ob-tained from breakage tests over a wide range of energies and particle sizes. Slurry transport isdescribed using the JKMRC’s latest model which incorporates the ef fect of grate design. This paperdescribes the overall structure of the model together with its main sub-processes.
* Av. Prof. Mello Moraes, 2373 São Paulo, SP 05508-900Brazil
** Isles Rd. Indooroopilly QLD 4075 Australia† Accepted: October 28, 2002
dynamics, particularly those related to the effect oflifter bar design and the estimation of mill powerdraw. These progresses have been based on physi-cally sound descriptions of the charge motion and theprincipal variables, which affect it. This scenario ofincreasing demand for a comprehensive model andthe development of better knowledge of chargedynamics, lead to the initiation of a new AG/SAG millmathematical model.
2. Objective
The main objective of this work is to describe theinf luence of the charge composition and motion onbreakage performance such that it can predict theperformance of the mill under all normally encoun-tered operational conditions. The derived modelshould then incorporate a number of operating con-ditions as they inf luence the charge dynamics andtherefore the breakage mechanisms involved inAG/SAG grinding as opposed to a rate process ap-proach.
3. Review of AG/SAG Grinding Process Models
Researchers involved with power prediction weremotivated by the possibility of reducing the largeamounts of energy consumed in comminution plants.Accordingly, the energy-size relationships, or “laws ofcomminution” were extensively used in attempts topredict the power draw by crushers and ball/rodmills, based on one characteristic of the broken mate-rial. However, the energy approach proved to be inad-equate for meaningful process simulation, specially inAG/SAG mills where the mill charge weight variedsubstantially.
The difficulty in maintaining the operation of AGmills in steady state motivated research groups todevelop models to predict and control their dynamicbehaviour. Such models were based on statistical cor-relations thus representing an intermediate stagetowards more comprehensive approaches (Kelly,1970). Three lines of models were since then pursuedto model AG/SAG mills i.e., matrix models, kineticmodels and perfect mixing models. However, follow-ing the evolution of computers, kinetic and perfectmixing models received much more attention fromresearch programmes, to the detriment of matrixmodels, which were eventually abandoned.
The majority of the models developed were essen-tially case-specific and strongly dependent on siteconditions. Moreover, they were not designed to take
into account the mechanisms involved in the process.Wickham (1972) first incorporated the perfect mix-
ing equation (Whiten, 1974) to AG/SAG modelling. Asimplified matrix form was used, in which a con-densed term adapted the model structure to ignoreboth load and discharge rate. Two distinct functionsfor rock breakage were considered i.e. impact andabrasion, but were non-ore specific.
Stanley (1974) published the first successful effortto model AG/SAG mills according to a mechanisticapproach, as a result of a series of survey campaignson both pilot plant and industrial mills. The underly-ing mechanism assumed was that AG/SAG mills aremixers in which both transport and breakage occurs.Furthermore, when rock fragments collide inside themill, they generate broken particles, which will be dis-tributed in other size fractions. Although the conceptsused by Stanley were essentially mechanistic, themodel created can be better classified as a phenome-nological, because the mechanisms involved weretreated as rate processes rather than genuine physicalinteractions, which could be predicted from simplegeneric laws.
Austin et al (1977) developed an AG/SAG modelstructure based on the kinetic model. The mean resi-dence time of the particles within the load was usedto correlate the batch grinding conducted in the labo-ratory, to the performance of pilot plant and industrialmills.
Leung (1987) used the perfect mixing model equa-tion in its full form as well as a mass transfer empiricalrelationship. Leung developed a combined ore-de-pendent impact and abrasion function for describingbreakage. Although average values were established,breakage rates were mill/ore dependent thus had tobe fitted.
Morrell and Stephenson (1996) incorporated a phe-nomenological mass transfer relationship to Leung’smodel, based on an extensive work carried out onindustrial mills.
3.1 The Perfect Mixing ModelThe basic concepts of the perfect mixing model
were developed by Whiten (1974) in which the rate ofchange of mill contents, due to breakage and f low,can be described by the following equation:
pidisifi∑i
j1aij rjsjrisi
where f i mass f low rate of size fraction i in the mill feed p i mass f low rate of size fraction i in the mill dis-
charge
KONA No.20 (2002) 209
s i mass of size fraction i in the mill loadr i breakage rate of size fraction ia ij appearance function (fraction of broken particles
from size fraction j which appears in size fraction i)d i discharge rate of size fraction i
The perfect mixing model equation represents themass balance of each individual size fraction of themill charge. Accordingly, the entering particles (millfeed plus broken particles coming from coarser frac-tions of the charge) balance with the leaving particles(mill product plus the broken particles going to finerfractions of the charge).
3.2 Breakage MechanismsMuch work has been conducted on the determina-
tion of breakage mechanisms prevailing in tumblingmills. The results obtained in the analysis of rod andball mill operation, which dominated the literature,are not adequate for AG/SAG mill load analysis as theparticle size range is more ample.
The majority of the authors dedicated to investigatethe subject (Wickham, 1972; Stanley, 1974; Austin etal, 1977; Manlapig et al, 1979; Goldman et al, 1988,Kelly et al, 1990, Loveday et al, 1997) have selected anumber of breakage mechanisms. Although a lot ofcontroversy still persists in the literature, mainlyderived from different nomenclatures for similar phe-nomena, the following mechanisms are considered tobe predominant in AG/SAG mills: impact, abrasion,chipping and attrition.
It is important to emphasise that much of the confu-sion in the literature originates from the indistinct dif-ferentiation between cause and effect. The former ishere defined as a combination of intensity and modeto impart energy to a fragment, while the latter is theresulted size distribution of broken fragments.
Schöenert (1993) affirmed that only the amount ofenergy imparted to a particle in any comminutionmachine should be considered to characterise thebreakage event. The form of interaction is thereforeirrelevant. However, both the breakage energy andmode are related to the motion of the charge. Hence,by relating the mode of breakage to charge dynamics,the energy associated with each mode can be deter-mined.
A number of different tests to characterise thephysical properties of material subjected to comminu-tion are reported on the literature. They can bedivided into those which are designed to reproducethe whole size reduction process within a mill (Bond,1952; Kjos, 1985; MacPherson, 1987; Mörsky et al,
1994), and the ones created to assess an individualfragmentation mechanism, specific of the AG/SAGmill process (Narayanan, 1985; King et al, 1993).
The characterisation tests relevant to the presentwork are those which correlate specific energy im-parted to a rock fragment and its correspondentdegree of breakage.
Based on the above discussions, this work consid-ers three main modes to impart energy to any particlein AG/SAG mills, which are showed schematically inFigure 1 and described below. • Impact, here referred as the action of a falling
charge element, including balls or rocks, onto theparticles lying on the exposed part of the charge.
• Abrasion, which includes the rubbing action of rockparticles against each other, against balls or mill lin-ers.
• Attrition, including the mechanism of particles be-ing nipped between steel balls and larger ore parti-cles rolling and sliding against each other.
3.3 Breakage RatesBreakage rates are associated with the frequency
breakage events. Leung (1987) assumed that thebreakage rates were fixed and calculated average val-ues for AG and SAG mills separately. The breakagerate distribution was not described by back-calculatedrelationships, but in terms of five values, at 128, 44.8,16.0, 4.0 and 0.25 mm. The intermediate values forother sizes are calculated by interpolation whichresults in a smooth breakage rate curve as shown inFigure 2.
The robustness of Leung’s model contrasts with thefact that breakage rates are affected by a number ofoperating conditions instead of depending only uponthe equipment. Morrell et al (1994) also showed thatthe inf luence of variables such as ball charge, ballsize, feed size distribution determines the perfor-
210 KONA No.20 (2002)
IMPACT ABRASION ATTRITION
Fig. 1 Fragmentation Mechanisms and the Resultant Size Distri-butions.
mance of the process, thus directly affecting thebreakage rate values.
As operating conditions determine breakage rates,difficulties were frequently experienced in predictingthe performance of the mill under conditions muchdifferent from those used to fit the model parameters.In addition, design of full scale mills where no pilotdata were available was limited to matching to thedesign of existing mills for which data were available.
The subject was investigated in detail by Mutambo(1992) in an attempt to empirically correlate breakagerate values with the operating conditions and designcharacteristics of a range of mills in the JKMRC data-base.
4. The New Model
4.1 DescriptionIn grinding mills the kinetic energy that the rota-
tion of the mill shell imparts to the grinding media issubsequently transferred to ore particles with whichthey are in contact, so causing breakage. The kineticenergy of these breakage events is related to both thesize and velocity of the grinding media whilst the fre-quency of these events is associated with the numberof grinding media and the rate at which they circulatewithin the mill. The process has a discrete nature, asit comprises many individual collisions or breakage‘events’. The product of these breakage events mayleave the mill via the discharge grate due to entrain-ment by slurry, or remain within the charge to un-dergo further breakage.
It follows from these arguments that for modellingpurposes it is necessary to have a description of atleast the following:• Energy associated with each breakage event and its
relationship to the charge.
• Frequency of breakage events for each size fractionand its relationship to the charge.
• Size distribution of the products from each break-age event.
• Classification performance of the grate.• Relationship between slurry hold-up in the mill and
its f low rate out of the mill.The assessment and modelling of each individual
element listed above are summarised in the followingsections.
The modelling approach adopted in this work isbased on the interaction between mill charge motionand size reduction mechanisms, which is believed toresemble a real mill operation. Although the individ-ual assessment of mill charge dynamics and size re-duction mechanisms have progressed substantially,none of the published AG/SAG models are directlybased on the interactions between them.
The charge is assumed to be comprised of two dif-ferent fractions i.e. the one which causes breakage,described as grinding media or ‘contactors’, and theone which receive the contacts, or ‘contactees’. Themotion of the contactors will therefore determineboth the frequency and the intensity of the size reduc-tion mechanisms. The two mechanisms selected torepresent the size reduction mechanisms in AG andSAG mills were impact and attrition, which thereforehave to be described according to the approachadopted in the charge motion model.
Modelling of the charge motion was based on theapproach adopted by Morrell (Morrell, 1993) for pre-dicting the power draw of tumbling mills. The modelassumes the mill charge to be comprised of concen-tric shells. The slip between the shells causes a shear-ing motion and creates the conditions necessary forattrition breakage where relatively small particles arenipped between grinding media as they slide againstone another. Impact breakage occurs predominantlyin the vicinity of the toe of the charge where thegrinding media impact after falling from the shoulderof the charge.
The Morrell model differentiates between the pow-er associated with each of these mechanisms individ-ually and provides separate estimates of impact andattrition power.
The grinding media are viewed as “contactors” inthe model and are used to determine the input energyfor breakage in each of these modes. The modelusing the rate at which the charge rotates as well asthe rate at which the shells slide against one anotheralso provided an estimate of the total frequency ofbreakage events in each mode.
KONA No.20 (2002) 211
1
10
100
0.01 1 100 10000
Size (mm)
Bre
akag
e R
ate
(1/h
)
Fig. 2 Breakage Rate Distribution as Obtained by Leung.
The relationship between contactors and contacteesis assumed to follow a pattern according to eachmode of breakage. Underlying each of these relation-ships is the assertion that the surface area of thegrinding media dictates the breakage frequency,whilst the probability that a contactee will be involvedin a collision with a contactor is related to the surfacearea of the contactee.
The model operates in an interactive manner, whichis believed to resemble a real mill operation. There-fore, after each iteration of the charge motion thegrinding media is re-calculated according to the sizereduction relationship. Accordingly, an arbitrary val-ue of grinding charge volume is initially used asmeans to start the calculation of the charge size distri-bution. The grinding charge is considered to reachsteady state after the constraint of fixed charge vol-ume is eliminated and the grinding charge loop runsfor a fixed number of iterations.
After each interaction the model calculates theslurry volume, which will fill the interstices of thegrinding charge and may eventually raise above thegrinding charge surface, thus giving rise to the for-mation of the slurry pool. If a slurry pool is formed,the next interaction will take into account its effect onthe falling grinding media. The net result is a reduc-tion of the impact velocity due to the buoyancy effectof the slurry pool.
The slurry volume is dictated by the dischargefunction and the mill throughput, together with theattrition mode of breakage, which is assumed to beprevalent on finer size fractions of the charge.
The mill charge motion is considered to be com-prised of a number of shells, which slide against oneanother. Attrition breakage therefore occurs in theinterstices between contiguous shells as well as inthe voids of the grinding charge. It follows that fora breakage charge volume and mill charge motionthere is a limited “volume associated to attrition sites”to be filled with particles. For situations where thecharge slurry volume is smaller than the volume ofattrition sites, no correction is necessary as any solidparticle in the slurry will be within the breakagecharge. However, as the slurry pool starts to build upin the mill chamber, the reverse occurs i.e. there willbe more particles than breakage sites which de-creases the attrition breakage performance of themill. The model therefore incorporates a correctionfactor to take into account the slurry pool effect onattrition breakage.
After the stabilisation of the grinding charge loop,the model iterates until the entire charge size distrib-
ution, charge volume and product size distributionstabilises.
One of the most prominent characteristics of themodel resides on its structure and consequently onthe mode in which it iterates. Instead of utilising theinformation to iterate backwards as most models do,the new model generates the necessary informationbased solely on the mill design characteristics, operat-ing conditions and ore characterisation results, asinput data. Therefore, the new model is not based onvariables that are inherently operation dependent ornecessitate scale-up procedures.
The fact that current AG/SAG mill models are notbased on mill charge dynamics determines a numberof limitations with them. Although a number of oper-ating variables and mill design characteristics havebeen carefully assessed, they were incorporated incurrent models by simplistic parameterisation thatlimited their application.
The load-interactive approach adopted in the mod-el incorporates a comprehensive description of thecharge motion. Initially designed by Morrell (1993) topredict the power draw, the Morrell model was basedon the location of the charge toe and shoulder foreach shell, as the bulk of the charge was divided. TheMorrell model was modified to incorporate Powell’s(1991) equations for describing the trajectory of par-ticles in contact with the lifter bars, including theeffect of the angle of the lifter bar on the trajectory tobe determined. Apart from the shell structure of thecharge no assumptions are made about the shape thatthe charge takes up.
The net result is a model which predicts the motionof the grinding charge as well as the power drawunder a wide range of operational and design condi-tions, and includes the effects of such factors as par-ticle size, lifter bar geometry, mill filling and millspeed. The effects of the grate design is also directlyincluded in the model as the discharge model isdetermined by grate open area and geometry. Thesefactors are therefore incorporated into the size reduc-tion part of the model.
The model also includes the prediction of the ballconsumption of the simulated mill, together with theball size distribution in the mill charge. The first is acharacteristic not found in the current AG/SAG millmodels even though it is valuable information in amill design scenario. The estimation of the ball sizedistribution in the mill charge represents a significantdecrease in the amount of input data to the model,which is also convenient for the user as this informa-tion is rarely available.
212 KONA No.20 (2002)
4.2 Model StructureThe model structure involves a number of sub
processes according to different levels in a rathercomplex scheme. Figure 3 summarises the mainstructure of the model showing the input data, calcu-lation loops and output data. Following the input ofmill design characteristics, operating conditions andfeed, the model begins execution by assigning an ini-tial estimate of the mill charge volume.
The initial charge has the same size distribution asthe mill feed, therefore resembling the start of themill operation. The initial charge enters the grindingcharge loop following an iterative process that pro-vides the charge volume and mill power draw basedon the mill charge motion and ore breakage charac-teristics. As the grinding charge loop reaches thestabilisation criterion, the model proceeds to the cal-culation of the mill discharge size distribution andthus finishing the cycle. Both grinding charge loopand mill discharge loop are further discussed in thefollowing sections.
4.3 Grinding Charge LoopFigure 4 shows in detail the schematic f low sheet
of the grinding charge loop. Initially, the chargemotion model provides the first estimation of the ini-tial charge breakage energy and frequency based onthe calculated characteristic media size. The totalbreakage energy and frequency are divided accordingto each of the breakage mechanism i.e. impact andattrition. The energy is then distributed to each sizefraction which results in the estimation of individualvalues of impact and attrition specific breakage ener-gies for all particle sizes.
The breakage of each size fraction according toboth impact and attrition are calculated consideringthe individual values of breakage energy togetherwith the ore breakage characteristics.
KONA No.20 (2002) 213
INPUT DATA
Mill OperatingConditions
INPUT DATA
Ore breakagecharacteristics
- Speed- Ball charge- Ball size(s)- Flowrate of solids- Flowrate of liquid- Solids’ size distribution- Density of the solids- Density of the liquid
INPUT DATA
Mill DesignCharacteristics
- Inside shell diameter- Inside shell length (EGL)- Mill cone length- Trunnion diameter- Lifter profile (length and angle)- Grate design parameter- Grate aperture- Grate open area
Initial charge(ore and balls)
Grindingcharge loop
Mill discharge loop
END
Mill Discharge
Charge Volume
Power Draw
Fig. 3 Schematic Flow Sheet of the AG/SAG Mill Model.
Mill dischargeloop
YES
Perfect mixing equation
Size distributionafter a breakage
event (appearencefunction)
Breakagefrequency for
each sizefraction (impact)
Total breakagefrequency (impact
and attrition)
Mill chargemotion
Characteristicmedia size
Initial charge(ore and balls)
Total slurrycharge volume
Slurry poolvolume
Is iterationcounter3
Ore breakagecharacteristics
NO
Grinding mediavolume and size
distribution
Breakage energyfor each size
fraction (impactand attrition)
Total breakageenergy (impactand attrition)
Mill ChargeVolume
Mill dischargefunction
Mill Power
Relationshipbetween contactorsand contactees for
impact and attrition
Fig. 4 Grinding Charge Loop.
The frequency of contacts follow the same proce-dure as the total amount of contacts is distributed toeach size fraction according to a relationship betweencontactors and contactees. The resulting breakage ofeach individual size fraction is then calculated on thebasis of breakage energy and frequency.
A discharge rate is associated with each size frac-tion using a hold-up f low rate model. Mathemati-cally the various sub processes are brought togetheraccording with a extended version of the perfect mix-ing model equation, as follows:
fidisi∑i1
jsj(aij
imprjimpaij
attrjatt)si[ri
imp(1aiiimp)ri
att(1aiiatt)]0
wherer i
imp impact breakage rate of size fraction i r i
att attrition breakage rate of size fraction ia ij
imp impact appearance function a ij
att attrition appearance function
Therefore, after each interaction the model esti-mates the total volume, which is discharged out of themill through the grate. The discharge rate is calcu-lated using a hold-up f low rate model (Morrell andStephenson, 1996) in combination with the classifica-tion function, resulting in the following equation:
diCiQ0.5A0.5g1.25f0.67D0.25Vm1
whereC i classification function at size IQ f lowrate through the grateA grate open areaγ mean relative position of the grate aperturesφ fraction of mill critical speedD mill diameterVm volume of the mill charge
The net result after the discharged volume calcula-tion is a new grinding charge volume and new grind-ing charge size distribution, which serves as thestarting values for subsequent interactions. At thisstage the model estimates the total slurry volume inthe mill charge comprising the finer fractions of oretogether with the water held-up in the mill.
As the model assumes that only part of the chargewill determine the frequency and intensity of thebreakage events, the structure was configured in away to first establish a stable grinding charge. There-fore, after each iteration of the charge motion thegrinding media is re-calculated according to the sizereduction relationship. The grinding charge is consid-ered to reach steady state after the constraint of fixedcharge volume is eliminated and the grinding charge
loop runs for a fixed number of iterations. After each interaction the model calculates the
slurry volume, which will fill the interstices of thegrinding charge and may eventually raise above thegrinding charge surface, thus giving rise to the for-mation of the slurry pool. If a slurry pool is formed,the next interaction will take into account its effect onthe falling grinding media. The net result is a reduc-tion of the impact velocity due to the buoyancy effectof the slurry pool.
4.4 Charge MotionThe motion of the mill charge is caused primarily
by the transfer of momentum from the mill shell tocontiguous particles according to a succession of con-tacts. As there is a slip between particles, part of theimparted energy is dissipated, resulting in a loss ofrotational rate among adjacent layers from the millshell to the inner surface of the charge.
Morrell (1993) established an experimental cam-paign in a laboratory glass ended mill from which hewas able to calculate a series of velocity profiles ofmill charge according to variations in mill rotationalspeed, mill charge volume, particle size, among oth-ers. He derived a series of expressions, which allowedthe charge angular velocity gradient to be calculated.He also derived expressions to calculate the positionof toe and shoulder angles as a function of selectedoperating variables.
The subject is in fact one of paramount importancefor mill operation, as it drives both the mill powerdraw and the comminution process performance.Accordingly, depending upon the amount of slip inthe mill charge, the energy imparted to the chargewill be split into attrition, abrasion or dissipatedthrough heat as a by-product of friction.
However, it was assumed in the Morrell model thatno slip occurs at the shell wall. Such a simplificationis a valid first approximation in the case of AG/SAGmills, as it does not significantly inf luence the powerdraw by this equipment, which in fact was the mainpurpose of the Morrell model. Nevertheless, as awide variety of lifter bar profiles are currently foundin industrial units the comminution performance ofthe mill can be altered depending upon the specificapplication. Moreover, there is an increasing interestof industry towards a means of predicting the trajec-tory of the outer shells’ particles as a function of thelifter bar profile. Most of that interest is motivatedby the consequences of inadequately designed lifterbars, which have reportedly caused severe damage tomill shells (Johnson et al, 1994).
214 KONA No.20 (2002)
It is important therefore to separate the behaviourof shells whose trajectories are directly inf luenced bythe lifter bars and those which are not. The formerare physically elevated by the action of the lifter barsurface thus showing no slippage with mill shell,whereas the latter are mostly inf luenced by the coeffi-cient of friction between neighbouring shells.
Two distinct treatments were therefore adopted topredict both the shoulder and toe angles of individualshells. A theoretical one comprising the motion ofthose shells directly inf luenced by the lifter bars andan empirical one for the inner shells.
The theoretical approach was based on the workinitiated by Vermeulen (1985) and further enhancedby Powell (1991), whilst the empirical one was basedon Morrell (1993).
Once the trajectories of the shells inf luenced by thelifter bar are established, the remaining shell trajecto-ries are determined based on Morrell’s expressionsto calculate the loss of rotational rate between con-tiguous shells, together with the empirical expres-sions for the shoulder and toe positions.
The net result of the above scheme was a modelwhich predicts the motion of the grinding charge aswell as the power draw under a wide range of opera-tional and design conditions, and includes the effectof such factors as particle size, lifter bar geometry,mill filling and mill speed.
Apart from the shell structure of the charge no fur-ther assumptions were made about the shape that thecharge takes up. However a lifelike prediction of thecharge motion is provided by the model and is typi-fied by the example shown below.
4.5 Breakage EnergyThe new AG/SAG model differentiates the break-
age processes occurring in AG/SAG mills into twomain mechanisms. Accordingly, the slip between theshells causes a shearing motion and creates the con-ditions necessary for attrition breakage where rela-
tively small particles are nipped between grindingmedia as they slide against one another. Impactbreakage occurs predominantly in the vicinity of thetoe of the charge where the grinding media impactafter falling from the shoulder of the charge.
The Morrell model estimation of the bulk powerassociated with each of these mechanisms was thebasis to establish the relationships, which associatesthe mill charge motion with specific comminutionenergy for all size fractions of the mill charge. Thegrinding media are viewed as contactors in the modeland are used to determine the input energy for break-age in each of these modes.
The separation of impact from attrition was a depar-ture from the way most models treat breakage. Untilnow it has been usual to describe breakage in termsof a single specific energy imparted to the particles,resulting from a combination from various size reduc-tion mechanisms.
The motion of the charge was therefore describedin terms of the breakage frequency and energy asso-ciated to each size reduction mechanism. Accord-ingly, the bulk power associated to the grindingcharge according to impact and attrition was distrib-uted to the entire charge of the mill. The interpre-tation of the physical mechanisms involved in thecharge motion was therefore the basis to model theselected size reduction mechanisms independently.
To fully describe the model, it was necessary tohave functions, which describe the way the totalbreakage frequency and energy is distributedamongst the size fractions of the contactees.
The total power associated with impact was directlyderived from the mill charge motion model. Thepower attributed to impact was thus calculated fromthe power consumed by each shell to elevate themedia elements and the frequency of contacts attrib-uted to the media elements. The power consumed byindividual shells was provided by the Morrell model.
The charge motion model adopted a shell descrip-tion of the charge according to which all grindingmedia elements follow a circular trajectory up to thepoint where they enter a free fall trajectory. The cycleis completed as the grinding element re-enters the cir-cular path at the toe of the charge.
To determine the rate at which breakage energy isimparted to the contactees, or the total number ofimpacts as shown in Figure 6, a simple approach wasadopted by assuming that impact is directly relatedto the motion of the charge. These two assumptionswere used to calculate the average energy associatedwith each impact event. From the shell description
KONA No.20 (2002) 215
Fig. 5 Simulation of Charge Motion Profile.
used by the model the mean energy associated witheach impact was then estimated.
Attrition breakage was considered to occur due tonipping in between media as they slide and roll overone another. It was further assumed that attrition hasan upper limit which is equal to the charge lower limitsize i.e. attrition mode of breakage is restricted to par-ticles smaller than those which form the grindingmedia.
The approach adopted to describe attrition energywas equivalent to the one described for impact. Ac-cordingly, the energy attributed to attrition was calcu-lated from the power consumed as a result of slipamongst contiguous shells and the frequency of con-tacts attributed to the media elements. The attritionpower consumed by individual shells was provided bythe Morrell model whereas the frequency of attritionevents was determined from the relative velocity ofcontiguous shells and their surface area, as schemati-cally described in Figures 7 and 8.
4.6 Breakage FrequencyThe frequency at which impact and attrition break-
age occur was considered to be the amount of im-pacts per particle per unit of time, according to thedefinition established by Morrell (1989). The defini-tion of what constitutes a breakage event and itssubsequent parameterisation was then necessary todescribe the frequency at which the size reductionmechanisms occur in the mill.
The approach adopted in this work was based onthe mechanistic description of the interactions be-tween contactors and contactees. A more detailedinterpretation was however necessary in order toestablish a procedure to predict the breakage fre-quency associated with impact and attrition accordingto each mill charge size fraction.
The equations developed to represent both impactand attrition breakage frequency were based on thesame approach i.e. the total number of breakageevents associated with the contactors was distributedamongst the mill charge particles according to a par-tition term. These partition terms were establishedon the basis of the mechanisms derived from thecharge motion and according to each specific sizereduction mode used.
The impact events generated by the motion of thegrinding media (impactors) are distributed amongstthe impactees according to a mechanism based onsurface area of the particles. Therefore, the estima-tion of impact breakage frequency involves two mainterms i.e. a specific impact generation rate as well asa partition term, which divides such a rate of eventsamongst each individual size fraction. A secondaryterm was introduced as recourse to calibrate the rela-tionship.
216 KONA No.20 (2002)
Fig. 6 Three-Dimensional Representation of a Shell Cycle. Fig. 8 Three-Dimensional Representation of the Surface FormedBetween Contiguous Shells.
Fig. 7 Surface Formed Between Contiguous Shells with Differ-ent Rotational Speeds.
The impact breakage rate was therefore estimatedas follows:
riimpΓ imp Pi
imp K iimp
where ri
imp impact breakage frequency of size fraction i Γ imp specific impact generation ratePi
imp impact partition term K i
imp constant
The average number of impact contacts per parti-cle comprises the ratio between the total number ofimpact contacts generated and the total number ofparticles which forms the grinding charge.
The total number of impact contacts was derivedfrom the Morrell model, which was based on thegrinding charge comprising solely of mono-sized par-ticles. This number was subsequently normalisedaccording to the number of grinding media particles.Numerically this relationship was expressed as fol-lows:
Γ imp whereNs
imp number of impact contacts per unit time givenby shell s
n number of shellsε total number of grinding charge particles with
an equivalent size equal to C, given by:
e wheresi volume of all ore particles contained in size frac-
tion isi
b volume of all steel balls contained in size frac-tion i
m size fraction which contains media size lowerlimit value
C characteristic media size
The specific impact generation rate is the averagefrequency with which a grinding media elementimpacts the toe region.
The impact partition term represents the distribu-tion of the impact breakage events provided by thegrinding media elements to the impactees. Accord-ingly, this term incorporates the mechanism attrib-uted to the interactions between impactors and
m
∑1(sisi
b)
C3πN6
∑n
1Ns
imp
e
impactees, according to which the surface area dic-tates the interactions.
The impacts generated by the entire ball chargewere considered to act indistinctly on all impacteesregardless of the particle size. It was assumed thatbelow the toe of charge steel balls re-transmit anyimpact they received. This energy was therefore con-sidered to be absorbed by the rock charge. Henceballs were not considered impactees.
As for impact, the attrition events generated by themotion of the grinding media (attritors) are distrib-uted amongst the attritees according to a characteris-tic mechanism based on surface area of the particles.However, the effective attrition contacts i.e. thosewhich cause attrition breakage, were considered torepresent a size relationship between attritors andattritees. Accordingly, the model assumes that only acertain size of particle provides adequate sites to cap-ture and subsequently break other particles by attri-tion.
4.7 Ore CharacterizationThe size distribution resulting from a breakage
event, or appearance function, comprises the combi-nation of the energy associated to the breakage eventtogether with the results of the energy-breakage rela-tionship calibrated for the ore investigated. Althoughtwo modes of imparting breakage energy to the parti-cles were presented and further parameterised, theparticle’s response in terms of breakage is consideredsolely on the basis of the corresponding fragmen-tation, which results from the amount of energyimparted, regardless the mode of breakage. This isequivalent to assuming that even though the mode ofapplying energy to a particle in a AG/SAG mill mayvary substantially, the resulting breakage will dependonly on the particle characteristics and the totalamount of energy received by the particle.
The ore breakage characterisation data resultedfrom two particular laboratory tests, which weredeveloped at JKMRC i.e. the drop-weight impactorand the tumbling test (Napier-Munn et al, 1996).
The drop-weight impactor is able to accommodateparticles in the size range 10-100 mm thus coveringthe range of sizes typically found in the grindingmedia of AG and SAG mills. It is used to generateenergy-breakage data comprising usually a 0.25 to 2.5kWh/tonne range of specific energies applied to par-ticles. The test reproduces breakage events carriedout on individual particles, even though in a typicalprogramme a number of particles are tested as tominimise the effects of ore heterogeneity as well as
KONA No.20 (2002) 217
experimental errors. Figure 9 shows a schematic ofthe JKMRC drop weight testing device.
The autogenous tumbling test was designed to cre-ate an environment where the breakage energy im-parted to each particle is very small thus resulting insize reduction typical of abrasion and chipping. Thedata generated from this test were re-interpreted notas a secondary parameter to the model but instead, interms of a energy-breakage relationship.
The experimental data obtained from drop-weightand tumbling tests were treated separately accordingto the procedures described in previous sections. Theinformation derived from such treatment were com-bined into a single system which constitutes the orebreakage characterisation, further used by the modelto calculate the appearance function.
The breakage characterisation system adopted bythe AG/SAG model consists of two complementarygroups of information. The first group involves therelationship between specific energy associated to abreakage event and a breakage parameter represent-ing a single point of the size distribution of corre-sponding broken particles. Accordingly, the specificenergy (kWh/tonne) values derived from the drop-weight test impacts were associated with a breakageparameter obtained from the sizing of broken frag-ments, in this case t10 or the percent passing at one-tenth of the original fragment size. The specificenergy (Ecs) and breakage parameter (t10) relation-ship was described in terms of a matrix, as shown inthe first two columns of Table 1. The information
obtained from the tumbling test was directly incorpo-rated to this matrix as noted in the first line. The com-bination of results from both drop-weight device andtumbling tests provided a comprehensive assessmentto the energy/breakage relationship.
The second group of information related the break-age parameter t10 to the entire size distribution of bro-ken fragments. The t10 was therefore associated witht2, t 4, t100 or the other t n’s which characterise the cor-responding size distribution. The full size distributionis predicted by successive interpolations conductedover the regressed t n values. The tumbling test re-sults were also included into the drop-weight t10/t n
matrix as an extra line, as shown in Table 1.
5. Validation
The model validation exercise represents a criticalstep in the analysis of the model’s ability to reproducea real mill operation and, by extension, establishesthe limits of the model’s application as well. Accord-ingly, the new AG/SAG mill model was evaluated onits predictive capacity to resemble the interactionsbetween the load and mill operating conditions. Thesimulations thus aimed to assess the load compo-sition as inf luenced by different conditions on theresulting breakage and power draw. The analysis in-cluded the load interaction with the following vari-ables:• Mill Throughput • Slurry Pooling• Grate Design and Open Area• Lifter Bar Design• Mill Speed • Ore Breakage Characteristics
Industrial AG/SAG mills have a characteristic rela-tionship between the load and the mill throughput,which tends to be more prominent as the ball chargedecreases. Accordingly, the load of an industrial AGmill increases with throughput up to a point wherethe increments will decrease progressively. This isequivalent to say that there is a non-linear relationship
218 KONA No.20 (2002)
Perspexenclosure
Guide rail
RockSteel anvil
5 kg leadweights
Adjustableheight (energy)
Large concretebase
Fig. 9 The JKMRC Drop-Weight Testing Device.
Ecs t10Parameter t (%)
(kWh/tonne) (%) t2 t100
6.0104 1.77102 1.87102 1.38102
0.50 20 63.1 07.5
1.25 30 84.2 11.4
2.50 50 99.9 20.2
Table 1 Relationship Between Ecs and t n.
between them. In terms of mathematical simulation of AG/SAG
mills the relationship between load and throughputdetermines the ability of the model to reproduce over-load conditions, which in industrial mills, often coin-cides with the filling of 35%.
To assess this relationship, the data obtained from aselected industrial mill was chosen as they representthe operation of a large mill (9.5 m in diameter) inconditions of high load level. The simulation resultsobtained with new and Leung’s model are shown inFigure 10.
It is clear from Figure 10 that the simulationsusing Leung’s model resulted in tendency of a linearrelationship between the mill throughput and millload whereas the new model showed a non-linearresponse. Accordingly, both Leung’s and new modelload level predictions coincides at the throughput of250 tonne/h which in this case was equivalent to 19%of mill volume. However, from this point onwardsLeung’s model predicts mill loads up to more than55% as the throughput increases whilst the new modelshows a tendency to f lat out at 40% of the mill volume.
Even tough the survey campaign carried out on theselected mill operation did not include a step changeprocedure to validate the above simulated results, thenew model clearly resembles the industrial mill oper-ation as opposed to the results obtained with Leung’smodel.
Although the new AG/SAG mill model was de-signed to incorporate a number of mill operating con-
ditions and design characteristics not included inexisting models, its predictive capacity was comparedwith Leung’s AG/SAG model. The comparisons wereconducted in terms of the most significant variablesof the mill performance i.e. power draw and dis-charge size distribution.
Each of the models was then applied to an indus-trial mill database and the relative error of their pre-dictions calculated. The comparisons were based onthe predictions relative to the mill power draw andmill discharge P80. Table 2 summarises the individualvalues obtained according to each data set and modelused. The mean relative error and standard deviationwere calculated for each set of model predictions.
The fact that the new AG/SAG model predictedsteady mill charges for all the 17 data sets as opposedto the other model tested indicated its superior capac-ity to reproduce the database. However, as Leungimposed no limits for the mill charge, it was decidedto conduct the comparisons using the charge volumesas predicted by the models.
The results showed in Table 2 indicated generallyvery high values of the standard deviation associatedwith the mean relative error. Accordingly, althoughthe mill power draw predictions showed relatively
KONA No.20 (2002) 219
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200
Mill Throughput (tph)
Mill
Loa
d (%
of M
ill V
olum
e)
Leung Model
New Model
Fig. 10 Relationship Between Mill Load and Throughput.Opera- Mill Power Draw Mill Discharge P80tion/ (MW) (mm)
Survey Exper. Leung New Exper. Leung New
Mill # 1
1 7.13 7.77 7.12 0.97 2.22 1.42
2 6.85 7.53 7.04 1.13 4.97 1.31
3 7.13 7.43 7.04 0.96 8.19 1.90
4 6.77 7.33 6.55 1.13 5.72 1.75
Mill # 2
1 5.76 3.85 3.91 0.24 0.27 0.42
2 2.34 3.72 2.60 0.82 0.34 0.32
3 3.28 5.15 4.60 1.02 0.33 0.55
4 3.93 5.76 4.89 0.86 0.32 1.50
5 6.07 5.02 5.79 0.69 0.34 0.60
6 5.72 4.55 4.80 0.58 0.28 0.50
7 6.07 6.24 4.82 1.08 0.33 0.47
8 5.68 4.40 4.98 0.26 0.28 0.28
9 5.95 5.41 4.37 1.43 0.32 1.73
Mill # 3
1 2.50 2.88 2.80 0.44 0.62 0.44
2 2.60 2.00 1.95 0.20 0.45 0.42
3 2.45 2.30 2.24 0.40 0.50 0.33
4 2.63 2.89 2.85 0.89 0.67 0.43
Relative Mean 7.1 1.7 78.2 8.4Error Std. Dev. 27.3 18.6 230.6 50.3
Table 2 Predictions of Mill Power Draw and Product Size Distrib-ution.
lower mean values the standard deviations varied inthe range of 18.6 to 27.3%. The new AG/SAG model isbetter than Leung’s as determined by the respectiverelative error means and standard deviations. Accord-ingly, the new model over predicted the power drawby 1.7% whilst the other model under predicted by7.1%.
The predicted mill discharge size distributions rep-resented by the P80 parameter showed a totally differ-ent picture as the new model resulted much superiorthan the other model. The new model provided thelowest standard deviation of the relative error (50.3%)whereas the other model resulted in a correspondingvalue of 231%.
Overall the new model provided the lowest meanrelative error and standard deviation for both millpower draw and mill discharge size distributions.
Additional Model Features
The slurry accumulation within the mill load wasinvestigated in terms of its effects on mill perfor-mance for all 17 data sets. A series of comparisonsbetween different circuit configurations showed thatthe effects caused by slurry pooling at both impactand attrition terms of the new model resulted in cor-rect tendencies of both mill power draw and mill dis-charge size distribution.
The simulations designed to assess the mill perfor-mance caused by grate design and total open areapredicted variations of slurry hold up in the millcharge according to the expected behaviour of a fullscale mill. The results should therefore be coupledwith effects of slurry pooling on the mill power drawand discharge size distribution.
The new model incorporated the effects of the lifterbar design on the mill performance. The simulatedmill performance ref lected accordingly the changesin the charge motion. Supplementary information wasobtained as the simulations indicated whether thepoints of impact associated with the outer shells wereonto the charge or the mill liner. This is a potentialfeature for optimisation of the lifter bar profile. Fig-ure 11 shows the representation of a simulatedcharge profile.
The effects of mill speed on the charge motionwere evaluated. The results indicated consistent var-iations of charge volume and corresponding millpower draw. The mill discharge size distribution re-f lected accordingly the relative variations of impactand attrition breakage mechanisms with mill speed.
On the basis of 17 AG/SAG mill data sets the new
model was found to provide consistent estimations ofboth mill power draw and product size distribution. Inboth cases the differences between the standard devi-ation of the relative error associated with the esti-mations were very close to the data measurementstandard error.
Even though the differences obtained for the millpower draw and product size distribution were rela-tively small, it should be emphasised that the highmagnitude of the data relative error which may not betolerable in greenfield estimations.
6. Conclusions
A model was developed to describe the influence ofthe charge composition and motion on breakage per-formance such that it can predict the performance ofAG/SAG mills under all normally encountered opera-tional conditions. The parameters derived from themechanistic description of the charge dynamics wereincorporated into distributions of both impact andattrition breakage frequency and intensity. The valida-tion exercise indicated that the new model predic-tions were better than an existing model as well asincorporates a number of additional features relatedto the mill design and operating conditions.
7. Notation
A grate open area (m2)a ij appearance function (fraction of broken
particles from size fraction j which appears in size fraction i)
a ijatt attrition appearance function
a ijimp impact appearance function
C characteristic media size (m)C i classification function at size i
220 KONA No.20 (2002)
Fig. 11 Simulated Charge Profile Corresponding to a Lifter Barof 120 mm and Angle of 90° for a 9.6 m diameter SAGmill.
D mill diameter (m2)D i discharge rate of size fraction i (h1)fi mass f lowrate of size fraction i in the
mill feed (t/h)K i
imp constantn number of shellsm size fraction which contains media size lower
limit valueNs
imp number of impact contacts per unit time given Pi
imp impact partition term pi mass f low rate of size fraction i in the
mill discharge (t/h)Q f low rate through the grate (m3/h)ri breakage rate of size fraction i (h1)ri
imp impact breakage rate of size fraction i (h1)ri
att attrition breakage rate of size fraction i (h1)si mass of size fraction i in the mill load (t)si
b volume of all steel balls contained in size fraction i (m3)
Vm volume of the mill charge (m3)ε total number of grinding charge particlesφ fraction of mill critical speedγ mean relative position of the grate aperturesΓ imp specific impact generation rate by shell s (h1)
8. Glossary
angle of the lifter angle formed between the lifterface and its base
appearance function size distribution of brokenfragments
breakage rates frequency of breakagecomminution process of size reductiondischarge function description of the probability of
a size fraction to be discharged from the mill cham-ber
grate perforated steel plate installed in the mill dis-charge end designed to classify the mill charge
greenfield estimation estimation not based on oper-ating mill or pilot plant campaign
grinding media or contactors coarse rocks andsteel balls contained in the mill charge
JKMRC Julius Kruttschnitt Mineral Research Cen-tre, University of Queensland, Australia
JKSimMet commercial software for mass balanc-ing, modelling and simulation of comminution
lifter bar steel bar installed in the mill internal wallto assist the charge lifting
matrix models mathematical models where all vari-ables are structured in matrices
mechanistic approach representing a phenomenonby its mechanisms
P80 size at which 80% of the mass passes of a givensize distribution
rate process approach mathematical description ofcomminution based on rates of change
reduction ratio ratio between the characteristicsizes of the mill feed and discharge solids
shoulder of the charge uppermost point reached bygrinding media
slurry hold-up pulp retention in the mill chamberslurry pool accumulation of pulp above the charge
in the mill chamberspecific energy energy per mass (kWh/tonne)
imparted to a fragmenttoe of the charge outermost point where the grind-
ing media impact after a falling trajectorytrunnion steel cylindrical projection forming the
mill feed and discharge endstumbling test test in which 3 kg of 5538 mm
fragments are tumbled in a laboratory mill for 10minutes
References
1) AUSTIN L.G., WEYMONT, N.P., PRISBREY, K.A.,HOOVER, M., Preliminary results on modelling of auto-genous grinding. Proc. 14th Int. Symp. APCOM, 1977,p.207-26.
2) BOND, F.C., The third theory of comminution. Trans.AIMME, 1952, 193, p.484-94.
3) GOLDMAN, M. and BARBERY, G., Wear and chippingof coarse particles in autogenous grinding: Experimen-tal investigation and modelling. Minerals Engineering,1988, 1 (1), p.67-76.
4) JOHNSON, G., HUNTER, I., HOLLE, H., Quantifyingand improving the power efficiency of sag milling cir-cuits. Minerals Engineering, 1994, 7 (2/3), p.141-152.
5) KELLY, F.J., An empirical study of comminution in opencircuit ball mill. Trans. CIM, 1970, 73, p.119-127.
6) KELLY, E.G. and SPOTTISWOOD, D.J., The breakagefunction; what is it really?. Minerals Engineering, 1990,3 (5), p.405-414.
7) KING, R.P. and BOURGEOIS, F., Measurement of frac-ture energy during single-particle fracture. MineralsEngineering, 1993, 6 (4), p.353-367.
8) KJOS, D.M., 1985. Wet autogenous mills. In: SME Min-eral Processing Handbook. WEISS, N.L., ed., SME-AIME, 1985, Sec. 3C, chap.4, p.3C-60/3C-70.
9) LEUNG, K., An energy based ore specific model forautogenous and semi-autogenous grinding. Ph.D. The-sis, University of Queensland, Australia, 1987.
10) LOVEDAY, B.K. and NAIDOO, D., Rock abrasion inautogenous milling. Minerals Engineering. 1997, 10 (6),p.603-612.
11) MANLAPIG, E.M., SEITZ, R.A., SPOTTISWOOD, D.J.,Analysis of the breakage mechanisms in autogenous
KONA No.20 (2002) 221
19) MUTAMBO, J.P.C., Further development of an autoge-nous and semi-autogenous mill model. M. Eng. Sc. The-sis, University of Queensland, Australia, 1992.
20) NAPIER-MUNN, T.J., MORRELL, S., MORRISON, R.D.,KOJOVIC, T., Rock testing determining the material-specific breakage function. In: Mineral comminutioncircuits their operation and optimisation. Napier-Munn, T.J., ed., Chap.4, JKMRC, Brisbane, 1996, p.49-94.
21) NARAYANAN, S.S., Development of a laboratory singleparticle breakage technique and its application to ballmill modelling and scale up. Ph.D. Thesis, University ofQueensland, Australia, 1985.
22) POWELL, M.S., The effect of liner design on themotion of the outer grinding elements in a rotary mill.Int. J. Min. Proc., 1991, 31, p.163-93.
23) SCHOENERT, K., 1993. Personal communications. 24) STANLEY, G.G., The autogenous mill: a mathematical
model derived from pilot and industrial-scale experi-ment. Ph.D. Thesis, University of Queensland, Aus-tralia, 1974.
25) VERMEULEN, L.A. 1985. The lifting action of lifter barsin rotary mills. Journal SAIMM, 85 (2), 1985, p.41-49.
26) WHITEN, W.J., A matrix theory of comminution ma-chines. Chemical Eng. Sc., 1974, 29, p.589-599.
27) WICKHAM, P. 1972. Comminution of pebbles and fineore. M. Eng. Sc. Thesis, University of Queensland, Aus-tralia, 1974.
222 KONA No.20 (2002)
grinding. In: Autogenous Grinding Seminar, 1979,Trondheim. p.A3/1-14.
12) MACPHERSON, A.R., Autogenous grinding 1987 update. CIM Bulletin, 1987, 82 (921), p.75-82.
13) MORRELL, S., Simulation of bauxite grinding in semi-autogenous mill and DSM screen circuit. M. Eng. Sc.Thesis, University of Queensland, Australia, 1989.
14) MORRELL, S., The prediction of power draw in wettumbling mills. Ph.D. Thesis, University of Queensland,Australia, 1993.
15) MORRELL S., FINCH, W.M., KOJOVIC, T., DELBONIJR., H., Modelling and simulation of large diameterautogenous and semi-autogenous mills. Proc. Eur.Symp. Comm., Vol. 8, Stockholm, 1994.
16) MORRELL, S. and MORRISON, R.D., Ag and Sag millcircuit selection and design by simulation. Proc.Advances in Autogenous and Semiautogenous GrindingTechnology. Sag 96, Vancouver, 1996.
17) MORRELL S. and STEPHENSON I., Slurry dischargecapacity of autogenous and semi-autogenous mills andthe effect of grate design. Int. J. Min. Proc. 1996, 112,p.53-72.
18) MÖRSKY, P., KLEMETTI, M., KNUUTINEN, T., KALAPUDAS, R., KOIVISTOINEN, P., The develop-ment of laboratory testing for autogenous grinding.Proc. Eur. Symp. Comm. Vol. 8, Stockholm, 1994, p.308-317.
Author’s short biography
Homero Delboni, Jr.
Dr. Homero Delboni, Jr. graduated in Mining Engineering from the University ofSão Paulo, Brazil. In 1989 he obtained a M. Eng. degree in Minerals Engineering atthe same university. He joined the Julius Kruttschnitt Mineral Research Centre inthe University of Queensland, Australia, where he obtained his Ph.D. degree in1999. He is currently a lecturer in the Department on Mining and Petroleum Engi-neering at the University of São Paulo, where he is involved in both teaching andresearch in mineral processing, particularly in comminution.
Steve Morrell
Dr. Steve Morrell graduated with Honours in Metallurgical Engineering from theRoyal School of Mines. He joined the Julius Kruttschnitt Mineral Research Centre JKMRC in the University of Queensland, Australia, where he obtained his M.Sc.degree in 1989 and Ph.D. in 1993. He is currently a researcher in the JKMRC,where he is involved in research in comminution.
KONA No.20 (2002) 223
1. Introduction
Various methods have been used to quantify theadhesive force between particles. Indirect methodsinclude those which measure adhesive force by deter-mining properties of powder beds such as angle ofrepose, shearing stress, f luidization threshold force,and degree of volume reduction. Direct methods thatinvestigate many individual particles include adhesiveforce measurement methods that use image process-ing or statistical processing, such as the centrifugalmethod [1, 2, 3] and the impact separation method.[1, 4] One method that works with a single particleuses a spring scale or other instrument to measurethe force needed to directly separate a particle from a
f lat surface or another particle, [5] but this method isusable only with particles that are at least 200 µmlarge, and it is meant for inorganic powders. The fineparticle adhesive force measuring apparatus (PAF-300, Okada Seiko Co. Ltd., Tokyo) used in this studyis capable of directly measuring, during visual obser-vation, the adhesive force between a f lat surface and afine particle, or between two fine particles, even downto particle sizes of about 10 µm. In other words, thisapparatus can focus on a single particle, tear it awayfrom a substrate or from an aggregate of fine parti-cles to which it is attached, and gauge the tiny forceneeded to dislodge it. Because the PAF-300 can use amicroscope or CCD camera to select the desired par-ticle and measure its adhesive force, it can determinethe relationship between the adhesive force and howit is attached or how it is released. This paper reportsalso on adhesive force measurement with the cen-trifugal method, and compares the results with thoseobtained with this measuring apparatus.
2. Sample Materials
Our sample powders were corn starch (CornstarchW, Nippon Syokuhin Kakou, Co. Ltd., Okayama), lac-
Yasuhiro SHIMADAa, Yorinobu YONEZAWAa, Hisakazu SUNADAa, Ryusei NONAKAb, Kenzou KATOUb and Hiroshi MORISHITAc
a Faculty of Pharmacy, Meijo Universityb OKADA SEIKO Co., Ltd .c HMI Inc.
Development of an Apparatus for Measuring Adhesive Force between Fine Particles†
Abstract
We developed an apparatus that uses the direct separation method to measure adhesive forcebetween fine particles, and between a fine particle and a f lat-surface substrate. This apparatus wasable to measure adhesive force with high resolution (approximately 2 nN) and monitor the behaviorof each particle with a microscope and image analyzer when separating particles from each other,and to calculate the adhesive force of the particles. Of the organic particles tested (corn starch,potato starch, and lactose), potato starch had the highest adhesive force, while lactose had the lowestadhesive force toward f lat-surface substrates. The diameter and size distribution of f ine particlesclearly affected their adhesive force.
Key words: Adhesive force, fine particle, organic particle, HPMC capsule, gelatin capsule
a 150 Yagotoyama, Tempaku-ku, Nagoya, Aichi Pref., 468-8503, Japan. TEL 052-832-1781 (Ext. 272)
b 4-27-8 Minami-karasuyama, Setagaya-ku, 157-0062, Tokyo,Japan. TEL 03-3308-1217
c Matsudo Palace 1002, 35-2 Koyama Matsudo-shi, 271-0093, Japan. TEL 03-3308-1217
† This report was originally printed in J. Soc. Powder Tech-nology, Japan. 37, 658-664 (2000) in Japanese, beforebeing translated into English by KONA Editorial Commit-tee with the permission of the editorial committee of theSoc. Powder Technology, Japan.
tose (Pharmatose 200M, DMV International), andpotato starch (refined starch, Hokuren AgriculturalCooperative, Hokkaido). In experiments measuringadhesive force between a fine particle and f lat sur-face, the materials used as the substrate for makingparticles adhere were slide glass (Micro Slide Glass,Matsunami Glass Ind., Ltd., Osaka), tablets formed bycompressing a powder of the same material as thesample particles made to adhere to the f lat surface,and gelatin capsule “0” (CLEAR Y, Shionogi QualicapsCo. Ltd., Nara), which is widely used in the pharma-ceutical field. We used the same gelatin capsule “0”for centrifugal method measurements in comparisonexperiments. We used gelatin capsule “3” and HPMCcapsule “3” (CLEAR 1, Shionogi Qualicaps Co. Ltd.,Nara) as the substrates when measuring adhesiveforce between fine particles.
3. Apparatus and Method
3.1 Measuring Basic Physical Characteristicsof Powders
Powder particle size was measured with a laser dif-fraction and scattering particle size analyzer (LMS-30,Seishin Kigyo Co. Ltd., Tokyo). Shape index was mea-sured with a high-speed image analyzer (LUZEX-FS,Nireko Co. Ltd., Tokyo). When performing these mea-surements, Eqs. 1 and 2 were used in measuring twoindexes: the index showing unevenness (ψ1), and thatshowing roundness (ψ2).
ψ14πA／PM2 (1)ψ24A／πML2 (2)
Where:A is the particle’s actual projected area,PM is the circumference of the particle’s projected
image, andML is the maximum length of the projected particle
image.
We used a differential scanning thermal scale (TG-DTA2000, Mac Science Co. Ltd., Kanagawa) to mea-sure the moisture content of powders.
3.2 Overview and Operation of the Fine Particle Adhesive Force Measuring Apparatus (PAF-300)
The apparatus used to measure adhesive force(Fig. 1) comprises a sensor unit (6) that measuresadhesive force, the computer (1-b) that controls thesensor unit, an image analyzer (1-a), a stereoscope (8)for monitoring the adhesive force measuring unit, and
a CCD video camera (9). A detailed view of the sensorunit (Fig. 2) shows it is composed of a contact needle(6-b) that comes into contact with the sample and dis-lodges particles, two plate springs (6-a) connectedto the needle, and a laser displacement gauge (6-c)behind the springs. When the stage (5-a) movesslightly in the direction of the large arrow, the contactneedle is pulled toward the sample substrate by theparticle adhering to the needle, stress is caused onthe plate springs, the needle moves to the left, and thelaser displacement gauge measures its change inposition. When the stage is moved slightly more tothe left, the stress on the plate springs exceeds theadhesive force between the particle and sample sub-strate, and the particle comes loose, which releasesthe stress on the springs. At that moment needle dis-placement is maximum, and computer processingconverts the displacement into adhesive force. Pow-ders were caused to adhere to the surface by passingeach power through a screen with 75 µm openingsfrom about 20 cm above the surface, and allowing par-ticles to fall freely. The experiment was performed in
224 KONA No.20 (2002)
3 6
42
1-b1-a 5
7 9
108
Fig. 1 Apparatus for Measuring Adhesive Force1-a: Image analyzer 05: Triaxial movable stage1-b: Sensor unit computer 06: Sensor unit2: Triaxial movable stage 07: Optical microscope
control box 08: Stereoscope3: Triaxial movable stage 09: CCD video camera
joystick 10: Video monitor4: Driving motor
8
5-b
6-b 6-d6-c
6-a
5-a
Fig. 2 Sensor Unit5-a: Triaxial movable stage 6-c: Laser unit5-b: Sample 6-d: Laser beam6-a: Plate springs 8: Stereoscope6-b: Contact needle
a laboratory where temperature was maintained at 20to 23°C and humidity at 50 to 55%. Adhesive forcebetween a f lat surface and fine particle was measuredin the following manner (Fig. 3-A): A particle wasattached to the surface and the contact needle wasattached to the particle, then the computer automati-cally dislodged the fine particle from the surface.Adhesive force between two fine particles was mea-sured in the same manner (Fig. 3-B). As an exampleof this latter type of measurement (Fig. 4), a particlewas attached to the contact needle, and then the stagewas moved under computer control to the left at arate of about 0.6 µm s1, at which time adhesive forcewas automatically measured. In the data plot obtain-ed in this operation (Fig. 5) the distance the stagemoved is on the horizontal axis, and the calculatedforce acting on the plate springs is on the verticalaxis. That force corresponds to the particle’s adhe-sive force. At the moment the contact needle dis-lodged the particle from the surface to which it hadadhered, the maximum value at point 4 was attained,after which the value instantly dropped. We deter-mined adhesive force to be the difference betweenthe center line and the maximum amplitude of thesprings’ free vibration, which steadily weakens. Be-cause the force acting on the two plate springs isgiven by the product of the spring constant k and dis-placement L in Eq. 3, finding k makes it possible tocalculate adhesive force F. Because spring constant kis given by Eq. 4, [6] the constant can be obtained byplotting Eq. 4 (Fig. 6).
FkL (3)k4π2(add.w.‐c)／(Ti2To2) (4)
KONA No.20 (2002) 225
3
4
2
2
A
Ca. 40µm
B
1
1
Fig. 3 Adhesion Force MeasurementA: Between particle and substrateB: Between particles1: Substrate 3: Contact needle2: Particle 4: Diamond head
4
3
0
0 5
5
10 15
100
200
2
6
1
Plat
e sp
ring
str
ess
(nN
)
Distance stage moves (µm)
Fig. 5 Separation and Adhesive Force1: Stage 2: Particle 3: Contact needle 4: Adhesive force peak 5: Net adhesive force 6: Distance stage moves
Fig. 4 Contact Needle, Particles, and CapsulePhoto A: Particles adhering to a capsule surfacePhoto B: An enlargement, showing particles just before
separation
Photo A Photo B
Where:add. w is the additional weight attached to thesprings,Ti is the characteristic frequency of the springs mea-
sured when the additional weight was attached,To is the initial characteristic frequency of the plate
springs, andc is the y-axis intercept.
From Fig. 6 we calculated the value of the sensorunit spring constant k as 0.18. Further, because thisapparatus pulls particles horizontally, we used Eq. 5to find the inf luence of a powder’s own weight onmeasurement, and considered the effect of the forceacting vertically.
Fg4π(d/2)3ρ α/3 (5)
3.3 Adhesion between Contact Needle andMeasured Particle
When the adhesive force between a particle and thecontact needle is weaker than that between the f latsurface and particle, it is necessary to somehowattach the particle to the needle. In our measure-ments of the adhesive force between potato starchand gelatin capsules, the adhesive force between thestarch and gelatin was greater than that between thestarch and needle, making measurements impossible
without using an adhesive. We therefore attachedindividual particles to the needle with an adhesive,which was a 40% aqueous solution of the macromo-lecular polymer hydroxypropyl cellulose (HPC-L,Nippon Soda Co., Ltd., Tokyo). However, we used noadhesive when the adhesive force between the needleand particle was greater than that between the f latsurface and particle.
3.4 Comparison of Centrifugal Measurementand PAF-300 Measurement of AdhesiveForce between a Flat Surface and Fine Particle
We used the centrifugal method to measure themean adhesive force F50 of potato starch to a gelatincapsule, and we used the PAF-300 to measure theadhesive force of a fine particle to a f lat surface, i.e.,that of potato starch to a gelatin capsule. A compari-son can be made because both methods were used tomeasure the adhesive force between a f lat surfaceand an individual particle. The centrifugal methoddetermines mean adhesive force F50 by applying aconstant centrifugal force on a group of particles,finding the particle size at which half the particlesbreak away, and then calculating the adhesive force.Thus it is possible to find the particle size that corre-sponds to mean adhesive force F50. With the PAF-300one can freely select the particle size one wants tomeasure, and our results in this study were those forcomparatively large particles of about 60 µm, a sizethat allows stable results. Both experiments were con-ducted at a temperature of 20 to 23°C and humidity of55 to 55%, conditions that make the effects of liquidbridging comparatively small. [7] Therefore we tookinto account only van der Waals force, and used Eq. 6to calculate the Hamaker constant H of the potatostarch from the adhesive force determined. The H ofhydrocarbons is reported [7] to be generally between4.0 and 10.01020 (J), and the constant calculatedfrom the adhesive force obtained was examined tosee if it conformed to the usual range. Adhesion dis-tance a corresponds to the distance at which van derWaals force is the maximum, and we used the value of0.4 nm found in the literature. [8]
FvdwHd/24a2 (6)
4. Results and Discussion
4.1 Measuring Adhesive Force between a FlatSurface and a Fine Particle [1, 9-11]
Table 1 presents the measurement results for aver-
226 KONA No.20 (2002)
10 20 30 40 500
10
9
8
7
6
5
4
3
2
1
0
Add
ition
al w
eigh
t on
plat
e sp
ring
(R20.998)
(105S2)Ti2To2
(2π)2
(10
2 g)
Fig. 6 Sensor Unit CalibrationFkLF is adhesive force, L is distance contact needle moves, To
is initial characteristic frequency of plate springs, and Ti ischaracteristic frequency of plate springs when additionalweight is attached.
age particle size, 10% diameter in cumulative distribu-tion, 90% diameter in cumulative distribution, shapeindex, and moisture content of the powders used inthis study. Table 2 gives the results obtained frommeasuring the adhesive force of these three powdersusing slide glass as the substrate. Adhesive forceincreased in the order from lactose, corn starch, andpotato starch, and the adhesive force of potato starchwas over four times greater than that of lactose. Theadhesive force of potato starch was larger than that ofcorn starch by the same extent. Table 2 also includesthe adhesive forces of the three powders when thef lat surface used for each powder was a tablet formedby compressing the same powder. Just as with slideglass, adhesive force increased in order from lactose,corn starch, and potato starch, although the differ-ences between them were not as great as when slideglass was the f lat surface. As seen in Table 1, theparticle size [1, 10, 11] and particle shape [9, 11, 12]would seem to be the biggest reasons. It would seemthat the more spherical a particle is, and the more itssurface is smooth and lacks roughness, the greaterits effective contact area, thereby reducing the meandistance between the particle and f lat surface, in turnincreasing van der Waals force. [11] A powder’s mois-ture content is another conceivable inf luence, whichwill be larger especially for adhesive force betweendifferent substances. The adhesive force of lactose,whose moisture content of about 5% is lower than theother two powders, was smaller than the adhesiveforce of the other powders, and moisture content was
thought to be one reason. The inf luence of a powder’sown weight when using this apparatus was provision-ally calculated with Eq. 5 to be 0.49 nN vertically forpotato starch (particle size 40 µm, true density 1.48 gcm3). Because this is about 1/1,000th the measuredadhesive force and hardly affects the results, wetreated it as part of measurement error.
4.2 Measuring Adhesive Force between FineParticles
Table 3 presents the results of measuring, asshown in Fig. 3-B, the inter-particle adhesive force ofcorn starch, lactose, and potato starch on a gelatincapsule surface. When the particle type changed wediscerned a clear difference, just as with the measure-ment of adhesive force between f lat surfaces andparticles in Table 2. Adhesive force in order of lowto high went from lactose to corn starch to potatostarch. As shown in Table 3, we likewise measuredthe inter-particle adhesive force of corn starch, lac-tose, and potato starch on the surface of an HPMCcapsule. Results were about the same as with thegelatin capsule, and we previously reported slight dif-ferences, [12] but we believe this is attributable to thedifference in the particle-attracting electrostatic adhe-sive force [13] due to differences between the gelatinand HPMC capsules with respect to material, capsulemoisture content, and electrification amount.
4.3 Comparison of Centrifugal Method andOur Method in Measuring Adhesive Forcebetween a Flat Surface and Fine Particle
Table 4 shows the results obtained when using thecentrifugal method to measure the mean adhesiveforce F50 between potato starch and a gelatin capsule,and the results from using the PAF-300 to measurethe adhesive force between a f lat surface and fine par-ticle, i.e., gelatin capsule and potato starch. Also givenin the table is the Hamaker constant, which was calcu-lated with Eq. 6 using these results. Table 4 showsthat measurement results obtained with the well-
KONA No.20 (2002) 227
D10 D50 D90Water
Sample (µm) (µm) (µm) ψ1 ψ2 content (%)
Corn starch 10.1 18.0 33.6 0.854 0.701 12.4
Potato starch 18.2 34.2 60.3 0.898 0.722 14.1
Lactose 05.7 28.8 80.6 0.557 0.511 05.2
Table 1 Physical Properties of the Samples
Adhesive force (nN)
Corn starch Potato starch Lactose
Glass platea 066.926.1 188.860.7 37.86.30
Tablet surfaceb 144.428.0 161.329.0 67.326.3
Table 2 Adhesive Force between Particle and Glass Plate, andTablet Surface of Same Substance
a Each value represents the mean S.D. (n5).b Each value represents the mean S.D. (n8).
Adhesive force (nN)
Corn starch Potato starch Lactose
Gelatin capsule 145.030.4 270.849.9 78.111.5
HPMC capsule 127.127.6 222.657.5 79.524.9
Table 3 Adhesive Force between Particles on the Gelatin Capsuleand HPMC Capsule
Each value represents the mean S.D. (n8).
established centrifugal method closely agree with theresults yielded by the PAF-300, and suggests that thePAF-300 can perform measurements of more or lessthe same accuracy as the centrifugal method. Fur-ther, both methods yielded values for the Hamakerconstant that are within or close to the range of 4.0 to10.01020 (J) for hydrocarbons found in the litera-ture. [7]
5. Conclusion
In this study we used an apparatus that, by directlydislodging adhering particles, can measure adhesiveforce between two particles or between a particle anda f lat surface, and we measured the adhesive forcesof three organic powders. The apparatus was able tomeasure clear differences in adhesive force. Whendislodging particles with the apparatus, particle be-havior was monitored with a microscope and animage analyzer, and recorded as an animated image,making it possible to calculate the adhesive force of asingle particle. Of the three organic powders used,potato starch had the highest adhesive force, followedby corn starch, and finally lactose. We found that lac-tose had an especially weak adhesiveness to slideglass in comparison to the other powders. It is likelythat particle size, shape, and moisture content hadthe most to do with the difference in adhesiveness,but it is conceivable that powder electrification alsohad some effect. By making comparisons with themeasured values yielded by this apparatus, we believeit will be possible to further explore adhesive forcechanges in the same powders under different tem-perature and humidity conditions, and to study theadhesive force equations that have been under inves-tigation for some time.
Nomenclature
a distance between two particles (m)A actual projected area of a particle (m2)
add.w additional weight attached to spring (kg)c y-axis interceptd mean Heywood diameter of particle
measured (m)D10 10% diameter in cumulative distribution (µm)D50 50% diameter in cumulative distribution (µm)D90 90% diameter in cumulative distribution (µm)F adhesive force (N)F50 mean adhesive force in centrifugal
separation (N)Fg force of gravity (N)Fvdw van der Waals force (N)H Hamaker constant ( J)k spring constant (N m1)L distance that contact needle moves (m)ML maximum length of projected particle
image (m)n number of samplesPM diameter of circle having a circumference
equivalent to the perimeter of the projected particle image (m)
Ti characteristic frequency of plate springswhen additional weight is attached (s)
T0 initial characteristic frequency of platesprings (s)
α acceleration of gravity (m s2)ρ density of particle (kg m3)ψ1 shape index based on PMψ2 shape index based on ML
References
1) Mizuno, M., H. Sunada, K. Iida, A. Otsuka, H. Sakashita,H. Tada and H. Kimura. “Measurement of the AdhesiveForce of Fine Particles on the Tablet Surfaces and ItsRemoval Method,” J. Pharm. Sci. Technol., Jpn., 57,181-189 (1997).
2) Okada, J., Y. Matsuda and Y. Fukumori. “Measurementof the Adhesive Force of Pharmaceutical Powders byCentrifugal Method, I,” Yakugaku Zasshi, 89, 1539-1544(1969).
3) Iida, K., A. Otsuka, K. Danjo and H. Sunada. “Measure-ment of the Adhesive Force between Particles and Poly-mer Films,” Chem. Pharm. Bull., 40, 189-192 (1992).
4) Otsuka, A., K. Iida, K. Danjo and H. Sunada. “Measure-ment of the Adhesive Force between Particles of Pow-dered Organic Substances and a Glass Substrate byMeans of the Impact Separation Method, I, Effect ofTemperature,” Chem. Pharm. Bull., 31, 4483-4488(1983).
5) Arakawa, M. and S. Yasuda. “The Measurement ofInteraction Force on Microparticles,” J. Soc. Mat. Sci.,Japan, 26, 858-862 (1977).
6) Matsumura, S., N. Kanda, T. Tomaru, H. Ishizuka and
228 KONA No.20 (2002)
Particle Adhesivediameter forcea,b H (J)
(µm) (nN)
Centrifugal separation 34.2 230.792.30 1.53.61020method
PAF-300 method 62.3 610.0175.8 2.64.81020
Table 4 Comparison of Centrifugal Separation Method and PAF-300 Method
a Each value represents the mean S.D. (n3).b Adhesive force of the potato starch to gelatin capsule.
K. Kuroda. “A Measurement of the Frequency Depen-dence of the Spring Constant,” Phys. Lett. A, 244, 4-8(1998).
7) Okuyama, K., H. Masuda, K. Higashitani, M. Chikazawaand T. Kanazawa. “Ni ryuushikan sougosayou,” J. Soc.Powder Technol., Japan, 22 (7), 451-475 (1985).
8) Massimilla, L. and G. Donsi. “Cohesive Forces BetweenParticles of Fluid-Bed Catalysts,” Powder Technology,15, 253-260 (1976).
9) Otsuka, A., K. Iida, K. Danjo and H. Sunada. “Measure-ment of the Adhesive Force between Particles of Pow-dered Materials and a Glass Substrate by Means of theImpact Separation Method, III, Effect of Particle Shapeand Surface Asperity,” Chem. Pharm. Bull., 36, 741-749(1988).
10) Shimada, Y., M. Sunada, M. Mizuno, Y. Yonezawa, H.
Sunada, K. Takebayasi, M. Yokosuka and H. Kimura.“Measurement of the Adhesive Force of Fine Particleson Tablet Surfaces and Method of Their Removal,”Drug Dev. Ind. Pharm., 26, 149-158 (2000).
11) Otsuka, A. “Adhesive Properties and Related Phenom-ena for Powdered Pharmaceuticals,” Yakugaku Zasshi,118 (4), 127-142 (1998).
12) Shimada, Y., T. Ito, Y. Yonezawa, H. Sunada, M. Yoko-suka and K. Takebayasi. “Measurement of the AdhesiveForce of Contaminative Particles on the Capsule Sur-face and Method of Their Removal,” J. Pharm. Sci. Tech-nol., 60 (1), 35-42 (2000).
13) Kulvanich, P. and Peter J. Stewart. “An Evaluation of theAir Stream Faraday Cages in the Electrostatic ChargeMeasurement of Interactive Drug Systems,” Int. J.Pharm., 36, 243-252 (1987).
KONA No.20 (2002) 229
Author’s short biography
Yasuhiro Shimada
March, 1998 Graduated from Faculty of Pharmacy, Meijo UniversityApril, 1998 Research Associate at Faculty of Pharmacy, Meijo UniversityApril, 1999 Entered Master Course of Faculty of Pharmacy, Meijo University March, 2001 Graduated from Master Course of Faculty of Pharmacy, Meijo
University April, 2001 Entered Doctor Course of Faculty of Pharmacy, Meijo University Research Work Analysis of Powder Adhesive Force and Removal Process
Yorinobu Yonezawa
March, 1967 Graduated from Faculty of Pharmacy, Kyoto UniversityApril, 1967 Research Associate at Faculty of Pharmacy, Meijo UniversityJuly, 1983 Ph.D. degree (Pharm. Sci., Kyoto Univ.)April, 1989 Assist Professor at Same UniversityApril, 1989 Associate Professor at Same UniversityAugust, 1983-August, 1985
Research Worker at University of Wisconsin-Madison (USA)Research Work Analysis of Dissolution Process of Solid Dosage Forms
230 KONA No.20 (2002)
Author’s short biography
Hisakazu Sunada
March, 1960 Graduated from Department of Pharmacy, Faculty of Medicine,Kyoto University
April, 1960 Entered Research Student, Kyoto UniversityApril, 1962 Entered Master Course of Pharmaceutical Science, Kyoto Univer-
sityJuly, 1963 Research Associate at Faculty of Pharmaceutical Science, Kyoto
UniversityApril, 1967 Associate Professor at Faculty of Pharmacy, Meijo UniversitySept., 1967 Ph.D. degree (Pharm. Sci., Kyoto Univ.)April, 1983 Professor (full) at Same University1992 KONA AWRD (Hosokawa Powder Technology Foundation)Research Work Powder Technology, Solid Dosage Form, SuspensionChairman of Standard Formulation Research Association
Ryusei Nonaka
March, 1997 Graduated from Faculty of Pharmacy, Tokyo University of Phar-macy and Life Science
April, 1997 Entered Master Course of Faculty of Pharmacy, Tokyo Universityof Pharmacy and Life Science
March, 1999 Graduated from Master Course of Faculty of Pharmacy, TokyoUniversity of Pharmacy and Life Science
April, 1999 Employed as a Staff of Technical Division in the Okadaseiko Co.,Ltd. in Tokyo Japan. He is now senior staff of technical division.
Research Work Tabletting, Measurement of Compression Force, CompressionEnergy Analysis
Kenzou Katou
March, 1986 Graduated from Faculty of Commercial Science, Aichi GakuinUniversity.
April, 1993 Employed as a Staff of Account Service Division in the Okada-seiko Co., Ltd. Chubu Branch, Nagoya Japan. He is now directorof account service division.
He contributed to development of GRANO (particle hardness tester), PAF300 (par-ticle adhesive-force analyzer) and many other machines.
Hiroshi Morishita
President, HMI Corporation, specializes in ultra-micro manipulation technology forMEMS (Microelectro-Mechanical Systems). He founded HMI Corporation in 1991to commercialize his ultra-micro manipulator system. He extended his interest andbusiness to the field of sensor-actuator systems for human-robot symbiosis envi-ronments. He graduated from the University of Tokyo (B.A., M.A., mechanicalengineering), and is in the final stage of preparing his doctoral thesis. He was avisiting researcher in Mechanical Engineering Department in 1992 and 1993, andat RCAST (Research Center for Advanced Science and Technology) of the Univer-sity of Tokyo in 1994 and 1995.
KONA No.20 (2002) 231
1. Introduction
Until now the usual way of synthesizing monodis-persed oxide particles on an industrial scale has beento use reactors that hydrolyze metal alkoxide (thealkoxide route).1-3 As in the reactor developed byRing4,5 and Fisher et al.,6 the principle of the system isas follows: when a hydrolyzed solution is put into apipe under ideal plug-f low conditions, nucleation andgrowth occur continuously and form monodispersedparticles. Consequently, it is difficult to maintain anideal plug f low in a large pipe for a long time. Wenoted that using a Couette-Taylor vortex to preparemonodispersed particles keeps a large quantity ofsolution at the ideal plug f low for a long time. Thisvortex is generated by filling the space between thewalls of two coaxial cylinders with a liquid, and gener-ating a Couette f low with the viscous frictional forceinduced by rotating the inner cylinder. Increasingrotation speed causes a transition from a Couette f lowto a doughnut-type Couette-Taylor vortex (C-T vor-tex) while spinning the inner cylinder (Fig. 1). Thediameter of the C-T vortex is equal to the spacebetween the inner and outer cylinders, and each vor-tex is independent.7,8 Each Taylor vortex generated
functions as a batch reaction vessel and brings abouthomogeneous mixing in the vortex. It is possible toimprove non-homogeneous mixing in a large reactionvessel. C-T vortices have already been used for con-tinuous seed emulsion polymerization in the prepara-tion of monodispersed Latex particles.9 We created atrial version of a reaction apparatus which uses vortexf low, and used it to prepare monodispersed silica col-loids.11 We found that monodispersed silica colloidscould be continuously prepared, while the hydrolysisand polymerization reaction of ethyl silicate (Stöbermethod10) was controlled, and the particle size distri-
Takashi OGIHARA and Mamoru NOMURADepartment of Materials Science and Engineering,Fukui University*
Continuous Synthesis of Monodispersed Alumina Particles by the Hydrolysis of Metal Alkoxide Using a Taylor Vortex†
Abstract
A continuous reactor was developed for industrial production of monodispersed alumina particlesfrom metal alkoxide. Taylor vortex f lows were used for solution mixing. Each of the Taylor vorticesfunctioned as a batch reaction vessel. Monodispersed spherical alumina particles were prepared byhydrolyzing aluminum alkoxide in a mixture of octanol and acetonitrile. The particles were contin-uously produced for 5 h by using this reactor. Particle size and distribution were comparable to thoseobtained by batch processing. We investigated the ef fects of Taylor number (Ta) and residence timeon the particle size, particle size distribution, yield, and particle number density of monodispersedalumina particles, which were obtained at Ta numbers from 50 to 150.
* 9-1, Bunkyo 3, Fukui-shi, Fukui-ken, 910-8507 Japan.† This report was originally printed in J. Soc. Powder Tech-
nology, Japan. 37, 722-727 (2000) in Japanese, beforebeing translated into English by KONA Editorial Commit-tee with the permission of the editorial committee of theSoc. Powder Technology, Japan.
Motor
Outercylinder(50 mm dia.)
Reservoir
Innercylinder(38 mm dia.)
1500 mm
Static mixer
Feeder
Alkoxidesolution
Watersolution
L
b
ω
Ri
Fig. 1 Schematic diagrams of Couette-Taylor vortex f low andreactor
bution of silica colloids obtained was the same as thatyielded in batch processing.11 This paper describesthe continuous preparation of monodispersed aluminaparticles by applying this vortex f low to the hydroly-sis of aluminum alkoxide, and relates our investiga-tion on the effect of reaction conditions on particleformation. Especially in the synthesis of monodis-persed particles12,13 from aluminum alkoxide, it is nec-essary to prepare the emulsion in a different kind ofsolvent mixture. Taking continuous reaction intoaccount, it appears that using a C-T vortex is veryeffective because the size and size distribution of theemulsion are inf luenced by mixing uniformity andstrength.
2. Materials and Methods
2.1 Starting solutionAl (sec-OC4H9)3 (ASBD, Takefu Fine Chemical Co.,
Ltd.) was used as the starting material, which wasprepared as described below. Water (Nacalai Inc.)was double distilled and deionized. Octanol (NacalaiInc.) and acetonitrile (Nacalai Inc.) were used to pre-pare an emulsion as an organic solvent. Organic sol-vents were dehydrated using a molecular sieve (3A,1/16) for 24 h. Hydroxy-propyl-cellulose (HPC, WakoChemical Co., Ltd., MW 100,000) was used as the dis-persant. For the preparation of monodispersed alu-mina particles, the starting solution was preparedaccording to concentration conditions for batch pro-cessing13,14 and the use of a continuous tube-typereactor.15 The concentration of HPC, which was dis-solved in the octanol at R. T., was 0.2 g/cm3. ASBDwas dissolved in the octanol at 50°C for 2 h underref lux, after which hydroxy-propyl-cellulose (0.2g/dm3) was added to prepare a 0.05 mol/dm3 ASBDsolution. Meanwhile, water was used to prepare a 0.05mol/dm3 solution in octanol (60 vol %) and acetoni-trile (40 vol %).
2.2 Preparation of alumina particlesThe apparatus (Fig. 1) consisted of a starting solu-
tion tank, a feeder for supply to the mixer, a T-typemixer, a C-T vortex f low reactor, and collector.15 Thereaction vessel consisted of a glass outer cylinder (50mm diameter, 1500 mm length) and a stainless steelinner cylinder (38 mm diameter, 1500 mm length)with a common axis. The sum of the vortices devel-oped in this reactor vessel was determined by divid-ing height (L) by inter-cylinder space width (b),which yielded a value of 125. The ASBD solution andaqueous solution were fed into the T-type mixer by
the feeder at the same rate (3104 dm3/s). Aftermixing, they were put into the reaction vessel wherethe emulsion formed. Solution residence was con-trolled by pushing the mixture upward, and residencetime is the interval starting when the mixed solutionsenter the reactor vessel, and ending when the mix-ture exits. We set residence time to a maximum of 1 hin these experiments. For the sake of convenience,reaction temperature was 25°C because the experi-ments were carried out in a room kept at 25°C. TheTaylor (Ta) number was defined as the determiningf low condition factor in the C-T vortex, and it wasdetermined by Equation (1).
Ta . 0.5
(1)
Where:Ta is the Ta number,ω is the angular speed of the inner cylinder (1/s),Ri is the inner cylinder radius (mm),b is the annular gap width (mm), andν is the f luid viscosity (m2/s).
The Ta number was controlled by the motor’s rota-tional speed, and ranged between 30 and 200. Uponleaving the reaction vessel, the solution containingalumina particles was collected in a beaker, and thealumina particles were separated from the mother liq-uid using a centrifugal separator. After washing thealumina particles ultrasonically with ethanol for 10min, an agglomerated chalk-like powder was obtainedby drying at 100°C for 24 h.
2.3 Characterization of as-prepared particlesWe used a scanning electron microscope (Hitachi
Co., Ltd., S -800) to determine the as-prepared parti-cles’ average size, geometrical standard deviation,morphology, and state of agglomeration. SEM pho-tomicrographs were analyzed to assess average sizeand geometrical standard deviation, and 200 particleswere measured for each sample. Particle numberdensity was calculated with Equation (2).
N (2)
Where:N is the particle number density (1026/dm3),Y is the yield (%),d is the particle density (g/cm3), andV is particle volume (cm3)
Particle volume was determined from average size,
YdV
bRi
ωRibν
232 KONA No.20 (2002)
assuming the particles are solid true spheres. Thedensity of α-alumina (3.98 g/cm3)16 was used as parti-cle density. Hence, these values are not accurate, butthey give us an idea of the relative tendency. Crystalphase was determined by powder X-ray diffraction(Macscience Co., Ltd., MXR-3V). Water and organicspecies contents of the particles were measured by athermogravimetric and differential thermal analysis(Rigaku Co., Ltd., PTC-10).
3. Results and Discussion
3.1 Comparison of C-T vortex reactor andbatch processing
Typical alumina particles shown in the SEM pho-tomicrograph (Fig. 2) were made with a C-T vortexreactor. Their Ta number is 92 and residence timewas 30 min. An SEM photograph of alumina particlesobtained by batch processing17 is also shown inFig. 2 for comparison with monodispersed aluminaparticles obtained from the C-T vortex reactor. As-prepared alumina particles are spherical and un-agglomerated. XRD showed that the crystal phaseof as-prepared powders was amorphous. DTA-TGshowed that the content of water, octanol, and unre-acted ASBD was about 40 wt% (Fig. 3). The particle
size distributions of alumina particles prepared by theC-T vortex reactor and batch processing are shown inFig. 4 (a) and (b), respectively. The average size andgeometrical standard deviation of alumina particlesobtained from the C-T vortex reactor were 0.2 µm and1.15, respectively. On the other hand, those of alu-mina particles obtained with batch processing were0.17 µm and 1.16, respectively, showing that the sizeof alumina particles obtained by the C-T vortex reac-
KONA No.20 (2002) 233
Fig. 2 SEM photomicrographs of monodispersed alumina particles prepared with a C-T f low reactor and a batch reactor
C-T f low reactor Batch reactor
Wei
ght l
oss
(%)
Temperature (°C)
0
20
40
60
80
1000 200 400 600 800 1000
TG
DTA
1200
Fig. 3 DTA-TG curves of monodispersed alumina powders
2 µm 2 µm
tor was comparable to that of particles made by batchprocessing.
3.2 Continuous preparationIt is apparent that this system is capable of prepar-
ing monodispersed alumina particles. We performedcontinuous production with this reactor for 5 h, dur-ing which time we collected 0.1 dm3 of solution at 30-min intervals and examined the change in averagesize (R), geometrical standard deviation (σg), yield(Y), and particle number density (N) of the monodis-persed alumina particles obtained after centrifugalseparation (Fig. 5). The Ta number was 92 and resi-dence time was 30 min. There were no changes in theaverage size, geometrical standard deviation, yield,and particle number density of alumina particles dur-ing any one of the five hours. It was therefore evidentthat the ASBD hydrolysis reaction was controlled bythis apparatus, which was able to maintain continuousproduction of alumina particles having uniform qual-ity. One can presume that there is little ASBD diffu-sion from one vortex to another because if ASBDreadily diffused among vortices, ASBD concentrationdifferences among vortices might cause non-unifor-mity in both the droplet size distribution and emul-sion number density. As a result, the average size,geometrical standard deviation, and particle numberdensity of alumina particles obtained in each vortexwould differ widely. However, as the variance in thesevalues for alumina particles was slight in this experi-ment, the diffusion of ASBD is controlled among thevortices to an extent at which the particle size and
yield of alumina particles are not inf luenced.
3.3 Effect of Ta numberWe investigated the effect of Ta number on particle
size, geometrical standard deviation, yield, and parti-cle number density (Fig. 6). Residence time was 30min. When the Ta number was less than 50, the appa-ratus produced polydispersed alumina particles with a
234 KONA No.20 (2002)
Y (
%)
N (
10
26/d
m3 )
R (
mm
)
σ g
Production time (h)
100
: Y: N
20
15
10
5
0
1.3
1.2
1.1
1
90
80
70
60
50
0.6
0.4
0.2
00 1 2 3 4 5 6
: R: σg
Fig. 5 Dependence of particle size, σg, yield, and particle numberdensity on production time
F (%
)
R (mm)
80
Size: 0.2 mmσg: 1.15
(a)
60
40
20
00 0.1 0.2 0.3 0.4 0.5 0.6
F (%
)
R (mm)
80
Size: 0.17 mmσg: 1.16
(b)
60
40
20
00 0.1 0.2 0.3 0.4 0.5 0.6
Fig. 4 Particle size distribution of monodispersed alumina particles prepared with a C-T f low reactor (a) and a batch reactor (b)
geometrical standard deviation of more than 1.2 and abroad particle size distribution. As a result, both theseparation between vortices and the mixing in eachvortex were incomplete because each vortex exists in
the boundary where the transition from a Couettef low to a Couette-Taylor vortex f low occurs. Monodis-persed particles were obtained when the Ta numberwas more than 50. The particle size and geometricalstandard deviation of alumina particles were constantin the Ta number range where monodispersed parti-cles were formed.
On the other hand, the alumina particle yield in-creased as the Ta number increased, with 85% yieldobtained at 150. Particle number density also in-creased as the Ta number increased. This is probablybecause the ASBD hydrolysis reaction was promotedby uniform mixing in the vortex when the Ta numbergrew larger. When the Ta number was greater than150, the yield and particle number density furtherincreased. However, unlike the alumina particlesobtained at Ta 92, those formed at Ta 160 wereagglomerated (Fig. 7), which indicated that the parti-cles were agglomerated by the high collision fre-quency that occurred during particle formation byvigorous mixing. This showed that when preparingmonodispersed particles using this apparatus, parti-cle agglomeration occurs even in the range in which aCouette-Taylor vortex with plug f low is formed. Con-sequently, monodispersed alumina particles were pro-duced in the range from 50 to 150.
KONA No.20 (2002) 235
Y (
%)
N (
10
26/d
m3 )
R (
mm
)
σ g
Ta
100
80
60
40
20
: Y: N
10
0
1.3
1
0
0.8
0.6
0.4
0.2
020 60 100 140 180
: R
(a) (c)(b)
: σg
8
6
4
2
1.2
1.1
Fig. 6 Dependence of particle size, σg, yield and particle num-ber density on Ta number. (a) Polydispersed region, (b)monodispersed region, (c) agglomerate region.
Fig. 7 Effect of Ta number on the agglomeration of alumina particles
Ta92 Ta160
2 µm 2 µm
3.4 Effect of residence timeWe investigated the relation among residence time,
average size, geometrical standard deviation, yield,and particle number density (Fig. 8). The Ta numberwas 92. Residence time was controlled by allowing thefeeder supply rate to change from 1.5104 to 9104
m3/s. Because the average size and geometrical stan-dard deviation of alumina particles were always thesame at a certain residence time, it was evident thatthese values were independent on residence time. Onthe other hand, yield rose to 86% at 1 h, and the parti-cle number density also increased. Fig. 8 indicatesthat because the size of alumina particles did notchange until the 1 h mark, the yield increase is notdue to the growth of alumina particles, but to theincrease in particle number density.
4. Conclusion
Monodispersed alumina particles were continu-ously prepared by the hydrolysis of aluminum alkox-ide using a C-T vortex f low reactor. We reached thefollowing conclusions:(1) Monodispersed alumina particles were amor-
phous, and the particle size and particle size dis-tribution were comparable to those obtained bybatch processing.
(2) The average size, geometrical standard deviation,yield, and particle number density of monodis-persed alumina particles were constant duringcontinuous preparation, and reproducibility ispossible.
(3) The Ta number range in which monodispersedalumina particles were formed was from 50 to150. Particle size and geometrical standard devia-tion were independent on the Ta number in thisrange, but the yield and particle number densityincreased as the Ta number increased. Aluminaparticles were also agglomerated when the Tanumber was greater than 150.
(4) The particle size and geometrical standard devia-tion of monodispersed alumina particles wereindependent on residence time, but yield in-creased with residence time. Yield increase is notdue to the growth of alumina particles, but to theincrease in particle number density.
Nomenclature
b Annulus width (mm)d Particle density (g/cm3)F Frequency (%)L Length of cylinder (mm)N Particle number density (1026·dm3)R Average particle size (µm)R i Radius of inner cylinder (mm)Ta Taylor numberV Particle volume (cm3)Y Yield (%)σg Geometrical standard deviation of average sizeν Kinematic viscosity (m2/s)ω Angular velocity
References
1) Ogihara, T., M. Ikeda, M. Kato and N. Mizutani. “Con-tinuous Processing of Monodispersed TiO2 Powders,” J.Am. Ceram. Soc., 72, 1598-1601 (1989).
2) Ogihara, T., M. Iizuka, T. Yanagawa, N. Ogata and K.Yoshida. “Continuous Reactor System of MonosizedColloidal Particles,” J. Mater. Sci., 27, 55-62 (1992).
3) Ogihara, T., M. Yabuuchi, T. Yanagawa, N. Ogata, K.Yoshida, N. Nagata, K. Ogawa and U. Maeda. “Prepara-tion of Monodispersed, Spherical Ferric Oxide Particlesby Hydrolysis of Metal Alkoxides Using a ContinuousTube-Type Reactor,” Advanced Powder Technol., 8, 73-84 (1997).
4) Ring, T. A. “Continuous Precipitation of Monosized Par-ticles with a Packed Bed Crystallizer,” Chem. Engng.Sci., 39, 1731-34 (1984).
5) Jean, J. H., D. M. Goy and T. A. Ring. “Continuous Pro-
236 KONA No.20 (2002)
Y (
%)
N (
10
26/d
m3 )
R (
mm
)
σ g
Residence time (h)
100
80
60
40
20
: Y: N
8
6
4
2
0
1.3
1.2
1.1
1
0
00 0.2 0.4 0.6 0.8 1 1.2
: R: σg0.5
0.4
0.3
0.2
0.1
Fig. 8 Dependence of particle size, σg, yield, and particle numberdensity on residence time
duction of Narrow-Sized and Unagglomerated TiO2
Powders,” Am. Ceram. Soc. Bull., 66, 1517-20 (1987).6) Kallay, N. and I. Fischer. “A Method for Continuous
Preparation of Uniform Colloidal Hematite Particles,”Colloids & Surf., 13, 145-9 (1985).
7) Kataoka, K. and T. Takigawa. “Intermixing over CellBoundary between Taylor Vortices,” A. I. Ch. E. J., 27,504-8 (1981).
8) Mizushima, A., R. Itoh, K. Kataoka, Y. Nakajima and A.Fukuda. “Velocity Distribution of Taylor Vortex Flowin an Annulus between Rotating Coaxial Cylinders,”Kagaku Kougaku, 35, 1116-21 (1971).
9) Imamura, T., K. Saito, S. Ishikura and M. Nomura. “ANew Approach to Continuous Emulsion Polymeriza-tion,” Int. Symp. Poly. Microsphere, Preprints, p. 151(1991).
10) Stöber, W., A. Fink and E. Bohn. “Controlled Growth ofMonodispersed Silica Spheres in the Micron SizeRange,” J. Colloid Interface Sci., 26, 62-69 (1968).
11) Ogihara, T., G. Matsuda, T. Yanagawa, N. Ogata, K.Fujita and M. Nomura. “Continuous Synthesis ofMonodispersed Silica Particles by Using Couette-Taylor
Vortex Flow,” J. Ceram. Soc. Jpn., 103, 151-154 (1995).12) Lee, S. K., K. Shinozaki and N. Mizutani. “Inf luence of
Mixed Solvent on the Formation of MonodispersedAl2O3 Powders by Hydrolysis of Aluminum sec-Butox-ide,” J. Ceram. Soc. Jpn., 101, 470-474 (1993).
13) Ogihara, T., T. Yanagawa, N. Ogata and K. Yoshida.“Formation of Monodispersed Oxide Particles byHydrolysis of Metal Alkoxide in Octanol/AcetonitrileSolutions,” J. Ceram. Soc. Jpn., 101, 315-320 (1993).
14) Mizutani, N., M. Ikeda, S. K. Lee, K. Shinozaki and M.Kato. “Preparation of Monodispersed Hydrous Alu-minum Oxide Powders,” J. Ceram. Soc. Jpn., 99, 183-186 (1991).
15) Ogihara, T. and N. Mizutani. “Synthesis of Monodis-persed Ceramic Particles from Emulsion Route,” Inorg.Mater., 3, 177-187 (1996).
16) JCPDS Card 10-173.17) Ogihara, T., H. Nakajima, T. Yanagawa, N. Ogata, K.
Yoshida and N. Matsushita. “Preparation of Monodis-persed, Spherical Alumina Powders from Alkoxides,” J.Am. Ceram. Soc., 74, 2263-2269 (1991).
KONA No.20 (2002) 237
Author’s short biography
Takashi Ogihara
Takashi Ogihara has been an associate professor of material science and engineer-ing at Fukui University since 1994. He received his B.S. degree from the Depart-ment of Synthesis Chemistry, Chiba University in 1983 and his M.S. and Dr. ofEngineering degrees from the Department of Inorganic Materials, Tokyo Instituteof Technology in 1986 and 1989, respectively. His research interests are the syn-thesis and sintering of functional ceramic fine powders derived from liquid phaseprocesses such as the sol-gel route, spray pyrolysis, and hydrothermal treatment.Recently, he has been studying the development of high-performance Li batterymaterials and Ti02 photocatalytic materials by nanotechnology.
Mamoru Nomura
Mamoru Nomura is a professor of chemical engineering in the Materials Scienceand Engineering Department, Fukui University. He graduated from Kyoto Univer-sity in 1964 and received his M.S. in 1966 and Ph.D. in 1976 from Kyoto University.His research interests are the kinetics and mechanisms, simulation, and reactordesign of heterophase radical polymerization such as emulsions and microemul-sion polymerizations. He has delivered several invitation and keynote lectures atinternational conferences such as those organized by the Gordon Research Foun-dation and the American Chemical Society. He started “The Ist Polymeric Micros-pheres Symposium” in 1980 in Fukui, which is domestically organized every twoyears, and celebrated its 20th anniversary in 2000. He also organized “The IstInternational Symposium on Polymeric Microspheres” in 1991 in Fukui.
238 KONA No.20 (2002)
1. Introduction
One way of obtaining fine particles from liquid is tofirst make the liquid into fine droplets, then removethe solvent by drying or other procedures to obtainsolid particles. Typical methods of atomizing liquidsinclude those using pressure energy such as binarynozzles and nebulizers, and methods that apply me-chanical vibration energy, such as ultrasonic sprayingand vibrating orifices. By contrast, electrostatic atom-ization [1, 7] applies electrical energy to liquid at thenozzle tip, thereby breaking the liquid column at thenozzle into fine droplets. Although it is possible tovary the size of the produced droplets from the sub-micrometer level to several millimeters, and to obtaindroplets of a comparative monodispersion, there iscurrently little promise of increasing its processingcapacity. The inf luence of a liquid’s surface tensionand its electrophysical characteristics on the electro-
static atomization is very large. For example, thereare few reports to use solutions with high conductiv-ity or high viscosity [12].
There are an interfacial reaction [3] and a mem-brane emulsion as the method to produce sphericalparticles from solutions [4]. For the interfacial reac-tion, silica particles are produced by mixing waterglass (a sodium silicate solution) into benzene, andthen solidifying at the droplet interface. As dropletfusion and dispersion occur at both the droplet for-mation stage and the solidification stage, it yieldsparticles with a broad size distribution. Membraneemulsion yields a monodispersion of spherical silicaby passing water glass through an inorganic mem-brane treated hydrophobic, and making droplets of auniform size. However, it is a complicated procedurethat has difficulty delivering particles bigger than 10µm. There are reports by Sato et al. [8, 9] on makingsilica particles by electrostatic atomization, but theyoffer little discussion on the effects of physical prop-erties of liquid.
We therefore used water glass with high conductiv-ity and high viscosity to explore the inf luence of theirphysical properties, supply f low rate, and applied volt-age on electrostatic atomization, and examined theconditions for making spherical silica particles of uni-form size in the several hundred µm range.
Yasushige MORI and Yuusuke FUKUMOTODepartment of Chemical Engineering and MaterialsScience, Doshisha University*
Production of Silica Particles by Electrostatic Atomization†
Abstract
Electrostatic atomization is a method typically used to produce fine liquid droplets with diametersbetween ten and several hundred micrometers and a relatively narrow size distribution. This methodis simple but its mechanism is not yet fully understood.
Our research involved producing fine silica particles by forming droplets of water glass no. 3 usingelectrostatic atomization, then dehydrating them and removing their sodium ions. The atomizationstate was classified into three modes according to applied voltage: dripping, uniform cone-jet, anddischarge modes. Uniformly sized droplets were produced only with the uniform cone-jet mode at apositive high voltage. The mean volume diameter of silica particles could be estimated as a functionof f low rate and applied voltage, as well as the surface tension, viscosity, and conductivity of thewater glass solution.
Key words: Electrostatic atomization, silica particles, sodium silicate solution, uniformly sized particles, highvoltage field
* 1-3 Tatara Miyakodani, Kyotanabe, Kyoto 610-0321 Japan.TEL: 0774-65-6626 FAX: 0774-65-6847E-mail: [email protected]
† This report was originally printed in J. Soc. Powder Tech-nology, Japan. 38, 90-96 (2001) in Japanese, before beingtranslated into English by KONA Editorial Committeewith the permission of the editorial committee of the Soc.Powder Technology, Japan.
KONA No.20 (2002) 239
2. Materials and Methods
An aqueous solution of sodium silicate, known aswater glass (water glass no. 3, made by Fuji ChemicalCo., Ltd.) was used. Water glass no. 3 contains 29% sil-icon in the form of SiO2, and its SiO2/Na2O molarratio is 3.2. Pure water was added to the water glassto change the physical characteristic values of theaqueous solution. The surface tension of the solu-tion was measured with a Wilhelmy tensiometer(CBVP-A3, Kyowa Science Co., Ltd.), viscosity coeffi-cient with a cone and plate type viscometer (ED,TOKIMEC INC.), and conductivity with a conductiv-ity meter (ES-12, Horiba, Ltd.). Table 1 shows thatadding more pure water brings a linear decrease insurface tension, and an exponential decrease in theviscosity coefficient, while conductivity maximized atthe condition added 40 vol.% pure water. This can beexplained by the declining concentration of sodiumsilicate (water glass) and the attendant change in dis-sociation.
Droplets were formed by the nozzle (N) in theschematic diagram of the experimental apparatus asshown in Fig. 1. It was a stainless steel pipe with anoutside diameter of 0.7 mm and an inside diameter of0.4 mm. Its tip was polished and finished to a 90°angle. Facing the nozzle was the earth electrode (E),a brass disk 60 mm in diameter and 2 mm thick. In itscenter was a 10 mm hole that allowed atomizeddroplets to pass through. The earth electrode was 6mm away from the nozzle tip. A high-voltage powersupply (HV; model HEOPS-10B2-PV made by Matsu-sada Precision) was used to apply a positive or nega-tive DC voltage between the nozzle and the earthelectrode. To prevent electricity leakage, we used amicrofeeder (JP-S, Furue Science) to supply siliconeoil (KF-96-100CS, Shin-Etsu Chemical Co., Ltd.) to
Volume ratio Sample of water Viscosity Surface Conductivity
No. glass No.3 (mPa s) tension (S m1)and water (mN m1)
30 100 : 00 139.3 71.0 3.46
31 090 : 10 037.3 66.7 3.79
32 080 : 20 021.7 64.0 3.83
33 070 : 30 010.8 55.7 4.09
34 060 : 40 006.7 52.3 4.11
35 050 : 50 004.3 48.5 4.05
Table 1 Physical Properties of Sample Solutions Measured at293 K
the sealed container (R1), thereby supplying a certainquantity of the water glass solution from R1 to thenozzle. Droplets formed by electrostatic atomizationwere captured in a polyethylene container (R2) hold-ing alcohol, where the droplets were instantaneouslydehydrated and solidified. Atomization was observedwith a video camera, video monitor, and a strobo-scope (S).
To remove the sodium from the water glass parti-cles solidified in the alcohol (solid particles of sodiumsilicate), they were separated from the alcohol andthen immersed for 5 min in a 500 mol/m3 aqueoussolution of dilute sulfuric acid. We used an opticalmicroscope to count out over 200 of the silica parti-cles thus made, and determined their particle size dis-tribution. To find the mean size we calculated themean volume diameter on a number basis fromcounted data.
3. Results and Discussion
3.1 Solution to Capture Water Glass DropletsWater glass becomes silica particles after reactions
to remove water and sodium. Accordingly, we experi-mented with a method of removing water and sodiumby dripping the atomized water glass droplets directlyinto a 500 mol/m3 aqueous solution of dilute sulfuricacid. Water glass reacted rapidly with the dilute sulfu-ric acid and immediately solidified, but it f locculatedinstead of becoming spherical particles, probablybecause of the low interfacial tension between waterglass and dilute sulfuric acid. We therefore decided toobtain spherical silica particles by forming an inter-
Oscilloscope
HV
Feeder
TV camera
TV monitorN
ES
R2
R1
Fig. 1 Schematic Diagram of Experimental ApparatusHV: High voltage power supply, N: Nozzle, E: Earth elec-trode, S: Stroboscope, R1: Vessel with water glass and sili-cone oil, R2: Container of alcohol solution
sometimes destroyed when interior water exits, fur-ther study will be necessary for choosing an appropri-ate capture solution.
3.2 Effect of Applied VoltageSilica particles were produced when a positive high
voltage applied on the nozzle with grounding theopposed electrode. The relationship between themean volume diameter and applied voltage showsFig. 3. Zone A, where applied voltage ranged up to4.6 kV, was an electrostatic drip zone where the sizeof the droplets gradually decreased as applied voltagerose. At 4.6 kV zone A suddenly became zone B, auniform cone-jet zone where small droplets wereproduced. Electrostatic force caused by the electriccharge accumulated on droplet surfaces, overcamesurface tension, and allowed the formation of uni-formly sized small droplets. We observed at this pointthat droplets emerging from the nozzle tip werestretched into cone shapes called Taylor cones [10].This uniform cone-jet mode continued at about 5.0 kVat the f low rate of 0.13 ml/min, and at around 5.2 kVwith a large f low rate of 0.32 ml/min. Further increas-ing the applied voltage, we noted a discharge atom-ization mode where the current amount suddenlyincreased (zone C). Average particle size was some-
face with the water glass, removing water and solidify-ing with alcohol, which has a dehydration effect, andthen immersing the particles in 500 mol/m3 aqueoussolution of dilute sulfuric acid to remove sodium.
Methanol, ethanol, and 2-propanol were tested toselect an alcohol suited to solidifying particles whilekeeping them spherical. Photomicrographs in Fig.2 were taken of the captured silica particles. Wewere unable to obtain spherical particles with 2-propanol (Fig. 2a) or ethanol (Fig. 2b). Using meth-anol yielded the most spherical particles (Fig. 2c).Sato et al. [9] used a 60 vol.% solution of ethanol whenmaking silica particles from water glass no. 3. Parti-cles dehydrated and solidified with methanol arealmost concentric circles as in Fig. 2c. Dehydrationand solidification begin at a droplet’s surface, withinterior water exiting later, which is likely what givesthe particles their hollow centers, and therefore theirconcentric circle configuration. Particles made with 2-propanol appear to have solid centers in the photomi-crograph. It would seem that when water exits slowlyand solidification proceeds unhurriedly, particleswithout hollows are obtained even though dropletshape cannot be retained, but when solidification israpid, one can obtain spherical, hollow silica particles.However, because hollow particles in the making are
240 KONA No.20 (2002)
Fig. 2 Effects on Particle Shape of Various Alcohols Used as Collection LiquidsExperimental conditions were the same as the uniform cone-jet mode in Fig. 4. (a) 2-propyl alcohol, (b) Ethyl alcohol, (c) Methyl alcohol
500 µm
(a)
500 µm
(b)
500 µm
(c)
ed our attention exclusively to the uniform cone-jetmode.
Next we investigated the effect of the polarity of thevoltage applied to the nozzle. When a positive volt-age was applied, uniform cone-jet atomization wasobserved across the range from 4.6 to 5.2 kV, butapplying a negative voltage yielded different results.When applying 4.6 kV there was an immediate transi-tion from zone A to zone C, and we observed no uni-form cone-jet atomization. Mori et al. [2] and Sato etal. [8] reported that it is easier to achieve uniformcone-jet atomization when applying a positive voltagethan when applying a negative voltage, which agreeswith our results. We conjecture the reason is the dif-ference between positive and negative discharge char-acteristics when a corona discharge arises betweenthe nozzle tip and the earth electrode disk as electro-static atomization proceeds. Specifically, when thereis a positive electrode corona discharge, nitrogen andoxygen atoms are ionized and move toward the earth
what larger in this zone because under these condi-tions some of the droplets were large, but the widerparticle size distribution produced a clear distinctionbetween zones B and C. As can be seen from the par-ticle size distributions of these two zones (Fig. 4) andthe photomicrographs of zone B (Fig. 2c) and zone C(Fig. 5), there was a very narrow particle size distrib-ution at 4.8 kV, at which the uniform cone-jet modearose (zone B), while the distribution was very broadat 5.5 kV, where discharge atomization proceeded(zone C). Because the purpose of this research was toobtain silica particles of uniform size, we then turn-
KONA No.20 (2002) 241
Und
ersi
ze (
%)
99.99
99.9
99
9590807050
3020105
1
.1
.01300 400 500 600
Q0.32 mL/min
f5.5 kV
f4.8 kV
Sample 31
Particle diameter (µm)
Fig. 4 Comparison of Particle Size Distribution in Uniform Cone-jet Mode (4.8 kV) with That in Discharge Mode (5.5 kV)
Fig. 5 Silica Particles Produced in Discharge ModeExperimental conditions were the same as those in Fig. 4.
10000
1000
A B C
1004 4.5
0.32 mL/min
Q0.13 mL/min
Applied voltage, f (kV)
Mea
n vo
lum
e di
amet
er, d
v (µm
)
5 5.5
Fig. 3 Effect of Applied Voltage on Mean Volume DiameterA: Dripping mode B: Uniform cone-jet mode C: Discharge mode
500 µm
decreased, the uniform cone-jet zone narrowed.When the f low rate was 0.06 ml/min, the lowest inour experiment, uniform cone-jet atomization oc-curred between 4.6 and 4.8 kV in Sample 31, andbetween 4.5 and 5.0 kV in Sample 33.
At a 5 kV applied voltage, the size distribution of sil-ica particles narrowed as the f low rate increased asshown in Fig. 7. But when the f low rate was reduced,average particle size decreased while the distributionbroadened. The reason appears to be that decreasingthe f low rate makes it hard to control, and even asmall variation in f low rate has a big effect on atom-ization.
3.4 Addition of Pure WaterWe manufactured silica particles from an aqueous
solution whose ratio of water glass to pure water wasvaried while maintaining a 5 kV applied voltage and a0.13 ml/min f low rate. Fig. 8 shows that undilutedwater glass (Sample 30) yields a two-peak distribu-tion. As the amount of added water increased, meanparticle diameter decreased and the distribution nar-rowed. One way to obtain small silica particles is toreduce the f low rate, but it is also effective to usewater glass whose viscosity has been attenuated byadding water.
As water content increases, it is anticipated thatdroplets will contract more during dehydration. Toinvestigate the contraction rate of droplets when turn-ing into particles, we made a comparison by conduct-ing an experiment in which atomized droplets werecaptured directly by silicone oil. When using a water
electrode, but under a negative electrode corona dis-charge, highly mobile electrons themselves move,resulting in dielectric breakdown and difficulty inobtaining a stable corona discharge.
The following equation provides the strength of theelectric field between the nozzle and disk [11].
E04f/doln(8L/do) (1)
When 5 kV were applied under the electrode condi-tions in Fig. 3, the electric field strength at the noz-zle’s tip, E0, was calculated to be 6.7 MV m1, whichwas greater than the 3 MV m1 dielectric breakdownstrength of air. Thus electrostatic atomization is pre-sumably difficult with negative high voltage. Resultsdiscussed below were obtained by applying positivehigh voltage.
As Fig. 6 shows the effects of applied voltage andvolumetric f low rate on the mean volume diameter ofsilica particles, the high-viscosity Sample 31 yieldedlarge silica particles whose sizes decreased onlyslightly when a high voltage was applied. But Sample33, whose viscosity was one-fourth that of Sample 31,was heavily affected by applied voltage. In all sam-ples, particle size was less affected by applied voltageat smaller f low rates.
3.3 Flow RateFig. 6 also shows the inf luence of f low rate. The
lower the f low rate, the smaller the silica particlesthat were formed. But we also found that as f low rate
242 KONA No.20 (2002)
Mea
n vo
lum
e di
amet
er, d
v (µm
)
400
300
200
100
0.06
0.19
0.32
Q [mL/min] Sample 31 Sample 33
4.5 5 5.5 6
Applied voltage, f (kV)
Fig. 6 Effects of Applied Voltage and Flow Rate on Mean VolumeDiameter in Uniform Cone-jet Mode
Und
ersi
ze (
%)
99.99
99.9
99
95908070503020105
1
.1
.01200100 300 400
f5 kVSample 33 Sample 31
Particle diameter (µm)
Q0.06 mL/min0.19 mL/min
0.32 mL/min
Fig. 7 Particle Size Distributions in Uniform Cone-jet ModeApplied Voltage was 5 kV.
distilled water, ethanol, and an aqueous glycerin solu-tion. Ogata et al. [5, 6] derived a correlation equationusing distilled water, ethanol, propanol, and an aque-ous glycerin solution for a solution up to 130 mPa s.Further, Yamaguchi et al. [13] made atomizeddroplets using an aqueous solution of calcium chlo-ride, an aqueous solution of glycerin, and a solutionmade by adding liquid paraffin and/or an antistaticagent to xylene, and described the relationshipbetween droplet size and physical properties. Al-though they propose a dimensionless correlation e-quation, a direct comparison is difficult because thedimensionless quantity differs from one researcher toanother. For that reason we made the following sim-plification to compare Eq. 2 with the dimensionlesscorrelation equations proposed heretofore.
As our experiment used only one nozzle, the ratioof its inner and outer diameters was fixed. Althoughwe did not measure permittivity, we made its contri-bution constant under the assumption that its valuewould not change very much due to the large amountof water. Using these assumptions, we summarizedthe dependency of physical properties in Table 2using dimensionless correlation equations in previousreports. There is no value for conductivity in the datafrom Mori et al. [2] because they did not include it.The dependence on physical property values exhibitsconsiderable differences among ours and the previ-ous four reports. Conductivity was especially large inour study: while it was under 0.2 S m1 in the previ-ous reports, it was in the high range of 3 to 4 S m1 inour study. Also, we examined the correlation with the
glass solution to which 10 vol.% pure water had beenadded (Sample 31), diameter contracted 5.8%, andwith a water glass solution to which 30 vol.% purewater had been added (Sample 33), contraction was7.8%. Far greater than this change was the change inaverage particle diameter, thereby demonstrating thatphysical properties of a solution are the larger inf lu-ence.
3.5 Estimating the Diameter of ParticlesFormed
Substantial changes occurred in atomization bydiluting water glass with pure water, but becausesome physical properties of the solution also changesimultaneously, it is unknown which physical prop-erty has the largest inf luence. For that reason we per-formed a multiple regression analysis for f low rate,applied voltage, surface tension, viscosity coefficient,and conductivity using the data for the uniform cone-jet mode under conditions of a 0.06 to 0.32 ml/minf low rate, and a 4.5 to 5.8 kV applied voltage. Theanalysis yielded the following correlation equation.
dv5.06104f1.56Q0.383γ 0.861η 0.313κ 2.29 (2)
Fig. 9 shows the relationship between the mean vol-ume diameter calculated with this equation, dv,calc, andthe measured value, dv,obs, has a high multiple correla-tion of 0.986, which is significant. Particle diameterwas most affected by conductivity, while the inf lu-ences of the f low rate and viscosity coefficient werelow.
Mori et al. [2] reported a correlation equation using
KONA No.20 (2002) 243
Und
ersi
ze (
%)99.99
99.9
99
95908070503020105
1
.01
.1
80 100 200 300 400
Q0.13 mL/min
Sample 35 34 33 32 31 30
Particle diameter (µm)
f5 kV
Fig. 8 Particle Size Distributions of Various SamplesApplied voltage was 5 kV and f low rate was 0.13 ml/min.
d v, o
bs (
µm)
500
400
300
200
100
00 100 200 300 400 500
Sample 30Sample 31Sample 32Sample 33Sample 34Sample 35
dv, calc (µm)
Fig. 9 Dimensionless Correlation of Mean Volume Diameter ofSilica Particles Produced under the Conditions of ThisStudy
size of particles formed. Specifically, particle diameterwas 5 to 10% smaller than droplet diameter, and theshrinkage factor was dependent on the amount ofwater added. For this reason, it would seem there is aslight difference between the correlation with dropletdiameter in previous reports and the correlation inour case.
Because Eq. 2 is an empirical equation, it is inappro-priate for understanding the phenomenon, and wetherefore derived a dimensionless correlation equa-tion from Eq. 2. Assuming that a relative permittivityof the solution is constant, we found the followingdimensionless correlation equation with the dimen-sionless quantity used by Yamaguchi et al. [13].
3.83109 0.917 0.65 0.382 1.3
(3)
The multiple correlation coefficient was slightlyworse, at 0.977. Comparison with the dimensionlessquantity range of Yamaguchi et al. [13] producesa considerably different conductivity range as dis-cussed above, so the index of the fourth dimension-less quantity in Eq. 3 is different. Further, the indexof the dimensionless quantity including u was also dif-ferent to adjust the dependence of f low velocity u.Judging from this, obtaining a general equation toestimate the droplet diameter in electrostatic atomiza-tion would require the accumulation of further dataon different physical properties.
4. Conclusion
We added various amounts of pure water to a solu-tion of water glass with high conductivity and highviscosity to change the solution’s physical propertiesand investigated electrostatic atomization, and arrivedat the following conclusions.
εf ε0uκdo
ηuγ
ρu2do
γε0E0do
γdv
do
244 KONA No.20 (2002)
1) As applied voltage was increased, the electrosta-tic drip mode, uniform cone-jet mode, and dischargemode were observed. It was in the uniform cone-jetmode that droplets of uniform size were obtained.
2) When the DC high voltage applied to the nozzlewas positive, we observed uniform cone-jet atomiza-tion, but making it negative caused a direct shift fromelectrostatic drip mode to discharge mode, with nouniform cone-jet atomization observed.
3) When the applied voltage increased, the highelectric field strength at the nozzle tip resulted in ahigher frequency of droplet ejection and a smallermean volume diameter, but the effect of the appliedvoltage on the particle size was small.
4) Decreasing the f low rate reduced mean volumediameter, but it was necessary to increase f low rate toobtain silica particles with a narrow size distribution.
5) Diluting the water glass with pure water resultedin silica particles having a small mean volume diame-ter and a narrow particle size distribution.
6) Based on the results of this study, we obtainedthe following empirical equation estimating to themean volume diameter of the silica particles formed.
dv5.06104f1.56Q 0.383γ 0.861η 0.313κ 2.29
Acknowledgments
This research benefited from the cooperation ofMr. Masaaki Mizuguchi at Suzuki Yushi IndustrialCo., Ltd. for the supply of water glass. We receivedthe advice from Professor Masayuki Sato of Depart-ment of Biological and Chemical Engineering inGunma University, and from Chief Researcher KeikoNakahara at the Research Institute of InnovativeTechnology for the Earth. Part of this research wassupported by RCAST at Doshisha University. Weexpress our appreciation to all these people and insti-tutions.
f low rate applied voltage surface tension viscosity conductivityQ φ γ η κ
this study 0.383 1.599 0.861 0.313 2.291
Mori [2] 0.430 0.510 0.022 0.124
Ogata [5] 0.667 1.111 0.111 0.444 0.222
Ogata [6] 0.667 1.111 0.208 0.250 0.222
Yamaguchi [13] 0.470 1.500 0.520 0.070 0.080
Table 2 Values for Dependence on Physical Properties
Power indexes of physical properties of sample solution and of operating conditions for the empirical correlation to the size of par-ticles produced by electrostatic atomization. Our results are compared with those of four previous studies.
KONA No.20 (2002) 245
Author’s short biography
Yasushige Mori
Yasushige Mori is a professor in Department of Chemical Engineering and Materi-als Science at Doshisha University. He graduated from Kyoto University, Depart-ment of Chemical Engineering in 1974, and received his doctorate in engineeringfrom the same University in 1980. His research interests include the formation ofnanoparticles of metals and/or semiconductors in liquid systems, measurementsof interaction and adhesion forces between particles and plates, particle size analy-sis, and applications of mesoporous materials.
Yuusuke Fukumoto
Yuusuke Fukumoto is an engineer at Matsushita Battery Industrial Co., Ltd. Hereceived his B.S. in 1996 and M.S. in 1998 from Department of Chemical Engineer-ing and Materials Science at Doshisha University.
Nomenclature
do outer diameter of nozzle (m)dv mean volume diameter of silica particle (m)E0 electric field strength of nozzle tip,
defined in Eq. 1 (V m1)L electrode gap (m)Q volumetric f low rate of sample solution (m3 s1)u linear velocity of sample solution
through nozzle (m s1)γ surface tension of sample solution (N m1)ε0 permittivity of vacuum (F m1)ε f dielectric constant of sample solution (F m1)η viscosity of sample solution (Pa s)κ electrical conductivity of sample solution (S m1)ρ density of sample solution (kg m3)φ applied voltage (V)
References
1) Cloupeau, M. and B. Prunet-Foch. “Electrostatic Spray-ing of Liquids: Main Functioning Modes,” J. Electrost.,25, 165-184 (1990).
2) Mori, Y., K. Hijikata and T. Nagasaki. “FundamentalStudy on Electrostatic Atomization,” Nippon KikaiGakkai Ronbunshu, B-hen, 47, 1881-1890 (1981).
3) Nakahara, Y. and K. Miyata. “Preparation of SphericalFine Particles by Interfacial Reaction,” Kagaku Kogaku,46, 541-546 (1982).
4) Nakashima, T. and M. Shimizu. “Preparation of
Monodispersed O/W Emulsion by Porous Glass Mem-brane,” Kagaku Kogaku Rombunshu, 19, 984-990 (1993).
5) Ogata, S., T. Hatae, K. Shoguchi and H. Shinohara. “TheDimensionless Correlation of Mean Particle Diameterin Electrostatic Atomization,” Kagaku Kogaku Rombun-shu, 3, 132-136 (1977).
6) Ogata, S., K. Shoguchi, T. Hatae and H. Shinohara.“Average Sizes of Droplets Electrostatically Sprayed,”Kagaku Kogaku Rombunshu, 4, 656-658 (1978).
7) Sato, M. “Production of Uniformly Sized Droplets byMeans of Electrostatic Methods,” J. Soc. Powder Tech-nol. Jpn., 29, 376-383 (1992).
8) Sato, M., T. Hatori, T. Ikawa, M. Saito and T. Ohshima“Production of Uniformly Sized Silica Particles with aWide Controllable Diameter Range,” Proc. Inst. Elec-trostst. Jpn., 20, 294-300 (1996).
9) Sato, M., H. Takahashi, M. Awazu and T. Ohshima.“Production of Ultra-uniformly-sized Silica Particles byApplying AC Superimposed on DC Voltage,” J. Elec-trost., 46, 171-176 (1999).
10) Taylor, G. “Disintegration of Water Drops in an ElectricField,” Proc. R. Soc. London, A280, 383-97 (1964).
11) The Institute of Electrostatics ed. Handbook of Electro-statics, p. 172, Ohm Sha (1983).
12) Watanabe, H., T. Matsuyama and H. Yamamoto. “TheFormation of an Immobilized Enzyme Particle by Elec-trostatic Atomization and Its Performance,” J. Soc. Pow-der Technol. Jpn., 34, 679-683 (1997).
13) Yamaguchi, M., A. Matsui, H. Murakami and T.Katayama. “Formation of Uniformly Sized Droplets ofNewtonian Liquids in a DC Electric Field,” KagakuKogaku Rombunshu, 21, 357-364 (1995).
246 KONA No.20 (2002)
Introduction
Polymeric f locculants, which are widely used in thef locculation and dehydration of suspensions, are gen-erally hydrophilic polymers and therefore have thedrawback that the f locs contain large amounts ofwater which cannot be easily removed. In our previ-ous paper (Sakohara and Nishikawa, 2000) we pro-posed the use of thermosensitive polymers as a wayto alleviate this problem.
Thermosensitive polymers in aqueous solutionsbecome soluble (hydrophilic) at low temperatures,but are insoluble (hydrophobic) at high tempera-tures. This hydrophilic/hydrophobic transition is re-versible and occurs at the transition temperature,which is determined by a primary structure of poly-mer (Ito, 1989). In our previous paper (Sakohara and
Nishikawa, 2000) by using the plunger test the com-paction of a highly concentrated kaolin suspensionwith poly(N-isopropylacrylamide) (polyNIPAM), arepresentative thermosensitive polymer, was exam-ined. The suspended particles were fully mixed withpolyNIPAM, and the mixture was heated to above thetransition temperature. Then by applying an appropri-ate external force, the compacted f locs was readilyobtained.
We proposed the mechanism illustrated in Fig. 1for the formation of such compacted f locs employingthermosensitive polymers. First, the polymer mole-cules are fully adsorbed onto the suspended particlesbelow the transition temperature (process 1, left). Ifthe conventional hydrophilic polymer is used, the par-ticles disperse stably under these conditions. But incase of thermosensitive polymer, by heating the sus-pension to above the transition temperature (process2, center), the adsorbed polymer molecules change tohydrophobicity, in turn making the surfaces of thesuspended particles hydrophobic, and resulting in thef locculation (f loc formation) of the suspended parti-cles due to the hydrophobic interaction. Applying an
SHUJI SAKOHARA, TAKASHI KIMURA and KAZUO NISHIKAWADepartment of Chemical Engineering, Hiroshima University*
Flocculation Mechanism of Suspended Particles Using theHydrophilic/Hydrophobic Transition of a Thermosensitive Polymer†
Abstract
We examined the f locculation of suspended particles using a thermosensitive polymer which under-goes a reversible hydrophilic/hydrophobic transition when heating or cooling its aqueous solution. Asa thermosensitive polymer poly(N-isopropylacrylamide) (polyNIPAM), whose transition tempera-ture is about 32°C, was used. Flocculation experiments were performed by the jar test using kaolinsuspension. In the case of operating temperature lower than the transition temperature of poly-NIPAM, there was an optimum polymer dosage, and by dosing excessively kaolin particles were dis-persed stably in the same manner as conventional polymeric f locculants. However, f loc formationwas observed by heating the suspension above the transition temperature under the excess polymerdosage. Furthermore, by cooling the f loc-containing suspension down to below the transition temper-ature again, the f locs were disorganized to the particles. These phenomena show that the f loc forma-tion caused by heating to above the transition temperature is due to the hydrophobic interaction ofpolyNIPAM molecules adsorbed on the particles.
Key words: Solid-liquid separation, f locculation, poly(N-isopropylacrylamide), thermosensitive polymer,hydrophobic interaction
* Higashi-Hiroshima 739-8527† This report was originally printed in Kagaku Kogaku
Ronbunshu, 26, 734-736 (2000) in Japanese, before beingtranslated into English by KONA Editorial Committeewith the permission of the editorial committee of the Soc.Chemical Engineers, Japan.
appropriate external force at this point will cause therearrangement of the particles, thereby forcing outthe water and readily allowing compaction. On theother hand, since the hydrophilic/hydrophobic transi-tion of thermosensitive polymers is reversible, bycooling the mixture down below the transition tem-perature (process 3, right) the f locs disorganize andreturn to stable suspended particles.
However, the plunger test in our previous paperwas meant to obtain the compacted f locs and did notallow us to adequately investigate this f locculationmechanism. In this research, therefore, we per-formed the f locculation experiments and examinedthe validity of this model by using an agitator tank.
1. Materials and Methods
As a thermosensitive polymer we used poly(N-iso-propylacrylamide) (polyNIPAM), which were synthe-sized by the same methods as in our previous paper(Sakohara and Nishikawa, 2000). The molecularweight is about 3.95106, and its transition tempera-ture in water is about 32°C. As a sample suspension,kaolin (Katayama Chemicals, Inc.) suspension witha concentration of 20 kg/m3, containing 0.5 mMsodium hydroxide as a dispersant, was used. Thetransition temperature of polyNIPAM in the aqueoussolution of 0.5 mM sodium hydroxide is about 34°C,slightly higher than that in water.
We performed the f locculation experiment with anacrylic resin agitation tank which had an inside diam-eter of 109 mm and a height of 135 mm, and whichwas fitted with six baff le plates. Into this tank we put1 dm3 of the test suspension, and submerged it in athermostatic bath at the prescribed temperature. Thesuspension was stirred at 300 rpm using a turbineblade (six f lat blades, 50 mm in diameter) installed athalf the liquid depth. After the temperature of suspen-
sion reached the prescribed temperature, the desiredamount of polymer was added, and the mixture wasstirred rapidly (300 rpm) and then slowly (150 rpm)under each of three experimental conditions de-scribed below. Although the slow stirring speed wasfaster than that generally used in the jar test, thisspeed was chosen to ensure good contact betweenthe suspended particles and the polymer molecules,or among suspended particles. The f locculation per-formance was evaluated by settling for 30 minutesafter stirring finished. The sample supernatant wastaken from the depth of 50 mm below the surface, andthe measurement of transmittance was performed ata wavelength of 600 nm using a spectrophotometer.
The f locculation experiment was conducted undereach of the following three conditions to confirm theviability of the mechanism proposed in Fig. 1.
(1) Flocculation experiment below and abovethe transition temperature
The mechanism in Fig. 1 assumes that the hy-drophilic polyNIPAM molecules adsorb onto sus-pended particles shown as in process 1 in the figure.To verify this we examined the f locculation perfor-mance at 30°C, below the transition temperature ofpolyNIPAM, and at 40°C, above the transition temper-ature. The desired amount of polyNIPAM was addedto the suspension after the suspension had attainedthe prescribed temperature, and the stirring was per-formed at high speed for 30 min, and then at lowspeed for 20 min.
(2) Flocculation experiment by heating We performed the following experiment to verify
process 2 in Fig. 1, that is, the formation of f locs byheating the suspension. PolyNIPAM was added at30°C, below the transition temperature, and the mix-ture was stirred at high speed for 10 min. The ther-
KONA No.20 (2002) 247
Thermosensitivepolymer
Adsorption of polymer onsuspended particles
(below transition temperature)
suspendedparticle
Hydrophobicinteraction
hydrophobicpolymer
Compaction
Floc formation
Re-stabilized particles
Heatinghydrophilicpolymer
q
w
eCooling
Fig. 1 Mechanism causing f locculation of suspended particles by using a thermosensitive polymer
mostatic bath water of 30°C was then quickly changedto water of 60°C, and the rapid stirring was continuedfor 20 min, followed by 20 min slow stirring. Thechange in suspension temperature is indicated by theopen circles in Fig. 2. Measurements of temperaturewere carried out with a thermocouple near the agita-tor blades.
(3) Flocculation experiment by cooling suspen-sion back below the transition temperatureafter heating
We performed the following experiment to verifyprocess 3 in Fig. 1, in which f locs formed by heatingwill again disperse when the suspension is cooledbelow the transition temperature (reversibility). Thesuspension was stirred at low speed for 20 min underthe heating conditions described above, and then thethermostatic bath water was quickly replaced withwater of 25°C, and slow stirring was continued foranother 50 min. The closed circles in Fig. 2 show thesuspension’s temperature change.
2. Results and Discussion
2.1 Effect of Temperature on Floc FormationFig. 3 shows the f locculation performance at 30°C
and 40°C. Since polyNIPAM is hydrophilic at 30°C,it acts like the conventional hydrophilic polymeric
f locculant: The transmittance of the supernatant in-creased with increasing the polymer dosage, and thendecreased after peaking. This means there is an opti-mum polymer dosage. At and near that dosage, thebridging adsorption of polyNIPAM on the suspendedkaolin particles encourages f loc formation, and thetransmittance of supernatant increases. But when toomuch polyNIPAM is added, the surfaces of the sus-pended kaolin particles are covered with polyNIPAM,and thereby disperse stably, which reduces transmit-tance (Sakohara et al., 1980). At 40°C, however, f locswere hardly formed no matter what the additiveamount of polymer, and the supernatant transmittanceremained low. It is considered due to the fact that theadded polyNIPAM molecules immediately becamehydrophobic and that they could not adsorbed ontothe kaolin. As a result, f locs did not form. Therefore,to make kaolin adsorb the polyNIPAM as in theFig. 1 model, the operation must be performed be-low the transition temperature.
We have seen no instances as in our experiment inwhich polyNIPAM was used as the f locculant, butthere are some reports of the f locculation of inor-ganic particle suspensions by copolymers of NIPAMand cationic monomers (Guillet et al., 1985; Deng etal., 1996). When this kind of cationic polymer is used,f loc formation has been observed even if the polymeris added to a suspension at the temperature higherthan the transition temperature. In this kind of poly-mer, the portion of polyNIPAM that has becomehydrophobic agglomerates through hydrophobic in-teraction, and forms polymer fine particles withcationic components on their surfaces. It appears that
248 KONA No.20 (2002)
polymer
Polymer
Tem
pera
ture
[°C
]
Time [min]
Cooling (set value: 25°C)
rapid30
rapid30
60
50
40
30
200 20 40 60 80 100 120 140
slow70
slow20
settling30 min
settling30 min
Heating
Heating & cooling
Heating (set value: 60°C)
Fig. 2 Temperature change in the f locculation tank
1.0
0.8
0.6
0.4
0.2
00.00001 0.0001 0.001 0.01 0.1
polyNIPAM 30°C(below transitiontemperature)
40°C(above transitiontemperature)
Tra
nsm
ittan
ce (
600n
m)
[–]
Polymer dosage [kg/kg-kaolin]
Fig. 3 Flocculation performance above and below the transitiontemperature (about 34°C)
these surface with cationic components function asf locculants. As a result, they cause f locculation evenabove the transition temperature.
2.2 Effect of Heating Suspension on Floc Formation
Fig. 4 compares the f locculation performanceobtained by heating suspension to 60°C after poly-NIPAM adsorption at 30°C, and that obtained at 30°C.By heating from 30°C to 60°C, the transmittanceincreased and then decreased with increasing poly-NIPAM dosage. By adding more polyNIPAM thetransmittance increased again, and then remainedfairly steady (range A in the figure). In this range thesupernatant had very low transmittance at 30°C,meaning that hardly any f locs were formed. Thisshows that f locs formed by heating the suspensionafter the surfaces of the suspended particles werecovered enough with polyNIPAM. In fact, before thetemperature of agitator tank was raised (when it wasstill 30°C), we did not discern f loc formation, butwhen the tank was heated we clearly discerned f locformation with the unaided eye at the point the tem-perature of suspension exceeded the transition tem-perature. This seems to bear out the mechanismillustrated in Fig. 1: By heating a suspension ofkaolin particles whose surfaces are covered enoughwith polyNIPAM, the polyNIPAM becomes hydro-phobic, which in turn makes the particle surfaceshydrophobic, thereby making particles adhere toeach other and form f locs due to the hydrophobicinteraction.
Even when the suspension was heated, the trans-mittance increased with the same polymer dosage as
the optimum dosage for 30°C (range B in the figure).The reason appears to be that f loc formation duringthe 10 min of rapid stirring after adding polyNIPAMto an almost optimum amount increased supernatanttransmittance. This fact suggests that even thoughpolyNIPAM adsorbed onto the surfaces of suspendedparticles might become hydrophobic, they do notreadily desorb from the suspended particle surfaces.As stated in our previous paper (Sakohara andNishikawa, 2000), this is likely because polymeradsorption onto the suspended particles is multipointadsorption by functional groups in the polymer mole-cules.
2.3 Reversibility of Floc Formation byHydrophobic Interaction
The closed circle in Fig. 4 shows one example ofthe f locculation performance by adding polyNIPAM,by raising the suspension temperature from 30°C to60°C, then by cooling it down to below the transitiontemperature. The polymer dosage was 0.02 kg/kg-kaolin. As the figure shows, the suspension return-ed to a nearly completely dispersed state. We alsoobserved clearly with the unaided eye that the f locquickly disappeared when the suspension tempera-ture fell below the transition temperature. This showsthat f locculation (f loc formation) caused by the hy-drophobic interaction occurs reversibly in response tothe change in temperature.
Conclusion
We investigated the f locculation mechanism utiliz-ing the hydrophilic/hydrophobic transition of poly-NIPAM, a representative thermosensitive polymer, byusing an agitation tank to perform a f locculation ex-periment on a kaolin suspension. Since f locculationhardly occurred above the transition temperature(about 32°C), the adsorption operation of polyNIPAMonto suspended kaolin particles needs to be per-formed in a hydrophilic state below the transitiontemperature. When the kaolin particle surfaces arecoated enough with polyNIPAM by increasing thepolymer dosage, kaolin particles disperse stablybelow the transition temperature, but f locs form byheating the suspension. When the f locculated suspen-sion is cooled back to below the transition tempera-ture, particles disperse again. From these results, itcan be concluded that the f locculation mechanismdue to the hydrophobic interaction proposed in ourprevious paper (Sakohara and Nishikawa, 2000) isvalid.
KONA No.20 (2002) 249
B
A
Tra
nsm
ittan
ce (
600
nm)
[]
Polymer dosage [kg/kg-kaolin]
1.0
0.8
0.6
0.4
0
0.2
0.00001 0.0001 0.001 0.01 0.1
polyNIPAM
30°C
30°C 60°C
30°C 60°C 25°C
Fig. 4 Effects on f locculation performance of heating and coolingthe suspension
diallyldimethylammonium chloride),” J. Colloid Inter-face Sci., 179, 188-193 (1996).
Guillet, J., M. Heskins and D. G. Murray. “Polymeric Floccu-lant,” U. S. Patent 4,536,294 (1985).
Ito, S.. “Phase Transition of Aqueous Solution of Poly(N-alkylacrylamide) Derivatives: Effects of Side ChainStructure,” Kobunshi Ronbunshu, 46, 437-443 (1989).
Sakohara, S., H. Unno and T. Akehata. “Turbidity Removalby Polymeric Flocculant: Analysis Through a SimpleBridging Model,” Kagaku Kogaku Ronbunshu, 6, 198-203 (1980).
Sakohara, S. and K. Nishikawa. “Flocculation and Com-paction of Highly Concentrated Suspensions by UsingThermosensitive Polymers,” Kagaku Kogaku Ronbun-shu, 26, 298-304 (2000).
250 KONA No.20 (2002)
Acknowledgments
Kohjin Co., Ltd. supplied the N-isopropylacrylamideused in this research. Mr. Shuichi Nakano (currentlyat Taiheiyo Cement Co.) and Mr. Hideaki Ootake(currently at Mitsui Chemicals, Inc.) cooperated insynthesizing the polymer and performing the f loccu-lation experiments. We wish to thank them for theirhelp.
Literature Cited
Deng, Y., H. Xiao and R. Pelton. “Temperature-SensitiveFlocculants Based on Poly(N-isopropylacrylamide-co-
Author’s short biography
Shuji Sakohara
A professor in the Chemical Engineering Department at Hiroshima Universitysince 1994. His major research interests are polymer technology, water treatment,and membrane separation. He received his B.S. and M.S. degrees from HiroshimaUniversity in 1974 and 1976. In 1983 he received a Dr. of Engineering degree fromTokyo Institute of Technology on the f locculation of suspended solids with poly-mers.
Takashi Kimura
Now working as an engineer at Sumitomo Mitsui Polyolefin Co., Ltd.
Kazuo Nishikawa
Now working as an engineer at Tokushu Paper Co., Ltd. He received his B.S. andM.S. degrees from Hiroshima University in 1999 and 2002.
KONA No.20 (2002) 251
1. Introduction
Tablets are the most frequently used form of phar-maceuticals. The main tableting method in Japanused to involve first making granules, and then com-pressing them into tablets by way of indirect (gran-ule) tableting, but the need in recent years forprocess validation, GMP, and automation of produc-tion processes has focused renewal attention on thedirect tableting method, which involves few steps.
Because direct tableting necessitates an activeingredient powder that excels in f lowability, bindabil-ity, mechanical strength, and other qualities morethan the materials for indirect tableting, there are cur-rently limited pharmaceutical tablets on commercialproduction that can be made by direct tableting. Forthat reason development of the design method ofactive ingredient crystals that can be directly tabletedhas been waited. As the model drug in our researchascorbic acid, which is difficult to tablet directly, was
used to develop directly compactable crystals withouta binder for direct tableting. The compactibility ofresultant crystals were evaluated.
Our design method involved using a process calledspherical crystallization developed originally by us[1], which allowed us to manufacture agglomeratedcrystals with two different internal structures thatwere suited to our purpose. After assessing the crys-tals’ f lowability and packability to ascertain theiradequacy as the powder for direct tableting, we con-ducted static and dynamic compression tests. We ana-lyzed the static compression process and determinedthe factors related to improving the granulated crys-tals’ compactibility. Further, anticipating the commer-cial production of tablets, we determined the effect ofcompression speed on compactibility.
2. Materials and Methods
2.1 MaterialsAscorbic acid was chosen as a model drug because
of its brittleness and its strong cohesive properties.As a control for assessing powder physical propertiessuch as f lowability and packability fine crystals (100mesh product, average particle diameter of 18.8 µm,made by Takeda Chemical Industries, Ltd.) was used,and for assessing compactibility it was coarse crystalswith excellent f lowability (FG product, average parti-
Yoshiaki KAWASHIMA, Misato IMAI, Hirofumi TAKEUCHI, Hiromitsu YAMAMOTOand Kazunori KAMIYAGifu Pharmaceutical University*
Development of Agglomerated Crystals of Ascorbic Acid by the Spherical Crystallization Technique for Direct Tableting,
and Evaluation of Their Compactibilities†
Abstract
Spherically agglomerated crystals of ascorbic acid for direct tableting were successfully prepared bythe spherical crystallization technique. This agglomeration dramatically improved the micromeriticand compaction properties of the original ascorbic acid crystals. The dominating mechanisms thatimproved compaction properties of the spherically agglomerated crystals depended on their fragmen-tation and plastic deformation during compaction. Support for this mechanism existed because thecompacted agglomerated crystals had higher stress relaxation and lower elastic recovery than theoriginal crystals. Spherically agglomerated crystals were tableted directly without capping by using asingle-punch tableting machine under dynamic compaction, although the tensile strength of tabletswith spherically agglomerated crystals decreased when the compression speed increased.
* 5-6-1 Mitahorahigashi, Gifu, 502-8585 JapanTEL: +81-58-237-3931 (ext. 244) FAX: +81-58-237-6524
† This report was originally printed in J. Soc. Powder Tech-nology, Japan. 38, 160-168 (2001) in Japanese, beforebeing translated into English by KONA Editorial Commit-tee with the permission of the editorial committee of theSoc. Powder Technology, Japan.
cle diameter of 425 µm, made by Takeda ChemicalIndustries, Ltd.). A control for both assessments wascommercially available granulated ascorbic acid fordirect tableting (hereinafter, “C97 granules,” averageparticle diameter of 422 µm, made by Takeda Chemi-cal Industries, Ltd.). C97 granules are produced in af luidized bed with 3% starch added as a binder. As themodel drug for plastic deformability we used potas-sium chloride (Japanese Pharmacopoeia, hereinafterwritten “KCl,” average particle diameter of 650 µm,produced by Yamazen Corporation).
2.2 Preparation of Ascorbic Acid AgglomeratedCrystals for Direct Tableting
Ascorbic acid was dissolved in 50°C purified water(a good solvent) to prepare a 0.4 g/ml saturated solu-tion. A pipette was used to quickly drop a prescribedamount of the solution into a 500 ml cylindrical agita-tor tank containing 300 ml of ethyl acetate (a poorsolvent, maintained at 5°C) while stirring with a four-bladed propeller-type agitator at either 300 or 800rpm. By choosing a water-to-ethyl acetate volumetricratio of either 1:100 or 4:150, we prepared sphericalagglomerated crystals of ascorbic acid by two dif-ferent crystal agglomeration mechanisms: sphericalagglomeration (SA), and emulsion solvent diffusion(ESD). We inserted baff les in the agitator tank to pro-mote granulation with SA, but with ESD we let granu-lation occur without using baff les so as to prevent thebreakdown of emulsion droplets. After stirring for 20min the crystal agglomerates obtained were suctionfiltered, washed with a small amount of methanol, anddried under reduced pressure for at least 24 h. Weused the agglomerate fraction in the 125 to 500 µmrange, obtained by classifying with a screen to bringthem into line with the C97 granule particle sizerange. This fraction’s yield was good at 70 to 80%.
2.3 Measuring Physical Properties of Agglomerated Crystals
A scanning electron microscope (JTM-T330A,JEOL., Ltd.) was used to observe the particle form ofthe original crystals (100 mesh product), coarse crys-tals (FG product), and C97 granules, and the surfaceproperty and cross sections of the two types of spher-ically agglomerated crystals (SA and ESD products).
Sample f lowability was measured and assessed byusing the pouring method to make them pile, thenmeasuring their angle of repose.
Sample packability was assessed by analysis of thetapping process with the Kawakita [2] (Eq. 1) andKuno [3] (Eq. 2) methods, and using the parameters
a, b, and k in the equations.
(n/C)(1/ab)(n/a), C(V0Vn)/V0 (1)ρfρn(ρfρ0)exp(kn) (2)
Where:a is the degree of volume reduction when the tap
number is infinity,b and k are constants for the apparent packing rate,V0 and Vn are the volume in the initial loosely packed
and the nth tapped state, andρ0, ρn, and ρf are the apparent density in the initial
state, the nth tapped state, and the most denselypacked state.
2.4 Tablet PreparationA screen was used to classify the test samples into a
125 to 500 µm fraction. We placed 150 mg of eachsample into a die with diameter of 8 mm, and usedan AUTOGRAPH (Instron type press) (AG5000D,Shimadzu Corporation) to tablet the samples at a con-stant rate of 10 mm min1 and at various compressionpressures between 50 and 300 MPa5%. Assumingcommercial production, we mixed 1% magnesiumstearate into each sample and used the universal ten-sile compression tester and a single-punch tabletingmachine (TabA11, Okada Seiko Co., Ltd.) to producetablets under a constant compression pressure of 200MPa5% and at various compression speeds. Thecompression speed of single-punch tableting machinewas calculated from the displacement rate of upperpunch when compressing.
2.5 Compression Behavior Analysis2.5.1 Heckel Analysis [4, 5]
We used Heckel’s equation (Eq. 3) to analyze thecompression process of agglomerated crystals, andassessed their compactibility.
1n [1/(1D)]KPA (3)
Where:D is the relative density of the tablets under compres-
sion pressure P (MPa; the ratio of tablet density tothe powder’s true density),
K is the slope of the straight portion of the Heckelplot, and
the reciprocal of K is the mean yield pressure (Py).
Eq. 4 gives the intercept obtained by extrapolating thestraight portion of the plots.
A1n [1/(1D0)]B (4)
Where:
252 KONA No.20 (2002)
D0 is the relative density of the powder bed whenP0.
Eqs. 5 and 6 give the relative densities correspondingto A and B.
DA1eA (5)DBDAD0 (6)
2.5.2 Stress Relaxation TestWe put 150 mg of each sample in a die with 8 mm
diameter the surface of which was coated with mag-nesium stearate in advance, then used the universaltensile compression tester to compress the samples ata constant speed of 10 mm min1. After the pressureattained 200 MPa, the upper punch was held in thesame position for 20 min, during which time we mea-sured the reduction amount of the stress applied onthe upper punch. [6] The result was corrected by sub-tracting from this measurement the relaxation mea-sured without powder in the die under the sameconditions. We used Eq. 8 to find the relationshipbetween relaxation ratio Y(t) and time t, calculatedthe parameters A s and Bs, and assessed relaxationbehavior. [7, 8]
Y(t)(P0Pt)/P0 (7)
Where:P0 is the maximum compression pressure, andPt is the pressure at time t.
t/Y(t)1/AsBst/As (8)
2.5.3 Tablet Elastic Recovery TestWe placed 150 mg of each sample in a die with 8
mm diameter and used the universal tensile compres-sion tester to compress them up to 200 MPa at theconstant speed of 10 mm min1. We measured thethickness of each tablet under maximum pressure(Hc) and at about 24 h after tablet ejection (He). Eq. 9was used to calculate the elastic recovery ratio (ER).[9]
ER[(HeHc)/Hc]100 (9)
About 24 h after the tablet was ejected, its weight,diameter, and thickness was measured, and its appar-ent density (ρa) calculated. Eq. 10 was used to calcu-late internal tablet porosity (ε) from true density (ρt),which was measured with an air comparison pyc-nometer (Model 930, Beckman-Toshiba, Ltd.).
ε1ρa/ρt (10)
2.6 Tablet Tensile Strength TestTablets were kept in a desiccator (silica gel) for
about 24 h, and then a hardness tester (GRANO,Okada Seiko Co., Ltd.) was used to measure a loadacross the diameter of each tablet at a compressionspeed of 100 µm s1 to find the hardness F whencrushing. Eq. 11 was then used to calculate the ten-sile strength T. [10]
T2F/πdL (11)
Where:d and L are a tablet’s diameter (m) and thickness (m).
We crushed the tablets made by compressing thetwo types of spherically agglomerated crystals, andobserved the fracture planes with a scanning electronmicroscope.
3. Results and Discussion
3.1 Spherical Crystallization Mechanism andPhysical Properties of Agglomerated Crystals
It was found that crystal agglomeration was possi-ble with two different types of mechanisms dependedon the amount of drug solution added to the system(poor solvent). When both solvents were mixed at asmall water-to-ethyl acetate volumetric ratio (1:100), aW/O emulsion formed at first. Then as the emulsiondrops cooled and the water and ethyl acetate counter-diffused, solubility in the emulsion drops decreased,and crystals precipitated on the surfaces of drops.Spherical agglomerates were obtained when crystal-lization completed. This agglomeration mechanism iscalled emulsion solvent diffusion, or ESD. On theother hand, when the water-to-ethyl acetate volumet-ric ratio was large (4:150) and the solvents did notmix, crystals precipitated in the same way after anemulsion formed. At this system a small amount ofwater that was liberated from the ethyl acetate phaseacted as a liquid bridging agent (forming a liquidbridge), which caused particles to randomly agglom-erate, and then become spherical under the shearingforce of stirring, after first passing through funicularand capillary forms. This agglomeration mechanismis called spherical agglomeration, or SA. Fig. 1 illus-trates the SA and ESD mechanisms, and Fig. 2 pre-sents electron photomicrographs of the surfaces andcross sections of the two types of ascorbic acidagglomerated crystals. Both types of agglomeratedcrystals were spherical.
As one can see from the agglomeration mechanism
KONA No.20 (2002) 253
in Fig. 1, while in the SA method the primary crys-tals randomly agglomerated, crystals in the ESDmethod grow toward the center. Owing to this differ-ence in the agglomeration mechanism, the two meth-ods yield two types of agglomerated crystals withdifferent internal structures.
The physical properties of the agglomerated crys-tals are shown in Table 1.
The angle of repose of agglomerated crystals wasclearly lower than that of the original crystals, andabout the same as that of commercially available C97granules. We used the equations of Kawakita andKuno to analyze the tapping process. The value a inKawakita’s equation was lower than that of the origi-nal crystals, while b in Kawakita’s equation and k in
Kuno’s equation were both higher. Both of theagglomerated crystals obtained had excellent f lowa-bility and packability, and in terms of handling prop-erties such as feeding into die, the agglomeratedcrystals were useful for direct tableting.
3.2 Compression Behavior AnalysisTo determine the compression characteristics of
the agglomerated crystals, Heckel’s equation [4, 5]was used to analyze the compression behavior ofagglomerated crystals (Fig. 3).
Except for KCl, none of the agglomerated crystaltypes exhibited a linear relationship at low com-pression pressures, while they did at high pressures.This shows that at low compression pressures therearrangement and crushing of agglomerated crys-tals proceeds simultaneously, and that at high pres-sures crystal particles are cohered and bonded withone another while undergoing plastic deformation.The initial portions of Heckel plot curves are a gen-eral indication of the tendency for particle fracturing.Doelker used the values for DA, D0, and DB calculatedfrom Heckel plots respectively, as an indicator of com-paction by the densest packing of rearranged andfractured particles into a die; an indicator of com-paction by initial packing; and an indicator of fractur-ing characteristics (compaction of a powder bed bythe rearrangement of primary particles and fracturedparticles). The higher the value of D0, the better the
254 KONA No.20 (2002)
Random coalescenceFunicular → Capillary
Compaction and spheronization
Precipitated crystalsand aggregate with
bridging liquid
Sphericalagglomerate
Precipitated crystals
Formulation ofemulsion
Crystallization
Liberated bridging liquid
SA method
ESD method
CrystallizationCounterdiffusion of
good solvent and poor solventwithout
coalescence
Fig. 1 Mechanism of spherical crystallization
Sphericalagglomerate
Sample Angle of repose (°) a1) b1) k2)
Original 56.12.3 0.508 0.066 0.021
C97 33.71.0 0.079 0.151 0.045
SA 33.82.6 0.224 0.176 0.065
ESD 33.01.6 0.133 0.155 0.063
1) Parameters in Kawakita’s equation: (n/C)(1/ab)(n/a) andC(V0Vn)/V0, where n is the tap number and V0 and Vn are thepowder volumes at the initial and nth tapped state, respectively.
2) Parameter in Kuno’s equation: ρfρn(ρfρ0)exp(kn), whereρf, ρn, and ρ0 are the apparent densities at equilibrium, the nth
tapped, and initial state, respectively.
Table 1 Flowing and packing properties
KONA No.20 (2002) 255
Fig. 2 Scanning electron photomicrographs of external appearance and cross-section of original ascorbic acid crystals, a C97 granule, potas-sium chloride crystals, and SA and ESD agglomerated crystals of ascorbic acid
a) Original crystals
50 µm
100 µm
50 µm
50 µm 10 µm
100 µm
100 µm
100 µm
b) Original coarse crystals
c) C97 granule d) Potassium chloride crystals
e) SA agglomerated crystal
Cross section
Cross section
f) ESD agglomerated crystal
initial packability in a die, while the higher the valueof DB, the greater the fracturing tendency exhibitedby a powder. [11] Analysis results indicated that theoriginal coarse crystals and KCl had high D0 values,which is probably because the surfaces of these crys-tals were comparatively smooth (Fig. 2), which madethem easy to pack into a die. Because SA agglomer-ated crystals had the highest DB value, it was evidentthat considerable fracture occurred during compres-sion (Table 2).
Plastic f low of the particles during compression
occurred mainly after rearrangement and fracture.Plastic deformability is generally evaluated accordingto mean yield pressure (Py), which was calculatedfrom the slope of the linear portion of plots. Py valuesin descending order were SA crystals, ESD crystals,C97 granules, and the original coarse crystals (Table2). All these values are higher than that of KCl, a sub-stance that tends to undergo plastic deformation, andthey are about the same with regard to plastic de-formability. They had lower elastic recovery valuesthan the original coarse crystals.
256 KONA No.20 (2002)
Fig. 3 Heckel’s plot for ascorbic acid and potassium chloride crystals at a compression speed of 10 mm min1
Straight lines were obtained by a linear regression analysis of data between 50 and 150 MPa. (a) Original coarse crystals, (b) C97 gran-ules, (c) SA agglomerated crystals, (d) ESD agglomerated crystals, and (e) KCl crystals
0
1
2
(a) (b)
3
0 50 100 150 200
ln
(1
D)
Compression pressure (MPa)
0
1
2
3
0 50 100 150 200
ln
(1
D)
Compression pressure (MPa)
0
1
2
(c) (d)
3
0 50 100 150 200
ln
(1
D)
Compression pressure (MPa)
0
1
2
3
0 50 100 150 200
ln
(1
D)
Compression pressure (MPa)
0
(e)
4
3
2
1
0 50 100 150 200
ln
(1
D)
Compression pressure (MPa)
To investigate compactibility in more detail, wemeasured stress relaxation, which is an indicator ofplastic deformability (Table 2). Fig. 4 shows theresults obtained by interpreting the relaxationprocess with Eq. 8. Good linear correlations wereobtained with all samples, and constants AS and BS
were determined from their slopes (Table 3). AS indicates the relaxation ratio at infinity time; the
higher the value, the greater the stress relaxation.1/BS indicates the time until the relaxation ratioattains AS/2, and means that the larger the BS value,the faster the relaxation rate. Spherically agglomer-ated crystals had larger stress relaxation than othercrystals, with that of SA crystals larger than that ofESD crystals. And because the AS and BS values werelarge, Table 3 shows that stress relaxation under sta-tic pressure was large, and that the relaxation ratewas rapid. Stress relaxation occurred because of par-ticle fracturing and rearrangement caused by pack-ing, and because of the plastic deformation of theparticles themselves. [12] It is thought that becausespherically agglomerated crystals were easily frac-tured during compression, their particle sizes becamesmaller, and their stress relaxation increased due torearrangement. By contrast, the original coarse crys-
tals and C97 granules had small relaxation values.This is likely because, as one can estimate from thevalues for D0 and DB calculated from the Heckel plots,the initial packing rate in the die was high, and littlerearrangement was caused by fracturing during com-pression. KCl had small stress relaxation. The smallAS value shows that stress relaxation under staticpressure decreased owing to the adequate stressrelaxation afforded by the strong plastic f low duringcompression (Fig. 3). Further, the low BS valuemeans that the relaxation rate under static pressurewas extremely slow.
3.3 Improving the Compactibility of SphericallyAgglomerated Crystals
We assessed the compactibility of agglomeratedcrystals samples according to the tensile strength oftablets (Fig. 5). [10]
KONA No.20 (2002) 257
SampleHeckel analysis Relaxation pressure Elastic recovery
Py (MPa) DA D0 DB(MPa) (%)
Original 127.42.9*** 0.7410.001*** 0.5610.013*** 0.1800.013*** 007.00.2*** 9.30.5***
C97 134.84.0*** 0.6820.001*** 0.4000.005*** 0.2820.006*** 028.40.4*** 5.10.4***
SA 168.83.5*** 0.7020.002*** 0.3300.011*** 0.3720.010*** 146.10.4*** 5.00.5***
ESD 142.92.9*** 0.7470.001*** 0.4090.010*** 0.3380.011*** 124.90.5*** 4.70.2***
KCl 035.41.6*** 0.5510.005*** 0.5230.017*** 0.0280.012*** 013.51.1*** 8.91.1***
The results are expressed as mean S.D. of four runs. There was a significant difference with the value for original coarse crystals at p0.001(***), p0.01(**) and p0.5 (*).
Table 2 Analysis of compaction behavior
Sample AS BS
Original 0.0580.001*** 0.0120.001***
C97 0.1680.002*** 0.0130.000***
SA 0.7780.004*** 0.0210.001***
ESD 0.6580.006*** 0.0290.001***
KCl 0.1030.005*** 0.0040.000***
The results are expressed as the mean S.D. of four runs. Therewas a significant difference with the value for original coarse crys-tals at p0.001 (***).
Table 3 Parameters of stress relaxation process
0
25000
20000
15000
10000
5000
t/Y
(t)
(s)
Time (s)
0 500 1000 1500
Fig. 4 Relationship between t/Y(t) and t() Original coarse crystals, () C97 granules, () SAagglomerated crystals, () ESD agglomerated crystals,and () KCl crystals
Capping of the original coarse crystals occurred atcompression pressures of 200 MPa and above. Owingto the small DB value of the original crystals, therewas less fracturing than agglomerated crystals andelastic recovery was high (Table 2), thereby allowingcapping. When ascorbic acid was made into crystalagglomerates by crystal agglomeration, tableting waspossible without the occurrence of capping. What ismore, the tensile strength of the resulting tabletsimproved dramatically; it was significantly better eventhan C97 granules, and displayed superior com-pactibility. The reasons for this are likely that as theDB value of spherically agglomerated crystals was sig-nificantly high (Table 2), making the crystals frac-ture easily under compression, this increased thepoints of contact among particles; the large stressrelaxation (Table 2) facilitated plastic f low, therebyincreasing the contact area; and new high-energy sur-faces appeared because of fracturing, which stronglybonded the particles. [13]
3.4 Effect of Compression Speed on the Compactibility of Spherically AgglomeratedCrystals
It was found that spherically agglomerated crystalsexhibited an excellent capacity for compactibility
under static compression. Nevertheless, powder bedsare compressed rapidly in the commercial productionof tablets. For that reason we mixed a lubricant (mag-nesium stearate) into the samples, and used a single-punch tableting machine as well as universal tensilecompression tester to investigate the effect of com-pression speed on tensile strength. Fig. 6 shows therelationship between compression speed and tensilestrength.
When the universal tensile compression tester wasused to compress the original coarse crystals, thetablets exhibited low tensile strength, but there was atendency for tensile strength to increase somewhat asthe compression speed increased. Although the com-mercially available C97 granules had a value higherthan that of the original coarse crystals, the tendencywas the same. KCl, which tends to undergo plasticdeformation, had a tendency for tensile strength todecrease as the compression speed increased. Whilespherically agglomerated crystals displayed the sametendency as KCl, under compression with the com-pression tester its tensile strength increased at acompression speed of 300 mm min1. But when com-pressing with the single-punch tableting machine, allsamples had about the same tensile strength, no mat-ter what the compression speed. When compressionwas performed with both the universal tensile com-
258 KONA No.20 (2002)
0.1
10
1
Tens
ile s
tren
gth
(MPa
)
Compression speed (mm min1)
1 10 100 1000
Fig. 6 Relationship between tensile strength of ascorbic acidtablets and compression speedSample: 150 mgCompaction pressure: 200 MPa(, ) Original coarse crystals, (, ) C97 granules,(, ) SA agglomerated crystals, (, ) ESD agglomer-ated crystals, and (, ) KCl crystalsTablets were prepared using an Instron-type hydraulicpress (closed symbols) or single-punch tableting machine(open symbols) at a 200 MPa compaction pressure. Theresults are expressed as the mean S.D. of four runs.
0
7
6
5
4
3
2
1
Tens
ile s
tren
gth
(MPa
)
Compaction pressure (MPa)
0 100 200 300
††
** *
*** **
*** ***
Fig. 5 Relationship between tensile strength of ascorbic acidtablets and compaction pressureSample: 150 mgCompression speed: 10 mm min1
() Original coarse crystals, () C97 granules, () SAagglomerated crystals, and () ESD agglomerated crys-tals †: Some tablets are capped during compaction. The resultsare expressed as the mean S.D. of four runs. There wasa significant difference with the value for C97 granules atp0.001 (***), p0.01 (**) and p0.5 (*).
pression tester and the tableting machine at the samecompression speed, tablets made with the compres-sion tester had the higher tensile strength. Weassume this is due to a characteristic of the compres-sion imposed by the tester, which is static compres-sion at a constant speed that places uniform stress onthe powder. By contrast, compression applied by thetableting machine initially has a high speed, thengradually slows. It is therefore characterized as dy-namic compression in which changes in the powderbed’s internal stress are non-equilibrium. Thus, it islikely that tablet tensile strength was low because thecompression energy was not effectively applied forpowder compaction and formation.
Fig. 7 shows the relationship between tablet poros-ity and compression speed.
Tablets made from the original coarse crystals withthe single-punch tableting machine had lower poros-ity than those made with the universal tensile com-pression tester. This is probably because when thecompression speed was high, the powder was sub-jected to a bigger impact, and brittle original crystalswas fragmented, rearranged, and compacted by com-pression. With respect to spherically agglomeratedcrystals, although no clear difference in ESD crystals
was found, when making SA crystals at the samecompression speed with the universal tensile com-pression tester and the single-punch tableting ma-chine, the tablets made with the compression testerhad lower porosity. This correlates to the above-notedfact that tablets made with the compression testerhave a higher tensile strength. To investigate thepacked state of crystals in tablets made with the com-pression tester we used a scanning electron micro-scope to examine tablet cross sections (Fig. 8).
At a low compression speed, solid bridges formedbetween crystals in both types of agglomerated crys-tals, but when the compression speed was high therewas no fusion between crystals, and the cross sec-tions were very similar to those of agglomerated crys-tals prior to compression. We assume this is becausewhen compression time is long, crystals undergo con-siderable plastic deformation. [6] In our examinationof tablets obtained from SA agglomerated crystals weobserved only the primary crystals that made up theagglomerated crystals, suggesting that compressionfractured the agglomerated crystals back down totheir primary crystals, which is the reason for thelarge DB value. On the other hand, examination oftablets obtained from ESD agglomerated crystalsrevealed that the internal structure of agglomeratedcrystals in the tablets was partially retained, sug-gesting that compression fractured only the outsidesurface of the agglomerated crystals. Because theinternal structures of agglomerated crystals differedaccording to the mechanism by which sphericallyagglomerated crystals were made, the agglomeratesalso differed with respect to the extent of fracturingduring compression and the arrangement of crystalsin tablets, which is likely the reason for their differentplastic deformability ( Table 2).
4. Conclusion
By applying spherical crystallization methods toascorbic acid with strong cohesive and brittle proper-ties, we were able to make agglomerated crystalswith excellent f lowability and packability, and withbetter compactibility than commercially availablegranulated particles for direct tableting, therebydetermining that these agglomerated crystals are use-ful as particles for direct tableting. In consideration ofthe drying conditions for this method, it is believedthat the ethyl acetate remaining in the agglomeratedcrystals is under the 5,000 ppm standard of the resid-ual solvent guideline. [14] We found that major rea-sons for the superior compactibility of spherically
KONA No.20 (2002) 259
0.06
0.16
0.14
0.12
0.10
0.08
Poro
sity
of t
able
ts
Compression speed (mm min1)
1 10 100 1000
Fig. 7 Relationship between porosity of ascorbic acid tablets andcompression speedSample: 150 mgCompaction pressure: 200 MPa(, ) Original coarse crystals, (, ) C97 granules,(, ) SA agglomerated crystals, (, ) ESD agglomer-ated crystals, and (, ) KCl crystalsTablets were prepared using an Instron-type hydraulicpress (closed symbols) or single-punch tableting machine(open symbols) at a 200 MPa compaction pressure. Theresults are expressed as the mean S.D. of four runs.
agglomerated crystals are the increased fragmenta-tion of granulated crystals and plastic deformability(f lowability) of fractured particles under compres-sion, and the low elastic recovery. An increase in thespeed of compression on spherically agglomeratedcrystals reduces the tensile strength of tablets, butour study showed that even direct tableting can bedone at high speed. Spherical crystallization can beused for any drug as long as an appropriate solvent ischosen. This is a useful granulating technology thatcan solve the problems of poor powder physical prop-erties and compactibility that make other drugs hardto tablet, and that can make them into powder that isresponsive to direct tableting.
Acknowledgements
We wish to thank Takeda Chemical Industries, Ltd.for supplying the samples used in this research.
Nomenclature
A total densification of powder bed due to die filling and particle rearrangement
AS constanta constantB densification of powder bed due to particle
fragmentationBS constantb constantC constantD relative density of powder at applied pressure PD0 relative density of powder when pressure is 0d tablet diameter (m)ER elastic recovery ratio (%)F crushing hardness (N)Hc tablet thickness at maximum pressure (m)He tablet thickness at 24 h after ejection (m)K slope of straight line by Heckel plot (1/Pa)
260 KONA No.20 (2002)
Fig. 8 Scanning electron photomicrographs of cross section of ascorbic acid tablets prepared by static compression
a) SA agglomerated crystalsCompression speed1 mm min1
b) ESD agglomerated crystalsCompression speed1 mm min1
c) SA agglomerated crystalsCompression speed300 mm min1
d) ESD agglomerated crystalsCompression speed300 mm min1
10 µmε0.1110.002 ε0.0850.002 10 µm
10 µmε0.1200.006 ε0.0970.006 10 µm
k constantL tablet thickness (m)n tap numberP applied pressure (Pa)P0 maximum pressure (at time t0) (Pa)Pt pressure after time t (Pa)T tensile strength (N/m2)Vo volume at initial state (m3)Vn volume at nth tapped state (m3)Y(t) pressure relaxation ratioε tablet porosityρ0 apparent density at initial state (kg m3)ρa apparent density (kg m3)ρf apparent density at equilibrium state (kg m3)ρn apparent density at nth tapped state (kg m3)ρt true density (kg m3)
References
1) Kawashima, Y. “New Processes Application of Spheri-cal Crystallization to Particulate Design of Pharmaceuti-cals for Direct Tabletting and Coating, and New DrugDelivery Systems,” Powder Technology and Pharmaceu-tical Process, edited by D. Chulia et al., 493-512, Elsevier(1994).
2) Kawakita, K. “Compression of Powder,” Kagaku, 26,149 (1956).
3) Kuno, H. Funtai (Powder Theory and Application), ed.by G. Jimbo et al., Maruzen, Tokyo, p. 342 (1979).
4) Heckel, R. W. “Density-pressure Relationships in Pow-der Compaction,” Trans. Met. Soc. AIME, 221, 671(1961).
5) Heckel, R. W. “An Analysis of Powder Compaction Phe-nomena,” Trans. Met. Soc. AIME, 221, 1001 (1961).
6) Kawashima, Y., F. Cui, H. Takeuchi, T. Niwa, T. Hinoand K. Kiuchi. “Improved Static Compression Behaviorsand Tablettabilities of Spherically Agglomerated Crys-tals Produced by the Spherical Crystallization Tech-nique with a Two-solvent System,” Pharm. Res., 12 (7),1040-1044 (1995).
7) Peleg, M. and R. Moreyra. “Effect of Moisture on theStress Relaxation Pattern of Compacted Powders,” Pow-der Technol., 23, 277 (1979).
8) Danjyo, K., A. Hiramatsu and A. Otsuka. “Effect ofPunch Velocity on the Compressibility and Stress Relax-ation of Particles and Granules,” J. Soc. Powder Technol.Japan, 35, 662-670 (1998).
9) Armstrong, N. A. and R. F. Haines-Nutt. “Elastic Recov-ery and Surface Area Changes in Compacted PowderSystems,” Powder Technol., 9, 287-290 (1974).
10) Fell, J. T. and J. M. Newton. “Determination of TabletStrength by the Diametral-compression Test,” J. Pharm.Sci. 5, 688-691 (1970).
11) Doelker, E. “Assessment of Powder Compaction,” Pow-der Technology and Pharmaceutical Process, edited by D.Chulia et al., 403-512, Elsevier (1994).
12) Cutt, T., J. T. Fell, P. J. Rue and M. S. Spring. “Granula-tion and Compaction of a Model System, II Stress Relax-ation,” Int. J. Pharm., 39, 157-161 (1987).
13) Kawashima, Y., F. Cui, H. Takeuchi, T. Niwa, T. Hinoand K. Kiuchi. “Improvements in Flowability and Com-pressibility of Pharmaceutical Crystals for DirectTabletting by Spherical Crystallization with a Two-sol-vent System,” Powder Technol., 78, 151-157 (1994).
14) Kojima, S. “ICH Guideline for Residual Solvents inDrugs,” PHARM TECH JAPAN, 16 (5), 7-24 (2000).
KONA No.20 (2002) 261
Author’s short biography
Yoshiaki Kawashima
Dr. Yoshiaki Kawashima is Professor of Laboratory of Pharmaceutical Engineeringat Gifu Pharmaceutical University. He received B.S. (1964) degree from NagoyaCity University and M.S. (1966) and Ph.D. degree (1969) from Kyoto University.He joined Gifu Pharmaceutical University as a faculty member in 1969. Since 1991,he becomes a visiting professor of Shen-Yang Pharmaceutical University. Hereceived FIP Colocon award and AAPS fellow ship in 1995 and 1996. He is chair-man of the society of Powder Technology, Japan since 1999. He developed spheri-cal crystallization techniques and his research interests are in the developmentand application of spherical crystallization for drug delivery system with nanopar-ticulate carriers.
262 KONA No.20 (2002)
Author’s short biography
Misato Imai
Misato Imai was born in 1975. She graduated from Gifu Pharmaceutical Universityin 1998 and received B.S. in Pharmaceutical Chemistry in Gifu PharmaceuticalUniversity. She worked in Gifu Pharmaceutical University from 1998 to 2002. Now,she is working in Pharmacy.
Hirofumi Takeuchi
Dr. Hirofumi Takeuchi is Associate Professor of Pharmaceutical Technology atGifu Pharmaceutical University. He received his B.S. (1979), M.S. (1981) and Ph.D.(1984) in pharmaceutical sciences from Kyoto University. He joined Gifu Pharma-ceutical University as a faculty member in 1984, and became Lecturer in 1988. Hespent 1 year as a visiting scientist at University of Alberta in 1989-1990. He hasbeen Associate Professor of Gifu Pharmaceutical University since 1991. Hisresearch interests are designing the novel solid dosage forms and dispersed sys-tems for drug delivery.
Hiromitsu Yamamoto
Dr. Hiromitsu Yamamoto graduated from Gifu Pharmaceutical University in 1992and obtained master degree in Pharmaceutical Engineering in 1994. He received aPh.D. degree from Gifu Pharmaceutical University in 1999. Since 1995, he is work-ing in laboratory of Pharmaceutical Engineering at Gifu Pharmaceutical Universityas assistant professor. His major research interests are development of drug deliv-ery system with microparticulate drug carriers and dry powder inhalation system.
Kazunori Kamiya
Kazunori Kamiya is a pharmacist, who received B.S. and M.S. degrees from GifuPharmaceutical University in 1996 and 1998.
KONA No.20 (2002) 263
1. Introduction
The dispersibility of fine particles in various sol-vents af fects the quality of the products in themanufacturing process treating suspensions. It isimportant to control the dispersion/f locculationbehavior of fine particles in various solvents in thefield of paint, printer ink, magnetic material, elec-tronic parts, etc. [1]. The DLVO theory, as is wellknown, explains the dispersion/flocculation behaviorof fine particles in aqueous solution. However, thistheory cannot be applied to the particles in organicsolvents, because the factors on dispersibility inorganic solvents are very complicated.
The dielectric constant of a substance is closelyconcerned with the dipole moment, and also thepolarity of a substance with high dielectric constantis considered to be large. Generally, the affinitybecomes higher between the solvent with large polar-ity and the metal oxide particle with large polarity.Therefore, dispersibility of fine particles in a solvent
may be concerned with the dielectric constant of thesolvent. On the other hand, Hildebrand [2] proposedthe concept of regular solution theory and gave theexperimental solubility parameter δ in order toexpand it to real solutions. However, this concept isapplicable only to nonionic solution with no dipoleinteraction. In order to extend this theory towardpolymer solutions, the Hildebrand’s solubility para-meter δ was divided into London dispersion effect δd,polar effect δp and hydrogen bonding effect δh byHansen, and then the applicability of these solubilityparameters was investigated for the solubility of pig-ments and polymers [3, 4, 5, 6].
In this study, the relationship between dispersibilityof fine particles and various properties of the solvent,such as dielectric constant and solubility parameters,was investigated in various solvents [7, 8]. Themedian diameters of fine particles of Al2O3, TiO2 andFe2O3 were measured in various solvents to evaluatethe dispersibility of particles, and also Hansen’s solu-bility parameters were used for the evaluation of dis-persibility of fine particles in various solvents.
2. Hildebrand’s solubility parameter andHansen’s solubility parameter
As the concept of ideal solution is not well applica-ble to real solutions, many useful approximations
Junji SHIBATA, Katsuya FUJII, Norihiro MURAYAMA and Hideki YAMAMOTODepartment of Chemical Engineering, Kansai University*
Dispersion and Flocculation Behavior of Fine Metal Oxide Particles in Various Solvents†
Abstract
The objective of this study is to investigate the relation between the f locculation and dispersion ofAl2O3, TiO2 and Fe2O3 particles and the properties of solvents such as dielectric constant and solu-bility parameters. The median diameter of these metal oxide perticles was measured in manyorganic solvents. The ef fect of the kind of solvent on the f locculation/dispersion behavior of metaloxide particles was evaluated from these results.
Hansen’s solubility parameters with three dimensions were applied to the evaluation of the f loccu-lation/dispersion behavior for fine metal oxide particles in organic solvents. The numeral balanceamong the Hansen’s solubility parameters of various solvents was plotted in a triangular chart, andthen the points of solvents with similar median diameter of the particle were linked. In the triangu-lar chart, these linked lines were not intersected each other and there was the specific point at whichthe best dispersibility of the particles was obtained.
* 3-3-35, Yamate-cho, Suita-shi, Osaka, 564-8680, JapanTel: +81-6-6368-0856, Fax: +81-6-6388-8869, E-mail: [email protected]
† This report was originally printed in Kagaku KougakuRonbunshu, 27, 497-501 (2001) in Japanese, before beingtranslated into English by KONA Editorial Committeewith the permission of the editorial committee of the Soc.Chemical Engineers, Japan.
have been made to real solutions. Hildebrand pro-posed the concept of regular solution theory and hegave the following equation to evaluate the solubilityof various materials [2],
δ(DHRT)/V 1/2 (1)
where R, T, DH and V are gas constant, temperature,enthalpy of vaporization and molar volume, respec-tively. The solubility parameter δ can be calculated bythe following equation [2],
δ3.75 (γ/V 1/3)1/2 (2)
where γ is surface tension of the solvent.On the other hand, the concept of regular solution
is applicable only to nonionic solutions in whichassociation and dipole interaction do not take placebetween solvent and solute. However, hydrogen bond-ing and dipole interactive force should not be ignoredin many solvents. It is important to extend the regularsolution theory to real solutions. Hansen dividedHildebrand’s solubility parameter δ into three termsas follows [3],
δ2δd2δp
2δh2 (3)
where δd, δp and δh are corresponding to London dis-persion effect, polar effect and hydrogen bondingeffect, respectively. In estimating the value of δh,Hansen noticed the fact that the hydrogen bondingenergy of -OH group was about 5kcal and then he pro-posed the next equation taking account of the contri-bution of -OH group to aggregation [5],
δhBN500N0 nN/V (4)
where n is the number of -OH group in a unit mole-cule.
The value of δp is calculated by the following equa-tion derived by Bottcher [9],
δp212.108/V 2･(e1)/(2enD
2)･(nD22)m2 (5)
where e is dielectric constant, nD is refractive indexfor Na-D ray and m is dipole moment. The value of δd
is estimated from the vaporization energy of the mate-rial in which the -OH and -CO groups do not exist.
As the dispersion phenomenon, similar to dissolu-tion, is related to the diffusion phenomenon, it is pos-sible to express the dispersion/flocculation behaviorof fine particles using Hansen’s solubility parameters.The fine particles of a-Al2O3, a-Fe2O3 and anatasetype-TiO2 were used as a model particle, and themedian diameters of these particles in various sol-vents were measured. The dispersibility of the fineparticles was considered from the obtained results.
3. Experimental
Fine particles of a-Al2O3 (Sumitomo ChemicalCorp., 0.5mm median diameter), a-Fe2O3 (TodaKogyo Corp., 0.7mm median diameter) and anatasetype-TiO2 (Ishihara Sangyo Kaisya Ltd., 0.2mm medi-an diameter) were used as a model particle. These par-ticles were dried in oven at 423K for 24hrs. Twentyseven types of solvents were selected as dispersionmedia. Table 1 shows the list of used solvents withsome physical properties. These solvents were dehy-drated with molecular sieves for 24hrs before prepar-ing suspensions. Each value of fd, fp and fh shown inTable 1 indicates the numerical balance among theHansen’s three solubility parameters, and these val-ues are calculated by the following equations, respec-tively.
fdδd/(δdδpδh)100 (6)fpδp/(δdδpδh)100 (7)fhδh/(δdδpδh)100 (8)
The particles and solvents were mixed at 10g/dm3
of slurry concentration, and then shaken at 300spmfor 24hrs. The particle size distribution in each sus-pension was measured by using a laser scattering par-ticle size analyzer (LA-910, Horiba Ltd.). The degreeof dispersion and f locculation was evaluated from thevalue of the median diameter in each solvent.
4. Results and discussion
The median diameters of particles in various sol-vents are shown in Fig. 1 as a function of dielectric
264 KONA No.20 (2002)
Fig. 1 Relationship between median diameter and dielectric con-stant of various solvents
00
10
20
30
40
50
60
20 40 60 80
18
1915
11
9 11 12
Med
ian
diam
eter
[µm
]
Dielectric constant []
Al2O3
TiO2
Fe2O3
090 Acetic acid 15 Acetone11 Pyridine 18 Acetonitrile12 1-Pentanol 19 Ethylene glycol
constant of the solvent. Each number in Fig. 1 meansthe kind of solvent listed in Table 1. The mediandiameter decreases with an increase in dielectric con-stant. In the range of dielectric constant over 5, thevalues of median diameter are under 10mm for manyparticle-solvent systems and good dispersion can beobtained under this condition. However, some parti-cle-solvent systems are confirmed to be against thistendency. For example, the values of median diame-ter are more than 10mm in case of Al2O3-pyridine(er12.3), Al2O3-acetone (er20.7), Al2O3-acetonitrile(er37.5), Fe2O3-ethylene glycol (er37.7) and TiO2-acetonitrile (er37.5) systems. The particles in these
suspensions indicate strong f locculation in spite ofhigh dielectric constant of these solvents. On theother hand, the median diameter for Al2O3-acetic acid(er6.15), Al2O3-pentanol (er13.9) systems is lessthan 0.6mm, and good dispersion is confirmed inthese systems though these solvents have low dielec-tric constant. In case of pyridine, Al2O3 particles havestrong f locculation (median diameter 20mm), whileFe2O3 particles indicate good dispersion (mediandiameter 2mm). For almost all of metal oxide parti-cles the dispersibility of particles tend to be related tothe polarity of solvent, but there are some systems forwhich the dispersibility of particles does not obey the
KONA No.20 (2002) 265
No. Solvent e δ δd δp δh f d f p f h
1 Hexane 1.89 07.24 7.24 0.1 0.2 94 02 04
2 Cyclohexane 2.20 08.18 8.18 0.2 0.2 96 02 02
3 1,4-Dioxane 2.21 10.01 9.30 0.9 3.6 67 07 26
4 Benzene 2.28 09.02 8.95 0.5 1.0 85 05 10
5 Xylene 2.37 08.79 8.65 0.5 1.5 81 05 14
6 Toluene 2.38 08.90 8.82 0.7 1.0 84 07 09
7 Trichloroethylene 3.40 09.28 8.78 1.5 2.6 68 12 20
8 Chloroform 4.81 09.21 8.65 1.5 2.8 67 11 22
9 Acetic acid 6.15 10.45 7.10 3.9 6.6 40 22 38
10 Aniline 6.89 11.05 9.53 2.5 5.0 56 15 29
11 Pyridine 12.3 10.60 9.25 4.3 2.9 56 26 18
12 n-Pentanol 13.9 10.59 7.81 2.2 6.8 46 13 41
13 1-Butyl alcohol 17.1 11.32 7.81 2.8 7.7 42 16 42
14 1-Propyl alcohol 20.1 11.97 7.75 3.3 8.5 40 17 43
15 Acetone 20.7 09.75 7.58 5.1 3.4 47 32 21
16 Ethyl alcohol 24.3 12.98 7.73 4.3 9.5 36 20 44
17 Methyl alcohol 32.6 14.49 7.42 6.0 10.9 30 25 45
18 Acetonitrile 37.5 11.95 7.50 8.8 3.0 39 46 15
19 Ethylene glycol 37.7 16.07 8.23 5.4 12.7 31 21 48
20 Formic acid 58.5 12.18 7.00 5.8 8.1 33 28 39
21 Water 78.3 23.43 6.00 15.3 16.7 16 40 44
22 Methyl isobutyl ketone 08.31 7.49 3.0 2.0 60 24 16
23 2-(2-butoxy ethoxy) ethanol 09.97 7.80 3.4 5.2 47 21 32
24 Diacetone alcohol 10.13 7.65 4.0 5.3 45 24 31
25 2-Ethoxy ethanol 11.44 7.85 4.5 7.0 41 23 36
26 Diethylene glycol 14.56 7.86 7.5 9.7 31 30 39
27 Ethanolamine 15.35 8.35 7.6 10.4 32 29 39
Table 1 Physical properties of solvents used in this study
ε : Dielectric constant, δ : Hildebrand’s solubility parameter, δd, δp, δh : Hansen’s solubility parameter
above tendency. Furthermore, it is very interestingthat water is not the best dispersion medium for metaloxide particles.
When the particles can be regarded as a completespherical body with radius a, the van der Waals attrac-tive energy VA is expressed as follows,
VA 2 ln (9)
where x is the distance between particles (L) dividedby the radius of particle (a), and A131 is Hamaker con-stant of particles in the solvent. Therefore, it is recog-nized from Eq.(9) that the van der Waals attractiveenergy between particles increases with an increasein the value of A131. When A11 and A33 are individualHamaker constants of particles and solvent, respec-tively, the Hamaker constant of the particles in thesolvent A131 can be approximated by the followingequation,
A131(BNA11BNA33)2 (10)
The relationship between the van der Waals attrac-tive energy and the dispersibility of the particles wasinvestigated. The relationship between Hamaker con-stant of particle A131 and dielectric constant of solventis shown in Fig. 2. In case of Al2O3 and TiO2 systems,some values of A131 are as high as 101020 J in therange of dielectric constant around 5. Because the vander Waals attractive energy of them becomes large,the particles tend to f locculate under the condition.In case of Fe2O3 system, A131 values is less than101020 J through all range of dielectric constant.The results indicate that the van der Waals attractive
x(x2)(x1)2
1(x1)2
1x(x2)
A131
12
energy of Fe2O3 is small in the solvents used in thisstudy and the particles have a tendency to disperse.Though high Hamaker constants are calculated in therange of dielectric constant more than 20, the electro-static repulsive energy by charged particles affectsstrongly dispersion and f locculation. From the aboveresults, it is difficult to evaluate the dispersibility ofparticles in a solvent by using only the Hamaker con-stant.
The Hansen’s solubility parameters were used toinvestigate the dispersibility of particles without us-ing dielectric constant and Hamaker constant. Thenumeral balance of Hansen’s solubility parameters foreach solvent was calculated from Eqs. (6)(8), andthen the value was plotted in the triangular chart. Thepoints of solvents with a similar median diameterwere linked to make the isometric particle lines.
Figure 3 shows the isometric particle lines forAl2O3. The intersected point of three broken lines inFig. 3 indicates the values of fd, fp and fh of the hypo-thetical solvent in which the best dispersibility isobtained. The point is defined as the optimal dis-persible point. The same examinations were carriedout by using TiO2 and Fe2O3 particles to evaluate theapplicability of Hansen’s solubility parameters to thedispersibility of several particles. In Fig. 3, the opti-mal dispersible point can be determined to be thecenter point of the largest inscribed circle for theclosed isometric particle line comprising the solventswith the particle size of 1.04.0mm. The values of theoptimal dispersible point for Al2O3 are fd44%, fp19% and fh37%, respectively. As fd, fp and fh valuesof a solvent approach to the optimal dispersiblepoint, the dispersibility of the particles becomesbetter. The solvents causing high dispersion to Al2O3
particles are acetic acid, formic acid, 2-(2-butoxyethoxy) ethanol, 2-ethoxy ethanol, diethylene glycol,ethanolamine and 1-pentanol, respectively.
The isometric particle lines of TiO2 and Fe2O3 areshown in Figs. 4 and 5, respectively. The optimal dis-persible point of TiO2 system locates at fd49%, fp18% and fh33%, and the good solvents for TiO2 areacetic acid, formic acid, 2-(2-butoxy ethoxy) ethanoland 2-ethoxy ethanol. In the case of Fe2O3 system, theoptimal dispersible point exists at fd55%, fp22% andfh23%, and the good solvent for Fe2O3 is pyridine.From these results, the specific optimal dispersiblepoint exists for each metal oxide particle.
Generally, the affinity between the two materials isconsidered to be high when the chemical and physi-cal properties of two materials resemble each other.For example, nonpolar materials can be easily dis-
266 KONA No.20 (2002)
0 20 40 60 800
10
20
Al2O3
TiO2
Fe2O3
Dielectric constant []
Ham
aker
con
stan
t A13
1[
1020
J]
Fig. 2 Relationship between Hamaker constant and dielectricconstant of various solvents
KONA No.20 (2002) 267
fd [%] fh [%]
fp [%]
10 20 30 40 50 60 70 80 9019
44
1090
80
70
60
50
40
4.110µm1.04.0µm
0.60.9µm
5060µm
1119µm2030µm
2117
19
161413
12
23 25 20 26
27
2410
1122
15 18
3
5
461
2
8
7
9
30
37
20
10
20
30
40
50
60
70
80
90
good solvents
090 Acetic acid12 1-Pentanol20 Formic acid23 2-(2-butoxy ethoxy) ethanol25 2-Ethoxy ethanol26 Diethylene glycol27 Ethanolamine
Fig. 3 Isometric particle lines on triangular chart for Al2O3 (Each number means a solvent listed in Table 1)
fd [%] f h [%]
fp [%]
10 20 30 40 50 60 70 80 9018
49
1090
80
70
60
50
40
5.010µm
3.04.9µm
2130µm 5060µm
1.02.9µm
1120µm
2117
19
2716
1413
12
23
2520 26
2410
1122
15 18
3
5
461
2
8
7
9
3033
20
10
20
30
40
50
60
70
80
90
Fig. 4 Isometric particle lines on triangular chart for TiO2 (Each number means a solvent listed in Table 1)
good solvents
090 Acetic acid20 Formic acid23 2-(2-butoxy ethoxy) ethanol25 2-Ethoxy ethanol
solved in nonpolar solvents, but hardly dissolved inpolar solvent. On the other hand, polar materials areeasily dissolved in polar solvents, but hardly dissolvedin nonpolar solvents. It can be also said that the dis-persibility of fine particles is related with the affinitybetween a particle and a solvent. Therefore, the val-ues of fd, fp and fh of a hypothetical solvent for whichthe optimal dispersible point is obtained may corre-spond to the values of fd, fp and fh of each particleitself. When the values of fd, fp and fh of a solventapproach to the optimal dispersible point, the particleis well dispersed in the solvent.
5. Conclusion
In order to clarify the relationship between the f loc-culation/dispersion of fine metal oxide particles andthe properties of solvents, the dispersibility of TiO2,Al2O3 and Fe2O3 particles in various solvents wasinvestigated in this study.
High polar solvents tend to disperse metal oxideparticles. The Hamaker constant of particles becomeslarge in the solvent with low dielectric constant, andthen the particles have tendency to f locculate. How-ever, some particle-solvent systems do not obey thistendency. It is difficult, therefore, to evaluate the f loc-
culation/dispersion behavior by using only polarity ofsolvent or the Hamaker constant of particle.
The dispersibility of particles in various solventscan be evaluated by using the numeral balance, fd, fpand fh of Hansen’s three solubility parameters. Thevalues of fd, fp and fh of the hypothetical solvent givingthe optimal dispersion exist for each particle. As thevalues of fd, fp and fh approach to the optimal dis-persible point, the fine particles are well dispersed ina solvent. The fd, fp and fh values for an optimal dis-persible point seem to be the values of fd, fp and fh ofthe particles themselves.
Nomenclature
A Hamaker constant [J]a Particle diameter [m]fd, fp, fh Numeral balance of δd, δp, δh [%]H Enthalpy [J mol1]L Distance between particles [m]n Number of -OH group in a molecule []nD Refractive index []R Gas constant [J mol1 K1]T Temperature [K]V Molar volume [m3 mol1]γ Surface tension [N m1]
268 KONA No.20 (2002)
fd [%] fh [%]
fp [%]
10 20 30 40 50 60 70 80 9022
55
38
1090
80
70
60
50
40
1120µm
3040µm3.05.0µm
1.02.0µm
5.16.0µm
2117
19
27161413
12
2325 20 26
2410
1122
15 18
3
5
4
61
2
8
7
9
30
2320
10
20
30
40
50
60
70
80
90
Fig. 5 Isometric particle lines on triangular chart for Fe2O3 (Each number means a solvent listed in Table 1)
good solvent
11 Pyridine
δ Hildebrand’s solubility parameter []δf, δp, δh Hansen’s solubility parameters []ε Dielectric constant []µ Dipole moment [C m]
References
1) Kitahara, F. and K. Furusawa: Saishin koroido kagaku,Koudansha Scientific, Tokyo (1990)
2) Hildebrand, J. H. and R. L. Scott: The Solubility of Non-Electrolytes, Interscience, New York (1950)
3) Hansen, C. M.: The Three Dimensional Solubility Para-meter and Solvent Diffusion Coefficients, Danish Techni-cal Press, Copenhagen (1967)
4) Hansen, C. M.: J. Paint Technology, 39, 104-117 (1967)5) Hansen, C. M.: J. Paint Technology, 39, 505-510 (1967)6) Hansen, C. M.: J. Paint Technology, 39, 511-514 (1967)7) Shibata, J., K. Fujii, K. Horai and H. Yamamoto: Kagaku
Kogaku Ronbunshu, 27, 497-501 (2001)8) Shibata, J., K. Fujii and H. Yamamoto: Kagaku Kogaku
Ronbunshu, 28, 641-646 (2002)9) Bottcher, C. F. J.: Theory of Electric Polarization,
Elsevier, Amsterdam (1952)
KONA No.20 (2002) 269
Author’s short biography
Junji SHIBATA
Dr. Junji Shibata is a professor of Chemical Engineering at Kansai University. Hehas had a research interest centered in Applied Surface Chemistry including theparticle dispersion, solvent extraction, f lotation, mineral processing etc.
Katsuya FUJII
Katsuya Fujii received the degrees of BS and MSc in the Department of ChemicalEngineering at Kansai University under the supervision of Prof. J. Shibata in 1999and 2001, respectively. He is researching as a student of Doctor Course at Gradu-ate School of Kansai University. His main research work is to clarify the mecha-nism of f locculation/dispersion behavior of metal oxide particles in varioussolvents.
Norihiro MURAYAMA
Dr. Norihiro Murayama is Research Assistant in the Department of Chemical Engi-neering at Kansai University, Japan. He received the degrees of BS and MSc inChemical Engineering from Kansai University in 1994 and 1996, respectively, andgot his Ph.D. degree from the same university in 2000. His research deals with thesynthesis of inorganic materials by using various metallic wastes, such as coal ash,incineration ash, aluminum dross and so on, as a raw material.
Hideki YAMAMOTO
Dr. Hideki Yamamoto is Associate Professor in the Dept. of Chem. Eng. at KansaiUniversity, Japan. He received the degrees of BS and MSc in Chemical Engineer-ing from Kansai University in 1982 and 1984, respectively, and got his Ph.D. degreefrom the same university in 1991. He has experience as visiting professor of Dept.of Chem. Eng., Texas A&M University. His research deals with environmental pro-tection engineering such as removal of toxic materials in water, harmless disposalof global warming gas from semiconductors manufacturing process.
270 KONA No.20 (2002)
The 36th Symposium on Powder Technology
Information Articles
The 36th Symposium on Powder Technology
Subject: “Industrial Development of Nanoparticles”
Session 1 Chairperson: Prof. Hitoshi Emi (Kanazawa Univ.)• Particle Electrification Prof. Hideo Yamamoto
(KONA Award Commemorative Lecture) (Soka Univ.)• Problems and Application of Material and Prof. Yukio Yamaguchi
Bio- Nanotechnology (Tokyo Univ.)
Session 2 Chairperson: Prof. Kiyoshi Nogi (Osaka Univ.)• Control of Powder and Nanoparticle properties Prof. Makio Naito
— Key to Creation of New Industries (Osaka Univ.)• Manufacture and Application of the Fullerenes Dr. Gohei Yoshida
(Honjo Chemical Corporation)
Session 3 Chairperson: Prof. Jusuke Hidaka (Doshisha Univ.) • Aerosol Deposition Method for Thick Film Coating Dr. Jun Akedo
on Electroceramic Material (National Institute of Advanced Industrial Science and Technology)
• Particle Engineering using Nano-sized Particles and Dr. Toyokazu. YokoyamaIts Application to Drug Delivery System (Hosokawa Powder Technology Research
Institute)
The 36th Symposium on Powder Technology washeld on August 30, 2002 at the Arcadia-Ichigaya inTokyo under the sponsorship of the Hosokawa Pow-der Technology Foundation and with the support ofHosokawa Micron Corporation. The symposium in
this year was also very successful with the atten-dance of 208 with about 20 academic people. Themain subject of this year was “Industrial Developmentof Nanoparticles”.
KONA No.20 (2002) 271
The 10th KONA Award
As the winner of the KONA Award, which is spon-
sored by Hosokawa Powder Technology Foundation
and given to the scientists or groups who have
achieved excellent researches in the field of particle
science and technology, Professor Hideo Yamamoto
of Soka University was selected.
Prof. Yamamoto has achieved remarkable results in
the field of particle science and technology, which
include those on the mechanism of contact electrifica-
tion of particles and preparation of functional parti-
cles.
On January 24, 2002, Mr. Masuo Hosokawa, Presi-
dent of the Foundation, handed the 10th KONA Award
to Prof. Yamamoto at the ceremony of presentation
held at the R&D Center of Hosokawa Micron Corpo-
ration in Hirakata, Japan.
272 KONA No.20 (2002)
Author(s)
J. Oshitani, M. Kondo, H. Nishi and Z. TanakaT. Sugimoto, H. Hirose, H. Mori and J. TsubakiM. Kimata, H. Tsujikawa and K. MatsumotoH. Ueda, J. Ueda and T. Sato
Y. Mori and Y. FukumotoJ. Oshitani, B. Trisakti and Z. Tanaka
T. Umekage, S. Yuu, K. Nakashima, T. Sugimoto and J. TsubakiK. Odagi, T. Tanaka and Y. Tsuji
M. Imai, K. Kamiya, T. Hino, H. Yamamoto, H. Takeuchi and Y. KawashimaK. Terashita, C. Kyoufuji and K. MiyanamiH. Kamiya and M. Yoshida
M. Konami, S. Tanaka, A. Iwai and K. MatsumotoY. Kanda, T. Nishimura and K. HigashitaniS. Morohashi, T. Tachibana, N. Takai and K. Hoshino M. Miyazaki, M. Kitamura, M. Kamitani,J. Kano and F. Saito
Y. Kobayashi
T. Ogihara, H. Aikiyo, N. Ogata, K. Katayama, Y. Azuma, H. Okabe and T. OokawaK. Terashita and K. Miyanami
T. Hotta, T. Fukui, H. Okawa, S. Ohara,M. Naito, S. Asahi, S. Endoh and K. NogiH. Itoh
M. Suzuki, M. Kobayashi, K. Iimura and M. HirotaT. Moriwaki
K. Hayashi, M. Ohsugi, H. Morii and K. Okuyama
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Academic publication concerning powder technology in Japan (2001)
Journal of the Society of Powder Technology, Japan Vol.38 (2001)
Title
<Research Papers> Separation of Silicastone and Pyrophyllite by Gas-Solid
Fluidized Bed Utilizing Slight Difference of Density Analysis of Settling Interface Formation Process in Sus-
pension Effect of Bulk Density and Flowability of Powders on the
Feed Rate of Screw Feeder Relationship between Water-holding Capacity of Powder
and Physical Properties of Granules Prepared by Agitat-ing Granulation
Production of Silica Particles by Electrostatic Atomization Evaluation of Particle Behavior in Gas-Solid Fluidized
Bed Composed of Different Size Particles by Measure-ment of Apparent Buoyancy
Numerical Simulation of Particle Sedimentation in Liquidand Experimental Verification
Compressive Flow Property of Powder in Roll-type PressesNumerical Simulation by Discrete Element Method
Development of Agglomerated Crystals of Ascorbic Acidfor Direct Tableting by Spherical Crystallization Tech-nique and Evaluation of Their Compactibilities
Agitating Granulation and Compression Compact forCompacting Detergents
Microstructure and Surface Behavior of Silica Gel Pre-pared from Metal Alkoxide
Transport Characteristics of Ultrahigh Bulk DensityGranules by Shot Type Plug Flow Transporter
Interaction Forces between Silica Surfaces in Wet Cyclo-hexane
Release Process of Enzymes From Baker’s Yeast by Dis-ruption in Agitating Bead Mill
Grinding Aluminum Hydroxide and its Effect on Proper-ties of Hardened Cement Material Forming Calcium Alu-minate
Crystallization and Densification of Cordierite Ceramicsusing Kaolinite as Raw Material
Particle Morphology and Battery Property of LithiumManganate Synthesized by Ultrasonic Spray Pyrolysis
Kneading and Dispersion of Positive Electrode Materialsin Lithium Ion Secondary Battery for High Density Film
Particle Composite Process by a New Vessel Type Mixer
Improvement of Property of Solid Oxide Fuel Cells Anodewith Fine and Coarse Yttria Stabilized Zirconia Particles
Effect of Hydrophobic Surface Treatment of Quartz Parti-cles on Packing and Flowability of Powder
Consideration on Dynamics of Decelerated AscentMotion of Grains in Inclined Disc Pelletizer
Improved Dispersibility of Iron Oxide Particle Coated byEther-modified Poly-Siloxane for Water-based paint
KONA No.20 (2002) 273
J. Oshitani, K. Kiyoshima and Z. Tanaka
T. Tashimo, Y. Lin and K. Kato
N. Iida, K. Nakayama, I.W. Lenggoro and K. OkuyamaE. Iritani, Y. Mukai and J.H. Cho
E. Iritani, Y. Mukai and C. Ueki
K. Uchida, Y. Kuriki, K. Shimada, K. Kamiya, H. Hayakawa, A. Kawai, A. Gotoh and F. IkazakiT. Ono
T. Yoshiyasu, T. Kakiuchi, T. Yamashitaand K. FurusawaK. Yamamoto, M. Shiokari, T. Miyajima,M. Kawamura and M. Sugimoto
H. Yoshida, S. Akiyama, K. Fukui and A. KumagayaE. Usuki, N. Asai, K. Oda and S. Suzuki
T. Kawaguchi, M. Suzuki and M. Hirota
A. Ema, K. Tanoue, H. Maruyama and H. MasudaJ. Oshitani, T. Kajiwara, K. Kiyoshima and Z. TanakaE. Iritani, Y. Mukai and H. Hayashi
M. Furuuchi, C. Kanaoka and S. Hara
H. Takase and A. Kojima
K. Terashita, S. Sugimoto, T. Ohnishi and K. MiyanamiS. Ando, T. Maki, Y. Nakagawa, H. Emiand Y. Otani
M. Kitamura, T. Sahara, M. Miyazaki, M. Kamitani and M. SennaA. Hashimoto, M. Satoh, T. Iwasaki and M. Kawasaki
H. Tsunakawa
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Material Separation from Automobile Shredder Dust byPneumatic Separation Method
Effective Sulfur Dioxide Removal by Powder-Particle Flu-idized Bed Using Fine Calcined Lime Powders Reformedby Inorganic modifiers
Oxidation Behavior of Spray Pyrolyzed Ag-Pb Alloy Parti-cle
Evaluation of Compression-Permeability Characteristicsbased on Vacuum Filtration Test Using Nutsche Equippedwith Floating Disk
Concentration and Desalination of Protein Solutions withSuperabsorbent Hydrogels
Effect of Surface-treatment Additive on Particle Charac-teristics and Catalytic Activity of Molybdenum SulfidePrepared by Wet Comminution
Improved Coal Pulverization Using Embrittlement due toCracks Generated in Pores of Coal
Dispersing Abilities of New Microbial Dispersants andTheir Derivatives
Particle Discharge Characteristics from a Nozzle of ThinTube Immersed in Liquid Subject to Ultrasonic WaveForce
Particle Classification with Improved Hydro-cyclone Sepa-rator
Development of Ceramic Shaping Device with Elec-trophoretic Deposition Method
Powder Characteristics of Filler for Molding Compoundof Thermosetting Plastics
Impact Electrification of Particles with Metal Plate inNitrogen Atmosphere
Material Separation from Automobile Shredder Dust byGravity Method Using Gas-Solid Fluidized Bed
Analysis of Filtration Process of Body-Feed Microfiltra-tion Forming Compressible Filter Cake
Recovery of Valuable Materials from Wasted PrintedWiring Board by an Impact Mill
Wet Agglomeration in a Suspension of Particles of Multi-ple Materials
Basic Study on the Resource Recovery of Metal PlatingSludge and Aluminum Dross Using Thermint Reaction
Coating of Pharmaceutical Particles by Spouted Bed witha Draft Tube Control of Seed Particle Circulation Rate
Preparation of Active Hydrated Alumina by MechanicalActivation and its Application to Rapid Cement Hardener
Application of Core/Shell Type Granulation Process forPreparation of Compression Molding Granules Contain-ing Fibrous Material and Powders
Estimation of the Critical Outlet Size to prevent Arch For-mation in a Miniature Silo under Centrifugal Force
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274 KONA No.20 (2002)
E. Hilmawan, S. Mori, M. Kumita and Y. TakaoI. Taniguchi and L.C. Kuang
M. Inagaki, K. Sakai, N. Namiki, H. Emiand Y. OtaniT. Ido, M. Mori, G. Jin and S. Goto
T. Hotta, M. Naito, J. Szepvolgyi, S. Endohand K. NogiT. Tsuyuki, Y. Iida and K. Okuyama
T. Tago, T. Hatsuta, R. Nagase, M. Kishida and K. WakabayashiM. Yokota, T. Nishimura, Y. Kawasaki and M. HayashiT. Hirai and I. Komasawa
E. Hilmawan, S. Mori, M. Kumita and Y. Takao
K. Nakahira, H. Abe, M. Naito, N. Shinohara, N. Miyagawa, H. Kamiyaand K. UematsuJ. Shibata, K. Fujii, K. Horai and H. YamamotoM. Aoshima, A. Satoh, G.N. Coverdaleand R.W. Chantrell
T. Kai, K. Makado, T. Takahashi, T. Tsutsui and K. SatoS. Yuu, Y. Nakano and T. Umekage
S. Yuu, T. Umekage, S. Kawakami and Y. JohnoH. Yoshida, S. Akiyama, K. Fukui, S. Taniguchi and A. MiyatakeM. Samata
R. Nagata, K. Koga, S. Gondo, Y. Uemuraand Y. HatateH. Sato, K. Suzuki and I. Komasawa
K. Kondo, K. Shimada and Z. Tanaka
K. Mishima, K. Matsuyama, A. Furukawa, T. Fujii, J. Shida, N. Nojiri,H. Kubo and N. KatadaK. Matsuyama, S. Yamauchi, T. Hirabaru,K. Hayashi, S. Hattori and K. Mishima
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Kagaku Kougaku Ronbunshu Vol.27 (2001)
Improvement in Coercivity of Magnetic Iron Fine Parti-cles Produced from a-FeOOH
Preparation of Spinel Lithium Manganese Oxide Fine Par-ticles Using Ultrasonic Spray Pyrolysis Method
Inf luence of Fiber Cross-sectional Shape on Filter Collec-tion Performance
Effect of mechanochemical Treatment on Gasification ofCarbon by Carbon Dioxiden in Stirred Mill Reactor
Effect of Rotor Shape on Particle Composite Process by aHigh-Speed Elliptical-Rotor-Type Mixer
Correlation Equation OF Nucleate Boiling Heat Transferfrom Horizontal Cylinder to Liquid Containing MovableParticles
Preparation of Silica-Coated Co-Fe3O4 Nanoparticles andtheir Magnetic Properties
Captive Particle Imaging during Combustion and Quanti-tative Evaluation
Preparation and Microscopic Structure Control of FineParticle Materials by Using Emulsion Liquid MembraneSystem as a Microreactor
Change in Particle Morphology During ProductionProcess of Magnetic Iron Fine Particles and Its Effect onthe Product Coercivity
Effect of Ambient Conditions on the CompressiveStrength of Granules
Dispersion and Flocculation behavior of Metal OxidePowders in Organic Solvent
Orientational Distributions of a Ferromagnetic Sphero-cylinder Particle in a Simple Shear Flow Analysis for a Magnetic Field Parallel to the AngularVelocity Vector of a Shear Flow
Decrease in Fluidization Quality by Mixing Two Types ofCatalyst Particles
Direct Numerical Simulation of the Flow Fields in aMedium Reynolds Number Non-Baff led Stirred Tank(Re4,500) and Experimental Verification
Computation of Air and Particle Motion in Bubbling Flu-idized Bed Using Distinct Element Method
Fine Control of Cut Size with Dry Cyclone
A Statistical Estimation of Precision in Sampling ofAerosol Particles by the Monte Carlo Method
Preparation of Calcium Alginate Micro-Gel Beads Using aRotating Nozzle
Kinetics of Coagulation of Ultrafine Particles in ReverseMicellar and Homogeneous Solutions
Morphology of TiO2 Particles Dispersed in Zinc Elec-trodeposition
Control of Polymer Coating Thickness of MicrocapsulesContaining Inorganic Microparticles Using Cosolvency ofSupercritical Carbon Dioxide
Microencapsulation of Proteins with Polymer-Blend byRapid Expansion of Supercritical Carbon Dioxide
Author(s) PageTitle
KONA No.20 (2002) 275
Author(s) PageTitle
Preparation of Gold Nanoparticles in Water-in-OilMicroemulsions
Mechanism of Nanoparticle Formation in Hydrolysis andcondensation of tetraeyhyl Orthosilicate
Orientational Distributions of a Ferromagnetic Sphero-cylinder Particle in a Simple Shear Flow Analysis for A magnetic Field Parallel to A Shear FlowDirection
Effect of Vibration on Particle Motion in Two Dimen-sional Fluidized Bed
Y. Mori, S. Okamoto and T. Asahi
Y. Saito and M. Konno
M. Aoshima, A. Satoh, G.N. Coverdaleand W. Chantrell
Y. Takemoto, Y. Mawatari, M. Yamamotoand K. Noda
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Hosokawa Powder Technology Research Institute has been founded for the new powder business of Hosokawa Group in the future
Hosokawa Micron Corporation recently announcedthat it will enter the nanotechnology-based/nanostruc-tured material industry in order to expand its range ofbusiness opportunities through exploiting its abun-dant knowledge and experiences in the powder proc-essing technology and microengineering. In line ofthis new strategy, Hosokawa Powder TechnologyResearch Institute (HPTRI) was established in Oc-tober 2002 to further promote R&D activities, in viewof the major importance and infinite potentialities ofnanotechnology and its application.
HPTRI consists of three divisions: R&D Division,Test Centers and Powder Contract ProcessingDivision. Within the R&D Division, NanoparticleTechnology Center (NPTC) was newly established inorder to carry out research in producing and proc-essing nanoparticles. Various methods to producenanoparticles are now being examined, and some ofthem are ready for commercialization/ready for themarket. One of them is Joule Quench Method, achemical-synthetic method using plasma technologywhich was recently introduced from NanoProductsInc. Colorado, USA. In a pilot plant at NTPC inHirakata, Osaka, sample nanoparticles have been al-ready produced and distributed for customers’ useand evaluation.
Another new and original technology of HosokawaMicron is Mechano-Chemical Bonding (MCB), amethod of creating new/nanostructured materialsthrough activation of nanoparticles. The MCB proc-essing systems are available for tests at HPTRI inHirakata and its branch laboratory at HosokawaBepex Division, Minneapolis, USA.
HPTRI has two test centers, one in Hirakata, Osaka
Pref., and another in Tsukuba, Ibaraki Pref. (nearTokyo). Most kinds of test machines are available tomeet the requirements of customers.
Also incorporated into HPTRI is Hosokawa Mi-crometrics Laboratory (HMLab). Originally foundedin 1958, its main function is to carry out contractR&D projects for particle design and particle engi-neering as well as for the development of new ad-vanced machines and systems for powder processing.
The Contract Powder Processing Division is also animportant part of HPTRI, with the growing needs forthe contract powder processing, which minimizesinvestment risks by cutting construction cost of pro-duction facilities, or enabling the customer to exam-ine products in small portions.
With these comprehensive R&D systems and cen-ters, the new research institute HPTRI is sure notonly to support but also pioneer the business opportu-nities and possibilities of the present and the future.
HOSOKAWA MICRON
I ..,
Process Technologies for Tomorrow
HOSOKAWA MICRON
Headquarter Locations; HOIOKAWA MICRON COilPOIIATION
5-14, 2-chome, Kawaramachi, Chuo-ku, Osaka 541-0048, Japan Tel: 81-6-6233-3968 Fax: 81-6-6229-9267 http:/ /www.hosokawamicron.com/japan