University of Alberta

DETERMINATION OF THE PHYSICAL PROPERTIES OF MELTS

STEVEN JOBN ROACH 0

A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfilhent

of the requirements for the degee of Master of Science in Chemical Engineering.

Department of Chemicai & Materiais Engineering

Edmonton, Alberta

Spring ZOO1

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ABSTRACT

It has been determined that surface tension is required in quantimg the fluid

dynamics of a stream exiting an orifice under the innuence of gravity under certain

circumstances. Liquids of high d a c e tension (i.e. melts) and low density typically

exhiiit low Bond numbers and indicate situations where surface tension must be included

in the formulation relating flow rate and head with the discharge coefficient.

A new formulation is presented that relates experimental qwtit ia of head and

flow rate, with d a c e tension, viscosity and density, facilitahg the calculation of dl

three properties. Experiments perfomed with molten aluminum as a f'unction of

temperature indicate that d a c e tension and density is within 6.5% and 2.5%

respectively of values obtained in the Iiterature. The viscosity has been d e t d n e d to be

significantly less than data reported fiun other sources. Resuits are aiso presented for

A29 1 D magnesiun alIo y.

The author wishes to thank his supervisor, Dr. Hani Henein, for his continuous

support, guidance, and dedication during the course of his degree. The author is also

indebted to his committee rnembers consisting of Dr. Suzanne Kresta, Dr. Zhenghe Xu,

Dr. Janet Elliott, and Dr. Tom W. Forest who have proven to be an excellent source of

information and guidance during the completion of this work. The author would like to

thank David Leon and other employees ûom Alcoa hc. for producing an excellent

collaborative effort. Financial support fiom the National Research Councii of Canada

made this work possible.

The Advanced Materials and Processing Laboratory provided an environment

where others contributeci significantly to the completion of this Thesis. Many Giendships

where forged in the process. The support of Dr. B. Wiskel, Craig Owens, A&d Prasad,

Manual Reider, Tuyet Le, Zaheer Champsi, and many others past and present is a

comastone of the author's expkence at the University of Alberta. Others in the

department to be acknowledged for design work and technical support are Bob Smith,

Bob Konzic, Bob Scott, and Walter Bodda. The author dso appreciates the aid of the

Business Development Bank of Canada in Toronto for services rendered durhg the

prùlting of this document.

Finally, the author wishes to express his gratitude to his family for the continuous

love and support. Thanks Mom, Dad and Mark.

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION

CHAPTER 2: LITERATURE REVIEW

Surface Tension of Molten Metals

2.1.1 Gibbs Adsorption Equation: Effects of Composition

2.1.2 Dependence on Temperature

2.1.3 Dynamic Surface Tension

2.1 A Techniques to Measure Surface Tension

2.1.5 Experimentai Data

Viscosity of Molten Metds

2.2.1 Theoreticai Determination of Vicosity

23.2 Techniques to Measure Viscosity

2.23 Experimental Data

Density of Molten Metals

23.1 Techniques to Measure Density

2 3 3 Experimental Data

The Saybolt Viscorneter

Conclnsions

CaAPTER 3: EXPERIMENTAL

3.1 Low Temperature Apparatus

3.1.1 Orifice Plates

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1

6

6

9

18

21

23

34

42

43

44

47

50

51

54

55

61

63

63

66

3.13 Procedure for Low Temperatme Experiments

3 3 Overview of High Temperature Apparatus

3.2.1 Orifice Plates

3.2.2 crucibles

3.23 Induction Furnace

33.4 PurgingGas

3.2.5 Metal Selection

3.2.6 Data Acquisition System

3.2.7 Oxygen Anaiyzer

3.2.8 Procedure for High Temperature Experiments

3.3 Conciusioas

CHAITER 4: CEIARACTERIZATION OF FRICTIONAL LOSSES

Flow From a Draining Vessel: Negiecting Surface Tension

4 . 1 Formnlstion

4.1.2 Results

Flow From a Draining Vessel: A New Approach

4.2.1 Formulation

4.2.2 Resuits

Considerations for High Temperature Fluids

Conclusions

CHAPTER 5: FORMULATION OF PHYSICAL PROPERTY MEASUREMENTS

5.1 Formulation of Surface Tension Merisurements: Fluids with Known Density and Viscosity

5.1.1 Error Andysis

5.12 Data Anilysis

5.1 3 Surface Tension of Water at 32 1.5 K

5.2 Formuiation for Simultaneous Determination of Surface Tension, Viscosity, and Density

5.2.1 Error Andysis

5.2.1.1 Surface Tension 52.1.2 Density 5.2.13 Viscosity 5.2.1.4 Surnmuy of Propagation of Errors

5.2.2 Data Analysis

5 3 3 The Surface Tension, Viscosity and Density of Aluminum at 1073 K

53 Conclusions

CEiAP'ïER 6: DISCUSSION

6.1 Density

6.1.1 Density of Afaminum

6.13 Density ofAZ91D

63 Viscosity of Aluminum and AZSlD Anoy

6 3 Stuface Tension

63.1 Surface Tension o f Alumintm

63.2 Surface Tension of AZ91D Ailoy

CHAPTER 7:

REFERENCES

APPENDIX A:

APPENDEX B:

APPENDIX C:

APPENDIX D:

MULTIPLE NON-LLIYEAR REGRESSION PROGRAM

SURFACE TENSION AND VISCOSITY OF ALUMINCTM (REGRESSION ON ALL THREE PROPERTIES)

OXYGEN PARTIAL PRESSURE

LIST OF FIGURES

Figure 2.1 :

Figure 2.2:

Figure 2.3:

Figure 2.4:

Figure 2.5:

Figure 2.6:

Figure 2.7:

Figure 2.8:

Figure 2.9:

Figure 2.10:

Figure 2.1 1:

Molecular forces acting at an interface separating a liquid from a gas.

Interface region representing the concentration gradient that exisit between phases a and p.

Surface energy for a varie@ of fluids plotted against the respective heats of vaporization [l O].

Surface tension of Al-based alloys as hctions of alloying composition at 973 K. Atmosphere and oxygen concentration are not specified. (From Lang, G. [ 1 11).

E f k t of oxygen present as a solute on the surface tension of molten iron. Temperature and atmosphere are not specified. (From Keene, B.J. [7]).

Effects of oxygen present in the gas phase on the surface tension of copper. Temperature and atmosphere are not specified. (From Keene, B.J. [q).

a) Interface region separating phases a and p. b) Dividing surface used in Gibbs Mode1 approximating the interface region separating phases a and p.

Surface tension of iron-3% carbon alloy with varying concentrations of chromium at 1623 K. Atmosphere and oxygen concentration are not specified. (Rom Whalen et al. [ 1 51).

Temperature dependence of d a c e tension as a hc t ion of lead concentration exhibithg positive values for do/dT. Temperame, atmosphere, oxygen concentration are not specified. '(Rom Joud and Passerme, [5]).

Characteristic times of a 0.01m diameter droplet to be saturateci with oxide at a total pressure of oxygen of lPa, for various metaliic systems (Rom Ricci et al. [40]).

Dimensions of sessüe droplet required for caldation using the analysis approach of BasMord and Adams [42].

Page #

7

8

9

10

11

12

14

Figure 2.12: Dimensions of pendant droplet required for calculation using formulation by Andreas et al. [43] (From lida and Guthne, [2]).

Capillary rise method for detennining the surface tension of a liquid.

Figure 2.13:

Sdace tension of high purity aluminum, and alumiaum deliberately cootaminated with oxygen (From Levin et al. [19]).

Figure 2.14:

Surface tension of aluminm and a l d a as a hc t ion of temperature, quoted fiom a variety of sources (From Kaptay [8]).

Figure 2.15:

Surface tension dependence on the coverage of N203 of pure aluminum detemiined experimentally [32], and theoretically [37] at 973 K.

Figure 2.16:

Surface of duminum subjected to coverage of Alz03: a) X < 0.3; b) X > O.S.

Figure 2.17:

Velocity profile of fluid subjected to extemai force. Figure 2.1 8:

Figure 2.19: Experimental viscosity of molten duminum as a function of temperature from different sources.

Viscosity of aiuminum and magnesium quoted in the Iiterature [ 1 7,521.

Figure 2.20:

Dimensions of the Saybolt viscorneter. Figure 2.2 1 :

Figure 3.1 :

Figure 3.2:

Figure 3.3:

Figure 3.4:

Low temperature apparatus.

Onfice plate design for low temperature apparatus.

Onfice plate dimensions for aluminum and A29 1 D experiments.

Schematic of clay graphite crucible used for aluminum and A29 ID experiments.

Time required to heat 1.275 kg Aluminm to 1 173 K. Aluminum Test# 29.

Figure 3.6%:

Figure 3.6b:

Figure 3.7:

Figure 4.1 :

Figure 4.2:

Figure 4.3:

Figure 4.4:

Figure 4.5:

Figure 4.6:

Figure 4.7:

Figure 4.8:

Figure 4.9:

Figure 4.1 O:

Figure 4.1 1 :

Time required to heat 0.62 kg A29 1 D to 1073 K. A29 1 D Test# 4.

Data aquisition systern used to acquire loadcell, thennocouple, and oxygen sensor data.

Schematic of draining vesse1 depicting flow rate of a fluid through an orifice placed at the bottom.

Controi element on stredine neglecting fictional losses.

Cumulative mass versus time for water at 293 K through a 0.003m Teflon orifice plate fiom an initial head of approximately 0.17m.

Head versus tirne for water at 293 K through a 0.003m Teflon orifice plate from an initial head of approximately O. 17m.

Cd venus Re, calculated using Equation (76) for a O.003m diameter orifice draining under the Uifluence of gravity. Ethylene glycol and water are presented at different temperatures.

Radius of curvature defining the gas-liquid interface of a fkee jet.

Pressure acting at orifice tip for Stream of liquid exposed to the atmosphere.

Cd versus R h , cdculated using Equations (90) for a 0.003m dimeter orifice draining under the influence of gravity. Ethylene giycol and water are presented at different ternperahires.

Dependence of the Bond and Froude relation on the density-dace tension ratio.

Relative magnitude of Bond nuxnbers for a variety of liquids. Density and surface tension are obtained h m rida and Guthrie [2].

Water: Acctnacy in neglecting d a c e energy for variable orifice design, for heads ranging h m O. lm to 0.0 lm.

Figure 4.12: Molten iron: Accunicy in neglecting d a c e energy for variable orifice design, for heads ranging h m O. lm to 0.0 lm.

Figure 4-13: Molten aluniinum: Accuracy in neglecting surface energy for variable orifice design, for heads ranghg fiom O. lm to 0.0 lm.

Experimental head measufenients for water at 32 1.5 K. Figure 5.1 :

Figure 5.2: Deviations between experimental head and calculated head for water at 32 1.5 K.

Cumulative mass as a fiinction of time for water at 32 1.5 K through a 0.003m diameter Tefl on orifice.

Figure 5.3:

Figure 5.4: Calibration for a 0.003m diameter orifice hole using water at room temperature.

Experimental surface tension as a function of head for water at 321.5 K for four separate calibrations.

Figure 5.5:

Figure 5.6: Maximum head height determineci for a specified error in srrrface tension for water draining through a 0.003m diameter orifice at 32 1.5 K.

Figure 5.7:

Figure 5.8:

Average surface tension of water at 32 1.5 K.

Emrs in property meamements as a function of h and Qap due to mr~ in Q, and Cd.

Erron in property mea~u~ements as a bction of Cd, due to mors in Q,, and Cd.

Figure 5.9:

Figure 5.1 O:

Figure 5. L 1:

Ermrs in property measurements as a function of r., due to in h a d Qap.

Volume within the cruciMe corresponding to a particdar head height.

Figure 5.12: Experimental head measurements for aluminum at 1073 K. AluminumTest#32.

Figme 5.1 3: Cumulative m a s versus time for aluminum et 1 073 K. Aluminum Test #32.

Figure 5-14: Frictional characteristics of O.OO5m orifice used for hi& temperature expaiments.

Figure 5.15: The experimental surface tension detefmined for aluminum at 1073 K, with expected error represented by the solid bars. Aluminimi Test #32,

Figure 5.16: The experimental viscosity detefmitled for aluminum at 1073 K, with expected error represented by the solid bars. Aluminum Test #32,

Figure 5.17: The experimental density detenrUIled for aluminum at 1073 K, with expected ermr represented by the solid bars. Alumininn Test #32.

Figure 6.1 : Density of 99.95% aiuminum as a fiinetion of temperature and compared with sources in the li terature [2,17].

Figure 6.2: Density of A29 1 D alloy as a hc t ion of temperature compared with theoreticai relations [ 1 71.

Figure 6.3: Viscosity of 99.95% purity aluminurn as a fhction of temperature compared with sources in the iiterature.

Figure 6.4: Viscosity of A29 1 D as a fimction of temperature.

Figure 6.5: SlItface tension of 99.95% aiuminum as a fhction of temperature compared with sources in the literature [2,7,321.

Figure 6.6: Surface tension of AZ91D as a fimction of temperature compared with sources in the literature [ 1 7,581.

Figure A. 1 : Velocity at reference points 1 and 2 indicated in Figure 4.1 as a finiction of the.

Figure A.2: Discharge coefficient as a fimction of Reynolds number taking into account transient terms in the formulation.

Figure C. 1 : Surface tension of aluminum as a fiuiction of temperature determhed through multiple non-Iinear regression on dl three properti-es.

Figure C.2: Viscosity of aluminum as a function of temperature determllied thmugh multiple non-linear regression on ail three properties. 187

Figure D. 1 : Represmtation for the partial pressure of oxygen as a fûnction of temperature during a purging and heating cycle. 188

Figure D.2: Oxygen partial pressure during the purging and heating cycle for Alumiaum Test #3 1 up to 973 K. 190

Figure D.3: Oxygen partial pressure durhg the purging and heating cycle for Aiurninum Test #38 up to 1023 K. 191

Figure D.4: Oxygen partial pressure during the purghg and heating cycle for Aiuminum Test #35 up to 1073 K. 192

Figure D.5: Oxygen partial pressure during the purging and heating cycle for Aluminum Test #39 up to 1 173 K. 193

Figure D.6: Oxygen partial pressure during the purging and heating cycle for A29 1 D Test #2 up to 967 K. 194

LIST OF TABLES

Page #

Surface tension of alimiinurn quoted h m a variety of sources. The temperature coefficient, atmosphere and purity are included. SD: Sessile hop . MBP: Maximum Bubble Pressure.

Table 2.1:

Surface tensions of aluminum and magnesium f?om sources in the literature [2,7,17,32].

Table 2.2:

Table 2.3:

Table 2.4:

Table 2.5:

Surface tensions of Mg-Ai-Zn-Mn alloys as a function of alloying composition [Sa] .

Viscosity of aiuminum and magnesium fkom sources in the literature [17,52].

Density of aluminum and magnesium from sources in the literature [2,17].

Standard dimensions of the Saybolt Universal viscorneter. Table 2.6:

Table 3.1:

Table 3.2:

Power requirements of induction fumace.

Percent of elemeats found as impurities present in alurninum [62].

Percent of elanents added to or containeci within A29 1 D ~ O Y Pl*

Table 3.3:

Table S. I : Polynomial constants that describe the discharge coefficient as a fbction of Reynolds number.

Cornparison between experimental d a c e tension and literatiae value for water at 32 1.5 K [6 LI.

Table 5.3:

Table 5.4:

PhysicaI properties of dinninum detennined by using different density values to caldate head at 1073 K.

Summary of remlts for aiuminum at 1073 K in cornparison to Iiterature guantities.

Table 6.1 : Density of 99.95% duminum detennined experimeutal1y.

Table 6.2:

Table 6.3:

TabIe 6.4:

Table 6.5:

Table 6.6:

Table 6.7:

Table 6.8:

Table 6.9:

Temperature dependence of density determined frmn experiments and fkom sources in the iiterature [2,17].

Density of A29 1 D alloy determined experimentally.

Temperature dependence of density determined from experiments, and h m the average values taken from sources in the literature [ 1 71. 154

Viscosity of 99.95% duminum detennined experimmtally. 155

Viscosity of A29 1 D alloy determined experimentally. 156

Surface tension of 99.95% aluminum determined experhentall y.

Temperature dependence of d a c e tension determined nom experiments and kom sources in the literature [2,7.17]. 162

Surface tension of AZ9 1 D dloy determined experimentally. 163

A = Constant in Arrhenius' formula (~slrn~).

A, = Cross sectional area for Bernoulli formulation (m2).

Ami = Resonant amplitude of oscillating plate method in air (m).

Am2 = Resonant amplitude of oscillating plate method in liquid (m).

Surface area (m2).

Polynomial constant describing 3rd order t m in polynomial fit of the discharge coefficient curve.

Constant in Arrhenius' formula (J/mole).

Bond number = p g W r (no uni&).

Polynomial constant describing 2nd order term in polynomial fit of the discharge coefficient cuve.

Discharge coefficient (no units).

Cumulative mass (kg).

Constant used in converting Saybolt Universal or Furol seconds to kinematic viscosiîy (m2/s2).

Constant used in convertïng Saybolt Universal or Furol seconds to kinematic viscosity (m2).

Poiynomial constant desmibing Ist order t e r - in polynornial fit of the discharge coefficient curve.

Polynomid constant descrîbing the y-intercept of the polynomial fit of the discharge coefficient m e .

Diameter of orifice of the Saybolt viscometer (m).

Outer diameter of the outlet of the orifice of Saybolt viscometer (m).

Dimeter of vesse1 or container of the Saybolt viscorneter (m).

Helmholtz fke energy (J).

Fo = Force 0.

Froude number = uk2/(2gh) (no units).

Gravitational constant (mls2).

Average head for Saybolt viscometer (m).

Liquid head above a point ofreference (m).

Constant fiom Bashworth and Adams table for sessile drop measmements (no dts) .

Equilibrium constant (no units).

Correction factor related to the shape of the meniscus for detacbment techniques (no units).

Length of orifice tube of Saybolt viscometer (m).

Number of moles (no units).

Pressure (Pa).

Flow rate (m3/s).

Constant fiom Bashworth and Adams table for sessile drop measurements (no utlits).

Radius of mature (m).

Reynolds numba = p2rou/p (no units).

radius (m).

Temperature (K).

Time (s).

Velocity (ds).

Internai energy (J).

Average velocity of liquid through the orifice tube of the Saybolt viscorneter (ds)*

Atomic volume (m3/mole).

Volume discharged fiom Saybolt viscorneter = 6.0x 1 0'' rn (60cm3).

Constant fiom Harkins and Brown tables for &op weight measurements (no lulits).

Awob = DiEerence in weight of object for Archimedean determination of density (N).

Maximum width of sessile droplet or pendant droplet (m).

Width dimension on pendant drop dependant on the dimension X (no units).

Mole fiaction (no units).

-2 -4 Apparanis constant for osdlating plate method (kg2s m ).

Shape factor fmom Andreas tables for pendant drop meamrements (no units).

Distance between geometric center and top af sessile droplet (m).

Distance on z-axis (m).

Symbol correspondhg to phase "a".

Symbol corresponding to phase "$.

Error in a meamrement Also reprsents standard deviation.

Interaction coefficient (no Uliits).

Surtace excess-concentration on gas4quid interface (moles/m2).

Activity coefficient (no uni&).

Viscosity (~sm**).

Interfacial tension (N/m).

Chemical potential (Jlmole).

Kinematic viscosity (m2/s).

Contact angle (degrees).

Density 0(g/rn3).

Surface tension of liquid (NIm).

Surface tension of liquid at equilibrium (N/m).

Pure dynamic surface tension of liquid (Nlm).

Shear stress (N/m2).

Frequency of oscillation for levitating-drop technique (Hz).

Kinetic energy correction factor for Saybolt viscometer (m).

Couette correction factor for Saybolt viscometer (m).

SUBSCRIPTS

cap: Capillary.

. Location describe by radius of cwature. m e "a"*

curve '%": Location descxibed by radius of mature.

d: Droplet.

exp: Experimental.

g: Gauge.

GS: Gas-Substrate Interface.

1: Chernical component 'P.

j: Iteration nimiber for mutiple non-hear regression andysis.

LS : Liquid-Substrate Interface.

rn: Melting point (or liquidus point).

Max: Maximum.

O: Orifice.

ob: Object.

poly: Polynomial.

r. Ring.

St: Saturation.

theo: Theoretical.

v: Vessel.

vap: Vaporization

a: Surface Tension.

SUPERSCRIPTS

s: Location conesponding to gas-liquid interface.

a: Denoting phase "CC'.

p: Denohg phase "fY"'

Knowledge of the physical properties of melts is of fundamental importance for

rnany metallurgid processes. The t m "melt" refers to molten materials such as metds,

salts, slags, etc. For the purposes of this thesis, this term refers only to these liquids and

not molten materials such as polymers or any other non-metallurgical liquids. The

productivity and efficiency of many high temperature applications rely on accurate

knowledge of surface tension, viscosity and density of the melt imda consideration.

Density is required in studies ranging h m simple m a s balance calculations to

the study of thermal natural convection phenornena in fumaces. m e r examples include

predicting the separation of slag/metd systems or calculating the terminai velocity of

inclusions submerged withh a melt. Dezisity is dso required to quanti@ other physical

properties such as surface tension and dynemic viscosity.

Viscosity is a quantity of nuidamental importance in fluid transport problems, as

well as issues conceming reaction kinetics in melt processing. The viscosity of molten

systerns ofien dictates the castability (or ability to fill a mold cavity) of many metais and

their alloys [l]. Furthermore, the mechanisms of solidification often depend on the

viscosity of the melt [2,3].

Surface tension is signifiant in terms of the efficiency to which atornization

pcesses operate in the powder metallurgy industry [4]. Of considerable significance is

the Marangoni effixt, which desmies the convection induced within a liquid fhm a

gradient in d a c e tension. This resuits, k m &ha concentration or temperature

diff'ces at the gas-liquid interfiice, in d a c e tension dnven flow that can of€en have

significant implications. An example is welding, where the penetration of the liquid

phase depends on the movements of the liquid pool [SI. This is also relevant in

steelmaking applications, where the Marangoni effect play; a crucial role in the corrosion

of refhctory material at slag-gas and slag-metal interfaces. The rate of nitrogen

absorption in iron (which impacts the mechanical properties) is also dependent on this

phcnomenon in steelmaking [6].

These processes exemplifjhg the fundamental significance of density, viscosity

and d a c e tension are merely a diminutive measure of the vast range of phenornena

requiring concise knowledge of these properties. In order to manipulate metallurgical

processes, a complete database of information should be available for these properties so

that fluid dynamics can be understood. Unfominately, there is much work that needs to

be done in applying property data to many processing endnmeats. For instance,

despite years of experimentation, large discrepancies in experimental viscosity values

exist for many pure metals such as iron, ahnihum, and zinc. This is atûibuted to the

highly reactive nature that many materials exhibit at high temperatures Contamination

issues are thus a continuous source of htration. In measuring d a c e tension, this issue

becomes monumentai since many of the contaminants, in particular oxygen, have a

drastic effect on the surface tension of metalIic liquids [5,7,8]. Consequently, many of

the techniques used in measuring the physid properties of low temperature liquids are

net applicable in consideration of these reallties. Material selection, temperature contml

and monitoring, and other mch notions place constraints on measurement techniques and

modes of operation.

D&g with melt systems ofien results in appreciably diffaent fluid dynamic

behavior than if low temperature liquids are used. A firmly established concept in

cornparhg low temperature liquids and melt systems is that densith are much larger in

metalIurgical processes. A less obvious concept is the contriiution of surface tension to

many high temperature appücations. Quantifyrng the fluid dynamics of melt systems

often r d t s in more complex relationships since d a c e tension is frequently requwd in

the analysis. This shidy focuses on such a case where d a c e tension has traditionally

been neglected. in the analysis of a liquid draining through an orifice under the influence

of gravity, potential and kinetic energies have conventionally been used to predict

throughput. Anomalies have been observeci in the prediction of flowrate of melts for this

system. This is aîûibuted to neglecting the d a c e tension in an energy balance.

Through proper characterization of potential, inertial, viscous as well as d a c e energy, a

more complete mode1 is fomiulated whae the effects of surface tension cm be analyzed.

A fortunate aspect of the drainhg vesse1 system is that d a c e tension, viscosiw,

and density are uiherently part of the formulation making it possible to determine dl

three properties by measuring processing v&ables. This has statistical advantages over

conventional measining techniques in that conditions change during the course of an

expriment making a series of detenninations possible. Also, the dynamic nature of the

experiments is advantageous over more stagnant conditions since the surface is

continuously replenished. Contaminants do not accumulate at the d a c e under such

conditions. Finally, the simultaneous measuranent of ail t h e pruperties using one

experimental setup is convenient and unique in cornparison with conventional methods.

In Chapter 2, this study will report theory, experirnental techniques, and results

that establish the riment status of kn&vledge of d a c e tension, viscosity and densi@ of

melts. The challenges in measuring these properties at high temperatures will be

emphasized not oniy in Chapter 2, but Chapter 3 as well, where a description of the

experimental apparatus used in this study is presented. Details of measurements at hi&

and low temperatures wül be given with information on heat supply, oxygen control, and

operational procedure.

Chapters 4 and 5 present the mathematical formulations necessary to detemiine

the physicd propenies using the new dynamic approach. Validation of the model will be

presented in both chapters. Chapter 4 illustrates the characterization of Wction through

the orifice using the new model. With a rigorous enor analysis included, Chapter 5

demonstrates how the d a c e tension, viscosity, and density can be determinad fiom the

formulation presented in Chapter 4.

A discussion of the method applied to systems of molten dumiaum and AZ91 D

d o y is presented in Chapter 6. The highly reactive nature of aluminum and AZ9ID

dloy with oxygen makes for challenging meaSUTements in this study. By measuring the

surface tension, viscosity and density of molten aluminum, it is possible to compare

results with data available in the literature and provide a discussion of the merits and

limitations of a draining vesse1 anaiysis. With measurements of AZ91D d o y

(approximateiy 9 1 %Mg-9W0.5%ZnZn0. 1 5%Mn), a valuable contriiution is made to the

cment status of information for cornmerciai dloys. The low density and excellent

strength of this material contributes to its success in automotive applications [8];

however, studies of the physical properties of this aüoy are lacking. From a fundamental

perspective, it is possible to test theones related to the physical propaties of metallic

mixtures in consideration of A29 1 D.

Finally, conclusions and recommendations will be presented in Chapter 7.

Important information fiom Chapters 2 through 6 will be highlighted and used to

generate recommendations for irnprovments on the technique. Systems of practical

importance in process metallurgy will also be considerd for fiiture experimentation.

CHAPTER 2: LITERATURE REVIEW

The physical properties of molten metals are fiindamental quantities used in

understanding many metaHurgica1 processes, as discussed in Chapter 1 . Theoretical

concepts must be understood in order to gain knowledge h m the information available

for d a c e tension, viscosity and densiîy. This chapter will provide theory descniing the

effects that composition and temperature have on each physical property. A review of

the literattue on the properties of molten alUmjIlum reveals that issues of oxygen

contamination are paramount in making these measurements. Finally, the current

methods used to masure surface tension, viscosiîy, and density will be discussed.

2.1 Surface Tension of Molten Metals

In defining d a c e tension, it is necessary to analyre fluids on a molecular level,

where attractive and rqulsive forces dictate the magnitude of cohesion between

moldes . Within the bulk of a pure fluid, attractive forces are bdanced in al1 directions.

However, when considering the interface between two separate phases, the resultant

forces are not of the same magnitude, nor do they unifody act in the same direction.

Refer to Figure 2.1 for an i11ustration of a gas-iiquid interface. An imbalance of the

cohesive forces at the d a c e results in the asymmetric resuitant force acting inward to

the direction of the buik liquid.

Gas

Figure 2.1 : Molecdar forces acting at an interface separating a liquid from a

R e f d g to Figure 2.2, there exists between pure phases a and j3, a region called

the interface region where the concentration of either phase varies and prophes change

fiom those characteristics of either phase. If a liquid-gas system is considered, the focus

of this thesis, the cohesive forces are much higher in the liquid phase [7]. The surface

tension can be defined as the property related to the intermolecular forces acting noma1

to the surface of the gas-liquid interface and has UILits of Newtons pa meter. The surface

energy of a üquid-gas system is the product of the surface tension and surface area

separating the two phases. The effect of surface energy is to minmiize the number of

molecules at the surface (Le. duce the d a c e area) [IO]. In this study, d a c e tension

WU always be r e f d to as the intediacial tension at a gas-liquid interface only. The

term interfacial tension, however, is used to descriie interfiiciial phenornena between any

two phases (e.g. gas-solid, solid-liquid, or gas-Liquid).

Distance

1 Phase

1 Phase a

l I O Concentration of fl

Figure 2.2: Interface region representing the concentration gradient that exisits between phases a and B

In deding with interfacial phenornenon, it is of intaest to note the high magnitude

d a c e energy that molten metals exhibit compared with other fluids. A useful approach

to quantimg d a c e tension is to relate it to other physical properties. This does not

condone the detennination of sinface energy b y cirnmiventing experimental techniques.

It does, however, provide useful insight into the relative magnitude of surface energy of

different fluids, so that the unique characteristics of molten metals c m be put into

perspective. For example, the heat of vaporization seems to be an indication of d a c e

energy (see Figure 2.3). The d a c e energy r e f d to in Figure 2.3 is detennined by

dividing the d a c e tension of the liquid by the d a c e excess concentration that will be

derived in Sedion 2.1.1. From analysis of Figure 2.3, rnetals clearly have the highest

surface energy relative to a wide range of fluids.

1 10 100 1000

Hest OF Vaporization ( k l l m o t l

3: Surface energy for a variety of fluids plotted ageinst the respect of vaporization. (From Utigard, T. [IO]).

ive heats

2.1.1 Gibbs Adsorption Equation: Effects of Composition

As explained previously, the surface tension of a particular liquid is a measure of

intermolecular forces that are asymmetric in nature at the interface between the liquid and

the gas. Often, solutes are "surface active" and preferentially adsorb at the surface, even

at low concentrations. The result is a signifiant decrease in the magnitude of the d a c e

tension because the cohesive forces between molecules at the d a c e are disrupted with

the presence of the solute moldes . This phenornenon is widely observed when

considering d a c e effects of molten metals. Figure 2.4 illustrates the surface tension of

alirminum doys with varying composition of copper, silicon, zinc, tin, antimony,

magnesium and lead. It is clear that elements such as bismuth and lead have a rnuch

greater impact on d a c e tension than other elanents.

Solute concentration (wt%)

Figure 2.4: Surface tension of Al-based aiîoys as fanctions of doying composition at 973 K. Atmosphere and oxygen concentration are not specified.

(From Lang, G. [Il]).

Interfacial effects c m often be greatly affectecl even by very low levels of

impurities. Many impurities drastically affect d a c e tension, especidy oxygen, d f u r ,

seleniun and teiiurium [12]. The presence of oxygen is of particular concem in high

temperatme systems since it is an impUnty that is hquently encountered. For a variety

of processing conditions, it is difficult to purge atmospheric oxygen an apparatus to

low enough concentrations to avoid d a c e oxidation. Figures 2.5 and 2.6 illusûate the

drastic impact that oxygen has on the d a c e tension of molten iron and copper,

respectively. The effects of oxygen contamination in aluminum systems have been

examineci thomughly in the litetaîure. This will be discussed in detail separately in

Section 2.1 .S.

Figure 2.5: Effect of oxygen present as a solute on the surface tension of molten iron. Temperature and atmosphere are not specifled.

@rom Keene, BJ. [q).

Figure 2.6: Effect of oxygen present in the gas phase on the surface tension of copper. Temperature and atmosphere are not specifîed. (From Keene, BJ* il).

To understand how a solute adsorbs at the d a c e of a Iiquid, the Gibbs

adsorption formulation is used. The presence of an interface introduces an additional

temi to the fiinction relating the changes in intemal energy with changes in volume (V),

entmpy (S), and molar quantities of species, i (ni) [5].

whae A: is the area of the interface and a is the d a c e tension of the liquid

The Helmholtz fiee energy is:

F=U-TS

The variation in HelmhoItz free energy is:

dF =dU - TdS - SdT

Substituthg Equation (1) into Equation (3) yields:

This is a useM relation in understanding the effects of pressure, temperature and solute

composition on the fne energy of a particular systern. When these variables are constant,

the thermodynamic dennition of d a c e tension can be stated:

The surface tension of a pure liquid is therefore a measure of the amount of Helmholtz

free energy that is necessary to extend a sinface by a unit area at constant temperature,

volume and composition. in the Gibbs mode1 for d a c e excess properties, the

concentration in the bulk of phase a is assumed to be constant up to a dividing d a c e

bat represents the interface (Figure 2.7). At the dividing surface, the concentration of

component i instantaneously changes to and assumes the concentration in the bulk phase

p. The interface region is thus simplified by a distinct dividing surface between phases a

and p. The number of moles of component i at the dividing surface is determined by

using knowledge of the total number of moles and the concentration in phases a and B:

Similady, the change in fiee energy at the d c e is:

dFS =dF-dFa -@B

D i s m l Interface

Phase a

' Concentration O?

O speciesi

i

Distance

1 Phase

11 + , - -. Dividing

1 Phase a

I b

O Concentration of species i

@) Figure 2.7: a) Intefice region separating phases a rnd $. b) Dividing surface

used in Gibbs Model approxlmating the interface region separrithg phases a and p.

Where the change in fiee energies in the bulk phases are aven by:

Whether component 'Y is associateci with phase a or p, its chernical potential is qua1 in

either phase when at equilibrium. Since the entropy of constituent subsystems is additive

[13], nibstituting Equations (4), (a), and (9) into Ecpation (7) yields the excess fiee

energy of planar interface, for a constant volume and constant temperature system.

From Euler's theorem for a dividing surface and the definition of the Helmholtz function:

Differentiating Equaiion (1 1) and substituting Equation (10):

Equation (1 3) is the Gibbs Adsorption equation:

where ss is the d a c e entropy per unit d a c e area, and the symbol Ti represents the

surface excess concentration which has units of moles per unit surface area.

Binary Systems

The significance of ri will now be made clear for binary liquids in contact with a

gas. Consider a . isothermal bhary (i.e. ssdT=O). Equation (1 3) can be written as:

Where subscripts 1 and 2 represent the solvent and solute constituents of the binary liquid

respectively. The dividing surface can be defined at the point where the surface

concentration of the solvent, Ti is zero. Equation (14) cm now be expressed as:

d o = -G( &f* (15)

r2(1) is Surface excess of component (2) given that the dividing surface was placed at the

location where there is no d a c e excas of component (1). It is theoretically possible to

calculate the surface coverage of the solute at the interface. Using Equation (6), and by

measuring the concentration of the solute in the liquid and vapor phases, the number of

moles of solute at the interface can be deâamined. The precision reqwred in this

detenninaîion, as well as pmctical limitations inherent with molten systems, are such that

these computations are rarely cairied out

At constant temperature, the change in chernical potential of species 2 at the

interface can be obtained by implementing the activity coefficient of a chernical species

in solution, y2 [ 141.

dc12 = R T ~ ~ ( ~ X , ) (1 6)

Equation (16) applies at quilibrium when pz = p;. The mole hction of the solute in the

liquid phase is x2. For a dilute solution, the activity coefficient is assumed to be uni@.

For solutions that are not considerd dilute, experimental determination of the activity

coefficient is required. Substituthg Equation (1 6) into Equation (1 5 ) yields the equation

for the adsorption in a binary system at constant temperature.

For dilute solutions:

A plot of 0 vs. ln(x2) provides an analysis where it is possible to determine the eEect of

concentration of a chemical specie on surface tension due to adsorption at a liquid-gas

interface. If en increase in surface tension is observed with increasing concentration, the

solute has preferentially trsnsfmed to the bulk phase fiom the surface. A decreasing

slope indicates that there is an affinity for molecules in the bullc to adsocb to the d a c e ,

typical of a d a c e active solute 1141.

Ternary Systems

The Gibbs adsorption equetion can prove to be a usehl relation in understanding

te- systems, where interesting interfacial phenornena have been observed. Figure 2.8

illustrates d t s obtained for iron-carbon-chromim alloys of varying chromium

compositions. Equation (13) wrïtten for a ternary system at constant temperature such as

the one depicted in Figure 2.8:

Similar to the analysis for binary systems, the dividing surface is deked at the position

where the surface excess concentration of the solvent is zero. It is not possible to obtain a

simple relationship between solute concentration, d a c e tension and surface coverage,

like Equation (1 7), due to complex interactions between constituents that ofien take place

at the interface. In Figure 2.8, it is clear that the surface tension of a three component

system are not additive because of the presence of a minimum at chromium levels

between 0.1 and 0.2 atom %. In order to predict this phmornenon, a formulation was

presented that makes use of "interaction coefficients" [16]. It is obtained by

differentiating Equation (1 8) with respect to ln(x3 and substituthg in Equation (1 6).

Where E: represents the interaction coefficients with respect to component 2, defhed as:

Kuowledge of activity coefficients is thus a requirement in this formulation. At the

minimum, the right hand side of Equation (19) equals z m . Belton [16] used this

formulation to predict the concentration of chromium at the minimum. He determined

this vahe to be 0.18 atorn fiaction, which c u ~ the minimum observed by Whden et

al. in Figure 2.8.

O 0.1 0.2 0.3

Chromium (atom hcti'on)

Figure 2.8: Surface tension of iron-3% carbon d o y with varying concentrations of chromium at 1623 K. Atmosphere and oxygen concentration are

not spedfied. (From Whaien et ad. [151).

2.13 Dependence on Temperature

From analysis of the Gibbs Adsorption equation (Equation (13)), the temperature

dependence of d a c e tension for a pure liquid is denned as the entropy per surface area

at the interface:

It is expected that the magnitude of dddT inmeases with temperature since entropy

increases with temperature. In the literatue, however, it is the n o m to express the

surface tension as a linear fiiaction with temperature [&7, 171. The ünearity is attri'buted

to the fact that measurements are made near the melting temperature relative to the

vaporization temperature. Non-linearity is expected as temperature approaches Tw since

entropy would rapidly increase near vaporization of the melt.

Rearranging equatioa (2 1 ) :

Integrating both sides for constant ss yields:

where o, is the d a c e tension at the melting point. Substituthg Equation (21) into

Equation (23) gives the traditional format in which d a c e tension is expressed as a

function of temperature [2,7,17].

For a multi-component system, and by applying the Gibbs adsorption equation, the

temperature dependence of surface tension is expressed as:

For a binary system, and in terms of activity coefficients and molar fiactions for constant

x2:

Equations (25) and (26) indicate that in multi-cornponent systems, the temperature

dependence of d a c e tension depends not only on the entropy at the surface but also on

the activities of the components in the bulk liquid as weU. In pure liquids, it is not

thermodynamically possible to have the d a c e tension increase with inmashg

temperature, as Equation (21) would indicate. in multi-component systerns, not only

does Equation (26) state that it is thennodynamically possible to have an increase in

surface tension with tempenihue, but it has been confïrmed experimentally to occur in

some instances. This has been observed with slag melts with high levels of Si02 in which

large cornplex molecular structures are formed. As temperature is increased, these

structures dissociate producing an increasing number of broken molecular bonds. The

increasing number of unsatisfied bonds increases the fiee energy at the surface, resulting

in an increase Ui surface tension [7]. Figure 2.9 illustrates the temperature dependence of

a silver based alloy with varying lead composition. This phenornenon is attnbuted to

strong surface segregation as temperature is increased [SI.

O 0.2 0.4 0.6 0.8 1 1.2 mole fraction Pb

Figure 23: Temperature dependence of surface tension as a funetion of Iead concentration enhibithg positive d u e s for dddT. Temperature, atmosphere,

oxygen concentration not speclfied. (From Joud and Passerone, 151).

2.13 Dynamic Surface Tension

For liquids in general, measuring the d a c e tension in the presence of d a c e

active substances requires that mass transfer and kinetic issues be considered. When an

interface between a liquid and gas is created, d a c e tension varies from its initial or pure

value (co) to its equiliirium value (a,) in the presence of sinface active substances. The

time it takes for this to occur varies h m approximately 10% to hours or days, depending

on the system under consideration [29]. For molten metais, the charact&stic times for

the surface to reach a saturated state with oxygen (ùidicating equih'brium condition) have

been predicted. This is accomplished through consideration of Knudsen diffusion and

imposing saturation values of oxygen pressure [40]. Figure 2.10 illustrates the t h e

required for melts to reach oxide saturation at oxygen pressures of 1Pa (in a vacuum).

By dehition, the "pure dynamic d a c e tension" is that meamrd at the instant of

formation of a new d a c e [5]. In this thesis, the tenn ''pure dynamic surface tension"

will refer to this definition. The term "dynamic d a c e tension" will refer to the surface

tension of the liquid at any instant before equilibrirnn is established. This is an

experimentally chdenging quantity to determine. Typically, equilibrium d a c e tension

is quoted in the literature with very little experimentd studies done on the dynamic

surface tension of molten metals. Ricci et al. [40] performed a study on liquid tin. The

review of the results is beyond the scope of this study; however it was detennined that

surface oxidation depends on the dynamics of metal and oxide vapor exchange at various

partial pressures. Also, it was determineci that the response of surface oxidation depends

on the gradient of temperature with the. More relevant to this discussion is the

experimental apparatus Ricci et al. used [40]. The sessile drop technique (explained in

the next section) was used in this experiment, which implemented an "ion-p" that

removed any oxides formed on the drop pior to taking measurements. The response

t h e of the expeiimental set-up ranges fian 0.5s to hours making it an especidy

pmctical procedure for anaiytuig the response of molten systems to kinetic and mass

transfer issues. The observable t h e s that the a p p m t u codd accommodate are within

the dotted lines indicated in Figure 2.10. The precise observation times are not stated

WI-

Figure 2.10: Characteristic times of a 0.01m diameter droplet to be sahirateci with oxide at a total pressure of oxygen of lPa, for various metaliic

systems (From Rlcci et ai. 1401).

2.1.4 Techniques to Measure Surface Tension

Techniques used to measure the surfâce taision of a liquid are based on a force

balance in which d a c e tension plays a signifïcant role. Again, for reasons of clarity,

the term d a c e tension refers to gas-liquid intafaces ody. Most rnethods rely, in some

fom, on the Laplace equation that dates the excess pressure (LU?) at a curved interface

with the radii of mature (Ri and R2) at a point on the surface:

Analysis of Equation (27) indicates that:

For a spherical surface (Ri=RfR): AP = 2 d R ;

For a cylindrical surface (Ri=R; R2=4: AP = o/R;

For a plauar mrface (Ri=R-): AP = 0.

The Bond number is a non-dimeasional number used to determine the magnitude

of the surface forces relative to the potential forces in a particular system. The potential

force often will take the fonn of gravity such as the weight of a droplet resting on a

d a c e or the weight of a droplet suspendeci from a capiilary. The techniques outlined in

this section will outline similar potential forces. The fomi of the Bond number may Vary,

but it always follows this convention:

When the Bond number is srnaII, indicating substantid d a c e forces, it is ofken possible

to measure surface tension by properly quantiwng relevant experimental variables. For

most d a c e tension measurement techniques, a curved intenace is usually present with a

s m d radius of m a t u r e resulting in a signifiant pressure ciifference according to the

Laplace equation. The sessile and pendant drop methods; drop weight, maximum bubble

pressure, capillary rise, and detachment techniques ail rely on these principle~.

Exceptions in the following discussion are the viirating jet and levitating drop techniques

that use the p ~ c i p i e s devehped by Raleigh 1411. These approaches involve the

inauence of d a c e tension on the instabilities inhermt to osciUations on a liquid surface.

Shupe Methodr- Sessile and Pendant Drop Techniques

Sessile &op (SD):

This technique uses the dimensions of a stationary droplet resting on a horizontal

d a c e . The resting drop assumes a shape in which a balance of gravitational forces and

d a c e forces is achieved. The Laplace equation is use& but due to the gravitational

enhament of the droplet, a cornplex fonn is required to desenie the d a c e

dimensions. Bashworth and Adams [42] detdned that the d a c e tension is related to

the dimensions of the droplet as follows:

i

Where q and j are parameters detmined from Bashforth and Adams tables [42] using

the meamrd values of X and Z illuseated in Figure 2.1 1.

I 1 I I

Figure 2.11: Dimeasions of sessile droplet reqdred for caiculation using the analysis approach of Bashford and Adams [42].

This technique faditates another analysis, which is descrhed by Young's

equation to obtain the difference in interfacial tension between the gas-substnite, ks, and

liquid-substrate, Irs, using the gas-üquid surface tension, CJ, and contact angle, 8.

Young's equation is defined as:

The d a c e tension is obtained fiom Equation (29) and substituted into Equation (30).

Note that in the SD technique, only one measurement of a and 0 is made per droplet.

Pendant Drop (PD):

Similar to the sessile droplet, the pendant droplet technique makes use of the

gravitational and surface forces that are in equili'brium, except that the droplet is hanging

h m the end of a capillary tube. Shape factors are also required to describe the d a c e of

the droplet. Refer to Figure 2.1 2.

Figure 2.12: Dimensions of pendant droplet required for caicalation usmg formdation by Andrea e t iL [431. (From Iidi and GntMe, (21).

A relationship involdg the dimensio~~~ of the pendant droplet (XIX'), and a set

of tables used to determine yet another shape factor (y) was proposed by Andreas et al.

[43]:

Both the sessile and pendant drop techniques describecl above rely on numerical

solutions that take the form of shape factors presented in tables. Consequently, there is

truncation error associated with the cdculations for surface tension. In recent years,

however, computerized numerical calculations, enhanced photographie resolution, and

effective image analysis techniques have yielded improved accuracy of redts. Even

with these improvements, many errors associate. with these techniques still exist.

Carnera-rnonitor distortion, discretization of the surface profile, and evaluation of the

system magnification factor (in deriving real drop profile from photograph) ai l contribute

to m r in measurements. in order to obtain the magnitude of error, the effect of each

source of error must be undeistood and quantified. Consequently, there are different

sources of m r s expected depending on the apparatus that is used. When dealing with

liquid metals, both techniques are aiso particulariy vulnerable to contamination with the

enviromnent since a mal1 quantity of liquid metai is used in a stagnant situation with the

surroundhg atmosphexe. The pendant drop rnethod is not a suitable technique to

detennine temperature variations. This is because there is a relatively small contact

M a c e between the droplet and the capiliary, making it difficult to maintain the droplet's

temperature. The capiilary is heated to the desireci temperature; however, there may be

signifiant temperature gradients between the capillary tip and various areas on the

hplet surface. Similar to the SD technique, the PD method wil l only provide one

measurement per droplet.

Drop Weight @lm: The basis of this technique utilizes the maximum weight a droplet achieves,

fonning fiom the tip of a capillary, before detachment takes place due to the influence of

gravity. Under ided circumstances, the gravitational force acting on the droplet at the

point of detachment is qua1 the d a c e force, and is given mathematicaily by:

m,g = 2m-O (32)

where, is the mass of the droplet and r,, is the radius of the capillary. in reality,

however, it has been detenniLled that the formation of the droplet is not as trivial as

Equation (32) suggests. Typically, as the &op grows, the neck of liquid comected to the

capillary elongates and prernahire detachment ensues. This o h results in liquid that is

still attached to the capillary that may even result in the formation of satellite droplets [7].

Harkins and Brown [44] produced tables of factors that relate the mal and ideal droplet

weights. A slightly modified form of Equation (32) is:

m,g = 2 5 0 6 (33)

The factor, % has been determined h m calibrations with low temperature fluids such as

water and 0th organic fluids. It has not yet been established if these factors can be used

for liquid metals. Since there is a smd contact erea between the heated capillary and

the rest of the droplet, signincmt tempexature gradients are expected making this method

an undesirable technique if the effect of temperature is of concem.

Maximum Bubble Pressure (MBP):

The maximum bubble pressure technique utiIizes the maximum pressure withiu a

bubble that is fomed before detachment from a capillary tube that is submerged at a

given location within a Iiquid. The maximum pressure is the summation of the static

pressure of the liquid at a depth, h, and the surface pressure induced due to the curved

surface of the capillary, Pa, dehed by r,.

The dmsity p, is the difference between densities of the liquid and gas and is

appmximately equal to the density of the liquid. When P,, is plotted versus h, the slope

will yield the density and the y-intercept wiil produce the surface tension of the liquid.

Equation (34) represents an ideal situation where it assumeci that the contours of the

menisci are spherical. However in many situations involving larger capillaries, and due

to gravitational effects, this assumption is renderd invaIid. SchrMinger [45] fomulated

a modifieci version of equation (34), which addresses this issue:

MBP is an effective technique in determining the temperature dependence of d a c e

tension since the ecpipment easily facilitates the use of thermocouples. Also, a k h

surface is created within the liquid, meaning that contamination due to the surroundings

is only possible through the introduction of impurities present in the inert bubbling gas.

Since gas suppliers can only guarantee a certain purity level in their pmduct, there is

dways a trace level of oxygen present that is expected to impact the surface tension

rneasurement. This will be disnissed in deM in Section 2.1 S. It is important when

using MBP that the "true" radius of the capillary is considered. This refers to cases when

the liquid wets the capillary resulting in spreading of the liquid to the outer radius of the

tip. This would r d t in a significant systematic error. There have been instances

published in the litemture where erroneous data was presented due to this phenornenon

[46]. Due to the fact that the bubble is submerged in the melt, it is not possible to make

visual observations of the bubble grneration. Abnormalities cannot be pinpointeci in the

experimental method via visual means because of this factor.

Detachment Methods:

This class of techniques is based on measurement of the maximum force that is

exerted by a body as it is pulled fkom the surface of a liquid. The body may be a ring,

plate, etc. The force that is required to detach fiom the surface is directly a fiinction of

the d a c e forces exhibited by the liquid. These techniques are also referred to as

" t ~ o m e t r i c methods". The equation used for a ring-shape body is the following [47]:

Where, F, is the force requUed detaching the ruig h m the d a c e of the üquid, r, is the

radius of the ring and 1 is a correction factor that is related to the shape of the menisci,

which is determined through calriration using a liquid of known surface tension. This

technique is lirnited to liquids that exhibit very good wetting behavior.

C'il[my Rise (CP):

A relationship used to calculate d a c e tension is based on the andysis of the

capillary nse of a liquid through a narrow tube. This technique has been used extensively

for orgmic liquids, but for practicaf misons, it has rarely been used for mo1ten metals [7].

When a capillary tube is immersed in a liquid, the levei will rise in the tube to a height,

hcap due to capillary action of the fluid. Refer to Figure 2.13. For a meniscus of a

spherical profile:

Figure 2.13: Capülary rise method for determining the s d a c e tension of a liquid.

The radius of curvature, R, is related to the contact angle and the radius of the

capillary, r,, by R=rdcosB. Equation (37) can be expresseci as a hction of contact

angie as:

Vibruting Jet Method (Va:

It is possible to determine the surface tension of a liquid flowing out of an

elliptical orifice. This orifice geometry resuits in oscillations on the liquid jet that

continue on the d a c e until they are dampened out due to viscous dissipation. The

formulation of the method is beyond the scope of this discussion; however, it was

determinecl that the d a c e tension is related to the fiequency of oscillations. The surface

tension acts as a restoring force, meaning that low d a c e tension results in relatively low

fkquency oscillations and long wavelengths. A series of rneaswernents may be taken on

the surface of the jet that corresponding to the length of time the surface is exposed to the

atmosphere. This facilitates time dependant d a c e tension calculations since the

distance fiom the orifice may Vary (refer to Section 2.1.3). Physically uarealistic surface

tensions are usually obtained f?om the fkst few wavelengths using this technique 1391.

Because of the large d a c e tension of liquid metals, break-up of the jet d l y occurs

very close to the orifice plate due to the disruptions on the liquid d a c e under these

circumstances. The viimting jet technique is, therefore, considered not to be an option

for molten metal systems.

Lwitating Droplet 0:

A relatively ment method for measuring surface tension, a levitating droplet

makes use of an electro-magnetic field induced by an induction coil. Approxirnately 0.5g

of an electrically conducting material is placed in the electromagnetic field where it

levitates and melts. The resuitant droplet oscillates due to perturbations inherent in the

system and the fiequency, a, is m d . Using the Raleigh equation [41]:

Where, m is the mass of the sample. This technique is attractive h m the point of view

that there is no contact betwem the droplet and any materials in the apparatus eliminating

contamination via that route. Howeva, the atmosphere must be of sufficient purity to

ensure that the sample is as clean as possiile. Since such a small quantity of sample is

used and it is the ody hot object in the apparatus, it is partidarly vulnerable to

contamhants in the atmosphere. Because electrical conductivity is a requkement for

materials subjected to LD, it is confined only to metallic systans. Finally, it is difficult

to obtain the temperature of the sample since it is not possible to insert thamocouples.

Pyrometric rnethods can be used; however, sufficiently high temperature must be used

such that emissivity data, if available, can be applicable.

Considerations For Molten Metals

Of al1 the rnethods that are introduced in this chapter, the sessile drop and

maximum bubble pressure method are most frequently used for measuring surface

tension of high temperature liquids mch as molten metals [2]. Practical issues such as

temperature control and measurement, and implications involving equipment design are

arnong the reasons why SD aM1 MBP are typically used. The sessile &op technique is

used because it is experimentally simple and it is possible to maintain good temperatine

control. Contamination issues, however, are at the forefront of limitations when applying

SD. The maximum bubble pressure technique is an attractive alternative fkom the point

of view of surface contamination. A fresh surface is created, submerged in the liquid and

is not in contact with the atmosphere mounding the liquid. The main source of

contamination is fiom the bubbling gas that must be of sufficient pur@. As mentioned

previously, it is not possible to make visual observations of the bubbling process since

the capillary is submerged in the melt It is dso important that the pressure aaa~ducer

used in determining the pressure within the bubble is calibrateci and making correct

measurements. However, fast bubbling rates can be applied so that under certain

circumstances, measurements can be made before the d a c e is completely oxidued.

This faciltates measurements that approach the ''pure dynamic d a c e tension". R d

h m Section 2.1.3 that this tam represents the d i i c e tension at the moment a fie&

d a c e is created. However, unda the best conditions for any liquid, the response tirne

for MBP is typically O. 1s to minutes [39]. Given the highly reactive environment at high

temperatures, obtaining the ' vue dynamic surface tension" is not possible using

conventional rnethods.

2.1 .5 Experimental Data

As dluded to in Section 2.1.1 and 2.1.4, measuring the d a c e tension of a pure

liquid metal is difficult due to the presence of oxygen that tends to act as a highly surface

active contaminant in most circumstances. It is often difficult to obtain experimentally,

the d a c e tension of a "pure" liquid metal since it is exûemely difficult to remove al1 the

oxygen fiom a particular system. The d a c e tension measurernents of molten metals are

done in a vacuum or within an inert atmosphae to ensure that oxygen is kept at a

minimum. The qudity of the equipment, and the measures taken for oxygen rernoval

Vary for different sources of data. Keene [q, in a ment review of the surface tension of

pure metals proposed a relationship for surface tension of molten aluminum as a h a i o n

of temperature. It takes the followllig fom:

Where Tm is the melting temperature (for alinninum, Tm = 933K (660°C)), and cm =

0.871 N/m is the d a c e tension at the melting point This relationship is based on an

average of a series of hctions that have been proposed in the litmture [10,17-341.

Table 2.1 srnarizes a number of sources and the conditions and methods of

rneasurements that were utilized.

- - - - -

In his review, Keene also acknowledged the fact that the data used to generate this

relationship are based on measwements in which a certain degree of oxidation is

expected. Levin et al. [19] performed a series of experheats and generated data that

were in reasonable agreement with other sources. The purity of the a l b u m he used

was greater than 99.99 %. As weiI, he implemented titanilmi getters to remove residual

oxygen h m the h e b atmosphere. As part of the analysis, Levin et al. purposely

contaminated a series of the duminum tests by re-melting the material in air prior to

experimeatation, consequentry increasing the mount of A1203 in the system. Figure 2.14

illusbates the d t s that clearîy indicate an increase of oxygen contamination has a

significant impact on the magnitude of surfàce tension. The Iinear reIatiomhip is the

Table 2.1: Surfrce tension of aiuminum quoted ftom a variety of sources. The temperature coefficient, atmosphere and purity are includeà. SD: Sessile Drop.

MBP: Maximum Bubble Pressure.

dofdT (N/mK)

- 0 . 1 5 ~ 1 ~ ~

-0.1 sx 10"

-0.16~ 1

-0. 1 5 2 ~ 1 0 - ~

-0. 15xl0"

- 0 . 1 2 ~

au(^, (N/m)

0.865

0.873

0.865

0.868

0.865

0.873

Pur@ (%)

99.99- 99.996

99.999

99.999

99.999

99.999

99.999

Authors

LeWietal.[lS]

Vatolin et ai. [30]

Yatsenko et al. [25]

Lang [29]

Gourimi et al. [14]

Pamies et al. [31]

Atmosphen

Helium

Helium

Vacuum

Ar

Vacuum

Ar

Yr

1968

1969

1972

1974

1979

1984

Method

SD

SD

SD

MBP

SD

MBP

recommended function presented by Levin et ai. in Table 2.1 and represents the

1

0.95

n 0.9

€ 1 0.85 w

5 0.8 - cn 5 0.75 l- 8 0.7 m 5 0.65 cn

0.6

0.55

0.5 1200 1300 1400 1500 1600 1700

Temperature (K)

Contaminated

Linear relation- - Uncontaminatd 1

Figure 2.14: Surface tension of high purity aiuminum, and aluminum deüberately contaminated with orygen (From Levin et al. [191).

In studying the effects of surface oxidation for an aiuminum-based system,

chernical eqdibrium between aluminum, oxygen, and aluminum oxide must be

oxygen as foilows:

The equilibrium constant for the formation of Ai& is l.23~10" at lûûOK

(723OC) [36]. The magnitude of this nimiber dictates that the reaction will proceed even

under exceptioaaily low oxygen partial pressures. An oxygen pressure of less than 10-

atm is needed to avoid oxidation [38]. From a pradcal point of view it is very difficult

to reach low enough pressures to avoid oxidation. Kaptay [8] proposeci that the d a c e

of aluminum in the presence of the oxide layer is, at relatively low temperatures, in a

state of super-cooled A&. This concept is illustrated in Figure 2.15, where it is

suggested that:

The temperature being referred to is the melting point of A1203.

oxidized moltea aluminum I moltec alumina

Figwe 2.15: S d a c e tension of a l d i u n and aiiimina as a fpnction of temperature, quoted fkom a variety of sources (From Uptay (81).

In the 1980's, insight into the suffixe tension of 'vuce" alimiirium was obtained

both theoretically and experirnentally. Chacbn et al. [37] theoretically calculated the

surface tension of pure alumitlum to be 1.184 Mm. Previous to this caldation, Gourimi

and Joud [32] also published experimental results that indicate that the surface tension of

pure duminum is indeed significantly higher than what has published in the Literature.

Goumllri and Joud used the sessile drop method to detennine the surface tension

of "pure" liquid aluminum. The extraordinary meames taken in this study to clean the

aluminurn of oxygen contamination consisted of a combination of heating and ion

bombardment of the surface. Using Scanning Auger electron spectroscopy (AES), the

surface concentration of oxide on the d a c e of aluminum-tin alloys was determined.

The principle behind this technique is the detection of emission of secondary electrons

from a specimen after the surface has been exciteci with electrons. This acts as a

fingerp~t of the chanical species on the d a c e of a specimen. The technique is

operateci at very low pressures (<1.0~10-' Pa), but allows for the incident beam to move

nom one specimen surface region to another for mapping of the elmental distribution on

the d a c e . The experimental r d t s from this study are presented in Figure 2.16.

Goumin and Joud have expressed the surface coverage of M203 in t m s of monolayer

units. When X = 1, the d a c e is considend to be covered by one layer of M203

molecules. It is clear fiom Figure 2.16 that the surface tension of aluminum decreases

rapidly at initial oxidation levels and much sfower at concentrations greater than one

monolayer. It is reasonable to say that because of these results, the d a c e tension

quoted fiom vanous sources pnor to îhis study correspond to "oxidized alurnînum". It is

proposed for low surface cuverage (X < 0.31, that oxide "islands" are present [8]. As the

oxide coverage inmeases (X > OS), the islands form a network that holds the specimen

together, which resuiîs in d a c e tension measurements that are more closely related to

the values of super-cooled &O3 [8]. Refer to Figure 2.17.

0.85 1 I I 1 1

O 0.5 1 1.5

X (monolayer Units)

Figure 2.16: Surface tension dependence on the coverage of Ai203 of pure aluminum determined experimentaiiy [32], and theoreticdiy 1371 at 973OC.

Figure 2.17: SIurace of aluminnm subjected to coverage of A1203: a) X < 0 3 ; b) X > O.S.

R e f d g to Table 2.2, the d a c e tension of aluminum and magnesium is

available in a number of reference books [2,17]. These sources incorporate the data that

was obtained fiom Men [57]. The method used by Men in detamining the d a c e

tension of aluminum and magnesiun is not specified in these refeiences. Keene's

thorough review of the mrface tension of pure metals is considered to be an excellent

source for the surface tension of pure metals. This is because the relation is based on the

average of a series of measurernents made by a variety of researchers. Of the 20 sources

referenced by Keene [10,17-341 for aluminum, 8 used MBP and 12 used SD. For the

magnesium relaîionship, 5 sources are refaenced, including 3 MBP determinations, 1 SD

detemination and 1 for which the method is not specified. Table 2.2 also includes the

surface tension of un-oxidized aiuminum obtained h m Gourmiri and Joud [32] that was

determined using SD.

Table 2 2 : Surface tensions of alaminm and magnesium from sources in the -

titerature [2,7,17$21. Source

melting point, a, (N/m)

Materid 1 Surlace tension at 1 Temperature dependence of

suface tension, da/dT

Liauid Metds 121, 1988; 2. Smithells Metais Reference Book [ 1 71, 1 998 Keene [q, 1996

Magnesium

Magaesium

A l h u m

Go& and Joud [32], i 982 (un-oxidized a l h u m )

0.577

0.559

0.87 1

-0.26~ 1 0è3

Aluminm

Magnesium

-0.35~ 1 o5

-0.1 55x 10''

1.050

NIA

NIA

N/ A

When discussing r d t s for A29 1 D d o y in Chapta 6, howledge of the physical

properties shodd be available to provide a complete anaiysis of the data. Unfommately

data were only found for surface tension. Regrettably, the data was only relevant at 1023

K. The surface tension of Mg-Al-Zn-Mn alloys at 1023 K is summarized in Table 2.3.

The source is h m Patrov et al. [58], who swnmarized a matrix of ailoy compositions as

follows:

Table 2.3: Surface tensions of Mg-Al-%-Mn ailoys as a hnction of aiioying composition et 1023 K. Atmosphere and oxygea concentration not specified.

(From Patrov et al. [SI). Aiioying Element (wt%) Surface Tension

0.570

0.522

0.522

0.552

0.522

0.539

0.496

0.57

0.57

0.566

Manganese

O

0.25

0.25

0.5

0.5

0.5

O

0.5

O

O

Aluminum

O

10

5

5

O

10

10

O

O

10

Zinc

O

2.5

5

2.5

5

O

5

O

5

O

2.2 Viscosity of Molten Metils

Viscosity is a physical property that quantifies the resistaace to flow when

subjected to an extemal force, F.. The shear stress that causes the relative motion

between layers of fluid is expressed as fùnction of the velocity gradient. For Newtonian

fluids:

Where s is the shear stress exerted on the fluid and u is the velocity which varies with

position, z. The proportionality constant, q, is the dynamic viscosity of the fluid (~sm").

Al1 liquid metals are considered to be Newtonian; however, it is important to keep in

mind that Equation (44) is only valid if the flow is Iaminar (refer to Figure 2.18).

Figure 2.18: Velocity profile of fiuid subjected to external force.

Figure 2.18 illustrates Couette fiow, a lamina flow pattern. The lower plate is stationary

and the upper plate moves with a uaifonn velocity. There is no pressure gradient in the

x-direction. The only forces acting in the ffuid are the shear forces due to the action of

viscosity descriid by Equation (44). This flow configuration is relevant to rotational

methods thai will be desded in Section 22.2. m e r Iaminar flow configuratioas used

to detennined viscosity are the Hagen-Poiseuille law for Iaminar flow in pipes. In this

case a parabolic velocity profile is the result of M y developed flow in ciradar pipes

where entrance effects are insignifiant. This flow configuration is relevant to capillary

methods that will also be describeci in Section 2.2.2.

2.2.1 Theoretical Determination of Viscosity

The Andrade formula is ofken used to predict the viscosity of melts at their

melting point [48]. The mode1 is based on rnomentum of atornic vibration. The

formulation produces the following relationship:

-Y Y ;rl, = L T , ~ M 6h 3 (45)

Where q, is the viscosity at the melting point, Tm is the liquidus temperature, M is the

rnolecular weight of the metal, p, is the density at the melting point, and L is a constant

deterrnined fiom viscosities of metals at their melting points. By plotting the known

viscosities of certain metals at their melting points verms T, ' ' *M ' '~~~~ , the constant, L,

is detennined fkom the dope. Hirai [3] quoted the magnitude of L to be 1.7~10"

(correlation coefficient of 0.95). In terms of varying composition and temperature, Hirai,

provided an analysis of estimating the viscosity of liquid alloys. For superheats that are

not excessive in relation to the liquidus temperature of the alloy, there appears to be a

linear relation between lnq and 1/T [3]. The Arrhenius' formula is thus used to

determine the temperature dependence of viscosity:

q = A ~ X ~ ( B I RT)

where A, and B are constants. A plot of h q vasus 1iT yields the dope B/R, which

changes in relation to the composition of the alloy. By experimentally detemiining the

value of B for a variety of rnelts, Hirai plotted B versus Tm and proposed the following:

B = 2 . 6 5 ~ ~ ' ~ (47)

The correlation coefficient for Equation (47) is 0.96. By substituting Equations (47), and

(45) into Equation (46), an expression for Constant A is determinecl:

As outlined by Hirai [3], in ternis of multi-component systems, p, and M, are detefmined

by taking the weighted average of the pure metals. For binary systems, the liquidus

temperature can be determined fiom a binary phase diagram [49].

2.22 Techniques to Measure Viscosity

There are a variety of techniques used to masure the viscosity of liquids.

However, due to constraints of working at high temperatUres, the methods applicable to

molten metais are limited. The definition of viscosity by Equation (44) only holds for

laminar flow. The techniques to measure viscosity that are described in this section al1

re1y on this fundamentai concept [2]. Some conventional methods for mwisuring

viscosity are the following:

a) Capiiiary Method,

b) The Oscillatin~Vessel Method,

c) Rotational Method, and

d) The Oscillating Plate Method.

These techniques will be qualitatively explained; however, formulations and the

procedural approaches are available nom Iida and Guthrie [2].

CapiIlav Method

The capiilary method masures the efflux t h e for liquid to flow through a capillary

under a given pressure. The tirne required to discharge a certain volume of fluid depends

on the viscosity of the liquid. A simple relationship used to relate the efflux tirne with the

kinematic viscosity is the following:

Where t is the efflux time and Ci and C2 are constants that are related to the dimensions

of the capillary. By using fluids of known properties, the constants are determineci by

caïbration. Visual observation is typically made through the viscorneter to determine the

time requireci for the volume tu be completely discharged. The material is thus

constnicted of heat resisting glass and quartz giass meaning that only low melting point

elements (Pb, Sn, Cd, etc.) are typically measured using this technique. The kinematic

viscosities of molten metals are much lower than those of organic liquids due to the fact

that density is of greater magnitude. It is thus necessary to construct a capillary of a

suitably mal1 radius so that the efaux time can be measured over a sufficiently long

period of the. The cleanliness of the maal is an important issue since even minute

inclusions wouid have a drastic impact on the eaux of the s m d capillary. Cleanliness in

this case =fers to solid inclusions and not Hnpurities in solution.

Oscillating Vesse1 Method

The principle behind this technique is monitoring the motion of a vessel or

crucible that contains the liquid and is set in vertical oscillations by a suspension rod.

Due to viscous dissipation in the vessel, the viscosity cm be determined by meamring the

decrease in the period of oscillation. This technique has been applied extensiveIy for

high temperature applications due to the relatively simple design and ease of

implementation. Unfortunately, there is no definitive analytical formula that relates the

viscosity to the period of oscillation. A number of equations have been foxmulated from

different sources and have been frequently used [50,5 11.

Rotational Method

This method makes use of a rotating vessel or mcible containing the liquid, and a

cylinder that is placed in the center of the vessel. The vessel is rotated at a constant

anpuiar velocity, which, due to the viscous nature of the liquid, exerts a torque on the

cylinder. The torque is registered by measuring the angular rotation of a suspension

fiba: The mathematics is relatively simple in this case. However, for non-viscous fluids

(typical of molten metals), the gap between the vessel and the Ulner cylinder must be

small enough such that the cylinder experiences suEcknt torque. This puts a difficult

co-t on the design capabilities, particularly at high temperatwes.

Oscillating Plate Melhai

The principle behind this technique is viscous dissipation monitored by a flat plate

immersed in the liquid that experiences oscillations. If the oscillations are operating at

constant force, the amplitude of the oscillations is a direct fimction of the viscosity of the

liquid. A simplified version of the formulaton is:

where Ami and Am2 are the resonant amp1itudes of the plate in air and in the liquid

respectively. Y is an apparatus constant which is determined through calibration

methods. The oscillating plate method is attractive from the point of view of equiprnent

design and the simplicity of tneasurcment The product pq can be determined over a

large temperature range because the amplitudes can be monitored as the liquid is heated.

The technique is unsuitable, however, for low viscosity fluids because a very large plate

would be required, which ofien presents serious experimental difficulties.

O h , experimental viscosities are of diffaent magnitudes than the theoretical

formulation derived in Equations (46-48). Theoreticaily, the Andrade approach is based

on a molecular basis (momentum of atomic vibrations). Di~similarly~ the experimental

approach is based on bulk flow in the laminar regime that produces shear stress exerted

by a d a c e on the fluid flowing in one direztîon (refer to Equation (44) and Figure 2. L 8).

Experimentally, however, the effect of temperature on viscosity, is often dacnied by

Arrhenius' equation (Eqpation (46)).

Despite the numerous measurements for many liquid met& that have been

perfonaed in the past one hundred years, there exist disc~epancies in the data reported for

certain metais, including aluminum, iron, and zinc [2]. The high reactivity of these

elements and the diffidties of taking measurements at high temperatures are fonsidered

to be among the main reasons for these dismepancies. Oxide contamiruted aluminum has

been quoted to have a viscosity 8% higher than melts that are nearly oxide fiee [52].

Figure 2.19 presents the results from a number of studies in mnisuring the viscosity of

aluminum. Both knes and Bartlett [53] and Kisunk'o et al. [56] used the principle of the

rotational method. Both Rothwell[55] and Yao and Kondic [54] used a rnodified version

of the oscillating plate method by incorporating a sphere rather than a flat plate. The

most ment results published by Kisun'ko et al., and Rothwell are within the closest

agreement compared with other researchm. Assuming that ment technological

advances have improved the accuracy of the measurernents, it is assumed that results

published fiom these raearchers are more reliable, and that the viscosity is much lower

than what was determined âom previous analyses. It is most interesthg to note the

tesults of Yao and Kondic that indicate a difference in purity between 99.96% and

99.9935% results in a dramatic difference in viscosity. The importance of providing

conditions of minimai contamination is illustrated fkom these resuIts.

800 900 1000 1100 1200 Temperature (K)

Figure 2.19: Experimentai viscosity of molten aiiimlnum as a fnnction of temperature fiom dhnerent sources.

- Theoretical (Andrade fomulat ion) [48] Jones and Bartlett [531

8 Yao and Kondic- 99.96% purity [54] Yao and Kondic- 99.9935% punty [54]

A Rothwe11[55]

o. 1

0.01 - ,

tl ( ~ s l r n * )

0.001

I I I

;a I a

R m

b:$, I I

- . q I

0.0001 -

A ..

Kisun'ko et al. [56]

The viscosity of a wide range of pure metals is available fiom ' n i e Viscosity of

Liquid Metals" fiom Liauid Metals [52]. The data are presented in the form of the

Arrhenius formula with constants A, and B included. SmitheIIs Metals Reference Book

[17] directly quotes the values obtained from this study. The Physical Prowrties of

Liquid Metals [2] does not include the variation of viscosity with temperature and is net

included in this study. Table 2.4 summarizes data for aluminum and magnesium. The

viscosities of aluminum and magnesium using these constants are illustnited in Figure

2.20 as a fhction of temperature. At the respective melting points, the viscosities of both

metals are sirnilar, however, the viscosity of magaesium appears to decrease with

temperature at a greater rate.

Table 2.4: Viscosity of ilumlnum and magnesium from sources in the iiterature

Source

1 . Srnitheils Metds Reference Book [ 1 71 2. "The Viscosity of Liquid Metals" fiom Liquid Metais WI

[l7,S2 1. Metal Viscosity at Constants for

melting point, q, Arrhenius' ( ~ s m - ~ ) Formulation

A (~srn-*) B (Jlmol)

Alurninum 1 .25x 1 O" A = 1 . 4 9 ~ 1 0 ~

Temperature (K)

Figure 2.20: Viscosity of aluminum and magnesium quoteà in the iiterature [17,52]

23 Density of Molten Metais

Density is a physical property of fûndamental importance. There have been

extensive data published in the literature on the density of pure metals; however, more

data is needed for high melting point rnetals and alloys. Nonetheless, in relation to

Mscosity and d a c e tension, there is g e n d y more information available for the

density of molten metals. h terms of alloy systems, it has ofien been found that the

atomic volumes of each alloying element is additive, indicating that the following

relation is of use [2]:

The tenns "$ and "x:' refers to the atomic volume (m3/mole) and mole hction of the

alloyhg elements respectively. The density is detennined by diving the molecular

weight by the atomic volume of the liquid (p = Wv). Equation (51) indicates that

metallic mixtures may behave as ideal solutions. This concept will be tested in Chapter 6

when Al-Mg-Zn-Mn alloys wili be discussed.

There appears, in most cases, to be a linear dependence of density with

temperature. It has been found that density can be represented by:

Where p, is the density at the melting point, and dp/dT is the linear temperature

coefficient of the metal.

23.1 Techniques to Meawre Density

Constraints, including contamination and reactivity as well as the difficdties in

operathg at high temperature are also pertinent in measuring density as they were for

surface tension and viscosity measurements. There are a variety of methods used to

rneasure the density of molten metals. Some are more advantageous than others

depending on the particular systems that are to be measured* Five techniques will be

briefly descriid.

a) Archimedian Method,

b) Pycnometric Method,

c) Dilatomettic Method,

d) Manometric Method, and

e) Maximum Bubble Pressure Method.

A full discussion of each is available in Iida and Guthrie [2]. A brief sumrnary

will be given below.

Archimedean Method

When a solid body of known weight is immmed in a liquid specimen, a new

apparent weight is observe& This is due to the buoyant effect the liquid has on the solid

object. The difference beîween the two weights is used to calculate the density of the

liquid, using:

where, Awob is the difference of the weight of the object before and afkr being

submergeci in the liquid, and Vob is the volume of the object. The apparent weight is

measured by hanging the object 60m a wire that is attached to the ami of a weighing

balance. This technique is attractive due to its relative simplicity; however it has been

observeci that there are d a c e tension eEects between the wire and the liquid that ofien

must be quantifieci in the analysis. Also the apparatus must be correcteci for themai

expansion if accunite measurements are to be made. Aithough rnetals are fiequently used

for the suspension wire, problems of reactiviw between the liquid metals and wire

material, as weU as the immersed object, are frequently encountered.

Pycnornenic Method

The basic concept of this technique is h p I e . The density is determined by

fïlling the iiquid mnal in a vesse1 of known volume and the m a s is measured following

solidification. The volume must be known with a great deal of confidence if this

technique is to provide reliable data The apparatus must be machined to appropriate

tolefaflces, and there must be no reaction between the walls of the vessel and the liquid

metal. Finally, the apparatus material must have a defined coefficient of thermal

expansion so that any modified volume h m heathg can be accounted for. Despite these

issues, accunite memements have been made using this method. It is worth noting,

however, that the temperature dependence of density is not practically rneasured ushg

this method since only one measurement cm be made at one temperature. This is

because the mataial is solidified der performing one test made at one particular

temperature.

Dilatometric Method

This technique has been widely used to measure the density of many molten

systems. It consists of a vessel of known volume that is fitted with a long nmow neck of

known dimensions. A finite mass of material is added to the apparatus where it is melted.

The height of the meaiscm of the melt is monitored in the neck portion to determine the

precise volume of that particular mass of liquid. This technique is useful in that it is

considaed to be quite accurate and it requires very little material. This technique can

only be used for low melting point rnetals, however, since Pyrex or quartz must be used if

the level is to be v i d y ascertained. Height measurements have been made, however,

using electrical contact methods with non-transparent materials.

Manometric Method

If a pressure of known magnitude is applied to one of the columns of a u-tube

monometer containing a liquid metal, a height différentid wiiî be established between the

cohmm of the u-tube. By measirring the diffaence in height, the density can be

calculated as follows:

Where P, is the gage pressure appüed to one of the columns and Ah is the resulting height

differentiai. Like the dilatometric method, visual observation can only be made if the

material is constructed of Pyrex or quartz.

Maximum Bubble Pressure Method

The final technique that will be discussed in this section is identical to the

technique of the same name that meamres d a c e tension in section 2.1.4. It was stated

that fiom anaiysis of Equation (34) that it is possible to measure both surface tension and

d e t y by vmyhg the depth that the capillary tube is submergeci in the liquid. The dope

of maximum pressure versus depth yields the density of the liquid.

23.2 Experimental Data

The density of molten rnetals is available h m a variety of sources. Table 2.5

summarizes the density of alumulum and magnesiun as a h c t i o n of temperature

represented by dp/dT. The refmences used here are quoted nom The Phvsical Properties

of Liuuid MeCals [2] as well as Smithells Metals Reference Book [17].

Table 245: Density of dauninam and magnesium fkom sources in the iiterature [2,17.

Source 1 Metal 1 Density at melthg 1 Temperature

Physicai Pro~erties

2.4 The Saybolt Viscorneter

Smithells Metals Reference Book

1171, 1998

A standard that meaSuTes viscosity deserving of considerable attention is the

Saybolt viscometer 165-781. The formulations and experiments performed in this thesis

have stRkllrg similarities with this device. By measuring the efflw t h e of a Iiquid h m

a vesse1 through an orifice of specific dimensions, it is expected that viscosity cm be

detennined since it is a function of the efnux time. in Chapters 4 and 5, it will be shown

that flow through the orifice is induced fiom the hydrostatic pressure of the liquid head

above the orifice much like it is in the Saybolt viscometer. This section will provide the

theoretical basis behind the Saybolt viscometer. Ofpartîcular celevance to this thesis are

the effects of d a c e tension at the orifice tip. It is of interest to detennine if d a c e

tension has played a role in the development of this device; and more importanîiy, if

&ce tension has been properly quantified in the formulation.

Aluminum

AlumYlum

Magnesium

point&, (kglm3

2380

dependence of density, dp/dT

( k g ~ n - ~ ~ ' ) -0.35

2385

1590

-0.26

-0.264

There are a variety of techniques that consist of orifice-type viscorneters. Among

them are the Redwood, Engler and Saybolt viscorneters. The Saybolt viscometer is used

pdominately in the petroleum industry and is most widely referenced when researching

this type of viscometer. All devices follow the same principle in that the efflw t h e

taken to drain a given volume of liquid can be expressed as a relative viscosity

measurement. For instance, the unit "Engler degrees" is the unit measure of viscosity for

the Engler device. This unit is the ratio of efflux time for the Iiquid being tested to the

time taken for water at 20°C. The Saybolt viscometer h p l y takes the efflux time and

quotes units of Saybolt Universal seconds (SUS) or Saybolt Fur01 seconds (SFS). The

Saybolt U n i v e d second is the measurement made through a calibrated Universai orifice

under specified conditions. The Sayblt Furol second is the measwement made through

a calibrated Furol orifice, which shouid be used if the Saybolt Universal second is greater

than 1000s as specified by ASTM standard D 88 - 94 [77].

The Saybolt viscometer was originally published in the Annual Book of ASTM

Standards in 1923 as ASTM D 88 - 21. Before this date, the device was accepted as a

standard fiom an initiative of G. M. Saybolt (the inventor of the device) and the Bureau

of Standards in 1917 [66]. To comprehend the theoretical basis of the Saybolt

viscometer, it is necessary to understand the work published at this time.

The principle of these viscorneters is similar to the capillary viscometers

disnissed in Setion 2.2.2 except that Hagen-Pouiseuille flow is catainly not established

within the short section of the orince length. For this flow to be established, the Iength to

diameter ratio of the orifice mus be greater that 10 [76]. This ratio for the Saybolt

viscorneter is approximately 7.0 [65,66]. For W y developed flow, the following

equation applies [65,66]:

For flow in capillary tubes, the tirne a certain volume takes to discharge (Vd) depends on

a difference in pressure, the diameter of the capillary (&) and the length of the capillary

) The viscosity, q, is calculated by quantifying each of the ternis in Equation (55).

This relationship has successfbUy been used to mode1 viscous flow in capillaries;

however it has been observeci that results have not agreed with this law when the velocity

was very high in the shortest of capillaries [65]. A correction factor has been proposed

that accounts for part of the pressure that is in reality expended in sening the liquid in

motion and not in overcorning viscous resistance [65,66]. A "kinetic energy correction

factor", represented by the symbol 5, is deducted h m the pressure difference to account

for this phenornenon. Another tm that accounts for "end effects" for a specified length

of tube is the "Couette correction factor", represented by the symbol y~ [65,66]. A

modified form of Equation (55) that accounts for these ternis is the following written in

The average velocity in the tube is represented by û Equation (56) states that hydrostatic

pressure of the üquid above the orifice induces the flow. Hence, the gravitational

constant, density, and the "average head", syrnboiized by & is introduced in the

formulation. The average head is considered a constant and is detennined using the

following relationship [66]:

The head before draining is hi and head after discharge is hz. Using the dimensions of

the device, most of the ternis in Equation (56) can be substituted with the exception of

values related to kinetic energy and Couette correction factors [66 1. Table 2.6 gives the

dimensions of the fkst standard SayboIt Universal viscometer in 1 9 1 7. These dimensions

are the same today as outlined in ASTM D 88 - 94 [77]. Refer to Figure 2.2 1 for a

representation of the Saybolt Universal viscometer. The Saybolt Furol orifice is different

thm the Saybolt Universal onfice in that d, = 3.1 SW.OO2m and dwa = 4.310.2rn [77].

Herschel rewrote equation (56) in temis of kinmatic viscosity, efflux tirne, and

two constants determined empirically since the kinetic energy and Couette correction

factors are unknown [65,66]:

Note that Equation (58) is of the same form as Equation (49), usai in capillary measuring

methods. This is not surprising since this device is modelled fiom p ~ c i p l e s of Hagen-

Pouiseuilie flow. The constants ci and Cz must be detennined through calibration using

fluids of known viscosities. Using a nimiber of fluids of varying viscosities, the constants

can be graphically detamhed. Dividing the left and right hand side of equation (58) by

t :

Plotting q/(pt) versus II? for a vaiety of liquids yields an intercept value of CI whiIe the

slope of the luiear relationship determines the value of Cz. This approach conducted by

Herschel in the standardization of the Saybolt viscometer was performed with a variety of

liquids that are referenced in [66]. It was determineci that water was an unsuitable

calfiration fluid because a departwe fiom linearity was observe- for Iow kinematic

viscosities associated with water. This is attributed to turbulent flow, which is an

indication that Equation (56) no longer applies since this relationship describes larninar-

viscous flow in a capillary only [65]. It has been observeci fiom experimental results that

when Reynolds nmbers are in excess of 1500 the Saybolt Universal viscometer is

unsuitable for testing [65,66]. Glycerol solutions were also determined to be inapplicable

as caiibration fluids due to issues concerning evaporation during the draining of the liquid

[66]. Sucrose solutions were also scrutinized for calibration purposes due to the high

d a c e tension of these liquids compareci with other calibration liquids. For the

standardization of the Saybolt viscorneta, Herschel desmied tests with sucrose solutions

that were consistent with one another, but produced Iower positions of the calibration

cuve than tests obtained with aicohol solutions. He directly attn'buted this difference to

the effects of surface tension, and stated that caiibration Iiquids must be selected with

d a c e tensions most neariy Bqual to that of oils, since Saybolt viscorneters are mainly

used for testing oils [6q. Although Herschel confirmai the influence of surface tension

effects on the dynamics of the Saybolt instrument in 19 17, there was no attempt in

quantifying this effect. In the fiterattire, there has been no fitrther reference made in

pursuing this matter [65-781.

The standardization of the Saybolt viscometer in 19 17 detefmined that kinematic

viscosity could be converted from Saybolt Universal seconds as follows:

Presentiy, the fom this equation assumes is similar. For example, in The Measurement,

Mmmentation. and Sensors Handbook r76L ci and Cz are said to equal2.226~ lo5 and

1.95 respectively. An ASTM standard exists today that publishes tables that convert

Saybolt Universal and Furol seconds to kinwatic viscosity values [78].

Figure 221: Dimensions of the Saybolt viscometer.

60

Table 2.6: Standard dhnensions of the Saybolt Universai viscorneter. 1 Dimension 1 Min 1 orm mal [Max 1 Length of outlet tube (capiliary), I,

2.5 Conciusions

Operating at high ternperatwes in particularly reactive environments, (Le. in the

presence of oxygen), poses many challenges in experimentally determining the physical

properties of molten metals. Techniques used for low temperature work (i.e. organic

Iiquids), do not apply in many cases due to such challenges. This will be clearly

demonstrated in the next chapter where a new apparatus for measlning the physical

properties of molten metals wiiI be describeci. It will be compared with another apparatus

based on similar principles, but operating at lower temperatures This wiîi iltustrate the

challenges in operating at high temperatures in a very practical mamer.

Anempts to understand the sensitivity of d a c e tension, viscosity and density to

temperature and composition have been made throughout the literature. Sinface tension

and densiîy are assumed to vary linearIy with temperature [2,7]. Viscosity, however, is

assumeci to vary with temperature according to the Arrhenius formulation [3].

(m) 1.750~ 1 0;'

L

Diameter of outlet tube (capiliary), kP

Outlet diameter of tube, dma

Height of overflow rim above outlet tube, hl

Diameter of vessel, d,

I 1 7 . 1 6 ~ 1 ~ ' 1 7.36~10" 1 7.56~10-' 1

1.225~ 1 O"

3 .OX 1 0"

1 .250x 1 O"

2.975~ 1 0"

1

1.2 15x 1 O-'

2.8~10--'

1.240~ 1 O*'

2 . 9 5 5 ~ 1 O-'

(m) 1.765~ 1 0-3

1 .235x 1

3 . 2 ~ 1 O-'

1.260~ 1 O-'

2.995~ 1 O-'

(m) 1.780~1

Theoretical determination using the Andrade formulation for viscosity is much lower

than experimental r d t s for duminum. For molten aliiminum, the magnitude of the

d a c e tension is a strong function of the amount of oxide that covers the d a c e of the

melt [8]. The surface tension of multi-component systems is often a complex issue;

however, the Gibbs adsorption equation has explained the results for a number of studies

[5,lS, 161. Finally, it has also been shown that the d a c e energy in molten systms is

much higher than systems of organic liquids. in fluid dynamic applications of

rnetallu~gicai processes, surface energy must be accounted for more often, and the

scarcity of accunite information is problematic. Such a situation will be explored in

subsequent chapters where the problern of fkee jets fiom small orifice tanks will be

discussed. These tests differ nom the Saybolt instrument in that the principle

experimentai variables are head and flow rate, and not simply the efflux tirne. There

have been numemus studies in the literature addressing this issue for low temperature

üquids, and throughput has traditionally been characterized by quantifying potential,

inertial and viscous energies in the system [59,60]. This system will be re-examined for

molten metals systems to determine if it is necessary to account for surface energy; and if

so, under what conditions.

This chapter will descnie the equipment used in generating controlled flow

through an orifice such that head and flow rate, the two principle variables, cm be

accurately measured. There are two purposes to this discussion. Fh t , this exercise will

provide a better understanding of the system and the limitations of the experiment.

Secondly, the difficulties intrinsic to high temperature applications will be clearIy

demonstrated by discussvlg the apparatus used in bo t . Iow-temperature and high-

temperature work. Issues dealing with heat supply and atmospheric control, relevant to

melts, wiII be addressed in this chapter. A full description of the experimentai procedure

will be presented as well as the specifications of metal purity and quality of the gases.

3.1 Low Temperature Apparatus

The apparatus for low temperature applications is illustrated in Figure 3.1. A

rectmgular Pyrex draining vessel (0.035m x 0.075m x 0.25ûm) was constructeci so that

visual observations can be made of fluid head. The fluid drains through the orifice plate

and is collectecl into a 1 litre beaker that is placed no less than 0.03m below the orifice

plate. The orifice plate and vessel are held together using a system of threaded rods.

The beaker is mounted on the loadcell as shown.

Scale

Collection Beaker

Orifice

Loadcell

Figure 3.1: Low temperature apparatus.

The loadcell (LCCA-25 supplied by Omega) is used to measure flow rate by

m&g the m a s pound through the orifice with time. It generates a voltage signal

that is detected by the data aquisition system desmibed in section 3.2.6. Ushg an

excitation of 10 Vdc, and outputthg 3mVN f 0.0075mVN (obtained fiom Omega), the

loadcell registers up to I 1 kg of mass. It is important that the collection beaker is placed

as close as possible to the orifice plate so that the Stream does not break-up before

impact. If this precaution is overlooked, an erratic signal will be registered by the

loadcell, directly resulting in scatter in data collection. The enatic signai is due to

discrete droplets formed der breakup that impact the loadcell at irrepuiar intervals. The

r e d t is a highly variabie detection of strain. A second order polynomial is fitted to the

cumulative mass that is plotted as a iùnction of time. This relation is differentiated,

which resuits in a new function desmibing flow rate as a fùnction of tirne. This will be

discussed further in sections 3.1.2 and 3-2.8.

The head of the fluid is measured in two ways. Visual obsewation through the

draining vessel can be made and recorded ushg a v i d a canera. A Sony color video

CCD canera (DXC-15 1) is used with a 35- leas approximately 1 m away to record the

experiment ont0 a VHS videotape. The head is also calculateci through careibl

caiibration of the draining vessel geometry. Pnor to experimentation, water samples of

known volume are related to head measurrd in the drainhg vessel. The volume is

m e a d indirectly by measuring the weight of the water, using an Ohaus GT 8000

scale. Temperature is measured so that the volume can be caldated using reiiable

density data [61]. The scaie used for visual observations as weii as for the calicbration of

the cruciible is accluate to 0.0005m (5ûûp).

31.1 Orifice Plates

Refer to Figure 3.2 for dimensions of the orifice plate. Teflon was used to

construct a 0.016m thick plate with a 0.003m orifice hole in the center where the fluid

drains through. The entrance of the orifice is chamfered so that entnince effects will be

lower than in the case of a square entrance. The holes for the threaded rods are also

indicated.

Orifice Hole

Figure 33: Orince plate design for low temperature apparatus.

3.1.2 Procedure for Low Temperatme Experiments

The thamocouple is inserted through the top and placed approximately 0.005m

fiom the orifice idet. The thennocouple is positioned at this distance to measure

the temperature at the orifice without interferhg with the dynamics of the

experiment . A stopper is placed through the orifice outlet to ensure that the fluid does not

begin pouring out once it is added to the draining vessel.

The draining vesse1 is filled to a head no greater than O. 1% registeied on the

adjacent scale.

Once it is detenniaed that the fluid appears still and the experiment is ready to

proceed, the stopper is removed and the fluid is allowed to flow into the beaker

placed on top of the loadcell.

The loadcell and temperature data are registered and recorded on the data

acquisition system and saved ont0 a floppy disk. A sampie rate of 5Hz (0.2s per

data point) is selected.

The data is imported into Excel (Microsofi corporation) where a polynomial is

fitted to the cumulative mass m e versus time data This function is

differentiated to obtain the experimental flow rate at the respective head heights

taken every 0.2s.

For an initial head height of 0.17m, the time taken to drain through the 0.003m

orifice is approximately 70s for water and ethylme glycol between 293K and

353K.

3 3 Overview of aigh Temperature Apparatus

There are a variety of design and implanentation challenges in measuring the

p hys id pro perties of molten metals. Besides providing equipment that measures head

and flow rate accurately, an apparatus is required that provides sufficient heat to rnelt the

materiai and that can be closely monitored and controlled. Material selection becomes

l a s trivial under these circumstaaces. As discussed in Chapter 2, since molten metais are

ofien susceptible to d a c e oxidation, conditions must be provided to ensure that oxygen

is kept at sufficiently low levels.

Refer to Figure 3.3 for a schematic of the high temperature apparatus. The

material to be melted is placed in the cnicile that rests on a bottom plate, 0.6m in

diameter and 0.04111 thick. The rest of the frame consists of a smaller plate that rats on

top of the crucible îhat provides a level and rigid surface. The h e is containeci within

a staidess steel shell that contains the atmosphere. Air in the shell is evacuated ushg a

vacuum pump (Speedivac supplieci by Edward High Vacuum Ltd. Manor Royal,

Crawley, Sussex, UX.).

Once air is removed, gas enters the shell and exerts an overpresmre of

approximately 34000 Pa (Spsig). The gas is purged out of the shell through a valve and is

replaced by eesh gas fiom cylinders located near the unit A sample of the purging gas is

analyzed using an oxygen seasor and monitored. A safety release valve is located on the

top of the towa and eomres that the pressure in the unit never exceeds 103000 Pa

(15psig). The material is heated using an induction finnace. Induction leads enter the

tower and connect to the coil that is wrapped around the aucible. The temperature in the

crucible is monitored using two k-type thermocouples, 0.00 12 m in diameter.

Temp LCD Display

Manual control of stopper rod r

O2 Sensor

Pressure Gauge

Acquisition w 1. Crucible 6. Pressure Relief Valve 9.b. Thamocouple to LCD 2. Frame 7, Induction Fumace- display 3. Sheli Power Supply 10. Stopper Rod 4. VacuumPump 8. InductionCoil 1 1. Collection Vesse1 5. Gas Supply 9.a Therrnowuple to data 12. Loadcell

acquisition

Figure 33: EIigh temperatare apparatus.

Before heating, the oxygen level that is obtained fiom the oxygen sensor must

reach 2ûpprn. It is not possible to obtain oxygen levels below this level before heating

using the existing apparatus. Once the matmal is molten and the oxygen content in the

unit has reached equilibrium, the material is poured through the orifice plate and onto the

loadcell (same as the low temperature work). During heating, a stoppa rod is placed

through the bottom of the orifice and released when the experiment is ready to proceed at

a specified temperature and oxygen content. The loadcell supplier recommends that the

loadcell never exceed 363 K. To ensure it is kept sufficiently cool, the melt is captured

ont0 a staidess steel pan 0.30 rn in diameter and 0.10 m high. For tests with duminuni,

the pan contains S i 9 (smd) for the purpose of dissipahg heat. Also, the sand makes it

possible to remove the materiai fkom the pan after it has solidified. For experiments with

AZ91D alloy, Mg0 replaces Si& due to concerns that magnesium may reduce Si02

resulting in an e x o t h d c reaction. uisulation is placed between the loadcell and the pan

for fiirther protection.

Similar to the low temperature work, the head of the melt is d e t d n e d using

precise knowledge of the vesse1 geornetry. Since a crucible is used, it is not possible to

make visuai observations of the head dwhg the course of an experirnent.

32.1 Orifice Plates

AI16 graphite, suppiied by Speer Canada Inc. (Kitchener, Ontario), is used

because of its dirrability and strength to machine orifices. The fictional characteristics of

the orifice may change if the materhl is brittie and susceptiik to Wear. It has been

obsened in practice that AI16 graphite is suitable for repeated use under these

conditions. Refei to Figure 3.4 for a schernatic of the orifice plate design. Larger holes

are required with molten metals than if low temperature Iiquids are used because of the

hi& d a c e energy these systems exhibit relative to low temperature systems. Since

mal1 orifice &es r d t in higher surface effects, the stream may break-up before

impacting the loadcell resulting in the erratic signal discussed in Section 3.1. If surface

effects are too hi&, a continuous streatn is not fomed at al1 and dripping ensues.

Figure 3.4: Orifice plate dimensions for duminam and AZ91D experimenh.

71

3.22 Crucibles

For molten aluminum and AZglD, clay graphite mucibles were supplied by

Morganite Cruciile Inc (Berkshire, U.K). Graphite is a suitable mataial for many high

temperature applications because of its ability to withstand high temperatures and its inert

characteristics with respect to aluminum and magnesiun dioys. The dimensions of the

cmciiles are illustrateci in Figure 3.5. The cnicible will provide a capacity of

approximately 0.9 litres of melt. A hole is machined through the bottom of the crucible

with a depression in which the orifice plate is inserted. The orifice plates are cemented to

the bottom of the crucible and cured at 366 K for 2 hours using "Graphi-Bond", a product

used for graphite materiais available from Aremco Products Inc.

3.23 Induction Furnace

An Inducto 20 mode1 fumace fkom Inductotherm Corp. was used for melting.

The mil was wrapped around the crucible nine times, providing sufficient coupling to the

mucible. Water is rn through the copper coil so that excessive heat that is generated

within the coi1 itself is removeci. It is possible to monitor the lag/lead of the current and

voltage @pals to the coi1 so that an appropriate capacitance can be selected to ensure that

power is being transferred efficientîy. Insulation is placed between the coi1 and the

cruaile to ensure no direct contact is established that wodd d t in a short circuit.

Table 3.1 Uldicates the momt of power the fumace generates in order to reach a specific

temperature.

3.5: Schematic of &y graphite crnrible used for duminom and AZ91D expriment%

Table 3.1: Power requirtments of induction furnace.

Figure 3.6a represents the time it takes to heat up aluminum to 1173 K. The

rnelting point at 933K can be seen as that location on the curve where latent heat is being

adâed with no change in temperature. The time required to heat AZ91D to 1073 K is

represented in Figure 3.6b. The liquidus temperature of 903 K for this alloy is observed

as that location on the curve where there is no change in temperature during heating.

1275g - 99.9% AIumiaum

12758 - 99.9% Alunhum

650g-A29 1D alloy

620g-A29 1 D dloy

660g-A29 1 D alloy

33.4 Rvging Gas

Power to Fumace (kW) Material

The gas used during these experiments was argon supplied by Praxair. The purity

of this gas is of Unportance since d a c e taision depends strongly on the degree to which

the atmosphere is contaminateci. The grade of argon used is "pre-purified" which

specifies a purity of 99.998%. The maximum amounts of oxygen and water present are

both Sppm. The maximum amounts of oxygen, water, carbon diode, THC and methane

Temperature (K)

1073

1173

903

1073

1173

4.5

6

3.5

5

5.5

do not exceed 2ûppm. During the course of one experiment, one cyiinder (49 litres) is

typically consumd contalliing 19MPa (2640 psig) of gas.

O 5 I O 15 20 25 30 35 40

Time (min)

Figure 3.6a: Time required to heat 1.275 kg Aluminum to 1173 K AIurninum Test# 29.

O 10 20 30 40 50 60 Time (min)

Figure 3.6b: Time required to heat 0.620 kg AZ91D to 1023 K AZ91D Test# 4.

3.2.5 Metal Selection

The aluminum used in these experiments is supplied by Alfa Aesar and takes the

fonn of 8-12mm granules. The surface tension is a strong function of the arnount of

i m p d e s present in the melt, a number of which are presented in Table 3.2. Alunhum,

Manganese, and Zinc are the principle alioying elements present in AZ91D. Silicon,

copper, nickel and iron are elements commody present as impunties [9]. Refer to Table

3.3.

Table 3.2: Percent of ele- found as impurities present In rluminnm 1621. Element 1 Percentage-metals basis (wt %)

l Nickel

Silicon

Zinc

Vanadium

0.037

0.00 1

0.003

Tabie 33: Percent of elements added to or contained wîthin AZ91D ailoy 191.

I Nickel (ma) 0,002

Element

1

Percentage-metais basis (wt %)

Manganese (min)

Zinc

Silicon (ma)

0.15

0.35- 1 .O

O. 1

Magnesium (balance) -9 f

32.6 Data Acquisition System

Voltages fiom the loadcell, thamocouple, and oxygen analyzer are recorded

using Instninet, a data acquisition system supplied by GW Instruments Inc. (Somerville

MA). Figure 3.9 illustrates how the system is connected. A network device box (0.10m

x O.12m x 0.25m) is comected to the controller board (inserted into PCI Siot of laptop

amputer) where devices are instal1ed (loadcell, thermocouple, and oxygen andyzer).

Instrunet software is displayed on the laptop monitor and data is saved on a floppy disk as

text files. The laptop system is NEC Versa P series, 75 MHz CPU, 8MB standard RAM,

16 KB cache RAM (intemal), 256 KB cache RAM (external), 256 KB ROM.

The loadcell requires an excitation voltage that is supplied directly from the

network control box fiom the VOu terminal. The strain is registered between the Vi, and

v,' terminais. By selecting the strain gage option in the program, Instninet recognizes

the application and outputs units of d. By manually measuring the mass that is

collected following the experiment and comparing that value to the strain on the loadcell,

a calibration constant is determined by taking the ratio of these two quatities. This

constant is used to convert strain into mas. The output on the loadcell is linear and

facilitates this caldation. The accuracy of the loadcell, as quoted frorn the supplier, is

0.037% fidl scaie.

Temperature is measmeci directly by measuring the difference in voltage between

the V*' and VL taminals. By selecting k-thennocouple in the hardware menu, voltage

is directly converted to degrees cetcius.

The oxygen sensor does not output unïts of concentration. A voltage is dso

measured between the V i l and v,+ terminal; howeva, this quantity must be converted to

concentration independently of the DAS. The conversion is explaineci in section 3.2.7.

Network Device Box

vaut Vin' - . Loadcell Gnd

vin- tn

Gnd IY K-Type . - Thermocouple 1 vin* in

Oxygen Sensor

I Laptop cornputer

Figare 3.7: Data acquisition system used to acquire loadceü, thermocouple, and oxygen sensor data.

32.7 Oxygen Analyzer

The oxygen semor used is mode1 2D-220 supplied by Centorr Vacuum Industries.

The principle behind the sensor is a voltaic cell that m m e s oxygen concentration. The

ratio of the oxygen partial pressures at the two electrodes dictates the magnitude of the

cell voltage. The electrolyte in the cell is solid yttria stabilized Zirconium dioxide

operated at 800°C, which ensures high mobility of oxygen. The concentration of oxygen

in air establishes the potential for the reference electrode, while the concentration in the

sample establishes the potential in the second electrode. The difference in potential of

these two electrodes is the ce11 voltage. There is an LCD display that indicates the

amount of oxygen in the gas Stream by converthg the voltage into parts per million units.

The quantity of oxygen is determined fkom the voltage by applying the Nemst Equation.

RT E = -log, (PO, ~ i r ) (PO, ~ i r )

= 0.0496 T Log,, 4F (PO, sample) (PO, ~ u r n ~ l e )

Where E is the voltage in miIli-volts, T is temperature in degrees Kelvin and 0.0496 is a

constant expressed in millivolts/K. Because the amount of oxygen in the sample is

inversely related to the cell voltage, an increase in oxygen content results in a lower

voltage in the cell. The oxygen content for each experiment is typidly less than 20ppm,

corresponding to an output > 150 millivolts. The cell voltage is comected to the data

acquisition system and recorded.

32.8 Procedure for HIgh Temperature Experiments

The crucible is mounted into the fiame of the apparatus, where two

thennocouples are inserted. From one thermocouple, the temperature is displayed

on an LCD display and fiom the other the temperature is recorded to the data

acquisition system. The materiai to be melted is added to the cruaile. The top

portion of the shell is bolted to the plate that the crucible rests on.

The pan containing SiO2 for aluITilnum and Mgû for AZ91D dloy rests on the

loadcell. The bottom portion of the sheH is bolteci to the plate. The stopper rod is

positioned at the bottom of the orifice plate.

Air is evacuated f?om the unit using the vacuum pump.

The vacuum is tumed off and argon is pumped into the apparatus until a pressÿre

of 34000 Pa (5psig) is registered

Steps 3 and 4 are repeated to ensure more complete oxygen removai.

Once 34000 Pa of argon is exerted on the unit, the purge valve is tmed on. The

gas flow rate is regulated such that the pressure is held constant despite the

presence of a continuous purge.

The oxygen content in the unit is monitored until 2ûppm is registered on the

oxygen sensor. This information is recorded on the data aquisition system every

30 S.

Once the oxygen content reaches 20ppm, the induction fumace is turned on.

R d 1 that 2ûppm is the minimal oxygen content that the existing apparatus can

achieve. Approximately 1 kilowatt (Power = Voltage*Current in induction coil)

is applied to the crucible for every 100 O C until the desired temperature is

reached. This information is dso recorded every 30 S.

9. When the material appmaches the desired temperature, the induction power is

tunied down until the temperature remains steady. The conditions are held for 20

minutes to ensure that the system is stabilized in tenns of temperature and oxygen

content.

10. When the melt is ready to pour through the orifice, the fumace is tumed off. This

is important because it elhinates induction sturuig that may seriously affect the

dynamics of the experiment.

I 1. Within approximately los, the stopper rod is removed and the melt flows from the

orifice ont0 the pan.

12. The loadcell, themiocouple, and oxygen sensor are recorded by the data

acquisition system at a sample rate of 5Hz (0.2s). The data is saved to a floppy

disk.

13. The data is importeci into Excel (Microsofi corporation) where a 2* order

polynornial is fitted to the cumulative mass c w e vernis time data. This function

is diffkrentiated to obtain the experimental flow rate at the respective head heights

taken every 0.2s.

14. For an initial h d height of 0.1 lm, the the taken to drain through a 0.005m

(5mm) orifice is approxirnately 35 s for molten aluminum (973K4165K) and

A29 1 D alloy (921K-1169K).

3 3 Conclusions

Both the low temperature and high temperature equiprnent is designed to provide

conditions where head and flow rate are measured with a minimal amount of uncertainty.

The high temperature apparatus efficiently provides heat and atmospheric control, a

necessity for such experimentation. By making use of the equiprnent and procedures, it is

possible to calculate the fictional characteristics of the orifice using measwements for

head, flow rate, and sotmd knowledge of the physical properties of melts. This is

discussed in detail in Chapter 4. Chapter 5 iflustrates how measurernents for head, flow

rate, and knowledge of the fictional characteristics of the orifice, make it possible to

measure the physical properties of a melt.

This chapter will present the Bernoulli approach to analyze the fluid dynamics of

a stream dralliing fkom a vessel. Two models will be presented. The first mode1 under

consideration will not include surface tension in the formulation. A second mode1 will

account for the surface energy of a stnam exiting an orifice. Non-dimensional numbers

will be inîroduced that provide insight into the relative magnitude of forces, a useful

analysis in designing similar dynamic systems.

4.1 Flow From a Drainhg Vessel: Negiecting Surface Tension

For a vessel having an orifice in the bottom, it is assumed that a fiee jet will form

when the vesse1 is filled with a fluid, and that flow rate is dependent on the head of the

fluid. To predict the flow rate, the Bernoulli formulation will be applied. This approach

is considered to be macroscopic meaning that exact solutions obtained from these

methods are correct "on the average" [80]. The assurnptions made in the derivation will

be clearly outlined.

4.1.1 Formulation

Refer to Figure 4.1 for an illustration of unsteady flow through an orifice. The

two reference locations under consideration are defimed at puits 1 and 2.

Figure 4.1: Schematic of draining vesse1 system depicting flow rate of a fluid through an orifice placed rt the bottom.

Bernoulli Approach

R e f d g to Figure 4.2, Wctionless unsteady flow can be coasidered dong a

stmmhe. Unsteady flow conditions can be considered using this method; however, the

moving boundary located at reference point 1 is not considered in this analysis. The

forces acting on the srnaIl cylindrical elment of fiuid that acts in the direction of the

streamline wül be applied dong with Newton's second law (Le. F,, = d(mu)/dt). This

formulation is outlined in Daugherty et al. [79]. The Bernoulli equation applied

specifically to a draining vesse1 system has been formulated in Whitaker [80]; however,

m i e n t terms were neglected.

Figure 4.2: Control element on streamiine neglecting frictional losses.

The forces tending to accelerate the fluid m a s are the pressure forces at the ends of the

element:

PdA, - (P + dp)& = d P a C (62)

Where P is the pressure exerted at the inlet of the eIement, dP is the change in pressure

across the element and A, is the cross sectional area of the element.

The weight of the element in the direction of motion is:

mg = pgdAC&

The sum of the forces expressed by Equatiom (62) and (63) equal the change in

momentum of the control element:

- dP&, + mdAc& = - dt

(64)

Daugherty et al. [79] considered the case of unsteady flow (velocity as a fiuiction of both

position and time). The following relationship is obtained:

Equation (65) can be expressed as:

Dividing by -p&:

The term du/dt is considered to be constant since the relation between velocity and time

at reference points 1 and 2 is essentially linear. Refer to Figure A.1 in Appendix A for

validation of the Iinear assumption. Integrating Equation (68) between points 1 and 2

yields:

Note that the formulation has thus far neglected viscosity effects in the derivation. The

balance is therefore considered to be valid for inviscid flow only. The frictional effits

will be charcterized by the discharge coefficient that will be introduced later in this

section. The t e m ~ (zz - zi) is the head of fluid above the exit of the orifice, h, as indicated

by Figure 4.1. The velocity at point 1 can be expressed as the velocity at point 2

An assumption is made at this point in the formulation. Since r, » r., ut = O [79].

Rearranging in terms of outlet velocity, u2, yields:

u2 =\12+ - (4 -4) -y&)) w g at

(7 1 )

The terni h/g(au/ût) represents the accelerative head term within the vesse1 [79]. This

term is neglected in the final fom of the equation. The assumption that the accelerative

head term is negiigible is validated in Appendix A. Another assumption will be

presented at this point. It is assumed that there is no pressure ciifference between points

1 and 2 (atmospheric pressure at the fiee d a c e and onfice tip). In section 4.2, a new

formulation will be presented, which states that there is in fact a pressure exerted at point

2 due to the effects of d a c e tension. Equation (71) becomes:

u2 =Ji& (72)

This is the classical expression that relates veiocity with head. Since finction is neglected

in the formulation, U* is considered to be the theoretical maximum velocity at the exit of

the orifice.

u, =&

Or in tenns of maximum theortical flow rate:

Q, = no2 ,lm A summary of the assumptions made in this formulation are the follohg:

1) The flow is quasi-steady state (vdidated in Appendix A).

2) Viscous dissipation is neglected.

3) The velocity at reference point 1, ui, is mal1 compareci with uz.

4) The velocity profile at the orifice exit is flat

5 ) The pressure at the inlet and outlet is atmopsheric pressure oniy (Le. Pi = Pd.

Equation (74) can be expressed in dimensionless form by introducing the Froude

number:

inertial Forces - u,' ( / m,') Fr = ,-= = I Potential Forces 2gh 2gh

The Froude number is aiways q u a i to unity in this analysis since viscous losses are

neglected.

Next, the discharge coefficient is used to characterize the Wction losses in the

orifice, and is defined as the ratio between experimental flow rate and theoretical flow

rate:

Qap is deiined as the experimental flow rate in rmits of m3/s. Clearly, Cd must always be

less than mity since viscous losses in the orince result in flow rates Iess than what is

computed ideally from Equation (74). Note that Equation (76) is dimensionless. The

physical significance of the inertial and viscous forces will now be discussed.

The Reynolds nurnber (Re) is introduced to characterize the inertial and viscous

forces at the orifice.

Where p and q are the density and viscosity of the fluid respectively, and b, is

experimental fluid velocity.

The next section will calculate the discharge coefficient expressed in Equation

(76) for water and ethylene glycol at different temperatures. This quantity will be plotted

against Reynolds number so that fictional characteristics in the orifice can be

determined.

4.1.2 Resuits

Ethylene Glycol and Water were used to test the formulation presented in this

section using a 0.003m diameter Teflon orifice. The viscosity of these fiuids is a strong

fùnction of temperature and makes it possible to explore a wide range Reynolds numbers

[6 LI. Refa to section 3.1 for an overview of the methodology for Iow temperature

experimentation. The tlow rate was determined fkom the cumulative mass measured with

time by the digital s d e (Ohaus GT-8000) and a stopwatch. A video canera recorded the

m a s and time bat was displayed by the instrumentation. The flow rate was calnilateci

by differentiating the cumuiative mass cume that was generated. Refer to Figure 4.3 for

the cumulative mass of water at 293 K for this system. The 3d order polynomial used to

desaibe the curve is included on the chart. It was determined that a 3" order polynomial

fit sufnciently desmies the data and that an increasing polpmial order does not

improve accmcy.

The fiindon takes the fonn:

Cm& =3.442~10-'(t)' -6.315x10-~(t)~ + 1.1 13x10"(1) +9.842x10"kg (78)

The standard deviation between the data points depicted in Figure 4.3 and the polynomial

curve is cdculated as follows:

The number of data points, n, is 75.

Equation (78) is differentiated to yield the flow rate on a mass basis, Le.:

Head was detennined through visual observation and recorded on video as well. Flow

rate and head were used in Equation (76) to calcuiate the discharge coefficient. Head is

ilIwtrated as a function of tirne in Figure 4.4. The scale used for visual observations is

accurate to 0.0005m.

R d t s from this anaîysis are represented in Figure 4.5. Each Liquid exhibits

different fictional ~haracte~stics, as Figure 4.5 indicates. The formulation presented in

the last section is reinvestigated in the next section to explain this behavior. By

accounting for other forces mch as d a c e tension e f f i , it will be observeci that a

different relationship is geaerated for the discharge coefficient and Reynolds numba

adysis .

20 40 60

Time (s)

Figure 43: Cumulative mass versus t h e for water at 293 K through 0.003m Teflon orifice plate from an initiai head of approximately 0.17m.

O 10 20 30 40 50 60 70 80

TÏme (s)

Figure 4-4: Head versus time for water at 293 K through a 0.003mTeflon orifice piate fkom an initial head of approximately 0.1711~

* Water 293 K A Water 321.5 K o Ethylene Glycol 298 K

Ethylene Glycol 333 K

Figure 4.5: Cd versus Reup, caicdated using Equation (76) for a 0.003m dameter orifice dralning under the influence of gnvity. Ethylene glycol and water are

presented at difierent temperatures.

4.2 Flow From a Drainhg Vessel: A New Approach

The formulation presented in section 4.1 did not consider pressure e k t s at

reference points 1 and 2 in Figure 4.1. The same system wiU be considered in this

discussion; however, pressures induced k m the effects of d a c e tension wiii be

wnsidaed as well. The new formulation will be tested and vdidated using the discharge

coefficient versus Reynolds number characterization using the same experimental data

that was used to generate Figure 4.5. Finally, a new dimensionless number will be

deîbed called the Bond number that indicates the magnitude of d a c e forces in the

system. This quantity assists in outlining the experimental set of conditions that result in

signifiant effects due to surface tension.

4 . 1 Formulation

Pressure that is induced by surface tension occurs at curved interface separating

the liquid kom the atmosphere. This occurs just below reference point 2 on Figure 4.1.

The Laplace equation relates the pressure difference across a curved interface to the radii

of curvature:

AP is the pressure difference across the liquidgas intdace, and and

qresent the radii of curvature that describes the shape of the surface. If there is a planar

surface, R+ 00, arîd there is no pressure induced as Equation (8 1) indicates.

At reference point 1 (top of the liquid in the vessel), it is a s m e d that the

pressure induced is negligible since the interface is considered to be planar and

approach Wty).

Duectly below reference point 2 (orifice tip), the stream exiting the orifice is

essentidly cylindncal with the matures iilustrated in Figure 4.6. At a location just

below the orifice (where the stream is first in contact with the atmosphere), is

taken to be the radius of the orifice, ri,. The second radius of curvatwe, Le%- is

assimied to be infinity since Uie stream is assumeci to be a perfect cylinder at this

location,

Figure 4.6: Radius of cuwature definhg the gas-iiquid interface of a free jet.

From the Laplace equation, the pressure induced due to the effects of d a c e

tension directly below the orifice is:

P=& R d t a n t Pressure

Referencc Point 2

Exerted at Point 2

Figure 4.7: Pressure acting nt orifice tip for a stream of iiquid erposed to the atmosp here.

Considering Equation (71), and assuming quasi-steady state conditions, an added

pressure at reference point 2 is inciuded in the formulation that corresponds to a

magnitude of air,

Pi is taken to be atmospheric pressure only because the fkee surface is considered to be

planar, which indicates no effkcts of d a c e tension. Equation (83) is considered to

represent the theoretical maximum velocity since ûictional losses are not considered ai

this point.

Or in terms of maximum theortical flow rate:

By rearranging Equation (85), it is possible to obtain the relative magnitudes of the

inertial, gravitational, and d a c e forces in a dimensionless format. This is useful in

detemiining the relative magnitude of these forces.

The Froude number appears on the left hand side of Equation (87). We now define

the Bond number as:

Potential Forces pgrh Bo = -- -

StirjtuceForces a

Equation (87) cm be expressed as the summation of the Froude number and reciprocal of

the Bond number

Similar to the analysis in section 4.1, the discharge coefficient is calculated using

Equation (85) and the experimental flow rate.

Similar to Section 4.1.2, in the next section will calculate the discharge coefficient

expressed in Equation (90) will be caiculated for water and ethylene glycol at different

temperatures. Equation (90) will be plotted against Reynolds number so that the

fictional characteristics in the orifice can be determined.

The surface tension of ethylene glycol and water was required for this analysis

[6 1,631. The results are presented in Figure 4.8. The trends of each liquid appear to

follow, more consistently, a dependence on Reynolds number. There is a transition zone

that is estimated to be approximately between 300 < Re < 3000. Laminar flow is likely

chmcterized by the portion that approaches the origin on the y-axis. The turbulent

@me (Re>2000) appears to have a sIight dope. Chapter 6 will provide further insight

into the turbulent regime in the discussion of expehental viscosity results.

Water 293 K A Water 321 -5 K o Ethylene Glycol 298 K o Ethylene Glycol 333 K

Figure 4.8: Cd versus Re- ralculated using Equation (90) for a 0.003m diameter orifie draining under the influence of gravie. Ethylene glycol and water

are presented nt dinerent temperatures.

4.3 Considentions for Bigh Temperature Fluids

In quantifjing surface energy in the momentum balance, the use of dimensiodess

numbers can be insightfd in terms of identimg for which systems and under what

conditions this new formulation should be considerd Inspection of Equation (89)

indiates thai as reciprocal of the Bond numbers incfeases, the Froude number must

decrease since the sum of these numbers must equal uni@. A srnall Bond number is

indicative of a systern where SUrfblce energy is playhg a significant role. The following

criterion is proposed conceming this issue:

1) As 1/Bo+O for a particular system, Fr+. By inspection of Equations (75) and

(89), flow rate and the âictional characteristics aui be reasonably approximated using the

classic approach outiined in section 4.1.

2) When !/Bo + 1, then Fr + O. This result c o b s the necessity to account for

surface tension using the newly developed approach outlined in section 4.2.

3) When 1iBo > 1, Fr < O meaning that continuous flow has stopped and that a

different formulation is required to desmie throughput (i.e. dripping supplied by

capillary action).

Through proper examination of the Bond number, it is possible to determine when

surface energy is expected to play a significant role for a pmticular system. For instance,

fluids with a relatively large surface tension to density ratio exhibit fluid dynamic

behavior in which surface forces are significant because surface tension appears in the

denominator and density appears in the numerator. Also, surface tension is expected to

exhibit greata infiuence on the system when a relatively small orifice is used. Finally,

and durhg the coune of an expairnent as head conditions get lower, surface forces

increase in relative magnitude since head appears in the numenitor as weli.

Densities of molten metals are known to be higher than those of fluids such as

water and a variety of orgsnic fîuids. Also, molten metals have cunsiderably higher

sinface tension values than iow temperature fluids such as water and organic liquids.

This has been discussed in Chapter 2. The innuence of the density-surface tension ratio

on the magnitude of the Bond number is obvious when comparing water and duminum

systems. Data collected for these systans is presented in Figure 4.9 for a 0.005m

diameta orifice design. It is immediately evident that the duminum systern is influenceci

to a greater extent by surface forces. This is due to the fact that dimiinwn's dmity-

surface tension ratio is 5.5 times l e s than it is for water (pmo = 988 kg/m3, cm0 = 0.069

N/rn at 3 13 K [6 11; = 2300 kg/m3 [Z], o = 0.83 Nlm [v at 1 173 K). Head conditions

corresponding to the water data vary between 0.13 and 0.01m. For aluminun the

conditions varied between 0. 12 and 0.02111.

m Aluminum 1 173 K II,,,,,, 1

Figure 4.9: Dependence of the Bond and Froude relation on the density- surface tension ratio.

Figure 4.10 illustrates the magnitude of the Bond number for a variety of fluids.

The head and orifice radius were hypothetically chosen at 0.01m and 0.004m respectively

because these design pararneters realistically enmre that a full scale Fr vs. Bo c i w e is

observed. Molten systems point to the fact that Bond numbers vary significantly

dependhg on the metal that is used. Mercury and lead are the only metals on this chart

that are within the same range as water and other orgaaic fiuids. Note that for other

values of head and orifice anas, only the magnitude of Fr and Bo WU Vary dong the

same h e shown in Figure 4.1 O.

Figure 4.10: Relative magnitude of Bond numbers for a variety of iiquids. Density and surface tension are obtained from Iida and Guthrie 121.

From a design perspective, the foUowing formulation can be very useful. By

takùig the ratio of Equatiom (84) and (73), Equation (9 1) is obtained:

For any processing condition, and if reliable pmperty data is available, one can detemiine

the flow regime that would be appropriate to consida before experiments are performed,

thus enabling the appropriate formulation to be utilized. The value compuîed h m

Equation (91) is an indication of the discrepancy if the effect of surface tension on

pressure at the outlet is neglected in the formulation. If Equation (91) approaches Uni@,

it is more reasonable to neglect d a c e energy in the formulation. Fimes 4.1 1,4.12, and

4.13 illustrate the discrepancies for head conditions between 0.1 and 0.01m for water,

iron and aiuminum systems respectively. These conditions are based on constant head

opaation. The properties of water were taken at 293 K [61] and those of molten

aluminum and iron at the melting points [2,7]. The results c o n h the significant

dependency on surface energy many melts exhibit relative to low temperature fluids such

as water. For instance, if a head of O.OSm (50cm) is utilized with a specified discrepancy

of 0.90, Figures 4.12 and 4.13 indicate that the radius must be in excess of 0.0030m

( 3 . b ) and 0.004 (4.01n.m) for Von and duminum respectively. When water is

considered, the orifice radius must only be in excess of O.OM7m (0.7mm). For the same

experimental conditions, molten metals have a higher value of IfBo than Iow temperature

organic liquids. Unfortunately, the density and surface tension of these Iiquids are often

unlanom.

dl- %O OW5

Figure 4.1 1 :

- - m0.05m head -0.02m head

.O001 0.0003 0.0005 0.0007 0.0009 Orifice Radius (m)

Water: Accmcy in neglectiag surface energy for variable orifice Y

design for heads ranghg from O.lm to 0.01m.

O 0.002 0.004 0.006 0.008 0.01 Orifice Radius (m)

-O.?m head - - e0.05m head *0.02m head *O.Oim head

Figure 4.12: Molten kon: Accuracy in negïecümg stuface energy for variable orifice design for heads rrngtng from O.lm to 0.011~~

103

-0.1m head - ~0.05m head

0.02m head -0.01 m head

Figure 4.13: Molten aluminum: Accuracy in neglecting surface energy for variable orifice design for heads ringing from O.lm to 0.01m.

4.4 Conclusions

The case of a fluid drainhg through an orifice is not a trivial problem that is

solved by accounting only for potential and inertial forces. la order to properly

characterize fictional losses in the system, conditions may exist where d a c e tension

must be implernented in the analysis. These conditions exist when, in relative temis,

fluid head and orifice radius are smd; and surface tension to density ratio is large. These

conditions are addresseci in the Bond number, which cm be useful h m a design

standpoint in detennining whether or not d a c e tension should be included in the

malysis. This approach is most relevant for molten metal systems where surface forces

are knom to be signifiant, and points to yet another example of the necessity to expand

the current available data of the liquid properties of hi& temperature systems. In the

next chapter, it will be shown how this formulation cm be used to calculate the physical

properties such as d a c e tension, viscosity and density. This is accomplished, however,

once the nictional characteristics of the orifice are quantified and calibrated using the

analysis desmieci in this chapter. Through proper caliratioa of the discharge

coefficient-Reynolds number relationship, the properties of liquids, in particular melts,

can be determined by measuring flow rate and head.

CHAPTER 5: FORMULATION OF PHYSICAL PROPERTY MEASUREMENTS

In this chapter, a formulation will be presented that calculates the physical

propdes of melts. A calibration relating discharge coefficient with Reynolds number,

coupled with experimental flow rate and head meaSuTernents, facilitates these

measurements because surface tension, viscosity and density are inherently part of the

formulation developed in Chapter 4. An approach to measure surface tension for systems

where density and viscosity are known will be fomiulated and validated using systems

involving water. This is a useful exercise in andyzing the sensitivity of the calculation

when low temperature liquids are used. By implementing non-linear regression

techniques it will be illustrateci how surfàce tension, density, and viscosity can be

detemineci simultaneousl y using data collected fiom one experirnent. This is relevant

when dealing with molten systems because it is often encountered that more than one

physical property is unknown. Molten aluminum is used in this analysis to validate the

model. A ngorous mor anaiysis is pdormed that identifies various sources of error and

predicts the uncertainties expected in the results. This is useful in detemiinhg for which

fluids, and under what conditions accurate measurments can be perfonned.

5.1 Formuiation of Surface Tension Measarements: Fiuids with Known Density and Viscosity

As explained in section 2.1.4, techniques that measure surface tension are

typically the product of a force balance in which d a c e forces play a signincant role.

By reatranging Equation (go), an expression for surface tension as a ftlnction of

experimental flow rate, head, and discharge coefficient is obtained:

A drainhg vessel system offers a distinct advantage compared with other

techniques. Conditions of flow rate, head, and discharge coefficient change continuously

during the course of one experiment. Consequently, by drainllig the vessel, a number of

rneasurernents can be made due to the variable conditions*

This new method for detemiining suface tension is based on the calibration of

fictional losses in the orifice described by Cd. This is accomplished using fluids of

hown properties for which under varying conditions of head and flow, a relationship

between discharge coefficient and Reynolds number can be determined. A 3d order

polynomial was chosen to describe the discharge coefficient cWee

For the work pdormed with water presented in section 5.1.3, it was deterniined that an

increase in the polynomial order did not result in an improved fit to the experimental data

(for 1000 < Re < 5500). Refer to Section 3.1.1 for this particular orifice design. For

molten aluminum, it will be revealed in section 5.2.2 that a lin- approximation

sufficiently descnia the discharge coefficient for 4000 < Re < 13000 and that constants

a and b are set to zero. Note that the discharge coefficient-Reynolds number relationship

is not considered to be linear. Certain portions of the awe, however, can be

approximated to be so. It wiil be reveaIed in Section 5.2.1, with the introduction of

multiple non-linear regression analysis, that this approach results in a simple

computational technique comparecl with a hifier order polynomial fit The orifice design

for the aluminum work is referenced in Section 3.2.1. Equation (93) cm be written in

terms of Q,, p, q and the polynomial constants, a b, c and d as follows:

5.1.1 Ertor Analysis

Enors in head, flow rate, and discharge coefficient will dl contribute to the error

Ui the calculation of surface tension. The propagation of unceaainties is used to

determine the effects and is written as follows [64]:

The value 6 0 is the expected deviation in d a c e tension. Quantitia, 6h, 6Q,,,

and SCd represent the standard deviations of head, flow rate and discharge coefficient

respective1 y.

The diEerentiaIs in Equation (95) are determined by taking the derivative of

E p t i o n (92) with respect to h, Q,, and Cd. TheSe relationships are represented in

Equations (96-98): The derivative of Equation (92) with respect to h is:

The derivative of Equation (92) with respect to Q, is:

(Recall fiom Equation (75) that u, = ,/2gh.Fr )

The derivative of Equation (92) with respect to Cd is:

Errors in Head

R e f d g to Equation (96), uncertainties in head will produce a deviation in

surface tension proportional to the product of p, g, and r,. This indicates that low-density

fluids and small orifice sizes are favorable in terms of accunicy of the surface tension

calculation. The derivative is independent of processing variables h, Qap, and Cd and

indicates the mors in the measurernent would be constant for any set of processing

conditions.

Enors in FIow Rate

In the presence of mors in flow rate, Equation (97) Uldicates that decreasing

hed, results in decreasing enor in the calcuiation. Low-density liquids are preferable, as

are large orifice &. Aiso, large discharge coefficients are favorable in minimin'ng the

effects of mor in flow rate.

Errom in Discharge Coq@cient

Similm to aors in fiow rate, diminishing head conditions and large discharge

coefficients irnprove the accuracy of the caldation h m analysis of Equation (98).

Small orifice designs and low-density liquids are more favorable as weii. By rearranging

Equation (98). an acceptable deviation with respect to a deviation in discharge coefficient

(do/ûCd) cm be imposed such that head never exceeds the following level:

This constraint will be put into practice in Section 5.1.3.

5.12 Data Analysis

Tests with water at 32 1.5 K were conducted to assess the feasibility of measuring

surface tension. Refer to Section 3.1 in Chapter 3. The 0.003m diameter Teflon orifice

plate was used. The cumulative mass was measured using the Ohaus GT-8000 scale and

a stopwatch. A video carnera was directeci at the scaie and stopwatch to record the mass

and tirne. The flow rate was detennined by differentiating the cumulative mass curve

that was genexated using a 2& order polynomial fit to the experimental data. Head was

determineci through Msual observation and recordeci on video as well. Four calibrations

were used to determine the polynomial constants a, b, c, and d required in Equation (93)

and (94). This was done using water at room temperature as a caliibration fluid. The

densiîy and viscosity of water at 293 K are 998 k91m3 and 1.002~10~~ ~ s l r n ~ respectively

[6 11. At an elevated temperature of 32 1.5 K, the density is 988 kg/m3 and the viscosity is

significantly less at 5.86~10" ~ s / m ~ [6 11. This corresponds to a decrease in viscosity of

41.5% resulting in operation at higher Reynolds nimibers. With reliable physical

pro- data and consistent cali'brations, the d a c e tension of water at 32 1.5 K is to be

calculated at any set of conditions, provided that Equation (92) properly quantifia

d a c e tension.

Meamring Head

Figure 5.1 illustrates head measmements that were taken at the respective times.

A 2Pd order polynomial relation was fitted to the data as illustrated. It was determined

that inmeashg the order of the polynomial fit did not improve the accuracy of the fit.

Error in head measurements can be represented by the standard deviation that is

calculated between experirnental numbers and the mathematical fiinction. The curve

takes the following form:

hmb = 229x1 O-' (t)' - 4.17~10" ( t ) + 1.95x10-' (m) ( 100)

O 10 20 30 40 50 60 70 80

Time (s)

Figwe 5.1: Experimentd Head measurements for water at 321.5 K.

The standard deviation of Equaîion (100) with respect to the experimental data points

presented in figure 5.1 is:

The quantity, n, represents the number of data points. h i e to the nature in which head

was mea~ufed, the m r represented by the standard deviation is %indom" and means

that each experimental data point has an equal possibility of producing either a positive or

negative deviation. When measuring head with a linear scale measuring length, random

behavior is encountered because values often have to be interpolateci. This results in

equal possibilities of either underestimating or overestimating the true dimension. Figure

5.2 illustrates the random deviations.

Figure 52: Deviations between experimentai head and calcuiated head for water at 3215 K.

Meanring Flow Rate

The cumulative mass m e is illustrated in Figure 5.3. Unlike relathg head with

the, the instantanmus flow rate is produced indirectly by analytically differentiating the

2" order polynomial m e that was detennifled to fit the data reasmably.

Cm,, = -6.228~10" ( t ) l - 1 .113x1 o - ~ ( t ) + 1 .246e-3 kg ( 102)

The standard deviation depicted in Figure 5.3 is:

The flow rate is:

dCm*pb = - 1.246~1 O-' (r) - 1.1 1 3e-2 kg / r dt

O 20 40 60 80

Time (s)

Cumulative

Figure 5.3: Cumuiative m a s as a functioa of thne for water at 321.5 K through a 0.003111 diameter Teflon orifice.

Errors associated with flow rate are of a different type than the random errors

exhibited in Figure 5.2, since they are considered "systematic" in nature. An analytical

expression is used to detemine the flow rate, which is an approximation to the actual

flow rate. Errors in the f o d a are systematic because they take the form of entire shifts

in magnitude rather than random deviations. Consequently, systematic errors produce

erroneous data that is not easily recopnized.

Meanring Discharge Coement

Figure 5.4 illustrates Cd as a fiinction of R h p detemiined for four different

calibration tests of the orifice.

Calibration 1 Calibration 2 Calibration 3 Calibration 4 - Polynomial Fit

Figure 5.4: Cilibration for a 0.003m diameter orifice hole using water at room temperature.

It is clear that there is little random scatter, yet there are differences that exist

between each calibmtion, even though they are generated under identicai conditions.

This is the result of systematic differences that are attnauted to mrs in the analfical

expressions for flow rate. A 3d order plynomial fit was used on aU four data sets

together making it possible to determine a standard deviation tem for discharge

coefficient that represents differences between the four calï'brations.

Cd = 2.587~10-~~(Re)' - 3.1 1 0 ~ 1 0 - ~ ( ~ e ) ~ + 1 .326x104(Fte) + 5.965x10-' (105)

The standard deviation in discharge coefficient was determinecl using Equation ( 1 05) and

each experimental data point represented in Figure 5.4.

Where a, the number of data points, is equal to 295 for al1 four calibrations combined.

5.13 Surface Tension of Water at 321.5 K

The data presented in Figures 5.1, 5.3, and 5.4 for water at 32 1.5 K were used to

test the validity of Equation (92). First, each of the four room temperature calibrations

was used independendy to aoalyze the propagation of mors theory. A 3" order

polynomial fit was used to desmie each o f the four calibrations. AU four calibrations

were also used in combination to produce a more statisticdly sound bction. This

hct ion is Ecpation (105) and is also represented in Table 5.1 as the "combination" data

set. The variability between the four re1ationsh.p~ is athiauted to random m r s in head,

and systematic errors in flow rate.

Table 5.1: Polynomlril constants that describe the discharge coefficient as a fiinction

Results for the -ce tension of water at 32 1.5 K are presented in Figure 5.5 for

each o f the four independent calibrations. The average value indicated on the chart

represents the average of ail points represented in Figure 5.5.

of Reynolds number.

O 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Head (m)

+ Calibrationl Calibration2 Calibra tion3 Calibration4

d

5 .83~ 10-'

5 . 6 0 ~ 1 O-'

6.1 8x 1 O*'

5 . 6 1 ~ 1 ~ '

5.965~ 1 o * ~

Figure 5.5: Experimentai sarface tension as a fiinction of head for water at 321.5 K for four separate caiibrntions.

c

1.52~ 1 o4

1 . 6 1 ~ 1 0 ~

1 . 1 8 ~ 1 0 ~

1 .76x1 0e4

1.326~ 1 o4

Caiibration

#l

#2

#3

#4

Combination

A

3.3 8x 1 O*"

2 . 9 2 ~ 1 0'12

2.53~ 10-l2

4.64~ 1 0-l2

2.587~ 1 O-"!

b

-3.80~ 1 O~

- 3 .71~10~

-2.84~ 1 o4

-4.84~ 1 o4

-3.1 10x10~

The propagation of m r s analysis, explained in section 5.1.1, was used to predict

the error in the detemination of d a c e tension. The standard deviation in head and

discharge coefficient was used to calculate the expected error, represented by the solid

arrow lines in Figure 5.5. The solid Iines were determined through application of

Equation (95). The partial derivatives with respect to h and Cd are Equations (96) and

(98) respectively. The standard deviations in h and Cd are determineci as indicated fk rn

Equations (1 0 1) and (1 06) respectively. The deviation with respect to flow rate was not

considered in the calculation. The propagation of m r analysis reasonably predicts the

magnitude of error in surface tension since scatter between the four calibrations follows

similar trends to the predicted deviation lines. This confirms, as predicted in section

5.1.1, that mors in surface tension increase with head. Also, there eppears to be greater

deviations between the four calibrations than is exhi'bited within each calibration. This

indicates that random erron related to head measurernents, appear to be insignificant.

Thus, enon inherent with the discharge coefficient seem to dominate the accuracy of the

surface tension measmement. Applying Equation (99) facilitates the maximum head to

be calculated resulting in a maximum amount of error in d a c e tension. As an example,

if the tolerance in the calculation is f0.0075 N/m, then substituting appropnate variables

in Equation (99) yields:

Recall that the deviation in discharge coefficient was determined fiom Equation (106) to

be 0.0035. The region indicated by the dashed arrows in Figure 5.5 predicts the range of

head conditions deemed acceptible in terms of aror in surface tension. The results

represented in Figure 5.5 confirm that for a tolerance of I 0.0075Nlm, the head should be

no greater than 0.063611~ Figure 5.6 represents the maximum h d that should be utilized

for a variety of hypothetical mors in d a c e tension for this system.

l/B0=0.90 l/Bo=O.06

O 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Head (m)

Figure 5.6: Maximum head height determined for a specified error in surface tension for water draining through a O.OO3m diameter orifice at 321.5 K o

Next, the polynomial curve that was fitted to ail four calibrations was used to

calculate the surface tension (combination that is illustrated in Table 5.1). By doing this,

a more sbtistically sound calibraîion is used since ail four calibrations are considerd

together and the nmber of data points used in generating the curve is increased by a

factor of four. Figure 5.7 illustrates the r d t s using this relationship. The standard

deviation of the data presented in Figure 5.7 is 0.002 Nlm. Results are presented and

compared with literame in Table 5.2.

Figure 5.7: Average surface tension of water at 321.5 K.

*&

Table 5.2: Cornparison between experimentd surface tension and literature value

*

for water at 321.5 K 1611. 1 Average Experimentai ( CRC Handbook of Chemistry 1 Percentage Difference 1 Sdace Tension 1 and Physics at 32 1.5 K 1

-4 3T%=

The validation of the mode1 is confirmeci since the average d a c e tension that is

calculateci h g this approach is in agreement with the accepted literature value at 32 1.5

K to within the experimental error.

+''

5.2 Formuiatioa for Sùnuitaneoas Determination of Surface Tension, Viscosity, and Density

6

Uncertainties associated with the values of density and viscosity will yield

systematic e n o ~ that may seriously impact the caldation of d a c e tension.

* O 0.02 0.04 0.06 0.08

Head (m)

Fortunately, the statistical nature of these experiments makes it possible to not only

measure surface tension, but density and viscosity as weli. The vast amount of data each

experiment produces faditates the simultaneous calculation of al1 three propaties ushg

non-linear regression analysis.

The following discussion outlines the formulation of the Gauss-Newton method.

The experimental head, hi,,, can be expressed as a fhction of experimental flow rate,

fQa) with a certain degree of error, m i i , , as follows:

h , = f ce,., 1 + &,ex, ( 1 07)

Where hi, and Qiap are experimental data points that are expressed in vector notation:

QI,

Qi.q

Q..m

Next, the fhction for d a c e tension in terms of Q , h, and constants a, b, c, and d,

dmcribed by Equation (94), is to be rearranged in ternis of one of the experimentd

variables. Using the format in Equation (107) the theoretical head is written in ternis of

Q, follows:

Flow rate, Q, is a volumeûic qwtity that is determiELed h m mass flow rate data.

Consequently, information on density is required so that the mass cm be converted to a

volumetric qumtity. Since density is considered an unknown in this malysis, the flux,

V,, cm be introduced to replace Q,:

Equation ( 1 10) can now be expresses as follows:

Equation ( 1 07) is now expressed in terms of flux:

h,.W = f (C., + 4.,

The non-hear model represented in Equation (1 12) is expanded in a Taylor series

around the unknown properties, cr, q, and p.

The subscript j corresponds to an initial guess, and, j+l is the r d t after a single iteration

of the algorithm. SubstiMing Equation (1 14) hto Equation (1 13) yields:

Equation (1 15) illustrates how differences between expaimental and calculated values

for head are minimized. Equation (1 15) can be represented in matrix notation:

{y} = [z, k 4 + w Where [Zj] is a matrix of partial derivatives:

The partial derivatives of Equation (1 12), for substitution into Equation ( 1 15), with

respect to o, q, p are:

f =- 1

au pgr,

The vector (Y} corresponds to the difference between experimental and calculated head

Vector {Ax} corresponds to the change in propeities:

{AE) is the error cissociated with the differences between experimental and

caldated head values. This quantity decresses as the solution converges. Applying

linear least square theory r d t s in the following rnatrix inverse relationship:

An initial guess is made, and new quaatities for 0, q, and p are determined iteratively

using Equations (124a) through (1 244.

=Ci +AQ;

A series of convergence critezia must be met when the solution is stated. Convergence is

met once the following quantities are mder than a chosen tolerance, E. For this study,

the tolerance was chosen to be 1 x 10".

The values k, e,,, E,,, correspond to the tolerance of each propcrty. I f one of the criteria

represented in Equations ( 1 25a) through ( 1 X c ) is not met, the algorithm is performed for

an additional itenition using the updated vaiues for cr, q, and p as the new initial guess.

The Matlab program used to perform this computational technique is presented in

The propagation of mors theoran c m be used not only to determine the

sensitivity of the surface tension dcuiation, but the sensitivity of the viscosity and

density caldation as well.

5.2.1.1 Surfâce Tension

Using non-hear regession, the prediction in uncertainty of surface tension is

identical to the approach outlined in section 5.1.1. The issues associated with enors in

head, flow rate and discharge coefficient are addressed in Equations (96) through (98).

Density

The propagation of mors theorem when applied to the calculation of density

requires Equation (92) to be r e m g e d in terms of density:

d

Applying propagation of mors theorem to Equation (126):

Similar to the error analysis with d a c e tension, the quantities 6h, SQ,, and SCd refer

to the standard deviations in head, flow rate and discharge coefficient. Before

proceeding, the following terms wiU be recalled h m Chapter 4:

The derivative of Equation (126) with respect to h is:

Substitutiug equations (1 28) through (1 30) into Equation (1 3 1) yields:

The derivative of Equation (126) with respect to Qap is:

Substituthg Equatious (1 28) through (1 29) into (1 33) yields:

The derivative of Equation (126) with respect to Cd is:

Substituting (1 28) through (1 29) into Equation (1 35) yields:

Ermrs in Head

Like surface tension measurements, mors associatecl with head produce error in

density rneasurments that are independent of the dynamic conditions (head, flow rate

and discharge coefficient). Low-density fluids with a high d a c e tension produce Less

uncertainty in tenns of density cdculations as Equation (132) indicates. A mal1 orifice

radius is also favorable to larger &es as are relatively high discharge coefficients.

Evors in Flow Rate

Like surface tension measurements, mors in flow rate produce higher deviations

in density me8suTernents when low-densi@ liquids are used that have relatively high

d a c e tensions. This is firrther reinforcd with the presence of the Bond number in

Equation (134). Discharge coefficients that approach unity r d t in favorable conditions

as well since discharge coefficient appears in the denominator. Like d a c e tension, it is

best to have larger orifice siza in the presence of erron in flow rate for more accurate

density measurements.

Errors in Discharge Co&cient

In tams of m r s in discharge coefficient, Equation (136) indicates that accurate

density measurements are facilitated when lowdetlsity Iiquids with relatively hi&

d a c e tensions are used. The presence of the Bond nimiber indiates that high d a c e

tension is fiivorable as well as conditions of low head. Again, discharge coefficients that

approach unity are favorable because the discharge coefficient is in the denorninator of

Equation (1 36).

5.2.13 Viscosity

In analyzing the sensitivity of the viscosity calculation, the task is not as trivial as

it is when studying surface tension and density. A problem arises when reaminging the

hct ioa in terms of viscosity because it cannot be solved for directly, as Equation (94)

indiaites. An assumption is made that Cd VS. Re curve is piece wise Iinear so that the

constants a, and b, are zero. This assumption is only valid for 4000 < Re < 13000, as will

be revealed in Section 5.2-1.

The propagation of errors theorem is applied to Equation (94), which is

rearranged in ternis of viscosity in this instance. The associated errors are assumed to be

head, flow rate, as well as uncertainty in constants c, and d that approximate the fiictional

characteristics of the orifice. Rearranging Equation (94):

Applying propagation of errors theorem:

The derivative of Eqyation (137) with respect to h are derived as foIIows:

Recall h m Equations (85) and (90) that:

Substitute (140) into (139):

R e d fkom Equation (75) that:

And h m Equations (88) and (89) that:

Substituting Equation (142) and (143) into Equation (141):

In order take derivatives of Equation (1 37) with respect to Q-, rewrite Equation (1 37) as

follows:

The derivative of Equation (145) with respect to Q+

Substitute Equation (1 40) into ( 146):

The discharge coefficient, Ca may be writîen in t m s of Qap.

Substituting Equation (148) into (147) and applying Equation (142):

The derivative of Equation (137) with respect to c is derived as follows:

Substituting Equation (140) into (1 50) yields:

The discharge coefficient, Cd, may be written in ternis of constants c and d. Substitute

Equation (148) into ( 1 5 1):

The derivative of Equation ( I 37) with respect to d is deriveci as follows:

Substituting Equation (140) into (153):

The discharge coefficient, Cd may be WRtten in terms of c and d. Substituthg Equation

(148) into (1 54). and applying Equation (142):

Errors in Head

Ref-g to Equation (144), the significance of constants c and d can be

determineci. These constants are an indication as to what shape the discharge coefficient

curve exhibits favorable conditions in meamring viscosity. It is clear that when the dope

(constant c), is shallow, that mors are expected to be minimal. Also, due to the presence

of the y-intercept (constant d), ii can be stated bat the discharge coefficient shodd be

relatively low in the presence of errors in h d . In short, the fnctional characteristics of

the orifice should be significant yet exhibit a srnail dependency on the processing

variables (represented by the Reynolds nurnber). Equation (144) indicates as well that

increasing head will result in lower errors when calculathg viscosity.

Errors in FIow Rate

Unlike the case with the d a c e tension and density measurements, Equation

(149) indicates that enon in flow rate are not as signifiant in terms of the viscosity

caldation if highdensïty liquids are used. It is also favorable to operate under high

head conditions. These concepts are reinforcecl due to the presence of the Bond nimiber,

which Uidicates in this instance that high potential forces are favorable relative to d a c e

forces. Large of ice radii are also favorable. The shape of the discharge coefficient

ciwe should have a steep dope (opposite to mors in head) with a small y-intercm A

steep slope indicates that the discharge coefficient exhiiits a strong dependence on

Reynolds nimiber.

Errors in Constant "c"

Emrs inherent with the slope of the discharge coefficient curve produce

deviations in terms of viscosity less significant when the slope is relatively steep (large

c), as Equation (152) indicates. The discharge coefficient should therefore exhibit a

strong dependence on Reynolds number.

Errors in Constant "d"

Equation (155) indicates that hi&-density fluids are favorable with srnall orifice

diameters if there are mors associated with the y-intercept of the discharge coefficient

curve. High flow rate conditions are favorable as well. A steep dope (large c) is

favorable as well, indicating that the discharge coefficient should be a strong function of

Reynolds number.

5.2.1.4 Summary of Propagation of Errors

The error analysis has provided a usefûl anaIysis of the set of conditions

necessary in measriring the d a c e tension, viscosity and density for varying degrees of

precision. Consider the presence of both mors in head and flow rate. It has been

observed that when dculating siirface tension and density conditions are favorable when

h and Q, are relatively mal1 (indicating smail potential and inatial energies).

However, in measuring viscosity, the opposite holds tnie for accuracy in the calcuiation

@gh h and Q, increases accuracy). This is qualitatively illu~sated in Figure 5.8 where

it is suggested that a balance of conditions should be established to provide a reasonable

degree of accuracy for d a c e tension, density and viscosity. The dashed arrows

intersehg the x-axis suggest a range of values for h or Q,, corresponding to a relative

error that can be specified on the y-axis. 1lBo

Absolute error in O, p, and ?

Experimental Variables, h or Qap

Figure 5.8: Errors in property mersurements as a function of h and Qu, due to errors in Q, and Cd.

The effect of increasing discharge coefficient cm be quaiitatively illustrateci on a

chart similar to Figure 5.8. Consider errots in flow rate and discharge coefficient. Figure

5.9 illustrates that a large discharge coefficient (indicative of an orifice design exhibiting

low frictional characteristics) is favorable in measuring both d a c e tension and deasity.

Absolute error in a and P

Discharge Coefficient, Cd

Figure 5.9: Errors in property measurements as a function of Cd, due to errors in Q, and Cd.

Consider the viscosity measurement. in the presence of errors in head, it is

desirable to have a low discharge coefficient with a small dependence on Reynolds

number (low c and low d). In the presence of errors in flow rate and constants c and d, it

is desirable for the discharge coefficient to have a strong dependence on Reynolds

number. This means that the slope, c, shouid be large to hprove accuracy.

The orifice radius is considerd in Figure 5.10 where erroa in head and flow rate

are accounted for. Enors in head result in deviations for di three propertks in the same

direction. Increasing the orifice radius increases the error in d a c e tension, viscosity

and density caidations. ConverseIy, in the presence of mrs in flow rate, inmeaskg

the orifice radius results in lower deviatiom in sinnlce tension, viscosity and detlsity. If

the inherent with measurements are properly characterized, the appropriate orifice

radius can be determined to improve on the accuracy of aii three properties. In the

presence of mrs in the discharge coefficient, increasing the orifice radius results in

increases in error for surface tension and density calculations. Finally, mors in the

intercept r d t in decreasing mor in the viscosity calculation as radius is decreased.

ln30

Absolute error in a 1?

and

Orifice Radius, r,

Figure 5.10: Errors In property measurements as a function of r, due to errors in h and Qap.

5.23 Data Anaïysis

Aluminum was melted using the induction fumace describec! in Section 3.2.3.

The surface tension, viscosity, and density were rneasured using the formulation

presented in this section. The m a s of duminum used was 1.275 kg and it was heated to

a temperature of 1073 K., corresponding to 413 K superheat. The 0.OOSm diameter

graphite orifice plate was useci. The m a s was cumulative!y measured as a hction of

time using the loadcelI and data acquisition system. The strain recorded by the loadceii

was converted to m a s knowiag the weight of aluminum that poured h u g h the orifice

and the strain before and &er experimentation. Similar to the low temperature tests,

flow rate is determined by differentiating the 2* order polynomial f'unction desmibing the

cumulative mass with the. Head was detennined in a different manner than it was for

low temperature work. Using the cumulative mass data, the volume remaining in the

cnicible is detennined at any time during the test. The crucible was caliirated such that

the head can be determined for any volume. The discharge coefficient versus Reynolds

number cuwe was (similady to the low temperature work) generated using water at

various temperatures. The m i l e dimensions are given in section 3.2.2. The onfice

plate that was uscd is illustrated in Section 3.2.1.

Measuring Head

The calibration curve used to relate volume left in the crucible with head height is

illutrateci in Figure 5.1 1. The density is, therefore, required to determine the volume left

in the crucible as the mass is cumulatively measured. Because density is considered an

unknown in this anaiysis, an obvious paradox exists. Deasity values quoted fiom Iida

and Guthne [2] were used to calculate the volume and hence the head left in the m i l e .

This paradox will be addresseci in the Section 5.2.3. Figure 5.12 represents the head

measurernents thst were determined £kom the aluminum experiment. A second order

polynomial fit was generated h m the data and used to determine the amount of random

m r by cdculating the standard deviation between the data and polynomial c m e , which

takes the following form:

= 6.25~1 0"(t)' - 5.13~1 0" ( t ) + 128x10-' (m) ( 156)

The standard deviation of Equation (1 56) with respect to the experimental data points that

are represented in Figure 5.12 is determined using the following relationship with O= 95:

Volume (m")

Figure 5.11: Volume within the crucible corresponding to a particular head height.

Sunilar to the low temperature work, the m r associated with head measuement

is considerrd to be random. For this case, however, the em>r is due to scatter registered

by the loadceli instead of uncertainties in reading the graduations firom a scaie. The

scatter is primarily due to the turbulent impact of the s t r m onto the loadcell systern.

1 + Head 1 - 2nd Oder Polynomial 1

Figure 5.12: Experimental head measurements for aiuminum at 1073 K. Aluminum Test #32.

Meancring Flow Rate

Similar to the low temperature work, the error associated with flow rate is

systematic since it is a product of differentiating the analytical expression describing the

cumulative mass with time. The mass that was c o k t e d is represented in Figurr 5.13.

The 2" order po1ynomia.i fit of the cumulative mass is represented by Equation (1 58):

c m . ~ & = -8.3 56x1 (t) + 6.49 1x1 (t) + 2.2 12x1 (kg) (158)

The flow rate is detennined by taking the time derivative of Equation (1 58):

+ Cumulative

O I O 20 30 40

Time (s)

Figure 5.13: Cumulative miss venus time for aluminum at 1073 K. Aluminum Test #32.

Meanring Discharge CMcient

Water was used as a calibration fhid to determine the aictional characteristics of

the graphite orifice used for the duminum and AZ91D tests. The results for two separate

calibrations are presented in Figure 5.14. The aluminum experiments were performed in

a regime on the curve that is approximately linear. For 4000 < Re < 13000, a linear

model is applied to approximate the Wctional characteristics of the orifice.

This relationship indicates that constants a, and b in Equation (1 12) are equal to zero, and

that c and d are 2.196~10~ and 0914 respectively. This is valid for 4000 > Re > 13000.

The linear model is illustrateci in Figure 5.14 over this Reynolds number range. Since the

majorïty of data points are scattered aromd the f'unction, it is assumeci that the linear

approximation is valid for this range of Reynolds ninnbers. The standard deviation of

Equstion (160) with respect to the 95 data points is range is:

Figure 5.14: Frictional characteristics of O.OO5m orifice used for high temperature experiments.

4 -

5.2.3 The Surface Tension, Viscosity and Density of Ainminurn at 1073 K

0.98

3 0.96 -. Y

Using the multiple non-linear regession analysis formulation developed in this

Chapter, the d a c e tension, viscosity and density were determined for a system of

a l h u m at 1073 K. The propagation of mors d y s i s is also included to determine

which experimental errors are relevant in the analysis of duminum. Density values

quoted h m Iida and Guthrie [2] were usai to estimate the head. The uncertainty in this

approach wiIi be discussed with the presentation of the density r d t s .

Water / 293 K i = 0.94 -

a3 Water 0.92

8 0.9 - O $ 0.88

5 0.86 O 8 0.84

0.82

0.8 O 2500 5000 7500 10000 A2500 15000

Reynolds Number (Re)

32 1 .SIC A

i K 1 - Linear -

-

l / Relation I

I l

1 i

i I 1

Suface Tension

The calculateci surface tension of aiuminum at L073 K is presented in Figure 5.15.

The values indicate an average d a c e tension of 0.842Nh with a standard deviation of

O.OZON/m. The propagation of enors aualysis predicts that the mor is 0.030N/m.

Reynolds numbers of this experiment were between 4000 < Re < 13000, validating the

linear assumption of the discharge coefficient. It is believed that the scatier depicted is

directiy related to error in head rneasurements. It has been stated in section 5.1.1 that

error h head results in random deviations an avenige value, while mors in

discharge coefficient and flow rate are of a systematic nature and deviate in one direction.

It is clear also, that mors are not a hction of the processing variables (h, Qa, Cd).

Finally, using propagation of mors, r d t s seem to be coafined within the solid lines

representing the predicted error in d a c e tension.

Viscosity

Results for the viscosity in the same experiment are presented in Figure 5.16. The

average value is 5 . 2 2 ~ 1 0 ~ ~sl rn ' with a standard deviation of 0.35x10%ldm2. Again,

the mdom scatter is related to m m in head rneasurements. The propagation of errors

analysis, depicted by the solid lines in Figure 5.12, indicates that r d t s are dependent on

processing variables to a certain extent. From theory and experimental evidence, it is

cl- that as head demeases, that m r s become more significant. This confirms the

propagation of ecrom analysis with respect to at least one variable. Equation (144)

indiates that large head conditions are favorable to the calculation.

The experimental density calculation for aluminum at 1073 K is represented in

Figure 5.17. The average density is 236 1 kg/m3 with a standard deviation of 46 kg+m3.

Errors associated with head are prevalent fiom the random scatter of the results. Similar

to measuring d a c e tension, it can be seen that there is no dependency on head as resdts

and propagation of mon indicate. The paradox in using hown density information in

determining head will now be addressed. An iterative approach is taken to calculate the

properties ushg published or estimated values as an initiai guess. The new density value

that is obtained fiorn the fïrst iteration is used in repeating the calculation. The iterative

process is repeated until density does not change appreciably (Le. converges). For the

purposes of these experiments, the convergence criterion was decidecl to be less than one

percent. The results from this approach are shown in table 5.3. It is clear that properties

rapidly converge to the tnie experimental values. The relative error in density d e r

applying data h m Iida and Guthrie [2] is 0.5 %. This is deemed acceptable for ali

subsequent properties reporteci in this thesis. Therefore, density data h m the literahire is

used to detennine experimentai head fkom the mass that is lefi in the cruciille.

Table 53: Physieai properties of iluminnm determined by using dinerent density values to dcuiate head at 1073 K. '

W O P ~ ~

Sinface tension (N/m)

Viswsity @Mn2)

p = 2371kglm3 (3d iteration) 0.850=t0.0 16

5. 18x10~kO.36~10~

p = 2328kgfm2 @da and Guthrie 121)

0.842I0.020

5.22~10~&0.35~10~

p = 2361kglm3 (2d iteration) 0.853I0.0 16

5.26x104f0.36~10~

0.5 0.04 0.06 0.08 0.1

Head (m)

Figure 5.15: The experimentai snrface tension determined for aluminum at 1073 K, with erpected error represented by the soiid bars. Aluminum Test $32.

1- - Average 1

0.04 0.06 0.08 O. 1

Head (m) Figure 5.16: The experimental Mscosity determinecf for duminiun at 1073 K, with

espected error represented by the soiid bus. Aluminuxn Test #32.

5 3 Conclusions

2100

2000

1900 -. 1800

The surface tension of water at 321.5 K has been successfully calcdated within

I

6 1

2% of the theoretical and accepted vdue reported in the literature. This is an important

0.04 0.06 0.08 O. 1

Head (m) Figure 5.17: The experimental density determined for duminom at 1073 K, with

expected error represented by the solid ban. AlumIourn Test #32.

validation of the formulation presented in this chapter. It was determineci that the

method and equipment used in the low temperature work is particularly susceptible to

m r ~ associated with the cal'bration of the discharge coefficient ciwe. Using

propagation of errors anaiysis, the standard deviation between four independent

calibrations was used to successfully predict the deviation in the surface tension

measurement This exercise not only determines appropriate pmcessing conditions, it

reinforces the legitimacy of the mode1 as weIl.

The surface tension, viscosity, and density of 99.95% pur@ alumuium have been

determined at 1073 K. This was accomplished by taking advantage of the fact that

voIuminous data is collecteci during the course of an experiment, which facilitates

nmultaneous measurements to be made on ail tbree pruperties using multiple non-linear

regression andysis. Errors associateci with head height were determined to be the

predominant source of inaccuracy in the rneasurement of al1 three properties. This was

determhed experimentally, and predicted utiluiag propagation of mors theory as well.

The physical properties of 99.95% purity aiuminum at 1073 K are summarized in Table

5.4 and compared with sources in the Iitemture. Recall that these values are produced by

using density values h m Iida and Guthrie [2] to detelmine experimental head fiom the

mass that is left in the crucible.

Table SA: Summary o f reauits for aiuminum at 1073 K in cornparison to iiterature quantities.

The resuits for surface tension and density are in reasonable agreement with data quoted

h m Keene [n and Iida and Guthrie [2] respectively. However, it is clear that t h e is a

sigaificant difference in the value of the viscosity reported in this work compared to that

obtained h m Srnitheus [17]. This is not the first instance that mch a discrepancy has

been reported when studying the viscosity of mdts. In fact, and as was discussed in

Chapta 2, a definitive quantity for the viscosity of pure duminum has not been M y

Density (kgirn? Surface Tension (Nha) L

Viscosity (Nam-')

Keene

VI 0.864

% Diff I I

This Study

0.842 I 0.020 2.55%

I

Smitheih

117 1 . 1 0 ~ 1 O-'

% Diff I

This Study

5.222 1 o4 1: 0.35x104

52.5% I

Uda and Guthrie

[21 2328

% Diff I

This Shidy

236 1546

1 23% I

established as of yet. This technique provides a unique opportunity to shed light onto

these ciifferences as wiU be shown in the next chapter. The next chapter will also explore

redts of implementing this formulation for duminum and AZ9 1D d o y over a range of

temperatures This is attractive fiom the point of view of d a c e tension, since the

dynamic nature of the experiment produces an interface that is rapidly replenished. The

measurements are thus considered to refiect, more closely, the pure dynamic d a c e

tension that was descnied in Section 2.1.3 (Le. no oxygen contamination).

CHAPTER 6: DISCUSSION

The Mique approach to measuring the d a c e tension, viscosity and density,

validated in the previous chapter, will now be utilized to determine the temperature

dependence of these properties for 99.95% alumiLlum and AZ9 1 D d o y . niere are two

pinposes of this discussion. The nrst is to relate r d t s of molten aîuminum with data

available in the literature. The second is to present results for AZ91D alloy, and to

provide an analysis on the effects of metallic alloys on these properties.

6.1 Density

Dmsity was deterrnined through implcmenthg multiple non-linear regsession

analysis on al1 three physical properties. Regression was perforrned using data

co~esponding to 4000 c Re < 13000 (refa to Figure 5.14). The experimental Reynolds

numbas were approximated using density and viscosity information âom Iida and

Guthrie [2] and Smithe1ls [17]. There is rmdoubtediy uncertainty with respect to Re;

however, imposing this constraint on the data ensures that the linear portion of the

discharge coefficient is used to calculate properties. The values from Iida and Guthne

w a e also used to deterrnine head fiom knowledge of cumulative mass data.

6.1.1 Density of Aluminum

Tests were conducted with aluminun between 973 K and 1173 K so that the

effects of temperature could be determined. The data is shom in Table 6.1 with m r

bars correspondhg to the standard deviation similar to the analysis presented in Figure

5-17,

The data presented in Table 6.1 is plotted in Figure 6.1. Sources h m the

literatine are included for cornparison [2,17j.

Table 6.1: Density of 99.95% aiuminum determined experimentdy. Test

Aluminum #23

Temperature 0 983 2352St

- - *Physical ProperOes of Liquid Metals [2] - - Smithells Metals Reference Book [17 - This Study - Linear

900 1000 1100 1200 1300 Temperature (K)

Figure 6.1: Density of 99.95% aluminum as a hinction of temperature and compared with sources in the literature [2,17.

Recail fkom Chapter 2 (Section 2.1.5) that density is usually expressed as a linear

bction of temperatwe. By fitting a linear relationship to the data in Figure 6.1, a new

f'unction is produced and illustnited in Table 6.2. Results fiom this study are in excellent

agreemmt with literature at the melting point. Evidently, this study yields a lower

dependence on temperature. At 1173 K; however, variation between the three

relationships is no greater than 2.5%. This is an important outcome in ternis of validation

of this model. By measuring flow rate and head, the density of 99.95% aluminum was

successfully determined using concise knowledge of the discharge coefficient curve.

Table 6.2: Temperature dependence of density determined from experiments and from sources in the merature [2,1q.

This Sîudy

Temperature dependence

-0.3 5

Source

Ii& and Guuine [2]

Densiîy at melüng point,

2380

2390 -0.15

6.13 Density of AZ91D

The Density of AZ9lD was detennined between 923 K and 1173 K and the

d t s are presmted in Table 6.3.

In order to compare density with literature quantities, the approximation for

atomic volumes of metallic mixtures is used. R e d Equation (51) h m section 2.3 in

Chapter 2:

Table 63: Density of AZ91D aiioy determinecl esperimentaily.

On thc basis of this fiulction, the d o y is preàominately made of altnninum (-9 wWo) and

rnagnesium (-91 wt%). Refer to Table 3.3 in section 3.2.5. Since the atomic volume

conesponding to Equation (5 1) is based on a molar basis, the wtO! must be converted to a

molar M o n . For AZ91D dey, x, = 0.90 and ql= 0.10. Manganese and zinc are

neglected h m this anaiysis since they are present at low levels relative to magnesium

Test

AZ9 1 D #2

Temperature 0 967 169M 13

and duminum. The values for the density of aluminum and magnesim are referenced

from Srnitheils [17] and are used in Equation (5 1).

R e d the liquidus temperatures for rnapesium and aluminum are 913 K and 933 K

respectively. The average molecufar weight is determined from the following:

The molecular weight of A29 1 D alloy is:

M,,,, = 26.98 kg l mole ( 164)

Equation (164) is divided by values obtained h m Equation ( 1 62) to obtain the density of

AZ9 1 D alloy. The following bction desmies the density as a hction of temperatme:

p,,,, = 1648 - 0.268(T - 903) ( m

The Iiquidus temperature for AZ91D dloy is 903 K and was obtained f?om a binruy

duminum-rnagnesim phase diagram [49]. Figure 6.2 presents the results obtained in

this study. Included is the expression represented in Equation (165) (indicated by the

predicted function) and the density of pure magnesiun [IV.

1800

1 750

P 1700

@g/m3) 1 6 ~ 1 A B 1 D alloy-This Shrdy

1 600 - Magnesiurn lm1 0-Predicted

1 550

1500

1450

1400 850 950 1 050 1150 1250

Temperature (K)

Figure 6.2: Density of AZ91D alioy as a huiction of temperature compued with theoretical relations Il 1.

The outcome in Figure 6.2 contrihtes signifimtly to the merits of this technique.

Clearly, the data is within reasonable agreement with the theoretical relation based on the

approach represented by Equation (165). There are essentially two key issues related to

the density of A29 I D doy. First, the technique successfiilly quantifies the addition of

an alloying elment since density obtained is significantly higher than the density for

pure magnesium. This conclusion is important for establishing confidence in the

formulation and execution of the technique. Secondly, the results wnfinn that metallic

doys behave ideally and that densities are additive [2].

A linear relation descriiing the data is presented in Table 6.4. The theoretical

mode1 based on the molar average of the magnesium-duminum mixture is included for

Table 6.4: Temperature dependence of density determinecl fkom experiments, and from the average vaiues taken from sources in the iiterature 117.

Recall: p = p, + dp/dT(T-T,,,)

The r d t s presented in this section used multiple non-linear regression on al1

three properties. Appendix C presents results for the surface tension and viscosity of

aluminurn using this regressioo analysis. Subsequent sections, however, will present

results where only d a c e tension and viscosity are caiculated from regression analysis

on only hKo properties. The density relationships developed in this study for both

duminum and A29 1D alloys (Tables 6.2 and 6.4) were implemented in the formuiation.

Refer to Appendix B for this program. It will be clarifiai in section 6.3.1 that a more

reliable anaiysis desmiing dddT is obtained when comparing results in Appendix C

with results obtained fiom regression on only two properties.

L

This Smdy (Experimentd)

6.2 Vlscosity of Aiuminnm and AZ91D AUoy

Temperatare dependence

-0.268

Source

Equation (1 65) (Theory)

The viscosities for both 99.95% aluminum end AZ91D dloy were detetmined

through multiple non-linear regretsion analysis on surface tension and viscosity only.

This was the procedure defined for data analysis so that m a in the density

m-ent would not result in systematic diffmces in the d a c e tension or viscosity

caldations. It is seen in Appendix C, however, bat there is little différence betweea

r d t s obtained with regression on ail three vanables and results obtained in this section.

Density at meltuig point,

1648

1651 -0.16

Theoretical viscosities of alurninum and A29 ID alloy were calculated using the

fondation presented in Section 22.1. R d Equatiom (46-48):

Ushg the methods outline by Hirai [3], the constants A and B were determined using the

molar averages for p, and M. The alloy is assumed to be predominately made of 10 %

alimiinum and 90 % magnesiun (molar basis).

Results for the viscosity of 99.95% purity aluminum and A291 D are presented in

Table 6.5 and 6.6 respectively.

Table 65: Viscosity of 99.95% aluminam determiaed experimentaily. - 7\

(~srn-~) (5 .1~1 .80)~ 1 o4

Test

Altmiinum #3 1

Temperature ( ' 973

These results are presented in Figures 6.4 and 6.5 with values obtained fiom the literature

and the theoretical calculations:

Table 6.6: V~iscosity of AZ91D aUoy detemhed expeRmentdy8

Temperature (KI

rn This study Kisun'ko et al. [56]

A Rothwell[55] - Smithells [17] - =Hirai Model [3]

rl (~sm")

(2.66H.397)~ 1 o4

Test

AZ9 ID #2

Figure 63: Viscosity of 99.95% purfty ainminum as a function of temperature compared with sources m the Uterature.

Temperature (K) 967

This Study aTheory-Hirai Model[3,1

~ ~ M a g e s i u r n [id 1

Figure 6.4: Viscosity of AZ91D as a fonction of temperature.

The experimental values for aluminurn obtained h m Rothwell [SS]. Kisun'ko et

al. [56], and SrnitheIls [17] are presented for cornparison. The viscosity of alurninum has

a maIl temperature dependence as shown in Figure 6.3. With A29 ID, temperature has

M e impact above 973 K. As the temperature decreases and approaches the liquidus

point (903 K), however, the viscosity sharply increases. This sharp increase near the

liquidus point has been observed experimentally by different researches [53,54]. These

references deait exclusively with aluminum based al1oys; however, there hasn't been

verincation of tbis phenornenon for AZ91D dloy near the liquidus point in the literature.

R d t s for aluminum are significantly lower than the experimental values obtained h m

other sources. AZ91D also exhi'bits low viscosities relative to pure magnesium

referacd in the iitemtme- The unique flow conditions in this technique mut be

emphasized in cornparison with other methods. Traditionally, techniques rely on laminar

flow mch that the viscosity is a constant relating shear stress with velocity gradient. This

is an essential criterion for the measuring techniques descnbed in Section 2.22 [2]. The

gradient is unidirectional and produced fkom the laminar no-slip condition. Recall

Equation (44) fiom Chapter 2:

The capülary, oscillating-vesse\, rotational, and oscillating plate method al1 rely on this

principle. Kisun'ko et al. used rotational prliciples and Rothwell used the principle of the

oscillating plate method (using a sphere instead) [55,56]. The technique fomulated in

this study, however, is perfonned with Reynolds numbers in excess of 4000. This clearl y

indicates that turbulent conditions dictate the dynarnics of the process. Further analysis

into the flow conditions of these experiments must be made before a definitive

explanation of the viscosity r d t s is given. Such an analysis is beyond the scope of this

study, however. There appears to be reasonable agreement with values obtained in this

study and the theoretical formulations presented in Table 6.5 and 6.6. The approach

taken by Andrade [48] to derive the theoretical expression is based on atomic vibration

mechanisms, and not the principle stated by Equation (44). The formulation of the

theoretical approach and how it may relate to this method is also beyond the scope of this

snidy. Simila to the Saybolt instrument descriied in Section 2.4, experiments at lower

Reynolds numbers (< 1500) rnay be considered to determine if experimental viscosities

wodd rdect values determined using conventional methods. Udortunately, the

dynamics of this rnethod makes it cM6cult to generate such low Reynolds numbers. This

is especially the case with molten metals where densities are particulaly high with

respect to viscosity.

63 Surface Tension

Similar to the viscosity calculation, the d a c e tension of 99.95% aluminum and

AZ91D alloy was determinecl using multiple non-linear regression analysis on only

viscosiîy and d a c e tension. It is seen in Figure C.l in Appendix C that for multiple

non-lin- regression on al1 three properties, modified r d t s are obtained compared with

results in this section. The following presents results for aluminum and A29 1 D alloy and

provides a discussion into their magnitude and dependence on temperature.

63.1 Surface Tension of Aluminum

Under equilibrium conditions with aluminum, the partial pressure of oxygen must

be below 104 atm [38] (1 o'.'~ Pa) to completely avoid oxidation ( R e d Section 2.15 in

Chapter 2). ûxygen contamination is surely expected since oxygen is present in these

experiments at levels no l e s than 2Pa (20ppm). Due to the highly dynamic conditions of

these experiments; however, it is possible that resuits are closer to the "pure dynamic

d a c e tension" (or the d a c e tension at the instant that the d a c e is created [SI). If so,

it is expected that unusually hi& surfkce tension values, corresponding to un-oxidized

aluminum will be pmduced Similarities between the d t s obtained nom Gourniri and

Joud 1321 (1.050Nlm at 973 K) and calculated h m Chadn [37l (1.184Nh) will be

expected if the rate at which the surface is replenished is fmter than m a s transfer and

kinetic issues controllhg oxidation. Table 6.7 presents d t s .

The data in Table 6.7 is presented in Figure 6.5. uicluded are the relationships

proposed by Keene [7] and presented in Iida and Gutbrie [Z]. The surface tension of

"pure" duminum obtained fiom Gourmin and Joud [32] is included as well. There are a

number issues pertaining to Figure 6.5. It is immediately evident that the d a c e tension

of 9995% aluminum, determined using this method, is closer to the oxidized values as

detenrilned h m a veety of sources [IO, 17-34]. This is an indication that there is a

certain degree of oxidation on the surface of aiuminum at the moment the stream exits the

orifice- This illustrates the diffidties in measuring the "pure dynamic d a c e teasion'' of

molten metds, even under the most dynamic circumstances.

Tibk 6.7: Siiflace tension of 9995% aiuminum determined experimentally. m / m )

0.846H.O 1 5 Test

AlUminum #3 1 Temperature (K)

973

- --

= This study

- Physical Pmperties 01 Liquid Metals [2] Gourmiri and Juud C321 - Linear (This study)

900 1000 1100 3200 1300

Temperature (K)

Figure 6.5: Surface tension of 99.95% alnminum as a function of temperature compared with sources in the iiterahve [2,7JZ].

There appears to be inconsisteacy in the data at higher temperatureS. A variety of

concepts have been considaed to explain such irregularities. The pur@ of the aluminwn

(99.95%) was scruhized so that the possibility of iucreasing activity of surface acting

contaminmts with temperature could be considered. The purity of the durninum that

previous researchers used was typically of a much higher quality. Table 2.1 in Chapter 2

indicates a number of sources in which the purity of the duminum used is approximately

99.999%. Refaring to Table 3 2 in Chapter 3, two major contaminants found in the

duminum used in this study are iron (0.0038%) and adcon (0.037%), two elements that

exhibit essentially no d a c e activity [Il]. The only elexnent that affects the d a c e

tension of duminum coflSidersb1y is lead that is present at levels < 0.0001%.

A plausible explanation is that the variation in surface tension at i n d g

temperatures is due to inaeasing reactivity ofoxygea Refer to Appendix D for insight

into the oxygen partial pressure in the apparatus for these tests. From the data given in

Appendix D, the oxygen content appears to decrease si@cantIy at temperatures above

1073 K when heating. This suggests that there are repeatability issues at higher

temperatures concerning the oxygen content of the apparatus. For this reason, results

between 973 K and 1073 K were only considered in determining the experimental

relatiomhip indicated in Figure 6.5 and presented in Table 6.8. The relationship quoted

k m Iida and Guthrie is based on data generated from one source. It is an important

validation of the technique developed in this study to gmerate results that are more

closely related to the formula developed by Keene, which is based on 20 independent

sources [10,17-341. In considering d t s between 973 K and 1073 K, the differences

between Keene and this shidy are no greater than 6.5%.

Table 6.8: Temperature dependence of sudace tension determined from experiments and from sources in the literature [2,7,l7.

R d fiom chapter 2: O = cm + da/dT(T-T,J

This Study

Temperature dependence of surfsce tension, dddT

(~m-' KI)

-0.35~ 1 O4

-0.1 55x 1 o - ~

Source

Iida and Guthrie (1988); and Smithelîs (1998)

Keene (1996)

S d a c e tension at melting point, aii

NI^) 0.9 14

0.871

0.868 -0 .25~ 1 o5

6.33 Surface Tension of AZ91D AUoy

Unlike density and viscosity, the d a c e tension of metallic alloys is very rarely

an additive property of the percentages of the doying elements. AZ91D is used in this

analysis to determine the effects of dloying elements on the surface tension of pure

magnesium. The results from this analysis are presented at various temperatures in Table

6.9.

These values are illustrated in Figure 6.6 with data in the literature for pure

magnesium [17] and the available results in the fiterature correspondhg to Mg-Al-Zn-Mn

alIoys [58]. The concentrations of alloying elements h m Patrov et al. that were

presented in Table 2.5 in Chapter 2 are included in Figure 6.6. Given the mges

presented in Figure 6.6, it is a reasonable assumption that A29 1D alloy would be within

the range that is presented.

Table 6.9: SurCace tension of AZ91D aiioy determined erperimentally. CF

(Nh) 0.539f0.035

Test

A29 1 D #2

Temperature 0 967

This study

- - +Magnesium [IV

8 Patrov et ai. [58]

- Linear (This stud y)

850 950 1050 1150 1250

Temperature (K)

Figure 6.6: Surface tension of AZ91D as a function of temperature compared with sources in the iiterature [17,58).

A linear regression is fitted to the data. Due to lack of data and the variation

between values; however, the resuits are considered inconclusive. There appears to be a

high degree of scatter between experimental data points making the argument that

repeatability may be an issue. Similar to measurements with aluminum at high

temperatures (>1073K), large fluctuations in oxygen partial pressure were observeci

during heating of the doy. Figure D.6 in Appendix D illustrates the decrease in oxygen

content after the alloy expdences rnelting. Nevertheless, considering the magnitude of

the lin= relationship, higher d a c e tension values indiate that the surface tension of

magnesiun appears to be affecteci by alloying additions of aluminum, zinc and

manganese. At the liquidus point (903 K) the surface tension of the experimental Iinm

relation is 8% higher than the case of pure magnesim. Due to complexities of the four-

component system, and the lack of thRmodynamic activity information for this system, it

is not possible to make a quantitative d y s i s of these r d t s . Data &om Patmv et al.

indicate that the surface tension of magnesium doys of similar composition is lower than

the linear relationship proposed in Figure 6.5. Speculation can be made, due to the

seefningiy lower experimental values at - 973 K and - 1073 K, that a minimum may

exist between these tempaatures. Such would be an indication of complex interactions

between the components in the alIoy as temperature is increased. Further studies must be

made using this technique to c o n h whether the surface tension is approximately a

linear relation with temperature, or if a minimum exists.

6.4 Conclusions

The results presented in this chapter have achîeved, with varying degrees of

success, the goals of perforrning experiments using molten aluminum and A29 1 D alloy.

The results for density have provided important validation to the technique in confimiing

that the density of 99.95% aluminum is in reasonable agreement with relationships

available in the literature. Furthemore, using AZ91D alloy, it was detennined that not

only can the density of an d o y be experimentaliy determineci using this method, but that

a molten metallic d o y behaves as an ideal fluid in temis of additive dénsity. The surface

tension of aluminum has been conf imd to refiect the oxidized values that have been

widely reprted in the Iiterature. Despite the highly dynamic nature of these experiments,

the "pure dynamic surface tension" was not obtained using this method. Results are

within masonable agreement with previous studies and contribute to the validation of the

experimental method Howeva; more work must be performed in providing a definitive

understanding of the d a c e tension of AZ9LD d o y as a fiuiction of both temperature

and composition. Also, in terms of viscosity, consideration into the highly turbulent

conditions must be made to determine whether or not the tme viscosity is cdculated

using ihis method.

Experiments pexformed in this study have focused on an experimental system that

has traditionaliy neglected surface tension. Using the analysis of a drainhg vesse1

through a mal1 orifice (0.002m-0.005m), it has been confimeci experimentally that

surface teasion plays a fundamental role under various circmstances. The traditional

energy balance, that is used to calculate the discharge coefficient, is insufficient in tenns

of characterizhg fnctional losses for certain liquids under certain processing conditions.

The new mode1 developed in this study is an extension of the traditionai energy balance

that indudes a d a c e tension t m in the formulation. The following conclusions have

been made fkom experimental r d t s :

The new formulation is relevant for low-density liquids with hi& d a c e

tensions compared with high-density and low surface tension liquids.

The new fonnulation is relevant, h m the perspective of design and operation,

for maIl orifice radii operating under low head conditions compared with

large orifice radii under high head conditions.

Low Bond numbers are an indication of conditions where the new formulation

is most relevant (i.e. Bo = pgrhh).

Molten metds should be considered in the new fonnulation more o h than

Iow temperature fluids due to larger d a c e tension values.

This approach c m be used to caldate the physical propdes of liquids since

surface tension, viscosity and density are inherent in the formulation. By accurately

measuring flow nite and head, these properties are detennined using multiple non-iinear

regression malysis. There is a statistical advantage to this technique o v a conventional

methods since a vast amount of data is used to calculate the properties (due to varying

head and flow rate). This technique is useful for molten metals because of the relatively

simple design of the equipment, couplecl with the sirnuitanaus seasurement of dl three

pmperties. There are also no opticai measurements required. Furthemore, and unüke

conventional methods, the surface tension is determined in a highly dynamic situation

where the Stream is replenished at a very high rate. The following conclusions are drawn:

5. Surface temion of water at 321 K was detennined to be 0.067M.OG2 N/m,

1.75% lower than values quoted in the literature. Errors associated with

discharge coefficient are predorninately the source of error.

6. Errors in calculating the d a c e tension, viscomty and density of molten

aluminum in this study are attnïbuted to enors in the determination of head.

7. The calculation of d a c e tension and density is favorable when low-

densityfigh surface tension liquids operate at low head conditions through

mal1 orifice designs exhibithg high discharge coefficients. This is

characterized by the Bond number, which accotmts for the density-dace

tension ratio (i.e. Bo = pgrW~). Conditions are favorable when 1 /Bo + 1.

8. The calcdation of viscosity is favorable when high-densityAow d a c e

tension liquids openite at high head conditions. Conditions are favorable

when L/Bo + O.

From experiments p e r f o d with molten aiuminum and AZ91D alloy, the

foUowing are concluded:

Experùnentally, the resu1ts for the sinface tension of 99.95% alUIIlifium are

closely related to the relationship proposed by Keene [7] as a hct ion of

temperature, providing an important validation of the technique.

The surface tension of 99.95% aluminum reflects the oxidized values that

agree with data available in the litmime.

Experimentally, the surface tension of AZ91D as a function of tempenihue is

approximately 8% higher than the d a c e tension values for pure magnesiun

quoted in the literature [7] if a linear estimate is assumed. There is evidence

of a minimum in the d a c e tension as a fiuiction of temperature between

temperatmes of 973 K and 1073 K.

Experimentally, the viscosities of 99.95% aluminum and AZ91D alloy are

approximately 50% lower rhaa values obtained h m the literature [17].

ExperUnentall y, the density of 99.95% aluminum agrees reasonably with

values obtained in the literature [2,17] and provides an important validation of

the technique.

The density of AZ9 1 D alloy reflects values predicted using the molar average

approach using hown data for aluminm and magnesim. This indicatm that

the metallic d o y behaves as an ideal Iiquid in this regard and provides M e r

validation.

This technique is considerd to be at the initial stages of development. Future

work is required in resolving a number of issues. These include lower viscosities

obtained in this shidy with respect to measurements made using conventional methods.

Since it was determineci in the Iiterature concerning the Saybolt instrument that Reynolds

numbers must correspond to laminar viscous flow, it would be of interest to experiment

under similm conditions. Also, more experiments with AZ91D alloy should be

perfomed so that a more detailed discussion cm be made into the effects of temperature

and composition. However, in light of the results obtained in this study there appears to

be Ognificant potentiai that deserves future consideration. The philosophy behind this

method is not to replace conventional methods but to provide an alternative where similar

processing conditions may be relevant. As an example, the conditions in this study are

very similar to atomization of melts in powder metallurgy. Aiso this method facilitates

rneasurernents at particularly high temperatutes. For instance, measuring the surface

tension of slag systems (> 1 500°C) in steelmaking operations will provide information of

tremendous practicd importance h m the perspective of corrosion of refkactory material

and/or gas adsorption.

Finally, a number of design issues cm be made to facilitate more accurate

measurements. For instance technology is available to electronically measure the melt

head as a function of time. independent meaSuTements of head and cumulative mass data

would reduce systematic m m in the calculation. Also, reducing the level of oxygen in

the apparatus cm be accomplished through irnplementing oxygen getters. Such

consideration is recommended to improve upon the potential of this unique method.

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Hirai, M: "Estimation of Viscosities of Liquid Alloys", ISIJlnt., 1993, vo1.33, pp. 25 1-258.

Yde* A.J. Dunkley, J.J: Atornization of Melts: For Powder Production and S~rav Dewsition, Clarendon Press, Oxford, 1994, p. 17.

Joud, J.C. Passerone, A: "Surface Propnties of Liquid AIIoys: Themodynamic Aspects and Chemical Reactivity ", Heterogeneous CherniSv Reviews, 1 995, ~01.2, pp. 173-2 1 1.

Mukai, K. Wang, 2: "Interfacial Phenornena of High Temperature Melts in Relation to Materials Processing", J. M. Toguri Symposium: Fundamentals of Metallurgical Processing, Met Soc, Ottawa, 2000, pp.265-279.

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APPENDM A: QUANTIFTING TRANSIENT TERMS

nie quasi-steady state approximation made in Chapter 4 for the Bernoulli

formulation will be validated in this Appendix. Water at room temperature was used.

The dimensions of the orifice and the crucible are illustratecl in Figures 3.4 and 3.5. The

radius of the vessel, r,,, is 0.045m and the radius of the orifice is 0.0025m.

From the Bernoulli formulation, Equation (7 1) was developed in Section 4.1 :

1

The accelerative head term, (h/g)(aulût), is included in the formulation unless the quasi-

steady state approximation is made. The pressures at the fiee d a c e and orifice tip are

also included for the purposes of this analysis. If the accelerative head t e m is considered

within the vessel and orifice separately, the following equation is stated:

This equation asmmes that there is an instantanmus change in velocity from ui and u2 at

the entrance of the orifice. Recall nom Chapter 3 that the height of the orifice plate is

0.0097rn (9.7mm). The temis hii/& and nit/& can be determinecl by plotting ul and u2

as a function of time. Refer to Figure A.1, which indicates a linear relationship. The

dope of the curves depictecl in Figure A.2 represents the gradients hii/& and duzldt.

Note that these velocities were detetmined experimentally.

+Velocity at point 1 (ul)

Figure A.1: Velocity at reference poiots 1 and 2 indicated in Figure 4.1 as a funetion of tirne.

The fictional characteristics of the orifice can now be determined using Equation

(Al):

Two cases wiii be presented. The first case will neglect surface tension in the analysis

(Le. Pi = Pd. The second case will state that there is pressure induced at the orifice tip

due to the effects of surface tension (Pi = 1 atm, Pz = Iaûn +oh,). This relationship will

be compared with the formulation that assumes the quasi-steady state approximation:

It is clear h m Figure A.2 that the quasi-steady state asmmption is a vaild one since there

is no difference between Equation (A2) and (A3). There is, however, a distinct

difference if pressure effects due to d a c e tension are neglecteà in the analysis. This

confirms that the quantification of surface tension in Section 4.2 is wt affecteci by

secondary effects deriveci fiom the transient effects of these experiments.

3000 4000 5000 6000 7000 8000

Reynolds Number (Re)

o Equation (A8)Surface Tension

o Equation (A9)Surfam Tension

A Equation (A8)-No Surface Tension

c Equation (A9)SJo Surface Tension

Figure A2: Discharge coefficient as a huiction of Reynolds number taking into account transient ternis in the formuiation.

APPENDIX B: MULTIPLE NON LINEAR REGRESSION PROGRAMS

Legend of Symbols for Prognuns

A =

At01 =

B =

Btol =

C =

Ctol =

cl =

c2 =

c3 =

c4 =

g=

h =

1 =

n =

ncount =

-=

nt01 =

Q =

r =

tol =

Surface tension (N/m).

Siuîace tension calculated nom previous iteration (N/m).

Density calculated f?om previous iteration (kg/m3).

Viscosity (Ns/m2).

Viscosity calculated from previous iteration (~dm').

Polynomial constant (Fte3 term) (no units).

Polynomiai constant ( ~ e ~ term) (no units).

Polynomial constant (Re term) (no units).

Polynomial constant (no units).

Gravitational constant (9.8 1 m/s3.

Head (m).

Iteration number and position of value in vextor (i = 1 to n) (no units).

Lmgth of vector containing data (no units).

# of iterations (no dts).

O when convergence is not met with respect to A, B, C.

Condition where all three properties converge within limit of tol (nt01 = 3 when solving for d a c e tension, density and viscosiv, nt01 = 2 when solving for surface tension and viscosity ody) (no UI1its). Flow rate (gis).

Orince radius (m).

Convergence tolerance for d a c e tension, viscosity and density (no units).

V = Flw (kg/m2/s).

Y = Vector corresponding to ciifference between experimental and cdcdated head data (m).

z = Matrix of partial derivatives with respect to A, B, C.

Program # 1: Solving for Sufiace Tension, ViPeosity and Density Simultaneously.

fiuzction value = surf2(h,Q,A,B,C,tol) % This program determines the coefficients for nodinear regession on % Surface Tension Viscosity and Density

% Insert vectors of data for flow rate and head here: Q=[l; h=[I; % Initiai Guess for Surface Tension: A=0.5; % Initial Guess for Density B=2000; % Initial Guess for Viscosity: C= 1 e-4; % Radius of orifice: F2.50/ 1000; % Constants related to 3rd order pol ynomid for discharge coeffcient % vs Reynolds number (assrmiing linear relation) % Cd=c 1 *Re3+~2*R*2+~3*Rek4: cl=O; c2=0; ~3=2.196E-06; c4= 0.9 14; % Tolenuice that calculation must reach for convergence criteaion: t01=0.00000 1 ; nt01 = 2 ; % Initiate count Ilcount =O; @.8 1; % detennine size of problem: n=length(Q);

% Calculate flux h m flow rate data: for i= 1 a

V(i, 1 )=Q(i)/( 1 Oûû*pi*(r)̂ 2); end

% Set Conditions for Convergence

% Convergence check loop wbile nt01 = 1

ncount~ncount+ 1 ; % Set up matrices to be solved. First Y matrix: for i = l:n

y(i, l)=@(i)+9.7/1000-0.0004)-1/(2*g)*(c 1 *B*V(i)"2*(2*r)"3/CA3 +~2*B*V(i)*(2*r)~2/C"2+~3 *B*(2*r)/C+~4*BN(i))~(-2)-A/(B*g*r);

end % Set up Z matrix: fori= l:n

z(i, 1 )= l/(B*g*r); z(i,2)=l/g*(c 1 *B*V(i)A2*(2'r)A3/CA3+c2*B*V(i)*(2*r)AZCA2

+d*B*(2*r)/C+c4*BN( i))"(-3)*(cl *V(i)"2*(2*r)"3/CY +c2 *V(i) *(2*r)A21CA2+c3 *(2%)/C+c4N(i))-A/);

z(i,3)= I/g*(c I *B*V(i)A2*(2*r)A3/CA3+c2*B*V(i)*(2?)A2/CA2 +~3*B*(2*r)/C+c4*BN(i))~(-3)*(3*cl *B*V(i)A2*(2*r)A3/CA4 +2*~2*B*V(i)*(2*r)~2/C~3+~3 *B*(2*r)/CA2);

end % Solve for x where [y]=[z] [XI:

x=inv(traospose(z) *z) *transpose(z) * r, % Maximum number of iterations allowed:

if ncount > 100 rehun

end % Determine new values of A,B,C:

A = A+x(l ); B = B+x(2); C = C+x(3);

% Tolermce check: nsum=O;

if abs((A-Ato1)lAtol) < toi nsum=nsum+ 1;

end

if abs((B-Btol)/Btol) < tol nsum=nsum+ 1;

end if abs((C-Ctol)/Ctol) < tol

nsinn=nsum+I; end

if nslnn =3 % if al1 variables meet convergence then nt01 = O;

end

% Redefine initial tolerance check variables Atol=A; Btol=B; CtoI=C;

end

% Output Results: SurfaceTension=A Density=B Viscosity=C

Program # 2: Solving for Surface Tension and Viscosity Simultaneously.

fûnction value = surfZ(h,Q,A,C,tol) % This program detennines the coefficients for nonlinear regression on %Surface Tension and Viscosity only % Insert vectors of data for flow rate and head here: en; h=O;

% Initial Guess for Surface Tension: A=O.5; % Initial Guess for Viscosity C= l e-4; % Radius of orifice: r=2SO/ 1000;

% Constants related to 3rd order polynomial for discharge coeffcient % % vs Reynolds nimiber (assuming linear relation) % Cd=c 1 *RtP3+c2*R&2+c3 *R*c4: cl+; c 2 4 ; ~3=2. I96E-06; c4= 0.914; % TOI-ce that caldation must reach for convergence criterion: t01=0.00000 1 ; nt01 =l; % Initiate count ncount 4; H.81; % determine size of problem:

% Calculate flux fiom fiow rate data: for i= 1 m

V(i, i)=Q(i)/(l OOO*pi*(r)̂ 2); end

% Set Conditions for Convergence Atol= 1 ; Ctol- 1 ;

%convergence check loop while nt01 = 1

ncount=ncount+ 1 ; % Set up matrices to be solved. First Y ma&: for i = 1:n

y(i, 1 )=(h(i)+9.7/ 1000-0.0004)-1/(2*g)*(c 1 *B*V(i)^2*(2*r)"3/CA3 +c2 * B *V(i) *(2*r)AMXHc3 * B *(2*r)/C +c4* BN(i))A(-2)-A/(B*p*r);

end % Set up Z rnatrix: for i = 1 3

z(i, 1 )=l/(B*g+); z(i,2)= 1 /g*(c 1 *B *V(i)A2*(2*r)A3/CA3+c2*B*V(i)*(2*)AZ/CA2

+c3 *B*(2*r)/C+c4*B N(i))"(-3)*(3 *c 1 * B*V(i)A2*(2*r)A3/CA4 +2*c2*B*V(i) *(2*r)AUCA3+c3 *B *(2*r)/CA2);

end % Solve for x where [y]=[z][x] :

x=inv(transpose(z)*z)* transpose(z)*~ % maximum number of iterations allowdd:

if ncount > 1 O0 return end

% Determine new values of A,B,C: A = A+x(l); C = C+x(2);

% Tolerance check: nSUm=O;

if abs((A-At01)lAtol) < tol nstlln=asum+l;

end if abs((C-Ctot)/Ctol) < tol

nsum=nsum+l; end ifm =2 % if aI l variables meet convergence then

nt01 = O; end

% Redehe initial tolerance check variables Atol=A; Ctol=C;

end

% Output Results: SwfaceTension=A Viscosity-C

APPENDK C: SURFACE TENSION AND VISCOSlTY OF ALUMINUM (REGRESSION ON A . THREE PROPERTDES)

900 1 O00 1100 1200 1300

Temperature (K)

Experirnental

- Keene [71

Figure C.1: Surface tension of duminum as a hinetion of temperature determined through multiple non-iinear regression on iII three properties.

Temperature (K)

-- -

rn This study Kisun'ko et al. [56]

A Rothwell [55] - Smithells [la - =Hirai Model [3]

Figure C.2: Viscosity of alaminnm as a fnnction of temperature determined through multiple non-linear regression on ail three properties.

APPENDIX D: OXYGEN PARTIAL PRESSZTRE

During the heating cycle, the oxygen content was measu~ed every 30s and

monitored as a function of temperature. The partial pressure of oxygen after purging is

approximately 2Pa (=20ppm) as discussed in Chapter 3. ûnce this level is achieved, the

duminum is heated to the desired temperature. Near the melting point, a rapid decrease

in oxygen content is observed, conespondmg to oxidation of the aluminm or AZ91D

dloy. This means that oxygen entering the tower is rapidly consumed in the reaction.

Under repeatable conditions, and once the material is molten, the oxygen level steadily

ascends to the original level(r+20ppm) indicatuig that the system bas stabilized. The melt

is held at the specified temperature for approximately 30 min to give the system time to

stabilue to the nominal oxygen pressure. If the oxygen partial pressure is ploned against

temperature, a m e ssimilar to what is represented in Figure 6.4 is produced.

num Oxygen Level = 20Pa . , . . . . . * . .

Begin Begin End -1 Begin

Heating Melting Melting Experiment

r

Temperature (K)

Figure D.l: Representation for the partiai pressure of oxygen as a function of temperatnre daring a piirgliig and heathg cycle.

A plot similar to Figure D. 1 was generated for duminum at 973 K (Figure D.21, 1023 K

(Figure D.3), 1073 K (Figure D.4) and 1 173 K (Figure D.5). A29 1 D d o y heated to 967

K is also represented in Figure D.6. Each data point on these charts represents a

measurement taken every 30 seconds.

It is clear from Figure D.5 that the oxygen did not reach the nominal oxygen

pressure (20ppm) in the apparatus when the experiment comrnenced. As the tempaahne

climbed past 1100 K, the oxygen partial pressure experienced aaother decrease with

temperature. This is typical of experiments with aliuninum when the temperature is

inaeased beyond 1073 K., and is attributed to an increase in reactivity* The same can be

stated for al1 experiments with A29 1 D alIo y. It is clear fiom Figure D.6 that the system

did not reach the nominai concentration of 20ppm due to the high reactivity of

magnesiun in the presence of oxygen. The conclusion drawn h m Figures D.2 through

D.6 is that alurninum experirnents above 1073K, and al1 A29 1 D experiments, were

perfomed under oxygen conditions cüffaent than the aiuminum experiments at lower

temperatures (< 1073 K).

600 800 1000

Temperature (K)

Figure D2: Oxygen partiai pressure during the purging and heating cycle for Aiuminum Test #31 ap to 973 K.

200

Figure D3:

Temperature (K)

Oxygen partiai pressure during the purging and heating cycle for Aluminurn Test #38 up to 1023 K.

Figure

600 800 1 O00

Temperature (K)

DA: Oxygen partial pressure during the parging and heating cycle for Aluminm Test #35 up to 1073 K.

200 400 600 800 1000 1200 1400

Temperature (K)

D.5: Oxygen partiai pressure during the purging and heating cycle for Aluminum Test #39 up to 1173 K.

Temperature (K)

Figure D.6: Oxygen partiai pressure during the purging and heating cycle for AZ91D Test #2 up to 967 K.