experimental and theoretical study on the agglomeration arising from fluidization of cohesive...

Chemical Engineering Science 60 (2005) 6529–6541

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Experimental and theoretical study on the agglomeration arising fromfluidization of cohesive particles—effects ofmechanical vibration

Chunbao Xu, Jesse Zhu∗

Particle Technology Research Centre, Department of Chemical and Biochemical Engineering, The University of Western Ontario, London,Ontario, N6A 5B9, Canada

Received 28 July 2004; received in revised form 2 May 2005; accepted 15 May 2005Available online 11 July 2005

Abstract

A novel technique that can prevent the disruption of agglomerates when sampling the agglomerates from a fluidized bed has beendeveloped and has been applied to the investigation of the agglomeration behaviour of cohesive particles during fluidization with andwithout mechanical vibration. A new model for the prediction of agglomerate size has also been established on the basis of the energybalance between the agglomerate collision energy, the energy due to cohesive forces and the energy generated by vibration. The accuracyof the model is tested by comparing the theoretical results with the experimental data obtained both in the present work and in theliterature. Effects of gas velocity and mechanical vibration on agglomeration for two cohesive (Geldart group C) powders in fluidizationare examined experimentally and theoretically. The experimental results prove that mechanical vibration can significantly reduce boththe average size and the degree of the size-segregation of the agglomerates throughout the whole bed. However, the experiments alsoreveal that the mean agglomerate size decreases initially with the vibration intensity, but increases gradually as the vibration intensityexceeds a critical value. This suggests that the vibration cannot only facilitate breaking the agglomerates due to the increased agglomeratecollision energy but can also favour the growth of the agglomerates due to the enhanced contacting probability between particles and/oragglomerates. Both the experimental and theoretical results show that a higher gas velocity leads to a smaller agglomerate size.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Cohesive particles; Fluidization; Mechanical vibration; Agglomeration; Modelling

1. Introduction

The significance of particle technology is apparent in thatapproximately one-half of the products in the chemical in-dustry and at least three-quarters of the raw materials are ingranular form (Nedderman, 1992) and it is estimated thatsales of $61 billion per annum in the chemical industry arelinked to particle technology (Ennis et al., 1994). The highsurface area-to-volume ratio and other special characteris-tics of fine particles make them very attractive in the in-dustries of advanced materials, food and pharmaceuticals,etc. However, handling of these fine powders becomes muchmore difficult as their sizes become smaller. Fine particles,

∗ Corresponding author.E-mail address:[email protected](J. Zhu).

0009-2509/$ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.05.062

30�m or smaller in size, classified as group C (cohesive)particles byGeldart (1973), are generally believed to beunsuitable for fluidization since they tend to form agglomer-ates as a consequence of strong interparticle forces (Baerns,1966; Chaouki et al., 1985; Pacek and Nienow, 1990; Ushiki,1995; Horio et al., 1996). Although for submicron- or nano-particles where the interparticle force is much stronger thanthe gravitational forces, the bed of particles may exhibit astate of self-agglomerating fluidization due to the formationof stable and roughly mono-sized agglomerates (Molerus,1982; Geldart et al., 1984; Rietema, 1984; Jaraiz et al., 1992;Chaouki et al., 1985; Morooka et al., 1988), for most ofthe group C particles where the interparticle forces are notstrong enough, the agglomerates formed in fluidization areunstable and normally have a severe size segregation, lead-ing to partial fluidization or even de-fluidization (Pacek and

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6530 C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529–6541

Nienow, 1990; Wang et al., 1998; Xu et al., 2004). It thussuggests that the fluidization behaviour of cohesive particlesstrongly depends on the properties (e.g., strength, size andsize distribution, etc.) of the agglomerates arising from flu-idization and the agglomeration behaviours during fluidiza-tion (Chaouki et al., 1985; Chirone et al., 1993).Several previous experimental works (Kono et al., 1990;

Li et al., 1990; Wank et al., 2001; Xu et al., 2004) havedemonstrated that the size/size distribution of agglomeratesarising from fluidization of cohesive particles is dependentnot only on the properties of the primary particles but alsoon the fluidization conditions such as parameters of fluidiz-ing gas (gas type, humidity and velocity) and the applicationof fluidization aids (e.g., mechanical vibration). Mechanicalvibration has proved to be an effective means to help flu-idization of cohesive solids due to the breaking of channelsand agglomerates (Mori et al., 1990; Dutta and Dullea, 1991;Mujumdar, 1983;Wank et al., 2001; Xu et al., 2004). Conse-quently, vibro-fluidized beds are commonly used in powderprocessing such as mixing, granulation, drying and coating.So far, however, a comprehensive study on the agglomera-tion behaviours of cohesive particles during fluidization andthe effects of mechanical vibration are still unavailable inthe literature.Due to the fragile structures of the agglomerates, the

biggest challenge in studying the agglomeration duringfluidization is the agglomerate–sampling techniques (Nodaet al., 1998;Wang et al., 1998;Venkatesh et al., 1998; Castel-lanos et al., 1999; Wank et al., 2001; Xu et al., 2004).A “freezing” method has been developed byPacek andNienow (1990), in which the agglomerate granules werefrozen by spraying of a binder solution of wax from thetop of the bed before sampling. Another technique, calledparticle/droplet image analysis, has been recently reportedfor direct measurement of the agglomerate size in the freeboard and the region close to the upper surface of the solidbed (Wank et al., 2001). However, there exists an obviouslimitation for these two techniques in that they are only ca-pable of the size measurement for the agglomerates in thetop bed. It is thus of a great significance to develop othertechniques, which are capable of sampling the agglomer-ates, without disrupting them in either sizes or structures,from any parts of the bed (top, middle or bottom bed). Inthe present study, a novel “on-line sampling” technique hasbeen developed, the details of which will be described laterin the experimental section.It is well accepted that theoretical study is a very useful

means for exploring the mechanism governing the processesof interest. Several theoretical studies on the prediction ofagglomerate size have been reported since 1985 (Chaouki etal., 1985; Morooka et al., 1988; Iwadate and Horio, 1998;Zhou and Li, 1999), where most of the models are based onthe principle of force balance.Bergstrom (1997)proposeda very simple model, where the agglomerate size was esti-mated from the force balance between the drag force due tothe gas flow and the interparticle force (van derWaals force).

Similarly, Iwadate and Horio (1998)predicted the agglom-erate size simply by balancing the bubble-causing expansionforce and the cohesive force between agglomerates.Zhouand Li (1999)assumed that the drag force due to gas flowand the collision force between agglomerates are balancedwith the buoyant gravity and the cohesive force. The predic-tions using these force-balance-based models have shownvarious degrees of agreement with the experimental data.On the other hand,Morooka et al. (1988)came up with amodel based on an energy balance, in which it is assumedthat the agglomerate tends to disintegrate when the energygenerated by laminar shear stress and the kinetic energy ofthe agglomerate are equal to the energy required to breakthe agglomerate (i.e., the energy due to the cohesive forces).However, in their model, the minimum fluidization velocity(umf ) rather than the superficial gas velocity was used incalculating the energy generated by laminar shear stress andthe kinetic energy of agglomerates, whichmakes the reliabil-ity of the model very questionable. Obviously, more studiesare needed to ameliorate these models for precise predictionof agglomerate size in fluidization of cohesive particles.In order to clarify the mechanism governing the forma-

tion and failure of agglomerates during fluidization of fineparticles under mechanical vibration, the present study willdeal with both the measurement and the modelling of thesize of agglomerates arising from the fluidization of cohe-sive particles with and without vibration. A new model forthe prediction of agglomerate size is developed based on theenergy balance between the agglomerate collision energy,the energy due to cohesive forces and the energy generatedby vibration.

2. Theoretical analysis

The phenomenon of size-segregation of agglomerates isoften observed in fluidization of cohesive powders, result-ing in a layered structure along the bed height: the smallerand usually more stable agglomerates exist at the top, whilethe larger and looser ones are present at the bottom (Xuet al., 2004). In this regard, the efforts on modelling of theagglomerate size are only meaningful for the top-bed sta-ble agglomerates. To simplify the analysis, the followingassumptions are made: (1) the agglomerates formed are allspherical in shape, same in size with a mean diameter ofda ,and of the same properties, (2) the wall effect is neglectedand (3) the van der Waals force dominates over other typesof the interparticle cohesive forces. It is also assumed thatthe agglomerate tends to disrupt or break when the total en-ergy due to collision plus external vibration (if applied) isgreater than that due to the cohesive forces. Accordingly, thefollowing energy balance may be attained at the breakingpoint for the agglomerate

Ecoll + Evib,eff = Ecoh, (1)

C. Xu, J. Zhu / Chemical Engineering Science 60 (2005) 6529–6541 6531

where the subscripts “coll”, “vib”, “eff” and “coh” denote“collision”, “effective vibration” and “cohesion”, respec-tively.

2.1. Collision energy

Similar to the work byZhou and Li (1999), the agglom-erates are assumed to be elastic bodies, and the maximumcompression displacement� can be calculated from the elas-ticity theory (Timoshenko and Goodier, 1970)

� =(1.25V 2

nm

)2/5

, (2)

whereV is the relative velocity between two agglomeratesin a collision, andn andm are given by

n =√

8

9�2(k1 + k2)2

da1da2

da1 + da2, (3)

m = m1 + m2

m1m2, (4)

wherem1 andm2 represent themass of the two agglomeratesin the collision andk is a function of Poisson’s ratio� andYoung’s modulusE, defined as

k = 1− �2

�E. (5)

According to the assumptions made,m1 = m2 = m =1/6�d3a�a, k1 = k2 = k andda1 = da2 = da , then one has

� = (0.313V 2�2k�a)2/5da . (6)

The collision force between the two agglomerates is (Zhouand Li, 1999)

Fcoll = n�3/2. (7)

Assuming the collision force remains constant during thecollision, the collision energyEcoll is then obtained as

Ecoll = Fcoll� = n�5/2. (8)

Substitutingn and� through Eqs. (3) and (6) into Eq. (8)gives

Ecoll = 0.104��ad3aV

2. (9)

Since all the agglomerates in the bed are moving aroundwithin the bed at certain unknown velocities, to determinethe relative velocityV between the two agglomerates incollision becomes more difficult. In the studies ofIwadateand Horio (1998)andZhou and Li (1999), the relative ve-locity V was estimated by the following correlation:

V = (1.5Ps,nDbg�b)0.5, (10)

wherePs,n is the dimensionless average particle pressure,�b is the bed voidage andDb is the bubble diameter. How-ever, the calculation based on the above correlation show

that the relative velocity is as high as the superficial gas ve-locity (ug), and in some cases the calculatedV is even muchhigher thanug, which is obviously too large to be practical.On the other hand,Morooka et al. (1988)adoptedumf of theagglomerates as the relative velocityV , but this approxima-tion is also questionable since it overlooks the effect of thesuperficial gas velocity(ug) on the agglomerate size, whilethis effect is significant as will be discussed later. Since thetwo agglomerates in collision are more likely moving ina same direction along with the fluidizing gas or bubbleswithin the bed, a more reasonable understanding is that therelative velocityV should be small. Thus, in this study,V isassumed to lie between 0 and the geometric average ofugandumf , i.e.,

V = �√ugumf , (11)

where� is the factor whose value is between 0 and 1.0. Bycomparing the predictions with the experimental results,�is fixed at 0.1 in this study.umf of agglomerates (generallywith a large size) can be estimated with the conventionalcorrelation byLeva (1959)

umf = 9.23× 10−3d1.82a (�a − �g)0.94

�0.88g �0.06g

, (12)

where�g and�g are the viscosity and density of the fluidiz-ing gas.

2.2. Vibration energy

As well known, the application of an external vibration tothe fluidization will help breaking the agglomerates downto small ones, so the contribution of the vibration should beproperly taken into account. However, a quantitatively studyin this regard is not yet available in the literature. For a massms oscillating with a simple harmonic motion of an ampli-tudeA and a frequencyf, it possesses an oscillating energyof (2�msf

2A2) (Morse and Ingard, 1968). Where, it shouldbe noted that the oscillating energy of an agglomerate, dur-ing collision with the other one, will dissipate only partiallysince its oscillation sustains after collision but with a slightlydecreased amplitude or frequency due to the damping effectof the collision. In order to account for the effective part ofthe oscillating energy that contributes to break the agglomer-ates, the effective factor, i.e.,�, is adopted, and the effectiveenergy due to vibration may be assumed as

Evib,eff = �2�msf2A2. (13)

Substituting the expressionms = 1/6�d3a�a into Eq. (13)gives

Evib = �13 �3�af2A2d3a . (14)

By comparing the predictions with the experimental results,� is assumed as 0.01 in this model.


2.3. Cohesion energy

Practically, the agglomerates in collision may break upunevenly into larger parts and smaller parts, but the averagevolume of the two portions in the bed should be equal, sowe have assumed that the agglomerate breaks into two equalparts to simplify the modelling process. To break an agglom-erate into half-and-half, the tensile strength due to cohesiveforces within the agglomerate must be overcome, and theenergy required for this process is the cohesion energyEcoh.Assuming the cohesive forces remain constant during thebreaking of the agglomerate,Ecoh can be calculated as

Ecoh=∫ Z

Z0

�4d2ad, (15)

where is the tensile strength of the agglomerate, is thedisplacement of the two parts of the agglomerate at thebreakage or the distance between the two departing particles,Z0 is the initial distance between the two adjacent particlesandZ is the displacement within which the tensile strengthof the agglomerate remains in effect. According toMolerus(1982),

= 1− �a�a

Fc

d2p, (16)

where�a is the voidage of agglomerates andFc is the inter-particle forces. As has been thoroughly discussed in the lit-erature (Krupp, 1967; Hartley et al., 1985; Staniforth, 1985;Seville et al., 2000), the interparticle forces that lead to ag-glomeration of fine particles may be of several types includ-ing the van der Waals forces, electrostatic forces, interfa-cial forces due to solid bridges and liquid bridges, as wellas mechanical forces resulting from static frictional contactor interlocking of irregular particle surfaces. Any of theseforces may be dominant in a particular circumstance. Al-though the relative importance of a particular form of in-terparticle forces is strongly dependent on the fluidized bedset-up, the original properties of the particles and the flu-idization conditions (such as moisture level), it is generallybelieved that the van der Waals force is much more signifi-cant than the electrostatic force and other types of interpar-ticle forces for finer particles of a diameter<100�m in theabsence of liquid bridges (Baerns, 1966; Visser, 1989; Wangand Li, 1995). In our experiments, tribo-electrostatic chargewas not observed for all the powders tested. Furthermore,in another study by the same authors (Xu et al., 2005), wehave also tested the effect of adding very fine metal particlesas flow conditioners to fine polyester powders (10–20�m),and it turned out that the addition of these electro-conductivemetal particles did not give better results on reducing thecohesiveness of the host particles, compared with the op-erations of other types of non-conductive flow conditioners(Al2O3, silica or TiO2). This thus suggests that even for thepolyester particles, a material very favourable for build-upof electrostatic charge, the electrostatic force is not the dom-

inant force among the interparticle forces in the fluidizedbed. Therefore, it is reasonable in this study to assume thatvan der Waals forces dominate, as stated in the previous as-sumptions for the modelling. According toKrupp (1967),Fvan between two particles can be estimated as

Fvan= h�

8�2R, (17)

whereh� is the Lifshitz–van der Waals constant, andR isdefined by

R = rp1rp2

rp1 + rp2, (18)

whererp1 andrp2 are the asperity radii for the two particlesin contact. By assuming the particles to be with smoothsurfaces,rp1 andrp2 can be radii of the particles, i.e.,rp1=rp2 = ra = dp/2 (Krupp, 1967; Morooka et al., 1988) andR=dp/4. By taking the number of contact points per particle(nc=1.61�−1.48

a ) (Jaraiz et al., 1992) into account, the overallcohesive forces per particle(Fc) becomes

Fc = ncFvan= 1.61�−1.48a

h�

8�2R. (19)

SubstitutingR = dp/4 into Eq. (19) and the substitutingEq. (19) into Eq. (16), one has

= 1.61�−1.48a

1− �a�a

1

dp

h�

32�2. (20)

Replacing h� with the Hamaker constantAH(h� =(4�/3)/AH ) (Krupp and Sperling, 1966; Krupp, 1967) gives

= 1.61�−1.48a

1− �a�a

1

dp

AH

242. (21)

Substituting Eq. (21) into Eq. (15) gives

Ecoh=∫ Z

Z0

�4d2a1.61�

−1.48a

1− �a�a

1

dp

AH

242d

= �96

d2a1.61�−1.48a

1− �a�a

AH

dp

(1

Z0− 1

Z

). (22)

The distance of maximum attraction or the initial distancebetween two particles at the point of contact,Z0, is normallychosen as 4A(=4× 10−10m). This value can be justifiedby the fact thatZ0 = 4A is slightly larger than the latticeconstant of weekly van derWaals-bonded molecular crystals(Krupp and Sperling, 1966; Krupp, 1967). Consequently,Z0is assumed as 4A in this work, andZ is arbitrarily assumedto be far larger thanZ0, i.e.,Z � Z0. With this hypothesis,Eq. (22) can be reduced to

Ecoh= �96

d2a1.61�−1.48a

1− �a�a

AH

dp

1

Z0. (23)

The Hamaker constantAH can be estimated by the followingequation (Israelachvili, 1992):

AH = 3

4kBT

(�1 − �0�1 + �0

)2

+ 3hve16

√2

(n21 − n20

)2(n21 + n20)

3/2 , (24)


wherekB is Boltzmann’s constant(kB=1.381×10−23J/K),T is the absolute temperature and�1 (�0) and n1 (n0) arethe dielectric constant and refractive index of the particulatematerials (the medium where the particles are present) (forvacuum or air,�0 = n0 = 1.0). Here,h is Planck’s constant(=6.626×10−34J s) and�e is the main electronic absorptionfrequency in the UV region, typically at around 3×1015s−1.Hence, for the particulate materials fluidized in air, Eq. (24)is rewritten as

AH = 1.036× 10−23T

(�1 − �0�1 + �0

)2

+ 2.635× 10−19 (n21 − n20)2

(n21 + n20)3/2 . (25)

The agglomerate voidage (�a) can be determined indirectlyfrom the agglomerate density (�a) and the particle density(�p)

�a = 1− �a/�p. (26)

Here, the value of�a can be obtained by direct measurement,but the experimental results ofZhou and Li (1999)havedemonstrated that�a for cohesive particles is approximatelybetween 1.15 times the aerated density (�ba) and 0.85 timesthe tapped density (�bt ) of the primary particles, dependingthe bonding strength of the agglomerate. To simplify,�a inthis study is approximated by�bt of the primary particles.Substituting Eqs. (9), (14) and (23) into Eq. (1) results in

da =�961.61�

−1.48a

1−�a�a

AH

dp

1Z0

0.104��aV2 + �13�

3�af2A2

. (27)

It should be noted that the relative velocity of agglomerates(V ) is of da dependence, referring to Eqs. (10)–(12), so thatEq. (27) must be solved by an iterative approach.

3. Experimental

The vibro-fluidized bed setup used in this study con-sists of a fluidized bed column made of Plexiglas (38mmi.d. and 500mm tall), a vibration generation system, a data

Table 1Fine powders used for fluidization experiments

Powders dpa Density (kg/m3) RH

b AORc,d Geldart group

(�m) �p �bld �ba

d (deg)

CaCO3 5.5 2700 1160 520 2.23 50.0 CTalc 4.1 2710 360 170 2.12 48.4 C

aThe volume-weighted mean diameter by laser diffraction (Malvern Mastersizer 2000).bRH (Hausner ratio)=�bt /�ba .cAOR, angle of repose.dAnalyzed by a Hosokawa Powder Tester.

acquisition system, and a gas flow control system. Com-pressed air stripped of trace humidity through a fixed bedof silica gel is used as the fluidizing gas, whose flow rateis controlled by a series of rotameters (Omega EngineeringInc.) and a digital mass flow controller (Fathom Technolo-gies, GR series). All the flowmeters are carefully calibratedwith a Wet Test Meter (GCA/Precision Scientific) beforeusing. A porous polymer plate serves as the gas distribu-tor. Pressure drops across the whole bed are measured witha differential pressure transducer (Omega PX163 series).Mechanical vibration is generated by a pair of vibratorsdriven by an ABB inverter with a vibration frequency (f)varying from 0 to 50Hz. Through changing the unbalancedweights of the vibrator, various amplitudes (A) between 0and 3mm (depending on the frequency used) can be ob-tained. In the present work, the vibration frequency and am-plitude are set at 50Hz and 0.3mm, respectively, unlessspecified otherwise.The fine particulate materials used are cohesive fine par-

ticles of Talc(4.1�m) and CaCO3 (5.5�m), which are typi-cal Geldart group C powders, whose key physical propertiesare listed inTable 1. The particles are loaded to the bed toa fixed height of about 100mm, and the whole particle bedis first loosened by a gas flow at 2.0 cm/s for 10min beforethe experiments start. In the case of no vibration, when thefluidization is attempted by slowly increasing the gas veloc-ity, the bed first behaves as that typical of group C particles,i.e., plugging and channelling, until a certain bed pressurebuilds up causing the particle bed to fracture. As the gas ve-locity increases further, the bed comes to a transition regionduring which the particles at the top-bed start to fluidize andself-agglomeration develops gradually, leading to the even-tual fluidization and agglomeration of the whole bed. On theother hand, the application of the vibration significantly im-proves the fluidization, e.g., the plugging, channelling andfracturing of the bed disappear and the agglomerate size de-creases, leading to smoother fluidization and higher pressuredrops.In order to sample the agglomerates out of the bed for

characterization while avoiding disrupting their size, shapeand structures, a novel “online sampling” technique that isillustrated inFig. 1 has been developed and applied to this


Fig. 1. Diagram of the “online agglomerate sampling” technique: (a)sampling the agglomerates from the top layer of the bed; (b) removingthe agglomerates from the upper layer by vacuum prior to the samplingfor the agglomerates on the lower layer.

study. The agglomerates are sampled in situ, without stop-ping the fluidizing gas or making any other changes to thefluidization conditions (e.g. gas velocity and vibration if ap-plicable), and with a sampling ladle from the top of thecolumn. To sample the agglomerates in the upper region ofthe bed, the ladle is used to pick up the agglomerates di-rectly. As for the agglomerates in the middle and bottomregions, an intensity-controllable vacuum is used to removeall the particulate materials very carefully above the sam-pling plane. More particles are removed as the measure-

20 40 60 80 100 120 140300

350

400

450

No vibration

Talc(4.1µm)

With vibration (30Hz/0.3mm)

da

(µm

)

t (min)

Fig. 2. Changes in mean diameters of the top-bed agglomerates of Talc(4.1�m) with fluidization time in air at 9.4 cm/s.

ments are continued further to the lower planes of the bed.In the experiments, the operations of both the agglomeratesampling and the vacuum agglomerate removal were manu-ally but carefully performed. In sampling the agglomeratesfrom the top layer of the bed with the ladle, particular carewas taken to avoid breaking the agglomerates during thesampling. In removing the agglomerates with the vacuumprobe, the suction intensity was controlled (by adjusting ei-ther the suction flow rate or the working distance betweenthe tip of vacuum probe and the suction objects) to be highenough to “pick up” all the agglomerates in the upper layerbut low enough to avoid removing the agglomerates in thelayer below. The agglomerates captured in the sampling la-dle were poured carefully onto a metal disk (4 cm in diam-eter), followed by gold plating and measurement of theirshape/size by scanning electronic microscopy (Hitachi SEMS-2600N). The mean agglomerate size is obtained by takingthe arithmetic average of over 100 agglomerates from onesample.In the present study, two experimental runs were carried

out for each given condition. The error of the average ag-glomerate diameter between two tests with the same pow-der under the same fluidization conditions was within therange of±(10.15)%, giving acceptable reproducibility forthis technique.Since the self-agglomeration of fine particles during flu-

idization is a dynamic process governed by the growing ofthe agglomerates due to the cohesive forces and the fractur-ing of the agglomerates due to the breaking forces, it maytake a certain length of time to achieve stabilization of theagglomerates in size and shape under certain fluidizationconditions (gas velocity, vibration intensity, etc.). The stable


sizes of agglomerates are particularly important and moremeaningful for the modelling of the self-agglomeration ofcohesive particles in fluidization. It is thus highly necessaryto first determine the stabilization time for the agglomerationprocess. Upon obtaining the stabilization time, one can fur-ther determine the sampling time, i.e., the fluidization timefor the particles before sampling the formed agglomeratesout for characterization. The sampling time should be equalto or longer than the stabilization time for the agglomerationprocess. In this regard, experiments are carried out using theTalc (4.1�m) powder fluidized in air at 9.44 cm/s with andwithout vibration (30Hz/0.3mm). The agglomerates formedduring fluidization are sampled from the top-bed after vari-ous lengths of time. The mean diameters of the agglomeratesat the fluidization time of 30, 60 and 120min are illustratedin Fig. 2. The results show that the sizes of the agglomer-ates attain a stable value after about 60min of fluidizationno matter whether the vibration is applied or not. It is thussafe to set the sampling time at 120min in every case.

Fig. 3. Microphotographs of the top-bed agglomerates of (a) CaCO3 at 18.88 cm/s and (b) Talc at 9.4 cm/s in air for 2 h without vibration: scale barsare 1mm and 50�m for the overhead views and close-up views, respectively.

4. Results

Fig. 3shows the overhead and the close-up pictures of thetop-bed agglomerates for CaCO3 (5.5�m) andTalc(4.1�m)

powders at specific superficial gas velocities in air withoutvibration. Clearly, with the new “online sampling” tech-nique, the original shapes and structures of the agglomeratesamples are well maintained. From the overhead pictures forthe agglomerates of the two powders, it can be seen that theagglomerates formed at the top-bed are in a good sphericalshape with a diameter of 200–500�m under the fluidizationconditions stated above. In particular, the sphericity of theagglomerates of Talc(4.1�m) is almost perfect. On theother hand, the microstructures of the agglomerate surfacesare clearly shown in the close-up pictures. The surfacesof both agglomerates show the structures of floc or den-drite, which may reveal one of the possible mechanismsgoverning the self-agglomerate formation during fluidiza-tion as has also been proposed in other previous works by


Fig. 4. Segregation for the agglomerates along the bed height for Talc(4.1�m) powder fluidized at 9.4 cm/s in air for 2 h (a) without and (b) with vibration.

Princen (1968), Vold (1960) and Wang (1995). The ag-glomerate formation in fluidization may be associated withthe following sequential steps: growing of the individualchains from the seed particles, growing of the dendritesfrom the individual chains, and formation of an agglom-

erate by folding of the dendrites due to collision andthe binding forces between dendrite/dendrite, agglomer-ate/agglomerate or dendrite/agglomerate. Despite the wideapplication of the fine particles in industries and the grow-ing interest of the research in fluidization of fine particles,


0

20

40

60

80

100

No vibration With vibration (30Hz/0.3mm)

Top

0

20

40

60

80

100 Middle

1000

20

40

60

80

100

50002000500

Bottom

da (µm)

Nu

mb

er%

un

der

siz

e

(a)

(b)

(c)

Fig. 5. Size distributions of the agglomerates sampled at (a) the top-bed;(b) middle-bed and (c) bottom-bed for Talc(4.1�m) powder fluidized at9.4 cm/s in air for 2 h with and without vibration.

the mechanisms governing the self-agglomeration for co-hesive particles during fluidization remain poorly under-stood, and more studies are obviously necessary in thisregard.Fig. 4 shows the microscopic photos of the agglomer-

ates sampled from the top, medium and bottom of the bedof the Talc particles(4.1�m) after being fluidized in airat 9.4 cm/s for 2 h with and without mechanical vibration(30Hz/0.3mm). Under no vibration, the maximum size ofthe top-bed agglomerates is around 600�m and the bottom-bed agglomerates around 6000�m. Under vibration, how-ever, the maximum sizes of the top-bed and the bottom-bed agglomerates are significantly reduced to around 500and 550�m, respectively. This observation shows a muchmore severe segregation of agglomerate size along the bedheight without vibration than that with vibration. The statis-tical size distributions of the agglomerate samples inFig. 4can be illustrated inFig. 5. It is found that the size distri-

0.0 0.5 1.00

500

1000

1500

2000

2500

3000

Top-bedBottom-bed

No vibration

Talc(4.1µm)

With vibration (30Hz/0.3mm)

da

(µm

)

z/Z0 (-)

Fig. 6. Changes in mean diameters of the agglomerates sampled in dif-ferent positions along the bed height for Talc(4.1�m) powder fluidizedin air at 9.4 cm/s for 2 h with and without vibration.

bution of the agglomerates sampled at any position of thebed is narrowed when applying the vibration, which indi-cates a reduced degree of the size-segregation. Moreover,the mean diameters of the agglomerates, calculated fromFig. 5, are plotted inFig. 6 against the different samplingpositions along the bed height. Clearly, both the averagesize and the degree of the size-segregation of the agglom-erates throughout the whole bed are significantly reduceddue to the vibration, the latter of which may be particularlyimportant for improving the fluidization quality of cohesiveparticles.With the mathematical model (Eq. (27)) developed in the

previous section, the agglomerate sizes for cohesive pow-ders can be calculated through the iterative approach. For theTalc (4.1�m) powder, for example, the calculated sizes ofthe top-bed agglomerates are 390 and 247�m, respectively,at a fluidizing gas velocity of 9.4 cm/s in air without andwith vibration (30Hz/0.3mm). The accuracy of the modelis tested by comparing the theoretical results with the ex-perimental data obtained both in the current work and in theliterature, as shown inTable 2. The experimental conditionsand the related parameters used in modelling are listed inTable 3. For the Talc and CaCO3 powders investigated in thiswork, the calculated results are in an acceptable agreementwith the experimental data regardless of whether or not thevibration is applied. For the other powders including TiO2(0.6�m), SiO2 (4.6�m) and SiC(1.82�m) by Zhou and Li(1999)and TiO2 (0.27�m) by Iwadate and Horio (1998),the calculation results are also in a reasonable agreementwith the experimental data.


Table 2Comparison between modelling results and experimental data of agglomerate size

Authors Powder da(�m) da,ca,b (�m)

No vibr. With vibr.c No vibr. With vibr.c

This work Talc 425 382 390 (−8%) 247 (−35%)CaCO3 362 326 230 (−36%) 190 (−42%)

Zhou/Li (1999) TiO2 482 n.a.d 415 (−14%) n.a.SiO2 300 n.a. 252 (−16%) n.a.SiC 597 n.a. 330 (−45%) n.a.

Iwadate/Horio (1998) TiO2 441 n.a. 560 (+27%) n.a.

aModelling (calculated) results.bThe number in the parenthesis is the % error between the calculation and the experimental data.cf = 30Hz, A = 0.28mm.dNot applicable.

Table 3Experimental conditions and parameters used in modelling

Authors Powder �p dp n1a �1a Dc u �a

(kg/m3) (�m) (m) (m/s) (kg/m3)

This work Talc 2720 4.1 1.79 1.0 0.038 0.094 357CaCO3 2700 5.5 1.64 8.0 0.038 0.189 1164

Zhou/Li (1999) TiO2 3880 0.6 2.46 114 0.033 0.52 1229SiO2 2000 4.6 1.54 3.7 0.033 0.32 217SiC 3210 1.82 2.56 10.2 0.033 0.52 1068

Iwadate/Horio (1998) TiO2 4250 0.27 2.46 114 0.044 0.46 1700

aFrom Bergstrom (1997).

5. Discussion

5.1. Effect of gas velocity

The velocity of the fluidizing gas is generally believedto be one of the most important factors affecting the ag-glomeration of fine particles during fluidization. However,the effect of the gas velocity on agglomeration is still de-batable. On the one hand, it has been suggested that thefluidizing gas velocity has little effect on the agglomeratediameter (Chaouki et al., 1985; Kono et al., 1987; Morookaet al., 1988); and on the other hand, the models proposed byIwadate and Horio (1998)and byZhou and Li (1999)sug-gest that a reduction in agglomerate diameter should occurwith increasing gas velocity. Clarifying the effect of gas ve-locity on agglomeration is significant for understanding theagglomerating behaviour of cohesive particles in fluidiza-tion or for exploring the mechanisms governing the forma-tion and failure of agglomerates during fluidization. In thisregard, experimental and theoretical studies are carried outusing Talc(4.1�m) powder fluidized under a mild vibrationcondition (15Hz/0.3mm) in air at a varying gas velocity of6.5, 9.4 and 14.2 cm/s. The mean diameters of the agglom-erates sampled at the top bed are plotted against the gasvelocity in Fig. 7, wherein the modelling results are also il-lustrated comparatively. Although with noticeable deviationbetween the experimental data and the simulation, the modelcan predict a same trend that was observed by experiments,

0 5 10 15 20 25 30 35 40 45 500

200

400

600

800

15Hz/0.3mm

Talc(4.1µm)

Experimental

Modelling

da

(µm

)

ug (cm/s)

Fig. 7. Effect of gas velocity on mean diameters of top-bed agglomeratesfor Talc (4.1�m) powder fluidized in air under vibration (15Hz/0.3mm).

i.e., the agglomerate size decreases with increasing gas ve-locity. This result strongly supports the previous conclusionmade byIwadate and Horio (1998)andZhou and Li (1999).


It is well accepted that the self-agglomeration of fine parti-cles during fluidization is a dynamic process between grow-ing of the agglomerates due to the cohesive forces and frac-turing of the agglomerates due to the breaking forces suchas the collision force between particles and/or agglomeratesgenerated by the fluidizing gas. A higher gas velocity there-fore tends to generate larger breaking forces, which mayresult in a smaller agglomerate size.

5.2. Effect of vibration intensity

In general, as has been shown inFigs. 4–6 andTable 2inthe previous section, the effect of vibration on agglomera-tion is evident, i.e., the vibration significantly reduces boththe average size and the degree of the size-segregation ofthe agglomerates in the whole bed. Another factor that mayaffect the agglomeration behaviour of cohesive particles influidization under vibration would be the vibration inten-sity, which is closely related with the vibration frequency(f) or amplitude (A). To quantify the vibration intensity, thevibration strength,�, defined as the ratio of acceleration ofvibration to that of gravity, i.e.,� = A(2�f )2/g, is used.From the present model (Eq. (27)), it may be concluded thata larger vibration intensity by increasing eitherf or A maylead to a smaller agglomerate size. However, this is neverthe case from the experimental data obtained, as shown inFig. 8. In this figure, the experimental and modelling resultsof the mean agglomerate sizeda for CaCO3 (5.5�m) at18.9 cm/s and Talc(4.1�m) at 9.4 cm/s are plotted againstthe vibration strength�. A reasonable agreement of themodelling results and the experimental data is shown for�lower than 0.25, showing a similar trend thatda decreaseswith �. When the vibration intensity increases further, how-ever, the experiments show that the mean agglomerate sizedoes not decrease but increases gradually with the vibrationintensity. Discrepancy between the modelling and experi-mental results becomes larger at a higher�. This suggeststhat precise prediction of agglomerate size for fluidizationof cohesive particles under mechanical vibration is difficultbecause the effect of vibration on agglomeration appears tonever be monotonic. The following gives a possible expla-nation: as has been discussed in the previous sections, theself-agglomeration of fine particles during fluidization is adynamic process between growing of the agglomerates andfracturing of the agglomerates. The experimental data shownin Fig. 8 suggest that the effect of vibration on agglomer-ation is two-sided. On the one hand, the additional energyintroduced to the bed due to the vibration can help to breakthe agglomerates, leading to a smaller agglomerate diame-ter. On the other hand, the vibration increases the contactingprobability between particles and/or agglomerates, whichthus favour the growth of the agglomerates in fluidization ofthe cohesive particles where the interparticle forces are verystrong. These two contrary effects compete with each otherduring the process of self-agglomeration in fluidization.

100

200

300

400

500

600

700

da

(µm

)

CaCO3 (5.5µm)

Experimental

Modelling

da

(µm

)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

100

200

300

400

500

600

700

� (-)

Talc (4.1µm)

(a)

(b)

Fig. 8. Effect of vibration intensity on mean diameters of top-bed ag-glomerates (a) for the 5.5�m particles of CaCO3 at 18.9 cm/s and (b) forthe 4.1�m particles of Talc at 9.4 cm/s.

Under these circumstances, the experimental data regardingthe effect of vibration intensity on agglomerate size canthus be accountable: at lower vibration intensities the for-mer effect can be predominant, while the latter may becomepredominant at higher intensities.

6. Conclusions

Due to the strong inter-particle forces, the handling of co-hesive powders in industries always suffers from the severeproblem of agglomeration, which often leads to poor flu-idization or even complete de-fluidization when attemptingto fluidize these particles. Mechanical vibration proves to bean effective means to help fluidization of the cohesive solids.However, a comprehensive study on the self-agglomerationof cohesive particles during fluidization, and the effect ofmechanical vibration on agglomeration behaviours did notreceive enough attention previously. In this study, a novel“on-line sampling” technique, which is able to prevent theagglomerates from being disrupted during sampling, hasbeen developed. Effects of gas velocity and mechanicalvibration on the self-agglomeration during fluidization ofcohesive particles have been examined experimentally andtheoretically using Talc(4.1�m) and CaCO3 (5.5�m) pow-ders. A new model for prediction of agglomerate size hasalso been established on the basis of on an energy balance,


where the collision energy between agglomerates, the en-ergy due to cohesive forces and the energy generated byvibration are taken into account. The accuracy of the modelis tested by comparing the theoretical results with the ex-perimental data obtained both in the present work and in theliterature. For the two powders investigated in this work, thecalculated results agree satisfactorily with the experimentaldata regardless of whether or not the vibration is applied.The results of the calculations are also within reasonableagreement with the experimental data by others. Withoutvibration, a severe segregation of agglomerate size alongthe bed height has been observed with small agglomeratesexisting at the top and bigger ones at the bottom. When thevibration is applied, both the average size and the degreeof the size-segregation of the agglomerates throughout thewhole bed are significantly reduced. Both experimental andtheoretical studies show that a higher gas velocity leads toa smaller agglomerate size. Meanwhile, it is found that theeffect of vibration is much more complicated. The meanagglomerate size decreases initially with the vibration in-tensity, but increases gradually when the vibration intensityexceeds a critical value. It thus suggests that the effect ofvibration on agglomeration in fluidization of the cohesiveparticles is two-sided: it can help to break the agglomeratesdue to the additional vibrational energy, and it can alsofavour the growth of the agglomerates due to the enhancedcontacting probability between particles and/or agglomer-ates. These two sides of the effect are competing during theself-agglomeration process in fluidization of cohesive par-ticles under vibration, one of which may become dominantdepending on the vibration intensity.

Notation

A amplitude of vibration, mAOR Angle of repose, degAH Hamaker constant, Jdp mean-particle size, mdai diameter of agglomeratei (i = 1,2), mDb bubble diameter, mDc diameter of fluidized bed, mE Young’s modulus, PaEvib energy generated by vibration, JEcoll collision energy between agglomerates, JEcoh cohesion energy of agglomerates, Jf frequency of vibration, HzFc cohesive force, NFcoll collision force, NFvan the van der Waals force, Ng gravity acceleration, 9.81m/s2

h Planck’s constant(=6.626× 10−34J s)ki function of Poisson’s ratio andYoung’s mod-

ulus, Pa−1

kB boltzmann’s constant(=1.381× 10−23J/K)

L0 static (unexpanded) bed height, mm function defined by Eq. (4)ms average mass of agglomerate, kgmi mass of agglomeratei (i = 1,2), kgn0 refractive index of medium, dimensionlessn1 refractive index of the solids, dimensionlessn function defined by Eq. (3)Ps,n dimensionless average particle pressurerpi asperity radii for particlei (i = 1,2), mra asperity radius for particle, mR parameter used inFvan calculation, dimen-

sionlessRH Hausner ratio(=�bt /�ba), dimensionlessT absolute temperature, Kug superficial gas velocity, m/sumf minimum fluidization velocity, m/sV relative velocity of agglomerates, m/sZ0 initial distance between two particles, mZ the maximum displacement within which the

tensile strength of the agglomerate remainsin effect, m

Greek letters

� maximum compression displacement, m the displacement of the two parts of the

agglomerate at the breakage, m�b average bed voidage, dimensionless�a agglomerate voidage, dimensionless�0 dielectric constant of medium, dimensionless�1 dielectric constant of the solids, dimension-

less� the effective factor for vibration energy, di-

mensionless� vibration strength, dimensionless�g gas viscosity, kg/m/s� Poisson’s ratio�e main electronic absorption frequency in the

UV region� the dimensionless factor in Eq. (11), dimen-

sionless�ba aerated bulk density, kg/m3

�bt tapped bulk density, kg/m3

�p apparent particle density, kg/m3

�g gas density,kg/m3

�a agglomerate density, kg/m3

tensile strength of the agglomerate, Pah� Lifshitz–van der Waals constant, eV

Acknowledgements

The authors are grateful to the Ontario Research andDevelopment Challenge Fund for supporting this study.


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Further reading

Mori, S., Wen, C.Y., 1975. Estimation of bubble diameter in gaseousfluidized Beds. A.I.Ch.E. Journal 21, 109.

experimental and theoretical study on the agglomeration arising from fluidization of cohesive...

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