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THES!S

MICHIGAN STATE UNIV

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3 1293 01566 3739

 

 

 

 

 

 

 

 

I

 

This is to certify that the
dissertation entitled

ELECTRORHEOLOGY 0F FLUID FOODS

presented by

Christopher R. Daubert

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Agricultural Engineering

 

 

and Food Science and Human Nutrition

4“» x? £4244,

Major professor

Date May 16, 1996

 

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

 

 

LIBRARY

Michigan State
Unlverslty

 

 

 

 

 

PLACE m RETURN BOX to remove We checkout trom your record.
TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

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MSU IeAnNfirmettve ActIoNEqueI Opportunlty InetIMIon

 

 

ELECTRORHEOLOGY OF FLUID FOODS
By

Christopher R. Daubert

A DISSERTATION

Submitted to
Michigan State University
in partial fitlfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Agricultural Engineering
Department of Food Science and Human Nutrition

1996

W

ELECTRORHEOLOGY OF FLUID FOODS

By

Christopher R Daubert

Electrorheology is the study of the effects of electric fields on the flow properties
of certain fluids. These fluids generally exhibit an increase in apparent viscosity and a
greater yield stress over an unelectrified sample. The phenomenon requires an electric
field and polar particles suspended in an insulating oil A standard concentric cylinder
viscometer, fitted with custom made electrical attachments, was converted into an
electrorheometer. This system allowed for control of the applied DC voltage, fluid
temperature, and shear rate while observing the resulting effects on the shear stress. Two
electrorheological fluids, milk chocolate and suspensions of wheat flour in oil, were the

materials examined in this study.

An experimental design was applied to the flour and oil systems to test for
significant effects and interactions among six important electrorheological variables:
voltage, temperature, concentration, flour type, oil type, and moisture content. One of the

variables, flour type, had no efl‘ect on the electrorheological response. At constant

temperature, the shear stress increases as the voltage increases for all fluid systems
studied. Also, shear stresses increase as temperature increases when fluids are subjected
to a constant shear rate and voltage. Although this response may have been predicted for
flour and oil suspensions, these results were tmexpected for a typical shear-thinning food,

milk chocolate.

Because a single mechanism explaining the electrorheological phenomenon has yet
been identified, dimensional analysis was applied to each electrorheological system in
attempts to model the response. Ten dimensionless groups were collected and
manipulated to create meaningful terms, like the Mason number - a ratio of polar and
viscous forces. Multiple regression was applied to the dimensionless groups, and

equations were developed to predict flow behavior for each fluid system

The effects of an applied voltage on the thermal conductivity of molten milk
chocolate was also studied. An applied electric field of up to 450 V mm'1 at 60 Hz was
found to have no significant effect on the heat transfer properties of milk chocolate. The
thermal conductivity was found to have an average value ofO. 163 W m1 K'1 over a

temperature range varying from 30 to 60 °C.

Cepyn'ght by
CHRISTOPHER RALPH DAUBERT
1996

W

T o my parents Harlan A. and Jeanne B. Daubert for their
unconditional love, guidance, and support.

T o my grandmother Alice H. Beaver for her infinite wisdom
and steadfast faith in my abilities.

To my brothers and sisters Suzanne, Nancy, Harlan, Alison, Elizabeth, and Aaron
for playing, fighting, laughing, and crying with me.

“When you steal from one author, it’s plagiarism; if you steal
from many, it’s researc ”

Wilson Mizner
( 1876-1933)

“There is only one proved method of assisting the advancement
of science - that of picking men of genius, backing them heavily, and
leaving them to direct themselves.”

James Bryant Conant
(1893- 1978)

W

I thank Professor James F. Stefl‘e for his support, guidance, and encouragement
throughout this experience. Dr. Steffe has been much more than a mentor. I am proud to

call him my fiiend.

I extend sincere appreciation to my committee members for their instruction and
time dedicated to this project: Dr. K Berghmd (Department of Chemical Engineering),
Dr. D. Smith (Department of Food Science and Human Nutrition), Dr. A Srivastava
(Department of Agricultural Engineering), and Dr. G. Strasburg (Department of Food
Science and Human Nutrition). In addition, special acknowledgement is made for Dr. D.
Gilliland (Department of Statistics and Probability) and Dr. J. Lloyd (Department of

Mechanical Engineering) for their assistance and advice during data interpretation.

I thank Hershey Foods Corporation for materials and technical support. I
acknowledge the use of facilities at Michigan State University: Food Engineering and
Rheology Laboratory, Engineering Research Complex, Department of Agricultural

Engineering, and Department of Food Science and Human Nutrition.

A very warm thanks is reserved for my special fiiends fiom Michigan: J. Briggs, D.
Campos, W. Chamberlain, J. Chick, R Fick, A Fogiel, M. Montross, S. Morris, J. Nuss,

L. Rayas, P. Rettew, G. Salthouse, E. Schluentz, S. Smith, J. Snook, R. Stowell, and A

Wedel. Special mention is made for the support and affection from Charles and Betty

Downs.

Finally, thanks to God.

 

 

 

 

 

page

LIST OF TABLES xi

LIST OF FIGURES xii

NOMENCLATURE xiv
1. INTRODUCTION

2. LITERATURE REVIEW 5

2.1. ORIGIN ................................................................................................................................. 5

2.2. THEORIES ............................................................................................................................. 8

2.2.1. Polarization Mechanisms .................................................................................... 9

2.2.1.1.Molecular Dipole Alignment and Interaction ..................................... 11

2.2.1.2.Water Glue ........................................................................................ 12

2.2.1.3. Interfacial Polarization (Maxwell-Wagner) ....................................... 14

2.2.2. Point Dipole Approximation (Electrostatic Polarization Model) ......................... 19

2.3. RIIEOLOGY ......................................................................................................................... 23

2.3.1. Yield Stress and Structure Development ............................................................ 27

2.3.2. Viscoelasticity ................................................................................................... 29

2.3.3. Dimensional Analysis ........................................................................................ 34

2.3.3.1.Mason Number (Mn) ......................................................................... 35

2.3.3.2. 11 Number (A) .................................................................................... 40

2.3.3.3.Peclet Number (Pe) ............................................................................ 42

2.3.4. Theoretical Models and Simulations .................................................................. 42

2.3.5. ER Rheometers .................................................................................................. 47

2.4. CHOCOLATE RHEOLOGY ...................................................................................................... 48

2.5. VARIABLES INFLUENCING ER BEHAVIOR ............................................................................. 50

2.5.1. Temperature (T) ................................................................................................ 51

2.5.2. Moisture Content (me) ...................................................................................... 53

2.5.3. Electrical Frequency (f) ..................................................................................... 55

2.5.4. Volume Ratio (ob) ............................................................................................... 57

2.5.5. Dielectric Properties (5) ..................................................................................... 58

 

2.5.6. Particle Size and Shape ..................................................................................... 60

2.5.7. Electric Field (E) ............................................................................................... 61

2.5.8. Shear Eaten") ................................................................................................ 62

2.5.9. Characteristics of Ideal ER Fluids for Mechanical Devices ................................ 63

2.6. ENGINEERING ER FLUID DEVICES AND APPIJCATIONS ......................................................... I. 64
2.6.1. Valves ............................................................................................................... 68

2.6.2. Clutches ............................................................................................................ 70

2.6.3. Interfacing ........................................................................................................ 70

2.6.4. Patents .............................................................................................................. 72

2.6.5. Miscellaneous Applications ............................................................................... 72

2. 7. THERMAL ENHANCEMENT FROM THE EIEC’I'RORHEOIDGICAL PHENOMENON ......................... 74
3. MATERIALS AND METHODS 77
3.1. EQUIPMENT ........................................................................................................................ 77
3.2. MATERIALS ........................................................................................................................ 80
3.2.1. Milk Chocolate and Cocoa Butter ...................................................................... 81

3.2.2. Wheat Flour ...................................................................................................... 81

3.2.3. Vegetable Oils ...... 82

3.3. PREPARATION OF ER SAMPLES ............................................................................................ 83
3.3.1. Milk Chocolate .................................................................................................. 83

3.3.2. Flour and Oil ..................................................................................................... 84

3 .4. DATA COLLECTION FOR ER FLUIDS ..................................................................................... 84
3.4.1. Shear Rate Ramp ............................................................................................... 85

3.4.2. Voltage Ramp ................................................................................................... 86

3.4.3. Temperature Ramp ............................................................................................ 86

3.5. CALCULATIONS ................................................................................................................... 87
3.5.1. Shear Rate ......................................................................................................... 87

3.5.2. End Effects ........................................................................................................ 87

3.5.3. Casson Model Parameters for Milk Chocolate ................................................... 91

3.6. STATISTICAL ANALYSIS ....................................................................................................... 91
3.6.1 Experimental Design .......................................................................................... 92

3.6.2. Fractional Factorial Design ............................................................................... 96

3.7. DIMENSIONAL ANALYSIS ..................................................................................................... 96
3.7.1. Description Of Physical System .......................................................................... 98

3.7.2. FLTQB System .................................................................................................. 99

ix

4.l

5.5

APPE

BIBL‘

3.7.3. [I Group and Prediction Equation Development ............................................... 100

 

 

 

3.8. THERMALPIIOIERTESOFMHKCHOCOIATENANEIECIMCFED .................................... 101

3.8.1. Heat Transfer Mathematical Model .................................................................. 102

3.8.2. Mirror Image Method (MIM) Plates ................................................................. 104

3.8.3. Overall Apparatus ............................................................................................ 104

3.8.4. MIM Testing Procedure .................................................................................... 106

3.8.5. Data Analysis ................................................................................................... 108

4. RESULTS AND DISCUSSION 109
4.1. EIECTRORHEOLOGICAL BEHAVIOR OF MILK CHOCOLATE .................................................... 109

4.2. STATISTICAL ANALYSIS OF FLOUR/OIL ............................................................................... 1 18

4. 3. II GROUPS RESULTING FROM DIMENSIONAL ANALYSIS ........................................................ 130

4.3.1. Prediction Equations ........................................................................................ 134

4.3.2. Dimensionless Rheograrn ................................................................................. 138

4.3.3. 11 Group Analysis ........................................................................................... 144

4.4. THERMAL ENHANCEMENT OF MILK CHOCOLATE ................................................................. 157

5. SUMMARY AND CONCLUSIONS 163
5.1. ELECTRORHEOLOGICAL BEHAVIOR OF MILK CHOCOLATE .................................................... 163

5.2. INVESTIGATION OF VARIABLES INFLUENCING ER BEHAVIOR ................................................ 164

5.3. DIMENSIONAL ANALYSIS OF THE ER PHENOMENON ............................................................. 165

5.4. THERMAL PROPERTIES OF MILK CHOCOLATE ...................................................................... 166

5.5. FUTURERESEARCH ............................................................................................................ 166
APPENDIX A 169
BIBLIOGRAPHY 179

 

 

 

 

 

 

 

 

 

 

 

Table Page
2.1. COMMON ER FLUID COMPOSITIONS. 6
2.2. DIMENSIONLESS TERMS OF ER. 36
2.3. COMMON CHARACTERISTICS OF ER FLUIDS. 52
3.1. END EFFECT DATA GIVING PERCENT TORQUE AT DIFFERENT BOB SPEEDS AND HEIGHTS FOR

SILICONE OH. 89
3.2. STATISTICAL LEVELS FOR ER VARIABLES. 93
3.3. PERCENT MOISTURE CONTENT FOR SOFT AND HARD RED FLOUR ACCORDING TO AACC

METHOD 44-15A. 95
3.4. 16 STATISTICAL TREATMENTS FOR FLOUR/OIL DATA. 97
4.1. CASSON MODEL PARAMETERS AND APPARENT VISCOSITIES FOR Mn.x CHOCOLATE DATA. ........ 110
4.2. ALIASED SETS FOR A 2“2 FRACTIONAL FACTORIAL DESIGN. 120
4.3. SS VALUES FOR COMPLETE FRACTIONAL DESIGN OF FLOUR/OIL DATA 121
4.4. SS PERCENTAGES FOR DESIGN EFFECTS AND ALIASES OF FLOUR/On. DATA. 122
4.5. OVERALL RANKING OF EFFECTS AND ALIASES OF FLOUR/OIL DATA. 123

 

4.6. ANOVA TABLE FOR FIVE MAIN EFFECTS AND LOWER ORDER INTERACTIONS OF
FLOUR/OIL DATA. 125

4.7. COMPARISON OF ER MATERIAL CONSTANTS FOR MILK CHOCOLATE AND FLOUR/OIL DATA. ..... 148

 

4.8. THERMAL CONDUCTIVITY (W M" K“) OF MILK CHOCOLATE EXPOSED TO VARYING
ELECTRIC FIELDS 160

 

43.

4.4. ‘

4.6. l

4.7. I

4.8, I

4.9, I

Figure Page

 

2.1. POLARIZABLE PARTICLE EXPOSED TO SHEAR AND ELECTRIC FIELDS

10

 

2.2. INTERFACIAL POLARILATION PATHWAYS

16

 

2.3. PARTICLE POLARIZATION GEOMETRY.

2.4. ELECTRORHEOLOGICAL MICROSTRUCTURES.

22
25

 

2.5. ER VALVE.

69

 

2.6. ER CLUTCH.

71

 

3.1. GENERAL CONFIGURATION FOR ER EXPERIMENTAL EQUIPMENT.

78

 

3.2. CROSSSECTIONAL SCHEMATTC OF THE ER BOB AND CUP.

79

 

3.3. END EFFECT DATA OF ER BOB IMMERSED TO VARIOUS HEIGHTS IN SILICONE OIL AT DIFFERENT

SPEEDS.

90

 

3.4. “MIRROR IMAGE” APPARATUS PLATE SERIES FOR DETERMINATION OF HEAT TRANSFER
PROPERTIES OF MILK CHOCOLATE

 

 

3.5. GENERAL CONFIGURATION FOR MIM EXPERIMENTAL EQUIPNIENT.

4.1. ELECTRORHEOLOGICAL CHARACTERIZATION OF AVERAGED MILK CHOCOLATE DATA AT
T = 35.0 °C.

 

4.2. ELECTRORHEOLOGICAL CHARACTERIZATION OF AVERAGED MILK CHOCOLATE DATA AT
T = 37.8 °C.

 

4.3. ELECTRORHEOLOGICAL CHARACTERIZATION OF AVERAGED MILK CHOCOLATE DATA AT
T = 40.6 °C.

 

4.4. THERMORBEOLOGICAL CHARACTERIZATION OF AVERAGED MILK CHOCOLATE DATA AT
300 VOLTS MM".

 

4.5. MILK CHOCOLATE FLOW BEHAVIOR DEPENDENCE ON TEMPERATURE IN THE PRESENCE OF
CONSTANT ELECTRIC FIELD AND SHEAR RATE.

 

4.6. FIVE-DIMENSIONAL STATISTICAL CUBE SHOWING MAIN VARIABLE AND INTERACTION
EFFECTS ON 7] AT 0.08 RPM OF FLOUR/OIL DATA.

 

4.7. FIVE-DIMENSIONAL STATISTICAL CUBE SHOWING MAIN VARIABLE AND INTERACTION
EFFECTS ON 27 AT 2.0 RPM OF FLOUR/OIL DATA

 

4.8. DIMENSIONLESS PLOT COMPARING ACTUAL AND MODEL VALUES OF 71/71, Vs Mn '
FOR FLOUR/On. DATA.

 

4.9. DIMENSIONLESS PLOT COMPARING ACTUAL AND MODEL VALUES or 17/17. VS Mn '
FOR MILK CHOCOLATE DATA.

 

105
107

111

113

114

115

116

128

129

136

139

 

4.1

4.1

4.1

4.1

4.1

 

4.1

4.1

4.10. DIMENSIONLESS SHEAR STRESS Vs DIMENSIONLESS SHEAR RATE AT DIFFERENT FLOUR/OIL

 

 

 

 

 

 

 

 

VOLUME RATIOS. 140
4.11. DIMENSIONLESS SHEAR STRESS Vs DIMENSIONLESS SHEAR RATE AT DIFFERENT FLOUR/OIL

TEMPERATURES. 141
4.12. DIMENSIONLESS SHEAR STRESS Vs DIMENSIONLESS SHEAR RATE AT DIFFERENT FLOUR/OIL

MOISTURE CONTENTS. 142
4.13. DIMENSIONLESS PLOT SHOWING BEST FIT LINE OF 17/1), Vs Mn' FOR FLOUR/OIL DATA. .......... 145
4.14. DIMENSIONLESS PLOT OF 17/17, Vs Mn ’ FOR MILK CHOCOLATE DATA IN COMPARISON

WITH THE BEST FIT LINE FROM FLOUR/OIL DATA. 146
4.15. DIMENSIONLESS PLOT SHOWING BEST FIT LINE OF ”/0. Vs Pe' FOR FLOUR/OIL DATA. ........... 150
4.16. DIMENSIONLESS PLOT OF q/n, VS Pe' FOR MILK CHOCOLATE DATA IN COMPARISON

WITH THE BEST FIT LINE FROM FLOUR/OIL DATA. 151
4.17. DIMENSIONLESS PLOT SHOWING BEST FIT LINE OF 17/17, Vs Re’ FOR FLOUR/OIL DATA. ........... 152
4.18. DIMENSIONLESS PLOT OF rI/q, Vs Re' FOR MILK CHOCOLATE DATA IN COMPARISON

WITH THE BEST FIT LINE FROM FLOUR/OIL DATA. 154
4.19. DIMENSIONLESS PLOT SHOWING BEST FIT LINE OF Re' Vs Pe' FOR FLOUR/OIL DATA. ........... 155
4.20. DIMENSIONLESS PLOT OF Re' Vs Pe' FOR MILK CHOCOLATE DATA IN COMPARISON

WITH THE BEST FIT LINE FROM FLOUR/On. DATA. 156
4.21. TRANSIENT BOUNDARY TEMPERATURES OF MILK CHOCOLATE: COMPARISON OF

ACTUAL AND THEORETICAL TEMPERATURES 158
4.22. MILK CHOCOLATE BOUNDARY TEMPERATURE DIFFERENCES BETWEEN ACTUAL AND

THEORETICAL VALUES 159

 

GO

0: In 2% K K1

k

.11

area, m2

Hamaker constant (kBT), J
proportionality constant
proportionality constant
proportionality constant

specific heat, J kg'l K'l

dipole moment, C m

electric field intensity, v m-1

unit vector in r direction

unit vector in 0 direction

electric frequency, Hz

polarization force, N

complex modulus, Pa

shear storage modulus, Pa

shear loss modulus, Pa

gravitational acceleration, 9.81 m s'2
bob height, m

effective bob height, m

ER material constant, dimensionless

consistency coefficient, Pa sn

thermal conductivity, W m’1 K’1
Boltzmann constant, 1.381 x 10'23 J K'1
chocolate layer thickness, In

torque, N m

D.

As.

double layer thickness, m

permittivity, CZN”l rn'2

dielectric constant of continuum, dimensionless

dielectric constant of particle, dimensionless

permittivity ofa material in vacuum, 8.854 x 10'12 CZN'l m"2
dielectric constant of suspension, dimensionless

complex permittivity, C2 N' m'2

relative permittivity, CZN'1m'2

dielectric loss, C2 N‘1 111'2

volume fraction, dimensionless

shear rate, 5.1

shear rate at the bob, s'l

apparent viscosity, Pa 5

apparent viscosity of continuum, Pa 5

plastic viscosity, Pa 5

apparent viscosity of suspension at infinite shear rate, Pa 5

it number, dimesionless
Modified 7. number, dimesionless
dimensionless group

modified dimensionless group
density of suspension, g cm'3
density of continuum, g cm'3
density of particles, g cm'3

Shear stress, Pa

shear stress at the bob, Pa

yield stress, Pa

angle between the line of centers of two adjacent particles and the electric field
vector, deg.

angular velocity, rad s'l

‘I‘ electric potential, V

 

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Rheology is the science of deformation and flow of matter (Stefl‘e, 1992). Rheology is
important to food science because it characterizes how materials respond to stresses and
strains applied during processing. Common properties determined during fluid rheological
measurements include viscosity and yield stress. Viscosity is a term that reflects the
tendency for a fluid to resist flow. The yield stress is a value corresponding to a minimum
stress required to initiate flow. Rheological measurements are useful for determining

quality, processing, and handling of food materials (Boume, 1982).

Electrorheology (ER), a discipline of rheology, is concerned With the efl‘ects of
electric fields on the flow properties of specific liquid suspensions that, upon application of
an electric field, show an increase in apparent viscosity and a greater yield stress. These
fluids require polarizable particles suspended in an insulating (non-conducting) oil. The
ER efi'ects result from formation of microstructures of the dispersed solid phase. In other

words, the field-induced microstructures attempt to span the fluid gap and cause reduced

ER suspensions generally respond as shear-thinning fluids regardless of an electric
field presence (Jordan and Shaw, 1989). That is, the apparent Viscosity diminishes as the

shear rate increases. Further investigation reveals that the major forces responsible for ER

 

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activity are polar, viscous, inertial, and hydrodynamic in nature. The field induced particle

chains are sensitive to shearing, and ER activity diminishes with high shear rates,
coinciding with viscous forces dominating polar forces. A dimensionless group devoted to
expressing the relationship between viscous and polar forces is known as the Mason
Number (Marshall et al., 1989). This term and others exist to describe competitive effects

in the ER phenomenon.

According to Block and Kelly (1988), there is little agreement about what induces
the ER phenomenon, and much experimentation needs to be pursued to research the many
ER parameters. Quoting Zukoski (1993 ), “Characterization of ER fluids requires an
understanding of the colloidal and rheological properties of suspensions, polarization
mechanisms in weakly conducting solids and liquids, and electrochemistry ill nonpolar
media. In addition, linking microstructures to flow properties involves study of the
interplay of viscous, thermal, and polarization forces as well as the strength of adhesion of
conducting particles held at small separations in a large field.” Among the numerous
variables known to impact ER activity are: volume fraction, temperature, voltage,

moisture content, dispersed and dispersant phases, electrical properties, and shear rate.

Electrorheological literature abounds with proposed ER devices, including shock
absorbers, engine dampers, and variable speed drives. Presently, there exists strong efforts
in the automotive industry to design ideal ER fluids for specific applications (Duclos et al.

1988; Hartsock et aL, 1991; Korane, 1991; Morishita and Mitsui, 1992; Stanway et al.,

 

1992).

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1992). With the development of more ideal ER fluids, ER applications and devices could

evolve into an annual multi-billion dollar industry (Jordan and Shaw, 1989).

For the food industry, ER technology may offer new potential in process design
and product development of foods responding to an applied electric field. Unlike designed
ER fluids for mechanical applications, fluid foods are not prepared to respond to an
electric field. However, certain materials of biological origin, such as milk chocolate,
respond naturally to an applied voltage. Through application of this technology, it may be
possible for the confectionery industry to externally control the flow properties of milk

chocolate by using a simple ER valve with no moveable parts.

ER materials have not only been studied for the ability to change rheological
properties, but reports have surfaced of ER fluids being able to improve heat transfer
capabilities (Zhang and Lloyd, 1993 ). The ER microstructures are believed to be particles
linking together and forming chains, which in turn orient parallel to the electric field
(Block et a1, 1990; Halsey, 1992). It is the microstructures that potentially increase the
directional thermal conductivity of ER materials, providing a particle pathway for heat

transfer.

The objectives for this dissertation cover four general aspects of the behavior of
ER food systems: 1) To evaluate the literature in electrorheology and milk chocolate
rheology; and to study the efl‘ects of shear fields and temperature on the flow behavior of
milk chocolate in the presence of an electric field. 2) To investigate the importance of six

primary ER variables and their interactions with each other by studying model ER fluids

molI

mlh

 

4
composed of different suspensions of wheat flour and vegetable Oil. 3) To employ

dimensional analysis to develop prediction equations for describing the ER phenomenon,
linking interactions between electrical, thermal, Viscous, and hydrodynamic forces in food
systems. 4) To describe the ‘Mirror-Image-Method” for measuring thermal properties of
molten milk chocolate; and to evaluate the thermal conductivity of molten milk chocolate

with and Without electric field effects.

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An electrorheological fluid consists of a polarizable, particulate phase dispersed in a
continuous, insulating medium In the presence of an electric field, the solid phase
polarizes and initiates structures attempting to span the electrode gap. The induced
structures result in increases in the fluid viscosity and yield stress. The potential of ER
fluids for flow control has been studied extensively, especially in respect to their use in
automotive mechanisms. However, the literature does not indicate any previous studies of
the potential for applying the ER phenomena to food processing techniques. Applications
of ER technology to the food industry may introduce new techniques for process design
and product development. Table 2.1 lists components, solids, liquids, and additives
comprising a variety of ER fluids. Numerous review articles have been written addressing
in great detail the ER phenomenon: Stangroom (1983), Deinega and Vinogradov (1984),
Block and Kelly (1988), Gast and Zukoski (1989), Jordan and Shaw (1989), Bares and

Carlson (1989), Pool (1990), Block et al. (1990), Halsey (1992), and Zukoski (1993 ).
2.1. Origin

The fibrillation of particles ill a fluid liquid suspension induced by an electric field
was first annormced by Willis M. Winslow in 1947. The Winslow Efl‘ect or

Electrorheology (ER) was accidentally Observed by Winslow while he was experimenting

 

Ca.

6

TABLE 2.1.
(Block and Kelly, 1988)

COMMON ER FLUID CODIPOSITIONS.

 

Particulate Phase Continuum Additive
Alginic Acid Polychlorinated biphenyls, Water
poly(tri-flurovinyl chloride), 0-
dichlorobenzene, p-
chlorotoluene, xylene, plus
mixtures of above
Carboxymethyl dextran Polychlorinated biphenyls, Water and sorbitan mono-
poly(tri-flurovinyl chloride), 0- oleate or sorbitan mono-
dichlorobenzene, p- sesquioleate
chlorotoluene, xylene, plus
mixtures of above
Cellulose Chlorinated insulator oil Water
Liquid paraffin or hydraulic oil Aqueous ammonium
or dibutyl sebacate or oleic acid chloride and other
or chlorotoluene or silicone oil electrolytes
Gelatine Transformer oil or olive oil or
mineral oil
Gypsum Transformer Oil or olive oil or
mineral oil
Poly(vinyl alcohol) Hydrocarbons Water
Starch (flour) Petroleum spirit or transformer Water and sorbitan oleate
Oil or laureate
Mineral or transformer oil or
olive oil
Hydrocarbons Water
Vaseline Oil Water

 

 

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with the Johnsen-Rahbeck efiea. The Johnsen-Rahbeck efl‘ect may occur when two

bodies in contact with a voltage potential between them experience considerable adhesion
(Johnsen and Rahbek, 1923). Winslow, an electrical engineer, used this technology to
design a photoelectric switch. To accomplish this task, he constructed a special clutch to
serve as a relay. This clutch consisted of a semi-conductive electrode rigidly held in a
brass cup by a shaft connected to a motor. The opposing electrode was suspended by a
torsion wire. The gap between the electrodes was filled with a powdered dielectric.
When a voltage was applied, attractive forces between the moving and suspended
electrode caused the latter electrode to rotate with the motored electrode. Oil was added
to the mechanism for lubrication. When an electric field was applied, the Oil enhanced the
attractive forces of the powder (Winslow, 1989). This was the earliest recorded

observance of the electrorheological phenomenon.

In his introductory ER publication, Winslow discussed many pertinent topics,
including applications and theories, as well as the role played by surfactants and water. He
credited voltage induced fibrillation as the mechanism responsible for the effect.
Fibrillation is the creation of particle chains, or fibril-like Structures, across the fluid gap.
Winslow also described an increase in bulk viscosity measured by a rotational electro-
viscometer. Later, Winslow established a company dedicated to researching ER fluids and
applications; he would go on to patent and demonstrate many ER devices (Winslow,

1949; Zukoski, 1993 ). However, lack of practical applications of this technology caused a
drought of ER research until the late 19605 (Stangroom, 1983). Within the past ten years,

ER has received renewed attention due to the rapid response time Of the fluids to an

 

clean
potell
1990;

deslgi

.Q
I
.9
o

no 511
1988
also I

flow _

8
electric field. Applications, such as shock absorbers and high speed robotics, could

potentially take advantage of the processing speed of present day microcomputers (Pool,
1990). A fluid which may easily be converted between a fluid and a solid may lead to

design improvements in many mechanical devices.
2.2. Theories

There have been numerous attempts to explain the ER response; however, there is
no single quantifying theory agreed upon by all that explains the effect (Block and Kelly,
1988; Jordan et al., 1988; Jaggi et aL, 1989; Pool, 1990; Block et al., 1990). BR fluids,
also referred to as smart fluids, present a complex physical Situation involving electric and
flow fields within a concentrated particulate suspension, complicating the development of
models and theories (Block and Kelly, 1988). However, there is general agreement that:
1) ER fluids consist of micron-sized polarizable particulates suspended in an insulating
medium; and 2) coulombic interactions existing between polarized particles lead to
aggregation and clusters acting as entities within the flow field, but may not extend

through the bulk.

It is generally accepted that the primary step for the ER response involves
polarization of the solid phase invoked by an electric field, leading to the formation of
microstructures within the continuum The initial polarization is followed by particle-
particle interaction, resulting in the ER phenomenon (Block and Kelly, 1988). The
polarization concept explains many features associated with ER fluids (Stangroom, 1983;

Zukoski, 1993).

 

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2.2.1. Polarization Mechanisms

Most theories associate electrostatic forces between particles with the origin of ER
activity, and are attributable to polarization alone. All ER fluids are composed of
randomly dispersed particles, polarized by an electric field. Polarization may be achieved
through two mechanisms, classified as interfacial or dipolar (Block et a1, 1990). Once
particle polarization is established, fibrillated structures follow from coulombic
interactions between particles. In shear flow, these structures are continuously destroyed

and recreated (Deinega and Vinogradov, 1984; Gast and Zukoski, 1989).

Polarization is influenced by the spinning of the particles in a shear field, commonly
referred to as flow modified permittivity (FMP). In rotational viscometry of ER fluids,
rotation and polarization of the particles occur simultaneously. Figure 2.1 shows a typical
particle exposed to shear and electric fields. Too fast a spin, and the field direction may
change too rapidly for effective polarization. At lower shear rates, the slower field
produces an enhancement of particle polarization. At large shear rates, the polar
interactions weaken and the ER structures deplete. However, fast polarization ill a shear
field involves a continuing tendency for ER structures to rearrange. Little permanence of

fluid microstructures exists under such circumstances (Block et al., 1990).

Presently, there is no evidence that ER involves a singular form of polarization
(Block et a1, 1990). Interfacial polarization involves the migration and movement of
charges and charge carriers about a partially or totally charged boundary. Molecular

Dipolar Alignment supports the rotation of dipoles, but not the migration of charges

10

 

 

 

FIG. 2.1. POLARIZABLE PARTICLE EXPOSED TO SHEAR AND ELECTRIC
FIELDS.

 

.4

he
PE
M

de

3p]

i1111

1 1
(Block et a1, 1990). Three main theories of electrorheology have received much attention

and support, they include: 1) Molecular Dipolar Alignment and Interaction, 2) Interfacial
Polarization, and 3) Water Glue. The following sections explore these three polarization
mechanisms. Other works addressing the role of polarization include: Usyarov et al.

(1965), Bezruk et a1 (1972; 1972b).

2.2.1.1.Molecular Dipole Alignment and Interaction

When Winslow first observed electrorheology, he attributed the special response to
particle polarization and fibrillation (Block and Kelly, 1988; Jordan and Shaw, 1989).
According to this theory, it is the strength of the interacting dipolar particles (the bridges)
which determines the magnitude of the ER response (Jordan and Shaw, 1989; Zukoski,

1993)

Dipolar polarization involves dipole rotation, not the dlifi of mobile charges.
Molecular polarization is based upon the concept that, due to a dielectric mismatch
between phases, particles polarize in an electric field and apply forces to surrounding
particles (Gamayunov and Murtsovkin, 1982; Jordan and Shaw, 1989; Zukoski, 1993).
Most molecules carry no net charge, but many do possess a dipole. Dipolar molecules
depend upon their environments and can change when transferred fiom one medium to
another (Gamayunov and Murtsovkin, I982; Israelachvili, 1992). In the case ofER, the
applied electric field induces the dipole and ultimately leads to polarization and
interactions. Dipole moment interactions in molecules induced by an electric field is a

unique electrostatic interaction known as molecular polarization (Israelachvili, 1992).

 

IN)
: .

IIlU

not
is. l
the
P101

198

10115 .
IHole

the f(

1 2
It has since been reported by Hill and Steenkiste (1991) that the ER phenomenon

occurs in the millisecond time fiame. A major criticism of dipole alignment and fibrillation
is that the response occurs too rapidly for extensive particle interaction and microstructure
formation which develops when an ER fluid is ill the presence of an electric field. (Block

and Kelly, 1988; Jordan and Shaw, 1989).
2.2.1.2.Water Glue

According to Stangroom (1983 ), certain requirements must exist for a fluid to
Show ER activity: 1) The base liquid must be hydrophobic; and 2) The particulate phase

must be hydrophilic and porous, allowing the solids to absorb water.

These criteria serve as the basis for the Water Ghle Theory, which incorporates the
notion that water absorbed by a solid particle is essential to elicit the ER response. That
is, the amount of water greatly influences the performance of the final fluid. Other
theories assume that the effect results from polarization alone; water and other additives
provide a mode for inducing charge mobility and interfacial polarization (Block and Kelly,

1988)

According to the Water Glue Theory, mobile ions exist in pores of the solid phase,
and these ions associate with water molecules. When an electric field is applied, mobile
ions move toward the oppositely charged polar end of the solid particle carrying the water
molecules. This action results in an uneven distribution of water ill the particle, leading to

the formation of "water bridges" between particles. Once the voltage is removed from the

 

 

1e

1 3
fluid, the water retreats into the pores of the solid, and the dipole is lost (Stangroom,

1983)

Uejirna (1972) showed results suggesting the adsorbed water essentially afl‘ects
particle surface charge density and the electric double layers, ultimately increasing the
solid phase dielectric constant. The Winslow efi’ect was enhanced with water adsorption
and was saturated at a constant amount. The adsorbed water was considered to be one of
two types: (1) adsorbed to the particle surface forming double layers, and (2) absorbed
within the particle. At lower amounts Of moisture, when the ER system was comprised of
the second type of water absorption, no electric double layers formed and no ER activity

occurred, indicating a requirement for water by the system for invoking an ER response.

Xu and Liang (1991) measured the rheological properties of a semiconducting
polymer-based ER suspension in transient, steady, and oscillatory flows. In these
suspensions, water was not necessary for polarization; although water still improved ER
performance. Considering the polarization mechanisms (interfacial or dipolar), it appeared
the overall degree of polarization afleaed ER fluid performance. At higher temperatures,
the anhydrous ER material had improved performances over water activated dispersions.

These results support the pursuit and development of dry ER fluids.

Kuramoto et a1 (1995) studied a suspension ofpolyanaline-coated copolystyrene
particles in silicone OiL This mixture was found to have a greater ER ability at higher

temperatures without the requirement of water when compared to other ER fluids. ER

1 4
data were nearly identical at 25 and 150 °C indicating ER activity Without water since the

physically absorbed water would desorb at higher temperatures.

The Water Glue Theory implies water is a necessity for the ER response.
However, recent development of anhydrous ER fluids clearly dictates that water-bridging
is not necessary. As an alternative mechanism, interfacial polarization may be a potential
candidate to explain the response in aqueous systems, and in particular, those systems

incorporating surfactants (Block and Kelly, 1988).

2.2.1.3. Interfacial Polarization (Maxwell-Wagner)

Interfacial polarization involves ionic migration through particle pores or along a
particle surface, as well as within the double layer. ER suspensions generally contain
sources for charge carriers, such as electrons, ions, or pores (Block and Kelly, 1988).
According to Block and Kelly (1988), ER fluids are based upon some type of charge
migration rather than dipolar orientation. The precise mechanisms for charge migration
may vary fi'om system to system There are various pathways that charge carriers may
follow: 1) bulk transport through the particle; 2) surface migration of carriers; and 3)
movement of charges ill a particle’s double layer (Block and Kelly, 1988; Block et al.,

1990)

When a potential is applied across the ER system without the passage of current,
the potential drop cannot exist in the electrodes or the dispersant, it must occur at the
interface according to Newman (1991) and Jordan and Shaw (1989). In other words, with

application of an electric field, free and bound charges accumulate at the interface

h

 

1 5
(Deinega and Vinogradov, 1984). Figure 2.2 depicts three potential interfacial

polarization pathways.

Double Layer. Double layer polarization is an example of numerous charge migratory
theories involving interfacial regions. It involves charges residing within the oil region
surrounding the solid phase, and is a likely source for the ER response particularly when
surfactants are present. Whenever surface reducing agents are in the ER solution, the

presence of a charged double layer is possible.

In colloidal systems, interfaces between solids and liquids almost always acquire
charges that may disturb the random distribution of charges in solution. In general, one
phase tends to achieve a positive and the other phase a negative charge. For example, in
the presence of an electric field, a positively charged particle will be surrounded by
negatively charged counter ions, culminating in a few negative ions bound tightly to the
particle surface. This monolayer of charges is called the compact layer. Concentration of
remaining charges falls ofl‘ gradually from the particle until the bulk concentration of
charges is attained. The outer region of freely moving ions, influenced by electrical and
thermal forces, is known as the diffuse layer. The total charged arrangement is commonly
referred to as the diffuse electrical double layer (Hunter, 1989; Jordan and Shaw, 1989;
Russel et a1, 1989;1sraelchivili, 1992). Application of an electric field causes movement
of the double layer toward the electrode having an opposite charge (Jordan and Shaw,

1939; Uejima, 1972).

1 7
The thickness of the electrical double layer is much less than the particle size

(Dukhin and Shilov, 1974). When two interfaces approach one another so that the double
layers overlap, the resulting force is usually repulsive (Hunter, 1989). However, with the
addition of an electric field, the charge on a particle and that in the diffuse layer have
different signs, and the charge cloud and the particle tend to move in opposing direction

(Russel et al., 1989).

Double layer processes involve the charges extending into the liquid phase of the
interface. According to Newman (1991) and Russel et aL (1989), a double layer is present
at an interface because: 1) some materials in solution sinme prefer positioning near the
solid; 2) application of an electric field causes a potential drop at the solid-liquid interface;

3) ionization of surface moieties; and 4) entrapment of ions.

Proponents Of the double layer theory believe that the electric field causes
movement and distortion of the diffuse double layer toward the oppositely charged
electrode. The problem with this theory is that double layer interactions and overlap may
not be strong enough to support the development of a yield stress (Jordan and Shaw,

1989).

A classical paper in ER by Klass and Martinek (1967) explained the primary ER
mechanism by induced interfacial polarization on and near the solid surface, resulting in
polarization of the electrical double layer. Electric field application, they contended,
caused a movement of the particle double layer towards the oppositely charged electrode.

Overlap of the double layers enhanced electrostatic interactions between particles, causing

1 8
ER structure formation. They reasoned that mass movement of particles through a

continuum would not be expected to follow an AC field; however, induced double layer
polarization would follow the alternating field since highly mobile charges are involved. In
this work, the ER behavior was found to be inversely proportional to the square of the
distance separating double layers. In addition, the viscosity of an electrified ER sample
was approximately proportional to the reciprocal of the shear rate and the square of the
field strength for a particular volume fraction. Similar rheological results were obtained
for 60 HZ AC and DC electric fields; yet, the ER efl‘ect decreased with electric frequency
of the field at constant voltage. The induced polarization of the double layer was found to

be more pronounced at higher temperatures.

This work led Klass and Martinek (1967b) to examine electrical properties
involved with the double layer polarization mechanism They theorized that shear stresses
in the transverse direction of the applied electric field, such as those for couette
measurements, perturb the induced structure formation. In the presence of electrical and
shear fields, a dynamic equilibrium is achieved between the rheological and electrical
properties of the fluid. Application of an AC field generates low-frequency interfacial
polarization between components in any system when the phases have difl‘erent dielectric
properties and conductivities. Higher temperatures, that do not cause destruction of the
double layer, enhance polarization due to a decrease in viscosity of the insulating
continuum and increased charge mobility. As concentration of the dispersed phase is

increased, distance between electric double layers shortens. In the presence of an electric

1 9
field, the polarized double layers are closer together, perhaps even overlapping, resulting

in a larger ER response.

In summation, in any system with an interface, a distribution of ions surround the
solid, dispersed phase in an attempt to gain stabilization. This distribution is represented
as an electrical double layer comprised of: 1) a monolayer, 1 ion thick, closely adhered to
the solid surface; and 2) a diflirse layer of ions extending into the continuum (Jordan and

Shaw, 1989).

Bulk Transport. In many types of particulate dispersions within an insulating continuum,
the possibility exists that the particles themselves serve as the charge carriers. In this case,
charges residing within the particle are induced to migrate towards the oppositely charged

polar end of the particle (Block and Kelly, 1988).

Surface Migration. Charges existing on the particle surface are influenced by an electric

field to drift along the surface toward the oppositely charged polar end of the solid.
2.2.2. Point Dipole Approximation (Electrostatic Polarization Model)

Electrostatic Polarization Models of the ER response are based on the concept that
dielectric constant mismatch between ER system phases (5,, at 3,) causes the solid phase
to polarize upon exposure to an electric field and apply a force to surrounding particles.
Many electrostatic polarization models consider the ER fluid as hard, dielectric spheres

suspended in a viscous, dielectric continuum, which is usually low in polarity and

conductivity (Adriani and Gast, 1988; Klingenberg et al., 1989; Gast and Zukoski, I989;

20
Zukoski, 1993). The spheres are treated with a “point-dipole” approximation - each

sphere interacts with a neighboring sphere and is replaced with a dipole at the center

(Klingenberg et al., 199 lb).

The electric field polarizes the particles and leads to induced charge at the particle

surface. The charged particle may be modeled as a dipole moment, d:
d = ,6 r: E [ 2.1]

with rp as the particle radius and E is the electric field intensity. ,6 is the particle dipole
coeflicient, representing the ability for a particle suspended in a dielectric continuum to
polarize ill the presence of an electric field. The dipole moment is enhanced by a large

difference in dielectric constants, reflected by new values for ,B (Adriani and Gast, 1988).

 

fl" P ° [2-2]

6,, and 6. represent dielectric constants for the particulate and continuum phases,

respectively. The energy, u, between 2 polarized point-dipoles is
d2
u(r,t9) = —,—(3cos2 6 — l) [2.3]
r

where r is the distance between particles and 0is the angle between the electric field

vector and the alignment of particle centers (Halsey, 1992).

21
Zukoski ( 1993) provides a detailed explanation of the electrostatic polarization

model and reviews simulations where this model serves as the foundation. When two
solid spheres, denoted as i and j, with radii rP are at a distance rij apart, and their lines of
center are at an angle 6;,- fi'om the electric field, E, each particle feels a force from the
polarization of the other sphere. Figure 2.3 shows the geometrical configuration for

polarization of a two-sphere system

Equation 2.3 (the electrostatic energy) is differentiated and manipulated to obtain

the polarization force (Fp) between two spheres:

Fp(r

ij’

“2‘“ 2611 '20 24
oij)x808crp fl E {(I) [(3005 ij— )8; +8111 ijegl} [ . ]

'1

where e' and e, are unit vectors pointing in the r and 9 directions of the cylindrical

coordinate system (Zukoski, 1993 ).

Equation 2.4 indicates that FF) is attractive when the sphere centers are aligned with
the applied field. In contrast, Fp is repulsive when the lines of centers are perpendicular to
the electric field (Zukoski, 1993; Halsey, I992). Electrostatic polarization interactions
between particle pairs provides the angular dependence associated with the ER columns

(Klingenberg et al., 1991c).

The electrostatic polarization models can account for much of the ER response.
However, it does not account for the effects caused by adding surfactants or water and the

efieas of electrical frequency. Incorporating these factors, a Maxwell-Wagner model may

 

 

 

 

 

 

”G- 2.3.

 

FIG. 2.3. PARTICLE POLARIZATION GEOMETRY.

way—cu

 

23
serve as the initial source for simulation development, since it involves the presence of free

charge carriers about the solid phase (Zukoski, 1993 ).

2.3. Rheology

In the absence of an electric field, the rheological behavior of an ER suspension is
similar to the flow behavior of any typical colloidal suspension (Marshall et al., 1989;
Zukoski, 1993). In the presence of an electric field, E, the increase in suspension viscosity
is rapid and reversible, typically occurring within 1 millisecond (Stangroom, 1983; Block
and Kelly, 1988; Klingenberg and Zukoski, 1990). BR fluids tend to be shear-thinning;
the apparent viscosity, 7], decreases as the shear rate, 7 , is increased (Jordan and Shaw,
1989; Otsubo et al., 1992). This behavior explains why ER suspensions usually have a
greatly enhanced viscosity at low shear rates. In addition, ER fluids exhibit a field induced
increase in shear stress, a, usually leading to a yield stress, 00 (Block and Kelly, 1988;
Block et aL, 1990). With an electric field, an ER fluid displays characteristics of a
Bingham plastic with the yield stress proportional to the square of the field, and has been
modeled as such (Uejima, 1972; Block and Kelly, 1988;1(raynik, 1989; Block et a1, 1990;

Halsey, 1992; Conrad, 1993):

O- : 00 + npl).I [2'5]

where 1],. refers to the plastic Viscosity.

The unique rheological response of ER fluids is directly related to microstructures

that form along lines parallel to an electric field. The ability of ER bridges to withstand

24
certain applied stresses supports the yield Stress notion, validating the application of the

Bingham model to describe ER properties (Jordan and Shaw, 1989). By definition, the
yield stress is a minimum force required to initiate flow. Below the yield stress, the ER
suspension is solid-like. Figure 2.4 shows the electric field induced structure formation
across the gap. When a shear stress is applied, the ER structure causes opposition to fluid

flow.

In Klingenberg et al (1991b), the Casson constitutive equation was found to best

represent the ER data:

[a(r'.1~:,¢)]yz = [00(E,¢)]% +[n..(¢)7']% [2.6]

This relationship showed improved performance over a Bingham relationship since it

considered shear rate, volume fraction (¢), and electric field intensity (B).

When an ER fluid is subjected to shear and electrical fields, an equih'brium must be
established between rheological and electrical properties to establish stability within the
fluid (Klass and Martinek, 1967b). Gamayunov and Murtsovkin (1982) observed that
when charged particles move through a dielectric continuum driven by an electric field, the
particles interact via polar and hydrodynamic forces. The polar interactions result from
induced dipole moments in the particles. The hydrodynamic interactions are caused by
particle motion through the liquid continuum, adding additional forces on the particle.

According to Gamayunov and Murtsovkin (1982), ER structure prediction must consider

A)

 

 

3)

FIG. 2.4. ELECTRORHEOLOGICAL MICROSTRUCTURES. A) PARTICLES IN
SUSPENSION WITHOUT A VOLTAGE; B) PARTICLE CHAININ G WITH A
VOLTAGE.

26
hydrodynamic interaction and interparticle polarization of the suspended solids ill shear

and electric fields.

With traditional parallel plate rheology, two plates are separated by a finite
distance with the sample fluid filling the space between the plates. One plate is set ill
motion relative to the opposing plate, placing a shear stress across the fluid. This force, at
a particular angular velocity is measured and related to fluid viscosity. For ER
measurement, the plates are two parallel electrodes separated by a gap filled with an ER
fluid. One electrode plate is stationary while the other is set in motion producing a shear
field (Jordan and Shaw, 1989; Halsey, 1992). It may be necessary to overcome a yield

stress for the plates to move at low angular velocities.

Results from Conrad (1993) estimated a maximum attainable shear strength in ER
fluids to be in the order of 49 kPa. Yang (1993) studied ER fluids comprised of a porous
solid aluminosilicate fine particulate as the dispersed phase. Results from this Study found
maximum shear strengths of 58 kPa when exposed to 2 MV In1 and a current density of
210 mA m'z. This same fluid demonstrated a rapid loss of ER activity under very high

shear rates.

Arp and Mason (1977) studied the simple shear behavior of electrically induced
linear chains of monodispersed spheres suspended ill a Newtonian dielectric fluid in
uniform electric fields. At low shear rates the chains rotated as single axisymmetric
particles; while at larger shear rates, the chains collapsed into smaller fragments. When

exposed to electric and shear fields, the chains responded as either rigid or flexible

27
particles depending on the interparticle gaps. Particle spacing strongly influenced the

orientation of the ER structures when exposed to electric and shear fields. Particle
behavior ill Shear and electric fields has been further discussed by Chafl‘ey and Mason
(1965), Chafi‘ey and Mason (1968), Okagawa et al. (1974), Okagawa and Mason (1974),

Arp and Mason (1977b), Seed et a1 (1989), Ceccio and Wineman (1993), and Filisko and

Gamota (1993 ).
2.3.1. Yield Stress and Structure Development

When the shear stress is less than the field induced yield stress, the ER materials
become solid-like. When the shear stress is equal to or greater than the yield stress, flow
is initiated. According to Jordan and Shaw (1989), the simple presence of a yield Stress in
an ER suspension indicates the presence of structure development. A threshold voltage
may be necessary to invoke ER activity, since a certain amount of polarization may be
necessary to overcome the forces separating the particles. Once the threshold voltage is
attained, the yield stress often increases in proportion to the square of the applied electric

field (Jordan and Shaw, 1989).

According to Block et al. (1990), the yield stress is not always a function of the
square of the electric field. Otsubo et al. (l992b) agrees that, for an ER fluid composed of
silica suspensions in silicone oil, the yield stress scales with the square of the applied field
for a volume ratio less than 0.3. However, with greater volume ratios the yield stress

varies with (¢E)2-4.

28
At a given electric field strength and temperature, the yield stress increases with

the volume fraction of the solid phase. The length of the particle bridges is a function of
the electric field strength and the particle concentrations (Usyarov et al., 1965). With
more suspended solids, the greater the potential for significant structure development.

The greater the integrity of ER structures, the greater the yield stress.

Not all ER fluids demonstrate a common response and stability with time, field,
and shear rate, but all fluids do exhibit the microstructures commonly alfiliated with ER
(Jordan et al., 1992). An understanding of field induced microstructures can allow one to
investigate rheological properties giving ER fluids their practicality (Halsey, 1992). On
applying the electric field, accompanying increases ill stress result from large changes in
the suspension, where randomly dispersed particles move to form cohlmns bridging the
electrode gap. Applying a shear field to an ER suspension degrades the structures, and
the additional work required to overcome the induced interactions is observed as an

increase ill apparent viscosity (Klingenberg et al., 1991c).

Other investigations have examined ER structure development (Jordan and Shaw,
1989b). Tao and Sun (1991 and 1991b) descn'be the 3 dimensional form of an ER
structure. The ground state of induced columns is proposed to be a body-centered
tetragonal lattice. Vorobeva et al. (1969) conducted a study of the change in time of the
ER structure size with the application of an AC field. The rate of structure formation
increased with concentration of the solid phase, and slightly decreased with increases to
AC frequency. Jordan et al. (1988) performed an investigation using turbidity

measurements to monitor the rate microstructure development in ER fluids undergoing

29
steady Shear. More turbid suspensions were found to have a lesser degree of particle

chaining.
2.3.2. Viscoelasticity

Progress has occurred in understanding the ER phenomenon under steady shear
conditions. Knowledge of the response is poor under dynamic or oscillatory conditions
(Klingenberg, 1993). Experimental investigation of the oscillatory response of ER has
produced various results. General conclusions agree that the storage modulus (G')
increases with electric field intensity, indicating a Stronger elastic component. Increasing
the solid phase concentration with a constant electric field strengthens the ER response,
evidenced by an increase in the storage modulus (Jordan and Shaw, 1989). Under
periodic deformation, ER fluid elasticity diminished as the amplitude of deformation

increased (Korobko and Shulman, 1989).

When a sinusoidal Strain is placed upon an elastic material, the resulting stress is in
phase with the applied strain. Should a similar strain be put on a purely viscous materiaL
the resulting stress is 90° out of phase with the oscillatory strain. A Viscoelastic material
produces a stress with components in and out-of phase with the loading. A complex
dynamic modulus, 6', considers both stress phases (Stefl‘e, 1992). In the linear
Viscoelastic region, the complex modulus is independent of oscillatory frequency, and at
high electric fields, the storage modulus achieves a plateau value (Zukoski, 1993 ). The

complex modulus is defined as:

G‘ = 0' +10" [2.7]

30
where G' and G" represent the storage (in phase) and loss (out of phase) moduli,

respectively. Measurements of the complex dynamic modulus generally use sinusoidal,

oscillatory flow (Jordan and Shaw, 1989).

As solid concentration of an ER fluid increases, G ' and G" are likely to diverge as
the electric field increases. In other words, the elastic contribution to the Viscoelastic
response becomes more important with higher fields (Jordan et al., 1992). Viscoelastic
measurements have shown that the shear rate dependence of the viscous and elastic
properties vary with electric field strength (Thurston and Gaertner, 1991). When the
electric field is removed, the ER structures weaken and are quickly destroyed, even at

small strain amplitudes (Korobko et a1, 1994).

Klingenberg expanded an earlier model based on the point-dipole approximation,
to study a dynamic, oscillatory shear response for ER fluids (Klingenberg, 1993). Most
experimental oscillatory data showed a broad dispersion with storage and loss moduli
reported to be insensitive to a large, oscillatory frequency range. Common attributes of an
ER fluid may be responsible for a broad dispersion of oscillatory data and must be
considered to improve mathematical models. These attributes include particle size and
shape, particle distribution, and nonlinear efiects. A significant result from this experiment
was that a relaxation mechanism was found from competition between polar and viscous
forces, resulting in a transition of the dynamic structure and rheological response as the

frequency was varied between small and large limits (Klingenberg, 1993).

31
Parthasarathy and Klingenberg, ( 1995 and 1995b) co-authored a series of papers

examining the transition from linear to non-linear rheological behavior for ER suspensions
under steady and oscillatory shear flow. The electrostatic polarization model served as the
foundation to describe various features of each of the shear mode responses. In each case,
the nonlinear deformation occurred from slight rearrangements of the ER structures, not
the rupturing of ER cohlmns. Model sirmrlations at low frequency found the
rearrangements to occur for strains above a limiting, critical strain, defined as the strain
when structures start to show an instability in the limit of zero deformation rate. For
oscillatory shear, the non-linear behavior was found to be induced by increasing strain
amplitude, or by decreasing deformation frequency or increasing electric field strength
(given the strain is higher than the critical strain value). A limitation of this model is that it
does not consider Brownian motion, buoyancy, particle sizes and shapes, dielectric

properties, and current.

Shulman et a1 (1989) studied oscillatory behavior of ER suspensions. The viscous
component of the complex modulus was seen to exceed the elastic component for weak
electric fields as the volume fraction was increased. Similar to other research, as the
electric field was strengthened, G’ increased to the point where it exceeded G" . With
volume fraction increases, G' increased in strength. As the strain amplitude was
increased, non-linear strain conditions were achieved, and the complex modulus became a
function of the strain amplitude. Studying the transition of linear tonon-linear behavior, a

threshold strain was achieved, accompanying the destruction of the ER structures.

32
McLeish et al. (1991) calculated a linear fi'equency-dependent modulus of an ER

system at low and intermediate concentrations using a particle string model The loss
modulus was afi‘ected by broken ER strings, while the storage modulus was dominated by
intact ER structures spanning the electrode gap. Results from this study showed that the
particle string model adequately accounted for general features of an ER dynamic

response.

Jordan et al. (1992) accompanied work from McLeish et al. (1991) and compared
Viscoelastic data for a mineral type ER fluid with concentrations varying between 0.02 -
0.10, electric fields between 0.1 and 5.0 kV mm'l, and strains of 0.2 - 15% with that of a
particle string model Broken and free ER strings contributed to viscoelasticity. As
concentration increased, G' and G" were more likely to diverge in the high electric field
limit. In other words, the elastic component of the complex modulus became increasingly
important with stronger electric fields. The particle string model failed at large strains,
with the loss and storage moduli becoming essentially equivalent. At larger strains, the
rheological behavior was clearly in the non-linear region, corresponding to a breaking of
ER structures beyond elastic limits and may be considered as a yield point for ER

materials under certain experimental conditions.

A parallel plate rotational rheometer was used to study the ER behavior of a
nematic poly n-hexyl isocyanate (PHIC) solution (Yang and Shine, 1992; Shine et al.,
1993). Storage and loss moduli at 5% strain were measured. The storage modulus was
observed to increase to a maximum, and then decrease. The G' maximum was a function

of oscillation frequency. Enhancement of the storage modulus for an electrified

33
suspension was seen to be greater at higher oscillatory fiequencies. At low electric field

strengths, the loss modulus was larger for higher frequencies. At larger field strengths,
this behavior was reversed. The PHIC is a helical polymer which forms a liquid crystal at
high concentrations in non-polar solvents. The molecules have a large permanent dipole
and rapidly orient ill the direction of an applied electric field. As a result, the mechanism
of polarization was understood to be from dipolar orientation, not interfacial effects. This
was a critical finding, since it demonstrated that polarization may occur through difi‘erent

mechanisms.

An aluminosilicate particle/parafin oil ER fluid was examined by Gamota and
Filisko (1991) for dynamic response to sinusoidal strains while exposed to an electric field
in the oscillatory frequency range of 300—400 Hz. The rheological response of the
material was in the linear Viscoelastic range for electric fields of 0.0 - 3 kV mm". Upon
exposure to an electric field, both the storage and loss moduli increased with increasing
electric field; i.e., the material showed greater Viscous and elastic behavior, where

G' = f(E“) and G” = f(E"l ). Additionally, the moduli showed a dynamic frequency

dependence, increasing as the electric field was strengthened.

Thurston and Gaertner (1991) described a method for measuring Viscoelastic
properties of an ER fluid consisting of corn starch in mineral Oil using oscillatory flow
through a thin rectangular tube. Results fi'om this study indicated that, at low field

strengths the microstructures degraded at strains less than 0.1, but with higher fields the

34
structures degraded at a strain near 1.0, essentially proving what other research has shown

- there is a much greater elastic contribution to the fluid ill the presence of an electric field.

Yen and Achom (1991) measured dynamic behavior of an ER fluid consisting of
hydrated lithium salt ofpoly(methylacrylate) dispersed in parafin 011. With an electric
field, the suspension displayed elastic behavior at low strains and plastic deformation at
larger strains accompanied by an electric field dependent yield stress. At low strains, the
elastic modulus exhibited an oscillatory fiequency independent behavior, confirming that
ER fluids behave elastically at low strains. The authors also studied the dynamic stress-
strain relationship of an ER fluid. The dynamic rheological properties were studied as
filnctions of an electric field, shear rate, vohrme fiaction, and oscillatory frequency. With
the application of an electric field, the ER suspension behaved elastically at low shear
fields and underwent plastic deformation, characterized by a field dependent yield stress,

as straining increased.

Other studies addressing the Viscoelastic response of ER fluids include: Korobko

and Shulman (1989), Gamota et al. (1993), and Korobko et al. (1994).

2.3.3. Dimensional Analysis

Dimensional analysis involves the identification of important variables affecting a
particular phenomenon. These variables are manipulated to form meaningful,
dimensionless groups, which are then compared and adjusted to properly describe an
observed quantity. Choosing dimensionless groups as ratios of physical quantities

provides a means for comparison of different forces (Russel et al., 1989). Gast and

35
Zukoski (1989) presented a review of dimensionless parameters and lists groups relevant

to ER, shown as Table 2.2.

Recent work has shown that the basic forces underlying the ER phenomenon are
electrical, viscous, and thermal in nature (Xu and Liang, 1991; Klingenberg et al., 1991c).
Electrostatic forces arise fiom a dielectric mismatch between the two ER phases. Without
an electric field, van der Waal's, electrostatic, and steric interaction forces are important
for stabilizing the suspension. In addition, thermal motion provides continual interaction.
With an electric field, the solid phase polarizes and interacts with surrounding particles
through dipolar-like forces causing the formation of chaining structures (Klingenberg et
a1, 1991c). In other words, polar forces dominate over colloidal and thermal forces
(repulsive electrostatic and attractive Van der Waals) and dictate the fluid behavior
(Klingenberg et a1, 1989). The stability of the fluid will be a direct reflection ofhow Well
the suspension balances all the competitive forces (Gast and Zukoski, 1989; Otsubo et al.,

1992b)
2.3.3.1.Mason Number (Mn)

A dimensionless group known as the Mason number (Mn) descrlhes the Viscous
and polar interaction of ER fluids. The Mn is the characteristic parameter representing
competition between dipolar forces and flow (Gast and Zukoski, 1989; Marshall et al.,
1989; Halsey, 1992). The viscous forces are associated with flow and tend to disrupt ER

microstructures developed fiom polar interactions. According to Jordan and Shaw

36

TABLE 2.2.
(Gast and Zukoski, 1989)

DIIVIENSIONLESS TERMS OF ER.

 

 

 

 

 

 

 

 

 

Ratio Dimensionless Group
van der Waals Arp
Thermal 246193]:
Electrostatic 4 as g r W2
. o c p
Thermal kBT
Pollinzatron _ ”3.5.1.3 (Mi):
ermal _
kBT
Viscous 67777 r 3);
“mm“ P6 = k '1:
B
V'sco s '
1. u. Mn.._27_cr_2_
Polarization 50 3c (p5)

 

A: Hamaker Constant, J
6: Electric Double Layer Thickness, nm
[/11 Electric Potential, mV

37
(1989), the Mn is a major factor ill ER since it incorporates shear rate (7 ), electric field

 

(E), and dielectric properties (,6).
= Viscous Forces [2.8]
Polanmtlon Forces
or
__'LZ.___ [2,]

' 2503,1329

The product of ( £05, ) is the dielectric permittivity of the continuous phase, where so is the

constant value for the permittivity in a vacuum and a. is the dielectric constant for the

continuous phase.

Marshall et al. (1989) established much of the preliminary groundwork associated
with the Mn and made comparisons of this dimensionless group with the Bingham plastic
model, based on the concept that structures within a suspension can withstand a certain
degree of stress. The Bingham model represents ER results well at low and high shear
rates (large and small Mn). The model was rearranged by dividing the expression with the

C

shear rate and continuum viscosity ( 77,}? ) to incorporate the Mn:

Ac ”G? ”c [ ° ]

allowing 1],, = r],,( ngis the suspension viscosity at large shear rates) and 0'0 to scale as

Mn'l since 00 at E2; substitution gives

38

%°=I§/Mn+"~ 77. [2.11]

with K being a material constant. Dividing through by "/7, gives

%Q=MnyMn+l [2.12]

with Mn’“ , the critical value of Mn, equal to K 7% . Numerous authors have

considered Equation [2.12]: Marshall et a1 (1989), Jordan and Shaw (1989), Klingenberg

et al (1991c), and Zukoski (1993).

The relative viscosity ratio of the of the electrified suspension viscosity to that of

the continuous phase viscosity ( % ) is a filnction only of Mn (Otsubo et al, 1992b).

Marshall et al. (1989) found that for a given volume ratio, the relationship between the
Viscosity ratio and the drear rate, electric field, and temperature can be expressed as a

single filnction of the Mn.

Typical plots of yr; as a function of Mn show a decaying curve, with the

C

dependence diminishing at a large Mn, corresponding to the critical Mn. Mn'“ is a material
property, also referred to as a dimensionless yield stress, of the ER fluid dependent upon
dielectric properties and particle concentration (Marshall et a1, 1989; Zukoski, 1993), yet

independent of the electric field and shear rate (Klingenberg et a1, 1991c). Mn‘“

39
corresponds with the transition from a Newtonian limit to a yield limit (Klingenberg and

Zukoski, 1990).

For field values where Mn << 1, the relative viscosity is observed to change in
proportion to MD"; while at larger Mn (Mn >> 1), the relative viscosity is independent of
the electric field. Temperature efi‘ects are incorporated through values of the continuum

viscosity, because no is strongly dependent upon temperature. (Marshall et a1, 1989).

Analysis of interparticle forces suggest, at high electric fields and low shear rates,

the Mn will be less than unity; therefore, the polar forces dominate.

a = 00(E); when Wm .., << 1 [2.13]

In the low shear rate range (Mn <<1) the stress transfer is purely electrostatic

(Klingenberg et al., I991c).

At large Mn, the viscous forces completely dominate the response and the fluid
behaves like it would in the absence of an electric field. According to Klingenberg et al.

(1991c) , when Mn >> 1, the electric field has no effect on the system viscosity, and

As Mn approaches unity, the polar forces become rivaled by viscous forces, and the ER
microstmctures are disrupted. When the Mn is approximately 1.0, the Bingham model

was expanded:

4o
a(E,;>) = a,(E) + 17,0}? + 0,,(E,;>) [2.15]

with ou(E,7) representing the intermediate Mn range, where hydrodynamic forces are

coupled with electrostatic forces (Klingenberg et al., 1991c).

Marshall et a1 (1989), Gast and Zukoski (1989), Klingenberg et aL (19910),
Otsubo et al. (1992b), and Zukoski (1993) further discuss importance and contributions of

the Mn to ER.
2.3.3.2. A Number (A)

When electric fields are considerably small, the ER effect may not be seen because
Brownian motion of the particles (random particle motion due to temperature) is so great
it overcomes the polar and viscous interactions. A dimensionless number, 21, has been
developed by Adriani and Gast (1988), relating forces arising from polar and thermal
interactions. 2. reflects the relative magnitude of dipolar forces to thermal (or Brownian)

forces:

_ Polarization Forces

 

 

xi -— [2.16]
Thermal Forces
127[£ a r3 2E2
,1 = ”(It/3 [2.17]
B

where kBT is the product of the Boltzmann constant and temperature.

41
Electrically induced microstructures are likely to be encountered when A is large

(2 >> 1), meaning the polar forces are dominating the response over the thermal forces
(Halsey, 1992). As the dielectric constant ratio approaches one (Hp/8091), the
polarization forces become negligible compared to thermal forces and A is small To
invoke ER activity, the dielectric constant ratio must be greater than 1, indicating that the
particulates polarize more easily than the continuum Generally, in all but the very
weakest of ER fluids, 2. will be much greater than unity; meaning that polar forces
dominate thermal forces when establishing the rheological behavior of a suspension (Gast

and Zukoski, 1989; Zukoski, 1993).

ER effects are not Observed for small electric fields due to Brownian motion of the
colloids. This ceaseless motion is caused by temperatures of the surrounding medium
The ordered microstructures are constantly being disrupted by the thermal motion of the
fluid. ER structures are likely to occur if the electrical forces can overcome the thermal
effects. For large xi, the particles are expected to form highly elongated structures
(Adriani and Gast, 1988). When A approaches unity, a transition occurs between the two

force regimes (Halsey, 1992).

Toor (1993) modeled ER microstructures using a multidimensional model based
on the point-dipole approximation, and observed a rapid increase of the characteristic time
scale with 2. of a model ER fluid. The characteristic time is a measure of the period
required for a particle, placed on the surface of a stable droplet, to move one particle

diameter. Above a critical 201,), ER structures formed and the column width increased.

42
Below 21., ER columns were not seen. At larger values of 2., the ER columns form rapidly

with the fibrillation time scale much shorter than the relaxation time scale (Toor, 1993 ).

2.3.3.3.Peclet Number (Pe)

The Peclet Number (Pe) is the ratio between Viscous and thermal forces:

_ Viscous Forces

Pe -
Thermal Forces

[2.18]

 

Pe = (mm) [2.19]
or
6 3 ‘
Pe = ——m’°r‘°7 [2.20]
kBT

Zukoski (1993) observed for Pe << 10, increasing the strength of the electric field
caused a transition fiom a liquid-like to a crystal-like packing, accompanying the transition
fiom thermal force to polar force dominance of the ER microstructures. At high Pe and
low A, a sliding string phase occurred, where the particles were oriented along lines of
constant velocity within the shear field. The phase was destroyed by increasing 7.. Few

publications dedicated to studying the effects of Pe on the ER response were located.
2.3.4. Theoretical Models and Simulations

Successfirl ER models rely on the understanding ofinterparticle interactions that

occur when fluids are exposed to shear and electric fields. A good model for predicting

43
ER behavior will be capable of considering how the response varies with other factors as

well: volume fiaction, particle Size, physical and chemical properties of particles, solvent

and solid-liquid interface (Gast and Zukoski, 1989).

Adriani and Gast (1988) modeled ER fluids as concentrated suspensions of hard
spherical particles, with dipoles induced by an electric field according to the point-dipole
approximation with the intent of investigating dipolar interactions in ER fluid rheology.
High frequency, small amplitude, oscillatory flow disrupted particle structures and
permitted calculation of the elastic shear modulus and the dynamic viscosity. The elastic
shear modulus and the dynamic viscosity each increased with particulate concentration.
The dynamic viscosity was insensitive to dipole strength, however, the elastic modulus
increased with dipole strength. This model ofiered a quantitative prediction of elastic
shear modulus and the dynamic viscosity, and was an important step towards modeling ER

fluids from a fundamental basis.

Klingenberg et al. (1989) also modeled the ER response as polarizable, spherical
particles in a nonconducting medium based on the point-dipole approximation. The model
incorporated particles exposed to polar forces from the electric field and to hydrodynamic
forces from movement through a viscous medium The continuous phase provided
hydrodynamic resistance to the particle moving through it. The modeled ER
microstructures were found to be independent of the electric field Strength and the
continuum viscosity. This model agreed well with experimental data for time scale and
appearance of structure formation. The work was aimed at gaining an understanding of

conditions required to simulate essential phenomena occurring ill ER fluids.

44
In the first of a series of papers, Klingenberg et a1 (1991) developed a molecular

dynamics-like simulation to investigate the ER response at small shear rates. The model
was extended from an earlier Simulation (Klingenberg et al., 1989), derived to mimic ER
suspensions and focus on small shear rates and the yield stress. Qualitative results from
the model predicted a dynamic yield stress dependent upon particle concentration.
Predictions agreed well with experimental data. Next in the Klingenberg series, the model
was extended to incorporate multipole and multibody contributions to electrostatic
interactions in attempts to predicting a yield stress. The extra considerations produced
larger magnitudes of yield stress values, indicating that accurate predictions for yield stress

could be made (Klingenberg et al, 1991b).

Whittle (1990) developed a Brownian dynamics computer simulation, also based
' on dipolar interactions, to model ER fluid behavior for viscosity, yield stress, and shear
modulus as a fimction of field strength. Actual rheological data were qualitatively similar
to simulation trends. Magnitudes of yield stress were comparatively low and indicated
that interparticle forces alone may not be able to account for the magnitude of the yield
stress. Experimental results indicated that G' and G" were comparable and both increased
with field strength at low fiequency. The simulation, however, showed G" < G' for low
field strengths. Thus, the simulation was not successful at low field strengths due to the

neglect of hydrodynamic forces by the model.

Bonnecaze and Brady (1992) developed a microstructural model to investigate
static and dynamic yield stresses of ER fluids. This model incorporated interparticle

energy to determine both yield stresses. The dynamic yield stress was correlated to energy

45
jumps occurring during the repetitious reformation and destruction ofER structures.

From this theory, a model was developed to predict the dynamic yield stress as a filnction
of concentration and dielectric properties. This model found that the dynamic yield stress
increases with the dielectric constant ratio, and a maximum yield stress occurred at a 40%
volume fraction. A rapid technique for predicting a maximum yield stress in an ER fluid is

provided by this research.

Klingenberg and Zukoski (1990) developed a model for yield stress and
continuous-shear response for ER suspensions. For steady shear conditions, the ER
suspension separated into two regions. One region behaved and flowed as a fluid, while
the other region contained ER structures aligned with the electric field, but slightly tilted
in the direction of the shear flow. The model was based on the concept that ER structure
regions degrade with increasing shear rates, and the stress transfer properties of ER fluids
are due to the destruction of induced ER bridges. Observations from this study suggested
that a critical stress exists and when surpassed, the structures continuously yield. Below
the critical stress, the structures deformed elastically. The primary goal of this
investigation was to explain the general features by considering only viscous and

polarization forces.

See and Doi (1992) developed a computer simulation to predict the response of an
ER fluid exposed to AC and pulsed DC electric fields. This work investigated the effects
of field frequency and the kinetics of ER structure development. It showed that ER stress
transfer passes through a minimum as the frequency is increased. Two reasons were

provided to explain the minimum fiequency. First, the dielectric properties were

45
frequency dependent and the real part of the complex permittivity was reported to

decrease with frequency. The second explanation was that ill an alternating field, the ER
structures were continuously being formed and destroyed, since the ER structure strength
stems fiom the altemating electric field. The coupling of this destructive mechanism with
a damaging shear field may be responsible for the decreased ER response at a minimum
frequency. The simulation produced results agreeing qualitatively with experimental

results.

Chen et a1 (1991) developed a model for particle-particle interactions in an ER
fluid, based on electric potential and ER chains extending across the electrode gap. The
electrostatic force between two spherical particles ill an infinite chain aligned with an
electric field was determined by considering dielectric properties of the ER phases. This
model gave interparticle forces in general agreement with experimentally measured values.

It was considerably more accurate than a point-dipole approximation.

Hill and Steenkiste (1991) studied the speed of an ER fluid response, with the
response time defined as the period of time between field application and the formation of
the first ER fibril. Response times for an ER suspension ranged from milliseconds to
seconds. The response time was observed to vary with volume fraction under AC and DC
electric fields. For AC conditions, the response time may be an order of magnitude longer
than DC response times. This was a valuable finding since response times for practical

applications should be within one millisecond.

47
Atkin et a1 (1991) analyzed and solved traditional constitutive equations for ER

fluids in concentric cylinder geometries. This included an ER rheometer composed of
concentric cylindrical electrodes, with radial distributions of velocity and potential existing
within the fluid gap. The model for this study considered the material as a dielectric
continuum based on a modified Bingham plastic constitutive equation with an electric field
dependent yield stress. The fluid was assumed a perfect dielectric with shear and current
flow considered fully developed, such that end efi‘ects were neglected. The effect of radial
field (electric and shear) distributions may be a considerable factor for yield stress-electric

field relationships determined in annular film shear and flow rheometers.

Bonnecaze and Brady (1989), Wang et al (1989), Lemaire et al. (1992), Lequeux
et al. (1992), Mokeev et a1 (1992), Lou et al (1993), Rajagopal et al. (1993), and Lee et

al. (1993) also proposed models to explain ER observations.
2.3.5. ER Rheometers

Janocha and Rech (1993) described requirements for ER measuring equipment.
The most important unit for measuring ER activity is the viscometer, which must be
subjected to an electric field. For cylindrical geometry, the field exists between the inner
and outer cylinders. It is essential to shield the torque sensors fiom the electric field,
preventing interference from stray voltage. Flow curves for ER materials may be obtained
using rotational viscometers, geometries include concentric cylinder, cone and plate,
parallel plate, cone and cone, and double cone and plate. Brooks (1992) presents a review

Of difi‘erent techniques for measuring ER behavior.

48
Voltage requirements of ER suspensions complicate viscometer design. Bailey et

al. (1991) provided instruction for the design and construction of an electroviscometer.
. This particular ER rheometer design was proven useful for studying stress transfer,

response time, and shear field efleas.

ER rheometers require a uniform gap without sharp edges, reducing electric field
edge efi‘ects. Practical designs generally include rounded edges with concentric cylinder
or parallel plate viscometers (Jordan and Shaw, 1989). Practically all viscometers used for
measuring an ER response Show a variation in the shear stress across the fluid filled

working gap (Stangroom, 1983).

Lou et a1 (1993) and Atkin et a1 (1991) used couette viscometers to characterize
the response of ER fluids. Lou et a1. (1993) revealed that ER fluids exposed to AC
excitation will yield accurate results only if the electric field fiequency is less than 0.1
times the natural frequency of the viscometer torque sensor. Atkin et al. (1991) found a

uniform shear rate profile was achieved at large rotational speeds for large electric fields.
2.4. Chocolate Rheology

Milk chocolate is a suspension of particles consisting of sugar, cocoa, and milk
solids in a continuous fat phase of cocoa butter (Chevalley, 1974). Chocolate processing
occurs with the product in the molten state. Understanding the rheology of this material is
crucial as the confectionery industry moves to more highly automated molding and

enrobing machinery (Minifie, 1980). Knowledge of rheology also provides the industry

49
with measurable properties to assess product quality and processing efliciency (Riedel,

1980)

Liquid cocoa butter behaves as a Newtonian fluid; however, with the addition of
the suspended particles, milk chocolate deviates from Newtonian behavior (Chevalley,
1974; Beckett, 1988). To accormt for the yield stress inherent to milk chocolate, early

attempts to model the chocolate flow behavior used the Bingham expression.

The model was inadequate in expressing the viscous behavior of milk chocolate
and Steiner (1958) proposed an alternative equation, known as the Casson equation, to

model the non-Newtonian flow properties of milk chocolate:
0°" = 03‘ + Kl(}-,)o.s [2.21]

where 00 and K1 are arbitrary constants determined from experimental data. In 1973, The
International Office of Cocoa and Chocolate (IOCC) adopted the Casson model as the
oficial equation for describing steady shear behavior of fluid chocolate (Beckett, 1988;
Steiner, 1972). The Casson equation has not been universally accepted and alternative
equations have been proposed (Chevalley, 1974). In a paper by Ofoli et al. (1987), a
general model (applicable to chocolate) was described for the rheological characterization

of inelastic foods:
0‘“ = 03' + K,(;'/)'12 [2.22]

Equation [2.22] permits additional flexibility by incorporating two flow behavior

indices, m and n;. For the Casson model, a, = n; = 0.5. The indices may vary with

50
temperature and chocolate composition. For example, Chevalley (1991) suggested using a

flow behavior index of 0.6 rather than 0.5 to better describe the behavior of milk
chocolate. Beckett (1988) states that the Casson equation has always given good
agreement with practical results. In attempts to develop equipment and techniques to
quickly and accurately measure the Casson parameters, many reports fiom the
confectionery industry have emerged over the years (Martin and Smullen, 1981; Pieper,

1986; Robbins, 1979; Bouzas and Brown, 1995).

Various factors may influence the flow properties of milk chocolate: fat content,
lecithin content, water content, conching time, particle size, temperature, degree of
temper, and thixotropy (Chevalley, 1974; Minifie, 1980; Beckett, 1988). The amount of
water has a great effect on chocolate rheology. Chocolate normally contains between 0.5
and 1.5% moisture, and if further minute amounts of water are added, the viscosity greatly
increases (Minifie, 1980). An explanation for the viscosity increase is that water may form
a layer of "syrup" about the surface of a sugar particle, increasing the friction between the
particles (Beckett, 1988). The presence of the emulsifier, lecithin, causes the hydrophilic
groups of the molecule to attach to the water on the sugar surface and the hydrophobic
groups to attach to the cocoa butter (Minifie, 1980) which lowers viscosity by neutralizing

the presence of water on the surface of the sugar.

2.5. Variables Influencing ER Behavior

The dependent variable, shear stress (a), is a function of numerous,

multidimensional variables:

51
a = function(E, f, T, me, (2, 77., 5,, 8p, )3) [2.23]

where f is electrical fiequency and me is moisture content. Table 2.3 provides a listing of
common ER fluid characteristics for each individual phase and the complete suspension.

The following subsections will address each variable and discuss the impact made on ER

activity.
2.5.1. Temperature (T)

The influence of temperature on ER is complicated. Typical ER fluids
demonstrate large increases to shear stress and apparent viscosity with temperature to a
certain point, followed by a sharp decline (Deinega and Vinogradov, 1984; Jordan and
Shaw, 1989). According to Nelson and Suydam (1993 ), the viscosity depends on
temperature for the complete measurement range between 5 and 75 °C. This response
may reflect dielectric properties, inasmuch as polarization tends to increase with
temperature (Klass and Martinek, 1967b; Uejima, 1972; Jordan and Shaw, 1989). The
increased polarization coupled with the lowered continuum viscosity leads to increased
charge mobility and a greater ER effect at higher temperatures (Klass and Martinek, 1967;

Jordan and Shaw, 1989).

At high temperatures, water evaporates and the ER response is lost for moisture-
based ER systems (Block and Kelly, 1988; Jordan and Shaw, 1989; Wong and Shaw,
1989; Halsey, 1992). Another factor that may lead to the loss of ER activity at greater
temperatures is that thermal forces resulting from Brownian motion become too strong

and overpower polar forces responsible for the particle chaining. The dimensionless

52

TABLE 2.3.
(Gast and Zukoski, 1989)

COMMON CHARACTERISTICS OF ER FLUIDS.

 

Continuum Properties

Relative Dielectric Constant gc = 2 .. 15
Low Field Strength Conductivity 10-7 , 10-13 mho m"
Viscosity ”c = 0.01 - 10 Pa 5
BMW pc = 0.6 - 2 g cm'3

Particle Properties

Shape approximately spherical
Size rp = 0.1 - 100 um
Relative Dielectric Constant gp = 2 - 40

Suspension Properties

Zero Field Viscosity 775 = 0.1 - 10 Pa 5
Volume Fraction ¢ = 0.05 - 0.50
conduCfiVIOl 10-6 _ 10-13 1111“) m-l

Typical Field Strengths E = 0.5 - 2 kV mm'l

 

53
parameter, A, is used to monitor these competitive forces (see Sec. 2.3.3.2). At low

temperatures (-20 °C), the ER response is diminished, because ice inhibits the response
(Block and Kelly, 1988). Most ER fluids are limited within a temperature range of-20 to

70 °C (Block et al., 1990).

Conrad et a1 (1991) determined electrical and rheological properties for an ER
fluid (zeolite/silicone oil) between 25 and 160 °C. They formd shear stress increased
substantially as the electric field and temperature increased. The fluid strength generally
increased with increasing temperature for the fields and temperature range investigated.
The fluid dielectric constant and DC conductivity were also found to increase with
temperature. Results showed an upper temperature limit, occurring between 120 and 150
°C. Once past this limit, the response no longer increased with temperature (Conrad et al.,

1991)
2.5.2. Moisture Content (mc)

Most ER fluids require water to respond to an electric field. With these fluids, the
absence of water may completely diminish the phenomenon. Nevertheless, too much
water leads to ER failure, i.e., the conductivity becomes too large to sustain the electric
potential across the electrode gap, eventually leading to electrical breakdown (Gast and
Zukoski, 1989; Block et al., 1990). The optimum moisture content for ER behavior is
between 5 and 10% by weight (Block and Kelly, 1988; Zukoski, 1993). As mentioned in
section 2.5.1., the presence of water ill ER systems limits the temperature range where the

phenomenon will exhlhit measurable results.

54
Except for a small class of anhydrous ER fluids, moisture content plays a critical

role ill producing ER activity (Wong and Shaw, 1989; Block et a1, 1990). Shaw (1993)
describes an approach for making anhydrous particulate phases with low [conductivities
while remaining highly polar. Jordan and Shaw (1989) report that the largest ER response
occurs in the range when water is strongly absorbed by the particles. Absorbed water
consists of two types. The first type is adsorbed to the solid surface, forming electric
double layers; while the other type is found at the inner part of the particle (Uejima, 1972).
It has been suggested that water absorbed by the solid phase affects the surface charge
density of the electric double layers, increasing the permittivity and leading to stronger
particle-particle interactions (Uejima, 1972; Jordan and Shaw, 1989). BR behavior is
strongly affected by adsorbed substances at the solid-liquid interface and the
understanding of polar forces due to surface agents may be a key to additional
understanding of the phenomenon. With the recent development of anhydrous ER
fluids, the contribution of moisture to the ER phenomenon is not yet clear (Kordonsky et

al., 1991).

Otsubo et al (1992; 1992b) studied the effects of adsorbed water on an ER fluid
consisting of silica particles suspended in silicone oil. Both reports concluded that the
physically adsorbed water enabled the ER response. Large amounts of water did not yield
excellent ER behavior. When this ER fluid was exposed to heat treatment, desorption of
the water followed, and subsequently a loss of ER activity. Otsubo et al. (1992) improved

the ER response by modifying the surface charge of the silica particles with the addition of

55
silanol groups. Similarly, Kordonsky et al. (1991) observed that water sorbed by a filler

and salt formation enhanced the ER efi‘ect.

2.5.3. Electrical Frequency (1)

Frequency has a large impact on ER behavior. The ER phenomenon occurs under
AC or DC conditions. For low fiequencies (50-60 Hz), practically DC, the shear stress
does not vary with frequency. However, as the frequency range increases to the range of
100 to 10,000 Hz, the rate ofmicrostructure formation diminishes (Vorobeva et al., 1969;
Block and Kelly, 1988; Jordan and Shaw, 1989; Jones, 1989; Block et al., 1990). Also, as
the frequency is increased, there is a decrease in ER material permittivity because the
dispersant does not have sufficient time to adjust and polarize in a large alternating field
(Jordan and Shaw, 1989; Yang and Shine, 1992). In support of this statement, Bezruk et
al. (1972b) observed a diminishing of the aggregate size with increases in the electric

frequency.

According to Hill and Steenkiste (1991), particle movement is linear under DC
excitation. However, with an AC field, the particles oscillate and delay formation of the
microstructures generating a greater response time. As the fiequency approaches zero,
corresponding to DC excitation, more time is available for the particles to polarize,
maximizing ER activity (Thurston and Gaertner, 1991). It is generally believed the ER
response is not present at larger frequencies because the particle fibrils cannot follow the
rapidly changing field direction. Hill and Steenkiste (1991) observed macroscopic particle

motion in a fluid consisting of water coated glass beads in silicone oil at fiequencies

56
approaching 10 kHz. This particular fluid displayed no loss of response as a fimction of

frequency. Uejima (1972) also observed ER activity at a large frequency (2000 kHz) and
concluded that the response time for the phenomenon was extremely fast. Thurston and
Gaertner (1991) compared viscoelastic measurements of a corn starch in mineral oil
mixture exposed to DC excitation and a 1 kHz AC field. Conclusions showed the

viscoelastic response of ER materials was similar for AC and DC fields.

See and Doi (1992 and 1992b) used computer simulations to observe frequency
effects on ER fluids. As the frequency was increased, the stress transfer was observed to
pass through a minimum. For this study, an electric field was applied as a pulsed on/ofl‘
response. The pulses were controlled and set to varying frequencies. Results from this
paper indicated that at low frequency pulses, the particles were able to follow the field and
the shear stress tended to increase. At higher fiequencies, the electric field was removed
before the clusters could completely form, leading to a shear stress decrease. Finally, at
very high frequencies, the electric field was reapplied before the clusters completely

collapsed and the shear stress again increased.

Jones (1989) further explained these results ill terms of dipolar alignment with the
applied field. For specific conditions imposed on the dielectric constants and conductivites
of the solid phase and carrier fluid a certain fiequency range causes ER microstructures to
align perpendicularly to the applied field causing a diminished efi‘ect. At lower and higher
frequencies, the chains still align with the electric field, culminating ill a greater torque

response.

57
2.5.4. Volume Ratio (¢)

Volume ratio, which describes the fiaction Of the total volume in the particulate
phase, is a very important parameter in the ER phenomenon. Generally, the shear stress
and apparent viscosity of ER suspensions increase with concentration (Klass and
Martinek, 1967; Gast and Zukoski, 1989). It has been observed that volume fractions are
generally in the range 0.1 5 ¢ 5 0.4 (Block and Kelly, 1988; Gast and Zukoski, 1989;
POOL 1990; Hill and Steenkiste, 1991). Below this range, there is generally no observable
Viscosity enhancement associated with ER However, high concentrations of solid matter
can cause the loss of fluidity of the material All optimum vohrme ratio exists where the
shear stress can be maximized while still maintaining fluidity when exposed to electric
fields (Jordan and Shaw, 1989). In addition, higher concentrations may lead to contact
across the electrode gap, essentially shorting the system, causing loss of ER activity

(Block and Kelly, 1988).

Vohlme fraction strongly influences the ER response time. Hill and Steenkiste
(1991) used high-speed imaging technology to observe fibril formation to estimate a
response time, where response time was defined as the time interval between field
application and the observation of the first developed fibril. For a volume fraction of less
than 10%, the response time may differ by an order of magnitude. Response times for an
ER fluid, consisting of water coated spheres suspended in silicone oil, spanned the time

range fiom seconds to milliseconds. For typical ER devices, the response needs to be in

58
the range of milliseconds. According to this study, the response time varied with vohlme

ratio for both AC and DC excitation.
2.5.5. Dielectric Properties (3)

Dielectric properties of a two phase ER system determine the magnitude of the
suspension response to an electric field. The continuum, usually an insulating oil, must
have a low dielectric constant so it can withstand exposure to large electric fields without
suffering from dielectric breakdown (Block and Kelly, 1988; Jordan and Shaw, 1989; See
and Doi, 1992; Zukoski, 1993). For water based ER materials, water absorbed ill the
particles create a large dielectric mismatch between the phases (scatsp). This is why many
researchers have conchlded that water is essential for a strong ER response. The
permittivity Of the solid phase is significantly greater than the insulator permittivity
(seasp ), allowing particle polarization to generate particle-particle interactions (Klass and
Martinek, 1967b). Ifthe solid phase has a dielectric constant equal to the surrounding
medium, both phases will polarize to the same degree resulting in no accumulation of

charge (Gast and Zukoski, 1989).

As stated in Section 2.5.1., permittivity increases with temperature, leading to
enhanced polarizability at higher temperatures (Klass and Martinek, 1967b; Block et al.,

1990; Zukoski, 1993).

The ability of a material to polarize is fiequency dependent, as reflected by the

complex permittivity (e):

59
e = e'(f) + ie"(f) [2.24]

The complex permittivity reflects the rate at which a material may polarize (Klass and
Martinek, 1967b; Pool, 1990; Block et al, 1990). When this permittivity is divided by a
constant known as the permittivity of a vacuum (so), that quantity is known as the
dielectric constant. The polarization of materials is conventionally examined by measuring
the relative permittivity (5') and the dielectric loss (5" ) as a filnction of frequency
(Uejima, 1972; Block and Kelly, 1988). Interfacial polarization oflen produces a
considerably higher 6' at a low fiequency for an ER fluid over the base medium,
supporting the idea that the solid phase is extremely important to polarization (Block and

Kelly, 1988).

ER response dependence on the electric and shear fields is not well understood,
because temperature, moisture content, and volume fraction each impact the relationship.
6" is dependent on the electric field strength, suggesting that polarizable components, such
as mobile charge carriers and surfactants are being activated (Block and Kelly, 1988;
Jordan and Shaw, 1989). The dielectric constant of a suspension (85), has a strong
temperature dependence saturating at 100 °C. as increases with the electric field intensity

because the degree of chaining increases (Conrad et al., 1991).

6' is strongly afl‘ected by shearing, a phenomenon commonly referred to as flow
modified permittivity (FMP) (Deinega and Vinogradov, 1984; Block and Kelly, 1988;
Jordan and Shaw, 1989; Block et al., 1990). During rotational flow, particles or

interacting clusters of particles spin and disrupt the principal axis for polarization, causing

60
a change in particle alignment and aggregate deformation. Shear defamation may disturb

the charge distribution surrormding a particle. The rate of spinning is what causes the e' to
have a shear rate dependence. For systems where the permittivity is shear sensitive, the
dependence of e on electric frequency is common. Increased particle alignment with flow
direction diminishes the a dependence on electric frequency. Likewise, at large
frequencies the a dependence on shear disappears (Deinega and Vinogradov, 1984; Block
and Kelly, 1988). Block and Kelly (1988) present a thorough review of the complex

permittivity for ER suspensions.

2.5.6. Particle Size and Shape

The optimum particle size is between 0.04 and 50 um; but, size and shape of
particulates are not crucial variables for invoking the ER response (Block and Kelly, 1988;
Jordan and Shaw, 1989). However, later work by Kanu and Shaw (1992) conflicts with
this statement. They examined the roles of particle geometry and electrical properties on
ER behavior and found that particle shape and size may be important since faster response

times were observed for smaller particles.

Also, particle size may impact the ER phenomenon because small particles (< 0.1
11m) are eiqlosed to Brownian motion from thermal effects. Thus, thermal forces compete
with the electrical forces for dominance over ER activity. Large particles react too slowly

to the applied electric field since hydrodynamic forces opposing particle mobility are

61
greater for larger solids. Nevertheless, an ER response has been reported with particles as

large as 200 to 5000 11m (Kanu and Shaw, 1992).

The size limits where no ER activity is observed are not certain (Jordan and Shaw,
1989). Typical ER fluids are composed of spheroidal particulates in the range of 0.1 to
100 um (Gast and Zukoski, 1989; Zukoski, 1993). The particle size distribution may be
very broad, as is the case with flour. Size and shape of the particles are poorly understood

ER variables deserving additional research (Gast and Zukoski, 1989).
2.5.7. Electric Field (E)

The electric field is responsible for inducing particle polarization, necessary for an
ER response. It has been well documented that apparent viscosity and the enhanced yield
stress of ER suspensions scales approximately with E2 (Klass and Martinek, 1967; Klass
and Martinek, 1967b; Uejima, 1972; Klingenberg and Zukoski, 1990; Conrad et al., 1991;

Atkin et al., 1991; Jordan et al., 1992; Katsikopoulos and Zukoski, 1992; Zukoski, I993).

Tao et al (1989) and Jaggi et al. (1989) described a critical electric field,
dependent on solids concentration and temperature, required to produce the transition
fiom a liquid to solid-like behavior. Up to a threshold electric field, the ER response is
very weak Once this field is achieved, resistance to shearing grows rapidly. The greater
the concentration of solids, the more pronounced the relationship between the shear stress

and electric field (Deinega and Vinogradov, 1984).

62
Rozakeas et al (1992) observed a reduction ill torque response as the electric field

intensity was increased. The authors claimed this was due to buildup of particle
concentration at the rotor surface resulting in a decreased solid concentration in
suspension. The study failed to look at various electrical frequencies. In addition, the
suspension did not appear to be a genuine ER fluid since the continuum consisted of an

aqueous medium instead of an insulating oil

2.5.8. Shear Rate (7 )

According to Jordan and Shaw (1989) and Deinega and Vinogradov (1984), the
ER response is strongest at low shear rates, with a diminishing response as the shear rate
increases. At large shear rates ( 1000 s"), the field induced microstructures degrade, and
the response curves are nearly independent of the applied field - corresponding to a large
Mn (Thurston and Gaertner, 1991; Lou et al., 1993). The imposition of a flow field tends
to disturb and distort particle bridges, ultimately rupturing ER microstructures. Particles in
a shear flow are constantly sheared with respect to one another, continually colliding,
agglomerating, and breaking up (Gast and Zukoski, 1989; Halsey, 1992; Otsubo et al.,
1992b). Microscopically, the shear field perturbs the charge distribution surrounding the
particle and counteracts the electric field induced dipole, resulting in a decreased solid
phase permittivity (Klass and Martinek, 1967b). Klass and Martinek (1967) and Uejima
(1972) report that the enhanced Viscosity scales inversely with shear rate (at a given

vohlme ratio) and electric field strength.

63

r1(E.¢)<IC% [2.25]

At a critical Shear rate, the stress in the electrified suspension approaches that of the
unelectrified suspension, indicating that the response is dominated by viscous forces

(Zukoski, 1993).
2.5.9. Characteristics of Ideal ER Fluids for Mechanical Devices

According to Block and Kelly (1988), Jordan and Shaw (1989), Lingard and
Bullough (1989), and Pool (1990), an ideal ER fluid would exhibit a low viscosity without
an applied electric field. With a field, the fluid would display a dramatic increase in shear
resistance. Low zero-field viscosity can be achieved by reducing the volume fraction of
the dispersed phase; however, dilute systems are not as effective and tend to require-
higher field strengths and larger mechanical devices. Ideally, the solid phase would not
settle; ie., the two phases would have similar densities preventing sedimentation. The fluid
should be non-abrasive, to not damage equipment of the designed ER application. Highly
abrasive fluids and particle settling may cause wear on ER devices, and the resulting debris
may produce an electrical short. Modern ER fluids address this problem by using sofi
polymer particles. The fluid should not be limited to a narrow temperature range. Finally,
in this day of enviro-consciousness, the ER fluid should be non-toxic and non-polluting.
Continued ER fluid development requires new ER materials be designed with sufficient

ER activity while attempting to exhibit ideal characteristics.

54
According to Xu (1992), the main requirements of ER fluids can be approximated

as: zero field viscosity < 1 Pa s; current density < 20 ILA cm'z; yield stress 2 - 15 kPa; and
a working temperature between 233 - 423 K Although high particle conductance
increases polarizability, the problem of larger current density is encountered, translating
into increased power consumption. A large vohIme fraction and higher temperature may
incite greater ER activity, but at the same time, conductance and current density will also
increase. An additional property for an ideal ER fluid would be a large polarizing

capability, while maintaining a relatively low current density.
2.6. Engineering ER Fluid Devices and Applications

The development and implementation of ER applications requires knowledge of
colloidal and surfactant chemistry, suspension rheology, physics, fluid dynamics, and
electrical properties (Duclos et al., 1988). The principal attraction of ER fluid devices is
their fast response time making possible feedback control systems for robotics and
automotive applications. ER fluid response time needs to approach the range of
milliseconds for effective device operation (Stangroom, 1983; Gandhi et. al., 1989b; Hill
and Steenkiste, 1991). A high response time of ER fluids is necessary for applications
where real time control of stress transfer removes the limitation of a slow response time
commonly encountered with electrohydraulic systems (Stangroom, 1983; Jordan and

Shaw, 1989; Zukoski, 1993).

While an ER fluid solidifies when exposed to an electric field, the material is not

particularly strong compared to most common engineering materials. A fluid which can

65
be readily and reversibly converted fiom a fluid to a solid could have important and

diverse applications, offering ways to make mechanical devices and feedback control
systems that take advantage of the calculational speed of modern computers (Block and
Kelly, 1988; Jordan and Shaw, 1989; Pool, 1990; Korane, 1991). Improvements in
computer processing speed have created a demand for mechanical systems able to
transform the quick computer signal into a correspondingly fast action. Intermediary
equipment, such as solenoids, pistons, and valves, may no longer be necessary to convert a
computer signal into a mechanical action since ER fluids can directly be controlled by an

electric field (Goldstein, 1990; Korane, 1991).

A unique feature of ER fluids is that rheological properties can be controlled
through electric field strength. This feature is useful for devices such as valves, clutches,
brakes, robotic control systems, reactive dampers and many other applications (Deinega
and Vinogradov, 1984; Block and Kelly, 1988; Jordan and Shaw, 1989; Brooks, 1989;
Bhadra et al., 1989; Gast and Zukoski, 1989; Goldstein, 1990; Block et al., 1990; Pool,
1990; Otsubo et al., 1992b). Proposed ER devices range fiom a simple hydraulic valve to
a complex tracking device for copying machines (Jordan and Shaw, 1989). The unique
damping (vibrational control) properties of ER fluids presents a controllable characteristic
ready to be exploited by devices and mechanisms, solving the problems of energy

transmission and control (Deinega and Vinogradov, 1984; Stanway et al., 1989).

ER designs in hydraulics, robotics, and damping systems seem to be the fi'ont-

running applications. Presently, the automobile industry is attempting to exploit ER

66
damping through innovative designs of engine mounts and shock absorbers (Block and

Kelly, 1988; Petek et al, 1989; Pool, 1990; Zukoski, 1993).

Hartsock et a1 (1991) and Duclos (1988) discussed requirements and necessary
fluid design data for ER materials to be used in automotive and other devices. This work
performed a feasibility study on numerous devices: engine damper, controlled torque
screwdriver, vehicle shock absorber, alternator variable speed drive, and engine accessory
variable speed drive. Each device was studied with three different ER fluids. Feasibility
was determined based on yield strength, current, and viscosity as fimctions of voltage and
temperature. With present ER fluids, Hartsock et a1 (1991) and Duclos (1988) agree only
the engine mount was feasible with the specified fluid properties. However, all the devices

could potentially operate with future advancements in ER material science.

Monkman (1991) added solid fabric materials to surfaces of an ER apparatus. The
layer of polar fabric, 0.7 mm thick porous cotton, served to roughen the apparatus surface
and polarized in the presence of an electric field. The addition of the porous fabric to ER-
activated clutches drastically increased the torque output, while slightly lowering the

current requirement.

A problem commonly‘encountered with ER fluids is sedimentation of the solid
phase. Thurston and Gaertner (1991) found that, although the suspension was constantly
agitated, repeatability of measured values was diflicult to achieve due to settling.

Variation of viscosity measurements up to 30% were observed for a fluid without an

67
electric field. Sedimentation is a problem which must be overcome to design ER fluids for

practical purposes (Jordan and Shaw, 1989; Thurston and Gaertner, 1991).

Block and Kelly (1988) mentioned sedimentation can be prevented using ER
technology itself; essentially, an electric field holds the solids in place. To prevent
settling, density matching between the two ER phases is desired. Density matching plays a
significant role in dispersion stability; therefore, higher density dispersing mediums are
desired. In addition to density matching, the use of classical stabilization techniques such
as srn'factants and adsorbents may be applied (Duclos et al., 1988; Jordan and Shaw, 1989;
Goldstein, 1990). Surfactants are substances used to keep particles in suspension. Also,
higher viscosity fluids are known to slow sedimentation, but may cause flow restrictions

when the voltage is removed.

Moisture content, voltage, and temperature are variables to be optimized when
designing ER applications (Stangroom, 1983). For example, a high water content may
induce a quicker response, but narrows the useful temperature range because heat drives
ofl‘ the water. Most water-based ER materials do not meet the necessary performance

requirements for engineering applications.

For a 6 °C temperature increase, the electrical conductivity of ER fluids doubles,
leading to greater power consumption (Goldstein, 1990). Interest in ER fluids has
recently been accelerated due to the development of anhydrous ER fluids, which broaden
the usable temperature range (Jordan and Shaw, 1989; Block et al, 1990). Power

consumption and heat transfer characteristics are important properties to consider for ER

68
fluid design (Duclos et al, 1988). Power consumption for ER fluids is low since the

current density is low, though large voltages are required. The current density is
influenced by the volume fi'action and E, affecting the power demand. A low current
density enables total power consumption to remain low, well within the capabilities of

typical electronic systems (Stangroom, 1983 ).

It has been projected that ER technology could develop into an annual multi-billion
dollar worldwide industry in the next ten years (Jordan and Shaw, 1989; Goldstein, 1990;
Korane, 1991; Zukoski, 1993). Although a simple ER fluid, such as cornstarch in
cooking oil, can easily be made, a marketable ER material must overcome many
shortcomings, such as temperature limitations and sedimentation. With all the suggested
applications, the problem to overcome is identifying the proper ER fluid for any given job.
Despite twenty years of research and development, a commercially successful ER device

has not appeared (Goldstein, 1990; Korane, 1991; Studt, 1992).

2.6.1. Valves

The simplest application and the cornerstone for ER technology is a valve with no
moving parts (Fig. 2.5) in an ER fluid pipeline. Ifthe fluid is passed through a channel
with an applied voltage across the gap, the flow through a pipeline can be varied or ceased
within a millisecond. In the absence of an electric field, the fluid can flow with the valve
remaining open. When a field is applied, the fluid thickens and essentially closes the valve.
Once the field is removed, the valve opens and flow again commences (Stangroom, 1983;

Deinega and Vinogradov, 1984; Jordan and Shaw, 1989; Pool, 1990; Goldstein, 1990).

69

ER Fluid Out
High Voltage Plate

   
 
 
 

Insulator

ER Fluid In

Ground Plate

FIG. 2.5. ER VALVE.

70
2.6.2. Clutches

ER fluids can be used to design controllable clutches, which are probably the most
technologically diflicult devices to design (Fig. 2.6). Common clutch designs involve two
disks separated by a thin layer of an ER fluid. One disk is connected to a rotating shafi,
while the other disk is attached to an output shaft. The chrtch is engaged upon
solidification of the fluid. Should the field be large enough, the disks behave as though
they were pressed together without a separating fluid. These clutches could be applied to
starting or operating electric motors adapted to drive bodies with a large inertial mass, or
in devices for creating a constant tension. Sedimentation is a particularly diflicult problem
with clutches, because centrifugation worsens the dilemma. ER clutches have been
discussed by numerous researchers: Stangroom (1983 ), Deinega and Vinogradov (1984),
Block and Kelly (1988), Duclos et al. (1988), Carlson and Duclos (1989), Jordan and

Shaw (1989), Pool (1990), and Goldstein (1990).
2.6.3. Interfacing

Interfacing between electronic controls and mechanical components presents
dificulty in engineering designs. ER technology permits mechanical devices to take
advantage of the possibilities of electronic controls. Electronics provide not only the
electric field, but also the signals at the proper time and form to produce the optimal
performance of the system As, microprocessor control becomes improved, the need to
take advantage of the rapid response time of ER fluids becomes more crucial (Stangroom,

1983)

High Voltage
Input Shaft

FIG. 2.6. ER CLUTCH.

 

71

 
 
 

 

 

 

 

 

\
ER Fluid

Insulating Seal

 

 

Output Shafi

72
2.6.4. Patents

Patent Number: 5,190,624 uses the polarizibility of an ER fluid, the induction of
dipoles in the particulates, and the ability to cause changes in pH within the ER fluid to
permit internal control of chemical processes. Patent Number: 5,213,713 deals with ER
solids. This work provides a means whereby an initially solid composition may be
electrically caused to fluidize or gel. Removal of the electric field enables the composition

to become a solid again (Reitz, 1993; 1993b).

2.6.5. Miscellaneous Applications

Other suggested applications of interest include robotic actuators, vibration
damping, new methods of separation and cleaning, catalysis and control of specific
chemical reactions, detection of electromagnetic energy, and enhancement of flexural

stimress (Deinega and Vinogradov, 1984; Zukoski, 1993).

Gandhi et a1. (1989) investigated a slider-crank mechanism featuring a connecting
rod embedded with an ER fluid. A new approach for the control of vibrations with a
transient responsive cantilever beam was proposed. This paper demonstrates the ability
for smart materials to acclimate their vibrational behavior by selecting an appropriate
voltage imposed on the internal ER fluid in the beam when subjected to vibrational
excitation. Thus, the connecting rod was able to adjust the natural frequency, stifliress,
and energy dissipation characteristics in real time. This technology could potentially be
employed in systems where it may be desired to rapidly change natural fiequencies of

structures to avoid resonance and vibration.

73
Gandhi et al (1989b) proposed that ER materials be used for active continual

vibrational control of structural and mechanical systems. This work evaluated cantilever
beams and the ability of ER fluids to change the vibrational characteristics of the beams.
Vibrational control of structures and mechanisms may accelerate the development of
advanced materials for defense, aerospace, and advanced manufacturing environments.
This technology, for example, may be used to develop an airplane wing that adjusts itself
when exposed to different loads without mechanical actuators since smart materials will
have the capability to select and execute specific functions intelligently in response to
changes in environmental stimuli (Studt, 1992). Others have studied the development of
controllable mechanical'damping devices (Oppermann et al, 1989; Coulter and Duclos,

1989; Margolis and Vahdati, 1989; Coulter, 1993; Austin, 1993; Lou et al., 1993b).

Morishita and Mitsui (1992) presented results of an ER squeeze-film damper for
controlling and reducing vibration amplitudes of a flexible rotor in a wide range of
rotational speeds. For each vibrational mode experienced, optimum damping could be
achieved. Stanway et al. (1989) studied an approach to identifying the damping law of an
ER fluid exposed to a vibration. As an electric field increased, the ER fluid underwent a
transition while the liquid material became more solid-like. Through this transition, the
damping force departed significantly from those associated with viscous damping,

becoming more elastic.

An ER clamp allows for devices to rigidly secure obstacles within the medium
between the electrode plates (Deinega and Vinogradov, 1984). Stanway et al. (1992)

described tests demonstrating the feasibility of ER fluids for squeeze-flow operation.

74
Squeeze-flow is an alternative mode for ER fluids which exposes the material to external

tension, and or compression, between two flat electrode plates. While operating in this

mode, ER fluids provide controllable damping and vibration isolating properties.

ER fluids have been used in the development of robotic fingers with elementary
tactile sensing (Kenaley and Cutkosky, 1989). The final system had the ability to generate
large 1ifiing forces with small grasp forces. This article investigated multi-element
fingertips for shape sensing and provides recommendations for design of practical ER

robotic hands.

2.7. Thermal Enhancement from the Electrorheological Phenomenon

Thermal conductivity (k) is a very important property because heat transfer
calculations are often essential for proper design and analysis of food processes. Heat
transfer calculations in food systems include heat treatment of foods to eradicate certain
pathogens and refiigeration of foods to extend storage shelf-life. k depends mostly on
product composition. Other factors which may influence thermal conductivity include:
void spaces, homogeneity, particle orientation, and temperature (Sweat, 1986; Cuevas and
Cheryan, 1979; Rahman, 1992). Inasmuch as biological materials are not homogeneous -
and may vary in cellular structure, composition, and air content - variation in conductivity
measurement is large (Mohsenin, 1980). Hence, many food engineers find it convenient to
estimate k using mathematical correlations (Cuevas and Cheryan, 1979). Several models
exist which predict the conductivity of foods based upon composition, such as the Choi

and Okos model (Sweat, 1986):

75
k = 0.61XW +0.20XP +0.205Xc +0.175Xf +0.135X. [2.26]

where the subscripts indicate the mass fractions of water (w), protein (p), carbohydrate
(c), fat (t), and ash (a). Equation 2.26 is a best fit expression between predicted and
experimental data points. Much has been written that review models and methods for
thermal property measurement of foods (Baroncini et al, 1979; Cuevas and Cheryan,
1979; Mohsenin, 1980; Ziegler and Rizvi, 1985; Sweat, 1986; Choi and Okos, 1986;

Zuritz et al., 1989; Rahman, 1992).

The complex nature of a fluid such as milk chocolate makes it difficult to use
predictive models and necessitates the use of experimental data to determine conductivity.
Milk chocolate is a multi-component system incorporating a suspension of particles
consisting of sugar, cocoa, and milk solids in a continuous fat phase of cocoa butter-
(Chevalley, 1974). The water component of a food is generally the most important factor
when determining conductivity (Rahman, 1992); however, this is not the case with milk

chocolate since it only contains between 0.5 and 1.5 % moisture (Minifie, 1980).

Electrorheological (ER) fluids are materials which change physical properties upon
the application of an electric field. Generally, an ER fluid displays a greater yield stress
and an increased apparent viscosity over an unelectrified sample, resulting from the
formation of microstructures in the dispersed phase. These microstructures are thought to
be particles linking together to form chains, which in turn orient in parallel with the
applied electric field (Block et al., 1990; Halsey, 1992). It is the microstructuring which

potentially increases the directional thermal conductivity of ER fluids. The fibrillar

76
particulate structures of an electrified ER sample consisting of zeolite particles in silicone

oil has been shown by Zhang and Lloyd (1993) to have increased thermal conductivity by
55%. Certain biological materials, such as corn starch and vegetable oil are well
established ER fluids. Controlling the heat transfer properties of fluid foods with a voltage

could have a very significant impact on a food process design.

A suspension of Aerosil in cetane with water serving as the activator was
investigated for thermal properties by (Shulman et al, 1974). Increasing the activator
content in the Aerosil/cetane suspension resulted in an increase of the thermal conductivity
when accompanied by electric fields of high intensity. The thermal conductivity increase
indicates that the ER structures have a lower thermal resistance compared to the original
unelectrified suspension. The transfer of matter (heat, mass, momentum, charge) by an ER

suspension will be dependent upon the applied electric field (Shulman et al., 1974).

Kaji et al (1988 and 1988b) found that heat transfer of a water droplet passing
through an immiscible liquid, silicone oil, could be improved with an electric field applied
across the fluid. The electric field frequency caused a continual changing of the water

droplet shape.

W

This chapter describes equipment, materials, and techniques used for evaluating

rheological and thermal properties of an ER response.
3.1. Equipment

Equipment required to perform electrorheological (ER) experiments, include 1) a
power source capable of generating a large electric field, 2) a unit for controlling
temperature of the sample fluids, 3) a viscometer to measure the torque response and
control speed, and 4) a data acquisition system to collect and record outcomes. Figure 3.1

presents the general configuration of the experimental equipment used in this study.

Viscometer. Electrorheological data were collected using a Haake RV-12 (Paramus, NJ)
concentric cylinder viscometer equipped with an M150 measuring drive unit having a
maximum torque of 1.47 N cm Fluid was sheared between an MV cup and a modified
MVI bob. The bob was tailored to accommodate ER measurements by connecting with a
high voltage cable from the power supply. This special sensor had the top and bottom
recesses removed to eliminate the threat of electrical arcing. To protect the viscometer
and computer from stray voltage, the bob was designed with a ceramic insulator and the
entire system was carefully grounded. Figure 3.2. shows a detailed drawing of the ER

bob. Dead weight cah'bration of the viscometer was performed to insure accurate torque

77

78

 

 

 

 

 

 

 

 

H Computer

 

 

 

 

 

 

 

 

 

 

 

 

FIG. 3.1. GENERAL CONFIGURATION FOR ER EXPERIMENTAL
EQUIPMENT.

79

   
 
 

Power Cable ER Ceramic Insulator

Water In

FIG. 3.2. CROSS-SECTIONAL SCHEMATTC OF THE ER BOB AND CUP.

80
measurements. Due to the modifications made to the bob, end effects were determined

using standard Newtonian fluids.

Power Supply. The voltage potential across the ER fluid was generated by a Trek Model
610C (Medina, NY) power supply, capable of generating a 0-10,000 DC voltage to the

test cell.

Data Acquisition System. To record readings of voltage field, bob speed, sample
temperature, current, and torque as well as permit control of the power supply, a P. 1.
Engineering (Williamston, MI) PIE818 Digital Acquisition and Control System was used.
This system consists of an AT-bus interface card with a fi'ont end Smartbay unit featuring
16 M11 sockets called channels. A single channel was used to monitor each variable.
The data acquisition unit is capable of operating at sampling speeds up to 100 kHz,
depending on the number of channels being operated. The measured data is recorded

directly into a spreadsheet program for immediate analysis and graphing.

Temperature Control. Sample fluid temperature was maintained by an Endocal
Refiigerated Circulating Bath Model RTE-9 (Portsmouth, NH). Sample temperatures

varied between 25 and 70 °C.
3.2. Materials

These experiments considered milk chocolate and flour/vegetable oil suspensions

as the ER fluids.

81
3.2.1. Milk Chocolate and Cocoa Butter

Hershey’s (Hershey, PA) milk chocolate bars were purchased from a local market
and used as the raw material for experiments. Cocoa butter, a milk chocolate ingredient,
serves as the suspending medium for the material, and was supplied for ER testing
purposes by the Hershey Foods Corporation. The viscosity of cocoa butter was
determined at each experimental temperature using a Haake (Paramus, NJ) RS- 100
controlled stress rheometer. Cocoa butter, a solid at room temperature, is a complex,
polymorphic lipid, with different factions melting at different temperatures. At the lower

temperatures of 35.0 and 37.8 °C, the cocoa butter displays shear-thinning behavior:

= 101007 ““8 [3.1]

773 5.0' C

77,,“ = 0.927 “2 [3.2]

At the highest temperature, 40.5 °C, the cocoa butter behaves as a Newtonian fluid:

= 0.15 Pa s [3.3]

”405' C

3.2.2. Wheat Flour

“Hard” and “8011’ are terms used to describe milling characteristics. Hard wheats
produce a course, gritty flour which is easily sifted, and soft wheats yield a fine flour
which may agglomerate causing difficulty when sifting. Hard wheat products include
yeasted breads and hard rolls; while soft wheat is used in cookies, cakes, and pastries. For

this study, hard red winter wheat and soft red winter wheat flours were selected. Hard red

82
winter wheat is characterized as a medium strength wheat, and soft red winter wheat is a

weak wheat. Wheat strengths reflect the ability of the flour to produce products of large
volume, good crumb texture, and good keeping properties. Generally, the stronger the
wheat, the greater the protein content (Kent, 1983). Polar functional groups define and
characterize protein molecules composing the flours; when exposed to an electric field, the
fimctional groups may polarize. When flours serve as the solid phase suspended in an ER
fluid, this technology may potentially exploit differences inherent to each wheat type.

Kent (1987) has provided tables for the temperature dependent dielectric permittivity of

flour. At 25 °C and 50 °C, the dielectric constants (5,) for flour are 5.58 and 6.68,

respectively.
3.2.3. Vegetable Oils

Canola and olive oils were the two edible oils chosen as carrier mediums for ER
wheat flour suspensions. The Haake RS-100 was used to measure the temperature
dependent Newtonian viscosity of each lipid: olive oil was found to have viscosities of
0.066 and 0.026 Pa 5; and canola oil to have viscosities of 0.053 and 0.023 Pa 5, at 50 and
25°C, respectively. The lipid composition of olive oil includes palmitic and linoleic, but
mostly oleic acids; while canola oil is composed of erucic, linolenic, linoleic, but primarily
oleic acids (Fennema, 1985; Belitz and Grosch, 1987). Olive oil has twice as many

saturated fats as canola oil, which may explain the greater viscosity of this fluid.

Kent (1987) has prepared a series of tables with electrical properties for many food

materials, including the dielectric constant for olive oil, 3, equal to 3.15. Although the

83
permittivity was not given for canola oil, other values for edible oils with a similar lipid

composition were supplied allowing a dielectric constant for canola oil to be estimated as

3. equal to 2.5.

3.3. Preparation of ER Samples

Separate preparation methods were developed for the milk chocolate and flour/ oil
experiments. The primary difference was that milk chocolate was in “final” form, so no
changes could be made to product composition. The flour/oil combinations were

developed according to a statistical design, testing for variable influences on the ER

response (Sec. 3.7).

3.3.1. Milk Chocolate

A fifty-one gram sample of solid milk chocolate was placed into the MV cup to
start each test. The cup was placed in the measurement position and the water jacket
temperature was set to the test temperature allowing the chocolate to melt. Care was
taken not to exceed the target test temperature due to the polymorphic behavior of cocoa
butter, ie., the fat crystals melt at different temperatures (Dimick, 1991). After the
molten chocolate attained a uniform temperature, the cup was removed from the
viscometer and temporarily set aside. Immediately, the ER bob was attached to the
viscometer and the sample cup, holding the molten milk chocolate, was put back into

measurement position. Sample preparation involved a preshearing step where the
viscometer was set to rotate the bob at 2 rpm while observing the resulting torque. When

the torque reading achieved a constant value, normal data collection was initiated.

3.3.2. Flour and Oil

Prior to running an electrorheological test, the flour/oil mixture had to be
prepared. The statistical design (Sec. 3.7) predetermined the volume fi'action, flour and oil
types, and testing temperature for each sample. A 300 ml sample was mixed in a 400 ml
pyrex beaker for each test. For example, a 20% volume fraction of a sofl red flour/olive
oil suspension indicates that 20% of the ER material is comprised of the soft red flour,
while the remaining volume is olive oil. The ER fluid beaker was placed on a stirrer/hot
plate with a stir bar placed inside. Agitation commenced until a homogeneous mixture
was achieved. For samples requiring heating, the hot plate was turned on with caution not
to exceed the measurement temperature. Forty-four grams of the prepared suspension
was poured into the viscometer cup, while the water bath controlling the viscometer jacket
temperature was set. The specially designed ER bob was placed into position, followed by
the filled sample cup. Once all experimental conditions were achieved, a brief preshearing
step was performed to eliminate any developed structures. At completion, ER testing

commenced.

3.4. Data Collection for ER Fluids

Two isothermal data collection techniques were employed to evaluate shear rate
and voltage efl‘ects. Milk chocolate samples were also subjected to a temperature ramp to
investigate thermal effects. The flour and vegetable oil statistical experiments involved

only the shear rate ramp.

85
3.4.1. Shear Rate Ramp
A constant voltage was placed on the sample fluid while increasing, then

decreasing the shear rate over a predetermined range. Initially, the viscometer speed was

set to 0.01 rpm (0.022 s“) and the apparatus was given two minutes to achieve steady
state conditions. Then 1000 data points for voltage, temperature, speed, torque, and
current were collected over a 45 second period, using the data acquisition system These
values were averaged, logged into a spreadsheet, and labeled accordingly. Next, the
voltage was removed from the sample to allow for the destruction of any nricrostructures
which may have developed from the ER phenomenon. The system was then ready for
another measurement and the above procedure was repeated for a new shear rate setting

in the ramping sequence. This technique continued until measurements were collected at

the maximum speed, 4 rpm (8.744 s"). At this point, the shearing speed order was
reversed, and data was acquired for a second set of torque values. Results for the up and
down ramp difl‘ered little and these points were averaged to produce a data set. This

procedure was repeated at specific voltages between 0 and 450 Volts mm".

During data collection from the flour/oil tests, viscometer speeds were ramped up
and down, and a torque value was recorded for each half of the ramping sequence. Then,
the sample ER fluid was deposited back into the mixing beaker containing the remaining
fluid still agitating on the stir/hot plate. At this point, a fresh sample was poured into the
measurement cup, followed by data collection from another shear rate ramping sequence

producing four randomly collected torque responses. For the statistical analysis, only two

86
shear speeds, 0.08 and 2.0 rpm, and their corresponding apparent viscosities were selected

for the 16 individual experiments. An AN OVA (Analysis-of-Variance) was performed on

the apparent viscosities to initiate the statistical analysis.

3.4.2. Voltage Ramp

This technique involved recording milk chocolate data at a constant shear rate
while the electric field was altered. Data were collected for each voltage while
maintaining a constant bob speed. Prior to recording the data, the system was given two
minutes to reach steady state conditions. Between each test, the electric field was
removed from the sample to eliminate any particle structures which may have developed.
Once the voltage ramp was complete, the tests were repeated in the order of decreasing
voltages. Data from each voltage were averaged. This procedure was repeated for each

bob speed.

Fresh milk chocolate samples were used for each ramping sequence. Because the
torque response under the same experimental conditions for each ramping technique were

similar, the vahres were averaged to produce a final data set.
3.4.3. Temperature Ramp

The milk chocolate temperature was slowly increased fi'om 35 to 70°C while
holding the shear rate and applied voltage at values of 300 Volts mm'1 and 0.219 s",

respectively. The temperature effect on the torque was monitored.

87
3.5. Calculations

Several calculations were performed to manipulate the raw data into the standard

forms needed for rheological modeling.

3.5.1. Shear Rate

Shear rates ()3 ) at the ER bob for all experiments were determined using standard

rheological methods for concentric cylinder geometry (Steffe, 1992). Specifically, the

Newtonian approximation was applied to calculate the shear rate at the bob:

 

7’1: = 2(Q)[ ?_ 1] [3-4]

a

where

ach
R

Q = 2m;fl1%0

All materials were tested at the following shear rates: 0.022, 0.044, 0.087, 0.175, 0.219,

0.437, 0.874, 1.749, 2.186, 4.372, and 8.744 5".
3.5.2. End Effects

It is important to consider the bottom of the ER bob since it comes in contact with

the fluid and may influence the torque response of the measuring system. To account for

88
this, an average end effect (ho) was determined and added to the actual bob height for

shear stress (0‘) calculations for the experiments.

To determine the end efl‘ect correction term, the rotating ER cylinder was exposed
to a Brookfield (Stoughton, Mass.) standard Newtonian fluid ( Silicone oil # 5000; 4800
cp) at 25 °C. Each test required filling the viscometer cup to a new level with standard
fluids. At each level, the bob was exposed to difl‘erent areas of fluid contact. The height
of the bob contacting the fluid was recorded for future calculations. For each of four fluid
levels, a torque response was recorded at five rotational speeds. Data (Table 3.1) are
calculated for three averaged readings and graphed (Fig. 3.3), producing a straight line for
each series of tests. The lines generated at each rotational speed were regressed and the
x-intercepts were determined by extrapolating to a value of zero torque. The five x-
intercepts from each measurement speed were averaged, allowing the end efl‘ect correction

to be calculated as 1.05 mm with a standard deviation of 1.42 mm.

With this general approximation for the end correction term, the shear stress at the

bob was determined as

M

0" = 2nR:(h+h,)

 

[3.5]

where:
ob : Shear stress at the bob, Pa
M : Torque, N m
R1, : Radius of the bob, 0.02 m
h : Height of the bob, 0.06 m

ho : End efl"ect correction term, 1.05 x 10'3 m

89

TABLE 3.1.

END EFFECT DATA GIVING PERCENT TORQUE AT DIFFERENT BOB
SPEEDS AND HEIGHTS FOR SILICONE OIL.

 

Height. 1.0 rpm 2.0 rpm 4.0 rpm 8.0 rpm 16.0 rpm
(cm)
3.6 0.80 1.62 3.17 6.21 12.44
4.1 0.94 1.80 3.51 7.06 13.86
4.6 1.02 2.03 4.04 8.07 I6.09
5.0 1.10 2.21 4.37 8.52 17.08

 

'Height of bob in contact with fluid

m.m

h< i=6 HZGU—dm Z.— mEQ—Hfl maze—fix» Oh. gummy—HES: may: In .mO <.—.<: BEN 62”.— .m.n .9:

so .22". as, 380 5 8m do :3»:

.mA—mmA—m Flag—E:

 

 

 

 

 

 

 

n né v m.m m
P n . L 8.6
59— Oil 0 '0. 1.
I 1-
&9 N l1 + . 8N
11011 .
r .
EB v - irdlll 8 v
u 8.0
W rl 0°.”
En.— m
. cod—
1 8.2
r 8.2
l u 8.3
En.— @—

 

 

8.8

anbxor. rem %

91
For these studies, the fluid only came in contact with the bottom of the bob, so a

cOrrection term was not needed to account for the top of the bob. Experimental data
confirmed that the end efl‘ects were minor in comparison to the shear stress magnitude.

Therefore, end effects were neglected throughout the analysis.
3.5.3. Casson Model Parameters for Milk Chocolate

Once the torque and shear rate vahres were calculated, regression analysis

(Microsofl Excel, Redmond, WA) was conducted using the Casson model:

0.5

0°" = 03" + K.r‘ [3.61
where:

00 : yield stress, Pa

K1 : consistency coeflicient, Pa 5”

Apparent viscosity (17), defined as the shear stress divided by the shear rate, at shear rates
of 0.219 and 1.749 s", was selected to compare the ER experimental results for milk

chocolate.
3.6. Statistical Analysis

The flour/oil data were subjected to a thorough statistical analysis to determine
significant variable contributions to the ER response. A fractional factorial analysis was

designed to incorporate each ER variable at a high and a low level. If6 variables are

involved, 64 ( = 26) individual tests would need to be m for a firll factorial design;

92

however, a fiactional analysis was used and 16 ( = 262) separate experiments were needed.
A fractional analysis minimizes the degree of erqaerimentation, while maintaining the
integrity of the research. Results fiom the analysis can reflect the significance of main
variables and lower order interactions. Running a minimum number of experiments has
advantages and disadvantages. A major advantage is that time is saved since fewer tests
are performed. The disadvantage is that treatments are aliased with other treatment
combinations. In other words, it is not completely certain which variable combination is
responsible for the outcome. To simplify data interpretation, higher order interactions are

often ignored, and for this particular study, four-way and above interactions are deemed
insignificant.
3.6.1 Experimental Design

Six ER variables were selected based upon their relative importance in invoking
the ER response: voltage, temperature, concentration, flour type, oil type, and moisture
content. To simplify notation, all factors were assigned a letter variable (Table 3.2). Each
factor was appointed two different levels for testing. The levels were selected to produce
noticeable differences in the outcomes, while keeping rheological measurements within the
physical limitations of the equipment. It was hoped to determine if ER could be applied to
discern between flour and oil types. The potential for using ER technology as an

analytical tool in cereal science was an important factor in the evolution of this work.

Electric Field. 0 and 300 Volts mm'1 were selected for testing. Preliminary analyses

indicated that these fields clearly demonstrate the effect voltage has on the samples. A

93
TABLE 3.2.

STATISTICAL LEVELS FOR ER VARIABLES.

 

Variable Factor Factor Level "Low" Factor Level "High"
A Voltage 0 Volts mm'1 300 Volts mm'1
B Temperature 25 °C 50 °C
C Concentration 20 % 40 %
D Flour Type Sofi Red Hard Red
E Oil Type Olive Canola
F Moisture Content 50 % 100 %

 

94

larger voltage was not chosen because it may have generated too large of a torque

response.

Temperature. 25 and 50 °C were selected to so as to not gelatinize or denature any of
the ER materials, since wheat flour proteins are known to denature above 60 °C
(Pomeranz, 1987). These temperatures were chosen to also affect the viscosity of the
carrier oils, since the viscosity decreases with temperature. Prior to performing the

analysis, viscosity measurements were taken for the oils at each temperature (Sec. 3.2.3).

Volume Fraction. According to the literature, concentrations producing the greatest ER
response falls between 5 and 40%. 20 and 40% concentrations were selected for the

study, producing a large ER efi‘ect while not peaking the torque measuring device.

Flour Type. Hard and soft red flours were chosen as the particulate phase for this study
(Sec. 3.2.2).

Oil Type. Canola and olive oils were the two fluids serving as the carrier mediums for the

ER suspensions (Sec. 3.2.3).

Moisture Content. Water serves as an activator for many ER fluids: too much or not
enough water tends to diminish the ER response. Therefore, the moisture content of the
flour was measured according to standard AACC Method 44-15A. 12.9 % water on a dry
basis was an overall average for the flour, with the soft flours at a slightly higher moisture
content (Table 3.3). The flour was then exposed to 50 °C to gently dry the flours. The

mass of the flour samples was recorded at periodic time intervals, developing a time-

 

95

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96
temperature relationship for drying flour at 50 °C. From this short study, it was learned

that approximately 50% of the moisture could be removed in a 3 hour time period. The
two levels of moisture content. were 12.9% ( equal to 100% of total moisture in the

powder) and 6.4% ( equal to 50% of total moisture) water on a dry basis.

3.6.2. Fractional Factorial Design

A 2M experimental design was used to analyze the data, that is a one-fourth
fraction of a fidl 26 design. A value added statistical technique determined the specific

variable combinations for individual tests. Table 3.4 shows the 24 factor combinations for

experimentation. Whenever the letter appears in a combination, the factor is set at the
high level. So, test combination 13 would consist of the following factor levels: 300

Volts mm", 25 °C, 20 % concentration, soft red flour, canola oil, and at 50 % moisture

content.
This design was constructed by adding factors E to ABC and F to BCD treatment
combinations of a complete 24 factorial. This is a resolution IV design allowing for the

estimation of all main effects and some interactions (Hicks, 1993).

3.7. Dimensional Analysis

Dimensional analysis is a powerful numerical method commonly applied when a
System response does not have a well defined theoretical basis, as is the case with ER
Conversion of the variables into meaningfirl dimensionless groups (IT) simplifies

BXperimentation by decreasing the number of independent variables. The objective of this

97
TABLE 3.4.

16 STATISTICSL TREATMENTS FOR FLOUR/OE DATA.

 

ae
bef
abf
cef
acf
bc
abce
df
adef
bde
abd
cde
acd
bcdf .

abcdef

 

98

analysis was to identify meaningful IT groups and predict relationships between them to

describe and model the ER phenomenon.

3.7.1. Description of Physical System

To employ dimensional analysis, all that is required is a knowledge of the principal

variables responsible for the effect. In this case, the ER effect is a function of shear stress,

electric field intensity, shear rate, viscosities, dielectric permittivities of the suspension

phases, volume fiactions, and others. A complete listing of important variables and their

symbols follow:

mppgxaV-eggwh

8
k3

mo
’10
T

: relative permittivity, dimensionless

: dielectric constant of continuum, dimensionless
: permittivity of a material in a vacuum, 8.8542 x 10’12 CZN'l rn'2
: volume fraction, dimensionless

: shear rate, s'l

: apparent viscosity, Pa 5

: apparent viscosity of continuum, Pa 5

: density of continuum, g cm'3

: density of particles, g cm’3

: electric field intensity, V mrn'I

: gravitational acceleration, m s‘2

: Boltzmann constant, 1.381 x 10'23 N m K"

: moisture content, dimensionless

: particle radius, m

: absolute temperature, K

The Buckingham 1T theorem was applied to the aforementioned variables to establish

dithensionless groups (Langhaar, 1951).

99
3.7.2. FLTQG System

The FLTQO system was employed for the dimensional analysis of ER variables.
[Q] is a dimension for electric charge. The standard unit of electric charge is the coulomb,
which is the force exerted by two unit charges separated by a distance of one meter in a
vacuum. [F], [L],[T'], and [8] are dimensions for force, length, time, and temperature,

respectively.

The ER variables and their FLTQG dimensions are:

[H] : dimensionless
[3.] : dimensionless

[6‘0] : I" L’2 Q2

[¢] : dimensionless
[2" l : T1

[17] : F L" T

[17.] : F L‘2 r

[p.] : F L‘4 T2

[p,] : F L" r2

[E] : F Q'1

[g] : L T2

[kg] 2 F L 9'

[me] : dimensionless
[rp] : L

[T] : 6

The dimensionless ER variables 5., ¢ , me, and ,6 are inherently dimensionless
groups. In addition, viscosity and density ratios (17/71. and pp/pc) were identified as
dimensionless. Therefore, five terms, ¢, mc, ,8, 77, and Fe. were pulled from the analysis

and immediately assigned to corresponding II groups.

1 00
3.7.3. IT Group and Prediction Equation Development

In this analysis, the dimensionless viscosity ratio was chosen as the dependent

variable, and expressed as a function of all the independent ER variables:
”Me = {(mca ¢a fl, EC, pp/pc, 77¢, E9 IP’ 60, k3. T, 7 9 pp, 8) [37]

According to Buckingham’s Theorem, each dimensional, independent variable is raised to

an unknown order to insure dimensional homogeneity,
n/nc = C 778 5" 0° 80“ ka‘ 1‘ 7' ”pp“ ai [3.8]

where C is a proportionality constant. Substituting the FLTQO dimensions for the ER

variables gives
[1] = [1] [FL’ZTJ’ [FQ"]b [L]c [F‘L'zQzld [FEST [9]f
...[I"]8 [F L" r21“ [LT2]‘ [3.9]

Checking rank, to guarantee linear independence between the FLTQB system
dimensions, the exponents were determined and results were simplified into four IT terms.
Adding the six predetermined dimensionless groups, gives a total often 1T terms.
Common ER dimensionless groups include the Mason number, the 7» number, and the
Peclet number. These terms may be written as combinations of IT terms from the current
analysis. Each IT group may be expressed as a relationship between the remaining

dimensionless groups:

1 01
11.: C nz'rlgbrL‘IIS‘rrngfl‘Issnghnm‘ [3.10]

The erqionents and proportionality constant of Equation 3.10 are determined using a
multiple linear regression technique to develop prediction equations to model the
phenomenon. During the natural logarithm transformation of the multiple regression
technique, the original 1T groups cannot equal zero. To counteract this limitation, 100

Volts mm'1 was added to each electric field intensity (E) value.
3.8. Thermal Properties of Milk Chocolate in an Electric Field

An apparatus was designed to simultaneously measure thermal conductivity (k)
and volume specific heat (pop), using a parameter estimation technique. The method is
based upon the mirror image concept (Danielson and Sidles, 1969). In this technique,
identical disks sandwich a heat source, and a constant heat flux (q) is split between the
two sides. Outside surfaces are well insulated and permit the assumption of an adiabatic
boundary condition. To firrther simplify calculations, disk thickness was kept small in
comparison to the disk diameter, allowing for the one-dimensional heat transfer

assumption. This technique was coined the Mirror Image Method (MIM).

Zhang and Lloyd (1993) calibrated the mirror image apparatus (the same one used
in this research) with water to ensure that the estimated thermal conductivity was
physically correct. The authors found that the procedure produced thermal conductivities
differing by 4.77% from the published data. Thus, the technique was validated as an

acceptable method for measuring thermal conductivity of liquids.

1 02
3.8.1. Heat Transfer Mathematical Model

The differential equation describing one-dimensional heat transfer is

6T 82T

—-- = — 3.11

at a 62’ [ l
where:

a : thermal diffusivity (kp"c,"). m2 s‘1

T : temperature, °C

t : time, s

z : position, 111

From the general difierential equation, the one-dimensional analytical solution for a flat
plate design insulated on one side and heated by a steady heat flux on the other is given

by Beck et a1 (1992) as

[exp(- n2 1t 2t )]cos(nrtz ) [3.12]

 

. . 1 . 1 .
T =t +——z +— 2
3 2(2)— 22;

n2
with the dimensionless variables defined as
T‘ = (ixr - To) [3.13]
qL
t. = g [3.14]
z' = _Lz_ [3.15]

1 03
Equation 3.12 is valid for the MIM with the following assumptions: negligible contact

resistance, homogeneous sample, one dimensional heat transfer, negligible heat transfer at

the edges (adiabatic), constant heat flux

The analytical solution of Equation 3.11 incorporates the following initial and

 

 

bormdary conditions:
T‘(z‘,t‘ = 0) = 0 [3.16]
— =0,t = 3.17
az.(z ) [ ]
2T. (2’ =1.t')= 0 [3.18]
62

The analytical solution given by Equation 3.12. requires a known value of the heat flux

defined as:

q =—— [3.19]

To solve for q, the parameters for Equation 3.19 were specified as follows: V, the AC
voltage to the heater, was equal to 12.5 Volts; R, the resistance of the heater, was equal to
10.0 Ohms; and A, the total surface area accounting for both sides was equal to 9.12 x
10'3 m2. Substituting these values into Equation 3.19 gave the total flux a numerical value
of 1713 W m'2; however, since only halfthe total flux is exposed to each side of the

"mirror", q equaled 856 W m'2.

1 04
The solution for a one-dimensional, transient heat transfer problem requires that

temperature be a function of time and position. Thermal properties are estimated from the

transient bormdary tenrperatures and the heating rate of the sample.
3.8.2. Mirror Image Method (MIM) Plates

The disks assembled on one side of the heater consists of an aluminum plate, teflon
O-ring gasket serving as the sample fluid reservoir, copper plate, followed by another
teflon O—ring gasket. Each disk was approximately 7.62 cm in diameter. The teflon
gasket included a small aperture permitting the injection of fluid into the system reservoir
that was 0.3 cm thick (L). All disks were clamped between two wooden blocks. The
purpose of the final O-rings and the wooden blocks were to add extra insulation to the
system, thereby satisfying the adiabatic boundary condition specified by Equation 3.18.

Figure 3.4 illustrates the overall plate series.
3.8.3. Overall Apparatus

To liquefy milk chocolate bars, a Brookfield (Stoughton, MA) Model EX-lOO
water bath was used. Liquid chocolate was deposited into the MINI sample reservoir, and
the constant heat flux boundary condition was satisfied by turning on a Hewlett Packard
Model (Boise, ID) 6024A DC power supply. This unit sent 12.5 Volts to the heating disk
(10.0 (2 resistance) at the center of the MIM plates. To monitor the sample temperature,
thermocouples (20 gage) were cemented at the center of the fluid side of each metal plate
(2 = 0 cm and z = L = 0.3 cm). The plates acted as the fluid border as well as electrodes

for the electric field. Fluid temperatures at the electrodes were recorded by a Fluke Model

ll

 

 

 

105

 

 

Heater

(A) Aluminum Plate, 0.1 cm; (B) Teflon O-Ring Sample Reservoir, 0.3 cm; (C) Copper

Plate, 0.1 cm; (D) Teflon O-Ring Insulator, 0.3 cm; (E) Wooden Block, 2.0 cm

FIG. 3.4. “MIRROR IMAGE” APPARATUS PLATE SERIES FOR
DETERMINATION OF HEAT TRANSFER PROPERTIES OF MILK
CHOCOLATE.

1 06
2625A data acquisition system The high voltage requirement was supplied by a power

amplifier. After testing, data was downloaded from the Fluke data acquisition system into
a personal computer for parameter estimation. Figure 3.5 depicts the overall experimental

setup for determining thermal properties.
3.8.4. MIM Testing Procedure

Two chocolate bars were melted at 40 °C using the water bath. Once liquefied,
approximately 6 ml of chocolate were injected into the sample reservoir of the MIM plates
using a heated hypodermic syringe. The milk chocolate temperature was monitored with
the data acquisition system to insure that the thermocouples were not damaged or
dislodged during the injection procedure. A constant temperature across the sample was
required as an initial condition for each test. Formal data collection was started once this

initial condition was satisfied.

The data acquisition system scanned temperatures at three second intervals. At
time zero, the high voltage power amplifier was initiated, sending a predetermined electric
field of 0, 300, or 450 Volts mm'1 at 60 Hz to the molten chocolate. The next step was to
apply the constant heat flux boundary condition by activating the power supply to the
heating disk. Boundary temperatures were scanned for approximately three minutes with
data collection continuing to occur at three second intervals. Milk chocolate temperatures

varied between 30 and 60 °C during each test.

Once the experiment had run for approximately three minutes, power to the

apparatus was turned off in the following order: the heating disk power supply, the high

107

   

   

 

        
   
       

 

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EQUIPMENT.

1 08
voltage power amplifier, and finally the data acquisition system Raw data, consisting of

temperatures at the fluid bormdaries and the times when sampling occurred, were stored

for later analysis.

3.8.5. Data Analysis

Equation 3.12 was programmed into a Microsoft Excel (Redmond, WA)
spreadsheet program This equation, along with recorded temperatures and the heat flux,
allowed for estimation of the thermal parameters at each thermocouple location.
Differences between the actual and theoretical temperatures at each boundary were
determined, then squared, and finally added together to produce a summation of the
squares value. The values of k and pep producing the lowest sum of the squares between
the actual to theoretical temperatures were selected as the optimal values. When the
differences are the smallest at each location, the predicted heat transfer properties more

accurately reflect experimental values.

A common statistical test was employed to compare the sample means of the
conductivities determined with a voltage and without a voltage. The t distribution test
statistic was used at a 95% confidence interval to determine whether the applied electric

field had a significant influence on the thermal conductivity (Hicks, 1993).

W

This chapter describes findings from the research and attempts to offer explanations for

the observations.
4.1. Electrorheological Behavior of Milk Chocolate

Data from this study give conclusive evidence that milk chocolate is an
electrorheological fluid. The work reported here is Imique because it is the first
documented research identifying an actual food product as an electrorheological
substance. Experimental results, shown as Table 4.1, offer a comparison of Casson model
parameters. Table 4.1 also gives the apparent viscosities calculated at two different shear
rates. Milk chocolate displays shear-thinning behavior regardless of an applied voltage.
As the shear rate increases, the apparent viscosity decreases. The coeflicient of
determination values (r2) for the data fit to the Casson model indicate good correlations
between data and model However, as the voltage is increased, some deviation fiom the

Casson model is observed as indicated by decreasing r2 values.

A transition (Fig. 4.1) occurs as the voltage is increased fi'om 150 to 300 Volts
mm‘1 at a temperature of 35.0 °C. To explain this transition, dimensionless groups have
been developed to compare the tendencies for different forces to dominate flow behavior.

The Mason number (Mn) describes the behavior of ER fluids as the ratio of viscous to

109

110

 

TABLE 4.1.
CASSON MODEL PARAMETERS AND APPARENT VISCOSITIES FOR MHK
CHOCOLATE DATA.
Volts mm’l Temp. r2 K 00 r] @ 17 @
0.033s-1 0.267s-1

DC °C (Pa s)0-5 Pa Pa s Pa s

0 35.0 0.97 5.8 7.6 494.4 133.9

0 37.8 0.98 5.1 8.7 427.2 109.1

0 40.6 0.98 4.6 5.1 330.3 85.3

150 35.0 0.93 6.3 7.0 489.6 153.4

150 37.8 0.92 5.6 7.4 481.6 138.5

150 40.6 0.92 5.6 4.8 315.0 124.5
300 35.0 0.94 6.0 8.7 464.4 178.1
300 37.8 0.93 6.0 10.8 552.0 190.6
300 40.6 0.93 6.4 10.6 577.3 201.0
450 35.0 0.88 5.7 19.6 950.5 265.0
450 37.8 0.77 5.2 20.2 993.1 270.9
450 40.6 0.96 7.3 5.0 328.2 150.8

 

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polar forces. It is possible that the transition period observed in Figure 4.1 is caused by

polar forces beginning to dominate the response over viscous forces. In other words,
polarized particles are beginning to form structures, causing a greater resistance to flow.
Figures 4.2 and 4.3 depict situations where the polar forces are dominating the effect at

larger temperatures: as the voltage increases, the resistance to flow increases.

One expects that the torque response for a fluid should decrease as temperature
increases, i.e., the material should becomes less viscous. However, in the case of ER
fluids, temperature increases the polar nature of the particles, enhancing the creation of
microstructures which deter flow (Fig. 4.4). At a constant voltage, the greatest torque
response is recorded at the highest temperature (40.6 °C). Figure 4.5 firrther supports the
effects of temperature on the ER response. This graph displays the apparent viscosity at a
constant electric field, 300 Volts mm", while the system temperature is increased. Clearly,
the resistance to flow increases with temperature in the presence of an electric field. In the
absence of an electric field, practically all fluid foods exhibit a decrease in apparent
viscosity at higher temperatures. The opposite response described here is typical of the

unusual behavior found in ER fluids.

A common characteristic of ER fluids is that the yield stress is a function of the
applied electric field, and milk chocolate is no exception. A yield stress is defined as the
minimum force required to initiate flow. Referring to Table 4.1, one can see a trend
developing where the yield stress is dramatically increasing at higher voltages (10 - 20 Pa).

According to the hypothesis, once the polar forces begin to dominate, the yield stress

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increases; hence, the force required to establish milk chocolate flow is larger due to the

presence of polarized particulate chains.

At the upper limits of the temperature and voltage range, erratic results were
experienced. At 450 volts and 40.6 °C, the system displayed a breakdown (Table 4.1).
Rather than continuing the trend of increasing yield stress and apparent viscosity with
voltage and temperature, the phenomenon disappeared. A possrble explanation for the
lost effect is that the cocoa butter faction of milk chocolate contains polar seed crystals
which liquefy at higher temperatures (Davis and Dirnick, 1989). Once the polar seed
crystals melt into the liquid medium, the non-polar continuum is gone and so is the ER

response.

Upon witnessing ER activity in milk chocolate, the question arose as to which
solid substance of the material, sugar, cocoa, milk solids, or combination, was responsible
for the microstructures commonly associated with the phenomenon. Milk chocolate,
consisting of approximately 31% fat, has a high composition of cocoa butter (15%) with
the remaining lipids supplied by the milk. It is understood that the lipid faction serves as
the nonconducting continuum for the two-phase system A preliminary rheological test
was performed on Hershey’s dark chocolate to determine the importance of milk solids to
the ER behavior of milk chocolate. Dark chocolate and milk chocolate have similar
compositions, with the exception that dark chocolate contains no milk solids. In the

presence of an electric field of up to 450 Volts mm“, no ER activity was observed for the

1 18
dark chocolate, leading to the conclusion that the milk portion was necessary for inciting

the ER phenomenon in milk chocolate.

Milk proteins consist of two classes, whey and caseins. According to Fennema
(1985), caseins exhibit a dipolar structure composed of a charged domain and a
hydrophobic globular domain at the normal pH of milk. The whey proteins are globular,
with a distribution of nonpolar, polar, and charged residues. Functionality of milk proteins
is strongly dependent upon the environment, i.e. pH, temperature, or polarity.
Manipulation of the protein fimctionality can be performed by adjusting these variables.
For example, by adjusting the system pH to the isoelectric point of caseins, these proteins
will display a net charge of zero. Understanding the polar nature of milk proteins validates
the notion that these macromolecules may be responsible for the polarizing the solid phase

of milk chocolate when exposed to an electric field.
4.2. Statistical Analysis of Flour/Oil

Main effects and lower level interactions of six ER variables (voltage, temperature,
concentration, moisture content, flour type, and oil type) were calculated using Yates
algorithm, a method to carry out calculations involved with an AN OVA - Analysis of
Variance (Hicks, 1993 ). The 16 treatment effects of the ER variables were determined
from a 2&2 fractional factorial design. As previously discussed, a drawback of a fractional
factorial design is that effects are aliased with other effects. For example, the main effects
are aliased with three-letter and above combinations. Higher order treatment effects are

assumed negligible for this analysis. Table 4.2 shows the 16 treatments and the aliased

1 19
treatment combinations. From this study, AN OVA tables, including F statistics and p-

values, were prepared.

The sum of the squares (SS) between treatments were calculated during the early
portion of the experimental analysis to measure variation among sample means (Table
4.3). SS was determined from the number of replications and the square of the estimated
effects from Yates algorithm with one degree of freedom. SS percentages were tabulated
neglecting the two three-letter interactions, reflecting the general importance of the
variable effects to the phenomenon. Table 4.4 shows the defining equations with the
confounding block efi‘ects and SS percentiles for each treatment at the two viscometer

speeds considered.

The initial analysis indicated that factor D, flour type, was insignificant to the ER
response, ranking 10th of 13 interactions in importance according to SS values. The
remaining five variables: voltage, temperature, concentration, oil type, and moisture
content ranked in the top seven efl‘ects for overall significance. Table 4.5 displays the

ranking for the treatment effects at the two rotational speeds and overall

Next, variable D was removed from the analysis, and the data were projected onto
the five remaining variables. Initially, the four observations for each treatment
demonstrated a non-normal distribution. The F-statistic of an AN OVA is based upon a
treatment being normally distributed with a homogeneous distribution. So, the natural
logarithms of each apparent viscosity were taken to generate a normal distribution and to

stabilize the variances. By examining the natural logarithms of the residuals composing

TABLE 4.2.

ALIASED SETS FOR A 2... FRACTIONAL FACTORIAL DESIGN.

 

 

(I I ABCE IBCDF I ADEF)
I ABCE BCDF ADEF
A BCE ABCDF DEF
B ACE CDF ABDEF
AB CE ACDF BDEF
C ABE BDF ACDEF
AC BE ABDF CDEF
BC AE DF ABCDEF
ABC E ADF BCDEF
ABCDE BCF AEF
AD BCDE ABCF EF
BD ACDE CF ABEF
ABD CDE AC F BEF
CD ABDE BF ACEF
ACD BDE ABF CEF
BCD ADE 1F ABCEF
ABCD DE AF BCEF
A: Voltage
B: Temperature
C: Concentration
D: Flour Type
E: Oil Type
F: Moisture Content

1 21
TABLE 4.3.

SS VALUES FOR COMPLETE FRACTIONAL DESIGN OF FLOUR/OIL DATA.

 

17 at 0.08 rpm 1) at 2.0 rpm
Treatments Est. Effects SS Est. Effects SS
1 42.8 2.2
ae 61.9 15330.1 1.9 13.9
bef -48.3 9316.0 -1.8 12.4
abf -57.5 13240.9 -l.7 12.2
cef 34.8 4830.7 2.2 . 18.8
acf 42.5 7213.6 1.2 6.2
bc -58.7 13805.3 -2.2 19.2
abce -45.3 8224.0 -1.5 8.6 2
df -27.7 3072.9 -0.6 1.6
adef ~19.2 1479.2 -O.9 3.0
bde 4.9 96.0 0.3 0.3
abd 16.1 1040.8 0.8 2.4
cde -20.4 1658.7 -0.4 0.7
acd -32.1 4114.9 -l.2 5.8
bcdf 45.1 8121.9 1.5 9.6
abcdef 35.5 5029.6 1.3 7.3
SS(A...ABCD) 91418.8 1 13.7

 

1 22
TABLE 4.4.

SS PERCENTAGES FOR DESIGN EFFECTS AND ALIASES

OF FLOUR/01L DATA.
1] at 0.08 rpm 1] at 2.0 rpm
Cumulative Cumulative
Effects ALIAS ALIAS ALIAS SS% °/o 88% %

 

ABD CDE ACF BEF
ACD BDE ABF CEF

A BCE ABCDF DEF 16.8 16.8 12.3 12.3
BC AE DF ABCDEF 15.1 31.9 16.9 29.1
AB CE ACDF BDEF 14.5 46.4 10.7 39.8

B ACE CDF ABDEF 10.2 56. 5 10.9 50.7

ABC E ADF BCDEF 9.0 65.5 7.5 58.2
BCD ADE F ABCEF 8.9 74.4 8.4 66.7
AC BE ABDF CDEF 7. 9 82.3 5 . 5 72. 1
ABCD DE AF BCEF 5.5 87.8 6.4 78. 5

C ABE BDF ACDEF 5.3 93.1 16.6 95.1

D ABCDE BCF AEF 3.4 96.5 1.4 96.5
CD ABDE BF ACEF 1.8 98.3 0.6 97.]
AD BCDE ABCF EF 1.6 99.9 2.7 99.8

BD ACDE CF ABEF 0. 1 100.0 0.2 100.0

 

1 23
TABLE 4.5.

OVERALL RANKING OF EFFECTS AND ALIASES OF FLOUR/OIL DATA.

RANK RANK Effects ALIAS ALIAS ALIAS ADD OVERALL
0.08 rpm 2.00 rpm RANKS RANK

 

ABD CDE ACF BEF
ACD BDE ABF CEF

2 1 BC AE DF ABCDEF 3 1
1 3 A BCE ABCDF - DEF 4 2
3 5 AB CE ACDF BDEF 8 3
4 4 B ACE CDF ABDEF 8 3
9 2 ABE BDF ACDEF l 1 5
5 7 ABC E ADF BCDEF 12 6
6 6 BCD ADE F ABCEF 12 6
7 9 AC BE ABDF CDEF 16 8
8 8 ABCD DE AF BCEF 16 8
l 0 1 1 D ABCDE BCF AEF 2 1 10
12 10 AD BCDE ABCF EF 22 1 1
11 12 CD ABDE BF ACEF 23 12

1—1
DJ

13 13 BD ACDE CF ABEF 26

 

1 24
each of the 16 treatments, the transformed data were randomly distributed with a

homogeneous variance.

Table 4.6 is the ANOVA table for the five main effects and their interactions. The
F-statistic is used to reveal the significance of the efi‘ects and their relative contributions to

the response variable, apparent viscosity. The F—statistic is a computed by the following

expression:
= 83/1 df
F SSE [4. 1]
/ 48 df

The error sum of the squares (SSE) is the pooled variations fiom the 16 total treatments
with four observations on each, accounting for 48 ( = 16 x (4-1)) degrees of fieedom,
representing a measure of the variation within samples. From the F distribution, the total
area under the curve is represented as 1.00. The p-value is the area under the curve to the
right of the F value for this distribution at 1 and 48 degrees of freedom Therefore, the
larger the p-value, the more insignificant the effect. For this analysis, the effect is
considered statistically significant for p-values less than 0.01. Four effects are recognized
as insignificant at each viscometer speed (boxed numbers in Table 4.6). Of the four

effects, three are common to each speed:
BCFEAEF, EFEABCF, and ACFEBEF

So, the two three-letter interactions are noted as having no effect on the response.

Because four-letter interactions are deemed insignificant fiom the outset of the study, the

125

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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1 26
EF interaction (oil type - moisture content) is the only two-letter interaction throughout

the analysis not to impact ER activity. Only one three-letter interaction had an efl‘ect on

the ER response, ABFECEF.

A noteworthy finding involves comparisons between F-values for the two
viscometer speeds. At the faster speed, 2 rpm, the fluid concentration was clearly more
critical to the response than at 0.08 rpm. This fact may be ermlained by analyzing the
shear-thinning behavior of ER fluids. A shear-thinning fluid displays a decreasing apparent
viscosity with an increasing shear rate. As the shearing (speed) is increased, the degree of
particle interaction and contact is heightened, ultimately interfering with flow behavior of
the suspension. An analogy can be drawn using a dance floor. When the dancers are
sparse, paralleling a low solid concentration, couples can move with ease. However, as
the concentration of dancers increase, the ability for the partners to move gracefully
becomes increasingly diflicult. Similarly, the inhibition of fluids to flow at greater speeds

is magnified with larger volume fractions.

Another interesting F-value comparison involves the voltage effect, A. At the
lower shear rate, the F-value for effect A is 334.24, while at the higher shear rate, the F-
value is 138.38. Hence, the voltage is clearly a more important factor at lower speeds.
Referring again to the Mason number (Mn), lower shear rates correspond to lower values
of Mn. Findings fiom this study support the notion that voltage effects are more

significant for lower values of Mn.

1 27
To demonstrate the five variable interactions more clearly, Figures 4.6 and 4.7

graphically depict the apparent viscosities for each viscometer speed considered. The
main axes of the cube incorporate the variables A, B, and F (voltage, temperature, and
moisture content). Low and high levels for the variables are considered as: A (voltage)
increasing from left to right, B (temperature) increasing fiom fiont to back, and F
(moisture content) increasing from bottom to top. At every corner of the three-
dimensional cubes are two-dimensional squares of the remaining variables, C and E
(concentration and oil type). The low and high variables are expressed similarly to the
main axes, where: C (concentration) increases fiom left to right, and E (oil type) changes
fiom bottom to top. Table 3.2 provides a listing of each variable and their experimental
values. The averaged apparent viscosities for each factor combination are placed at the
proper position on the statistical cube. According to Table 4.6, two two-level
interactions, temperature - concentration (BC) and electric field - temperature (AB), were
found to have a large impact on the ER response at each shear rate. Observations fiom

multiple-variable interactions are made for each figure.

For Figure 4.6 at 0.08 rpm, when the temperature effect (B) was low (25 °C),
corresponding to the front face of the statistical cube, the concentration (C) had a large
effect on the apparent viscosity; the opposite holding true when the temperature was in the
high position (50 °C), corresponding to the back wall of the cube. When the temperature
factor (B) was low, the electric field (A) had a positive efl‘ect on the apparent viscosity;
however, when the temperature was high, the electric field had little effect on the ER

response. Of the 16 treatments, the five largest viscosities occurred in the presence of the

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1 30
high voltage, with all but one of these five viscosities occurring while the moisture content

(P) was at the greater value (12.9%).

Similar results were obtained at 2 rpm (Figure 4.7). While the temperature was in
the low position, the larger concentration created greater apparent viscosities. However,
when the temperature was high, the concentration had inconclusive effects on the viscous
response. The largest viscosities were recorded when concentration and voltage were in
the high positions for the lower temperature condition. Nevertheless, the eight averaged
viscosities were larger for temperatures of 50 °C opposed to the eight averaged viscosities
for 25 °C. By comparing the high moisture viscosity values (12.9%) with the low
moisture values (6.4%), the higher moisture invoked a greater viscosity in each case but

0116.

Comparison of the two cubes finds the largest viscosities recorded at the same
cubic positions for each figure. For each instance, these positions coincide with the larger

voltage and concentration conditions for olive oil at the lower temperature setting.

4.3. 11 Groups Resulting from Dimensional Analysis

Buckingham’s Theorem was applied to the list of ER variables, and the following

dimensionless groups were defined:

111 = mc [4.2]
Hz = ¢ [4.3]
113 = fl [4.4]

IL = a. [4.5]

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[4.10]

[4.11]

Upon firrther inspection of the H groups, some basic relationships among primary

forces involved with ER were revealed. l'I groups 7 - 10 each represent a ratio of an

important force involved with ER activity to the gravitational force:

Polarization Force

 

 

 

 

n7 '3 . .
Gravrtatronal Force
H ___ Thermal Force
8 _ Gravitational Force
11 = Viscous Force
9 - Gravitational Force
11 _ Hydrodynamic (Inertial) Force
10 =

Gravitational Force

[4.12]

[4.13]

[4.14]

[4.15]

1 32
It has already been noted that polar, thermal, and viscous forces are important in

the ER phenomenon. However, 1110 the inertial force term, may also play a crucial role in
predicting behavior. This group represents a kinetic energy term (mass 0 velocity’), and
may be considered as a force imposed by a mass of fluid in motion. This force is different

fiom the viscous force term, related to internal fluid forces resisting shear flow.

Three major dimensionless groups have received much attention in ER literature,
the Mason number (Mn), the Peclet number (Pe), and the 7» number (2.). Variables

comprising these terms are taken from Table 2.2:

 

 

 

 

677,}? = Viscous Forces [4 16]
8:08.},(flE)2 Polarization Forces '

A _ ”soar: (.313)2 = Polarization Forces [4 l7]
kBT Thermal Forces °

Pe = 67K: 77,7 = Viscous Forces [4.18]

 

kBT — Thermal Forces

From the current dimensional analysis, the 10 11 terms can be manipulated to generate the

above groups:
Mn = 6n;’r1;‘rl;‘rl, [4.19]
,1 = nflinfifig' [4.20]

Pe = (Mn)(2) = sang‘n, [4.21]

133

Several variables remain uniform and are replaced with constant values for the

analysis. These variables include pp, p, , rp, 6,, g, and 1rB . P. was compared for olive and

canola oil at the two experimental temperatures of 25 and 50 °C. Results validated that
oil type and temperature had no effect on the continuum density. Substituting the

constants for the uniform variables gives the new groups:

o:1

 

 

IT,5 cc 1; H6 =a6(l); 1'1:s = l—a—s—l [4.22]

117 at E2; l'I7 =a7 E2; 1'1'7 = I-gll [4.23]
7

1'18 0: T; 118 = 013 T; H; =|:I—:| [4.24]

11, cc 77.7; II. =0. 71.7; H; = IL]; [4.25]

1110 at 72; 11,0 =a10j/2; 11:0 = '23 [4.26]

These newly formed 11' groups, along with the previously mentioned groups (I'll-1'15),

serve as the basic terms for the analysis.

The common ER dimensionless groups (Mn, Pe, and 2.) are adjusted to consider

the variables remaining unchanged throughout the analysis. These terms are distinguished

 

 

with a prime (') symbol.
. 77.7
II/ 71.7 , 152
Mnoc 9 ,; Mn=a ; Mn=— 4.27
1'17 Mn E2 laml [ 1

134

 

 

 

 

E2

n' E2 ’1—
,1 /.; 2:0. —; 2'=— 4.28
m Us A. T lall [ 1

. . 0.?

1'1/ 77.7 . T
P 0: 9 ,; Pe=a ; Pe = 4.29
e H. p, T lap, [ 1

Additional inspection of the 11 groups lead to the identification of another popular
dimensionless number, the Reynolds Number (Re). Reynolds Number is a ratio comparing
the inertial to viscous components, and provides an indication of fluid flow regions:
laminar, turbulent, or transitional This term is beneficial for classifying flow regimes

where sedimentation may be encountered with ER suspensions. The Reynolds group is

defined as
L
I ' 2
Re cc [1%, ; Re: am —7—,; Re' = i [4.30]
9 ”c lake

 

4.3.1. Prediction Equations

Flour/Oil. Dimensional analysis was applied to the flour/oil data to gain insight into the
ER behavior of milk chocolate and other fluids. Ten dimensionless groups were

developed to describe the ER response of flour/oil suspensions, with the viscosity ratio,

’7 77 , serving as the dependent variable. The remaining IT groups were regressed, using

1 35
Microsoft Excel (Redmond, WA) software, to determine the following prediction

equation:
H5 ___ e4488.43ni.73n§.29n;158.44n;133.361-I;0.34n;-864.96n;-124.94n$2.09 [431]

01'

%c = e4488.43(mc)l.73 (¢)0.29(fl)-158.44(gc )-133.46 . ..

(E2 )0.34 (T)-864.96(17c}', )-124.94 (7 2 )62.09 [432]

r2 for this expression is 0.80. Figure 4.8 shows the actual and predicted viscosity ratios
for the flour/oil data plotted against Mn'. This plot also reveals trend lines representing

regressions of the actual and predicted data.

1'1;I , a term proportional to temperature, had a very large exponent, -864.96. The
variables 77c and a both considered temperature dependencies. Since temperature

variations were considered in these variables, 11; was pulled from the dimensionless

groups, and the analysis was rerun. The new prediction equation was found to be
H, = 8407611138112.”Hg]0.12n;10.80n;0.34n;-3.45n;(1).34 [433]

01'

%¢ = e-10.76(mc)l.38(¢)0.75(fi)—10.12(£c)-10.80(E2 )0.34(ncy)-3.45(7 2 )1.34 [434]

136

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1 37
with an r2 value of 0.74. Although the I; value is less than that found with Equation 4.32,

the magnitude of the exponents is much more reasonable.

Milk Chocolate. To validate the prediction equation determined from the flour/oil
experiments, the model was applied to ER data of milk chocolate. Certain variables from
the flour/oil data were not involved or remained uniform for the milk chocolate analysis.
These variables included moisture content (mc), volume fraction (¢), and the permittivities
(a and fl). Because these factors remain unchanged, they are incorporated into overall
constants, C1 and C2. To determine these constants, the milk chocolate viscosity ratio was
regressed against the remaining H groups using the exponents from the flour/oil prediction

equation (Eq. 4.33).

ns : C1[e-io.76n;o.34n;-3.4s[1:334l+C2 [4.35]
01'
% =116.32[e"°‘76(E2)°'”(77c}°/)‘3'4’(72)”4]+4918 [4.36]

The expression was fit to a linear model, and values for the constants, C; and C2, were

calculated as 116.32 and 49.18, respectively, with a correlation (r2) determined to be 0.90.

A prediction equation was also determined from the milk chocolate dimensionless

groups. Multiple regression was employed and the prediction equation found as

H, = e15l.93n;0.l7ng-26.19n;-1.02H;3.22 [4.37]

138

01'
y = 6151.93 (E2 )0.l7(T)-26.l9(n 7)-1.02 (72 )0.22 [438]
77c c

with an r2 of 0.99. Figure 4.9 shows the predicted and actual apparent viscosity ratios
against Mn' for the milk chocolate data. In addition, this plot shows trend lines
representing regressions of the actual and predicted data. At the lowest milk chocolate
temperature studied (35.0 °C), the fluid behavior is strongly shear-thinning and the data do
not conform to the additional data fiom higher temperatures. These values are clustered
together and shown as the data group in the lower right comer of Figure 4.9.

Nevertheless, the model accurately reflects data fiom all experimental temperatures.

4.3.2. Dimensionless Rheogram

A conventional rheogram consists of the shear stress plotted against the shear rate.

The dimensionless groups were manipulated to produce a dimensionless rheogram, where

the dimensionless shear stress is the product of % and Mn' , and the dimensionless

shear rate is represented by Mn’. Data from the flour/oil statistical experiments were
applied to the new rheogram to graphically show the effects of ER factors: volume
fraction, temperature, and moisture content. Figure 4.10 - 4.12 represent best fit

expressions and depict significant trends in the ER response.

Figure 4.10 demonstrates the concept that concentration enhances the

phenomenon. At the larger volume fraction, the dimensionless shear stress is much

139

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1 43
greater than the response at 20% concentration. In addition, Figure 4.11 efl‘ectively

shows the strong efl‘ect temperature plays in ER At higher temperatures, the ER activity
is stronger, due to increased polarization and particle mobility coupled with a decrease in

continuum viscosity.

Figure 4.12 illustrates the role water plays in ER It has been well documented
that moisture increases ER activity and is often a requirement for many ER fluids. For the
flour/oil data, two moisture levels of 12.9% and 6.4% (% water on a dry basis) were
compared. As expected, the higher moisture content promoted ER activity. However, the
enhancement was not as significant as one might expect. At 50% total moisture content,
ER activity of flour is slightly diminished. The lack of impact on the ER response may be
supported by examining the statistical analysis, where moisture content ranked fifih of the

six primary factors for significance on ER activity (see Table 4.5).

An interesting observation from Figures 4.10 and 4.11 is that in each graph, the
variable changes are characterized by lines running non-parallel to one another. Parallel
lines would indicate that the ER variables, volume fraction and temperature, do not
interact with Mn' , the independent variable. Therefore, ER variable efl‘ects from volume
fraction and temperature are influenced by changes in Mn’. For example, as Mn' is
increased, the larger volume fraction line shows a growing significance, 'Le., volume
fraction has a greater importance at higher Mn' values. Similar observations can be made

for temperature effects. Figure 4.12, however, shows two lines running fairly parallel

1 44
through the Mn' range due to the influence of moisture content. This means moisture

content changes do not interact with Mn’.

4.3.3. H Group Analysis

% Vs Mn' . Much ER literature has been dedicated to studying the relationship

between the Mn and the viscosity ratio. Equations 2.12 and 2.13 are equations
representing this relationship, where the values for K and Mn‘“ are suspension dependent.
Log-log plots of the viscosity ratio against the Mn are characterized by a linear portion
with a negative slope for lower values of Mn. As Mn increases, the viscous efl‘ects begin

to dominate the response causing the graph to tail and approach a constant value

corresponding to 77% . In other words, the electric field has no efl‘ect on the fluid with

large shear fields causing the viscosity to approach that of an unelectrified suspension.

This study also examined the aforementioned relationship. Figures 4.13 and 4.14

show curves for 7% Vs Mn' for flour/oil and milk chocolate, respectively. A best fit

power law curve was calculated for the flour/oil data and applied to the milk chocolate
graph (Fig. 4.14). At the highest milk chocolate temperature - when the carrier medium
(cocoa butter) behavior was Newtonian - the data corresponded well with the flour/oi]

best fit line.

145

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Figure 4.14 shows the temperature effects on % Vs Mn' for milk chocolate.

Temperature had a definite impact on the ER behavior, illustrated by a data cluster in the
lower right comer of the graph (similar to Fig. 4.9). The temperature regions may result
fi'om values of the continuum viscosity, 7],. At the lowest temperature, the cocoa butter
was strongly shear-thinning resulting from large values for the continuum viscosity. At
the highest temperature, 40.6 °C, the cocoa butter responded as a Newtonian fluid, and

the viscosity ratio was comparable to the flour/oil results.

For the flour/oil graph (Fig. 4.13), the data were studied for two different volume
fractions and temperatures. From a power law expression, values for Equations 2.11 and

2.12 constants, K and Mn *’ , were calculated. Since Mn *' scales with the Mn'value

when the electric field no longer efl"ects the ER response, one would expect that increasing

the volume fraction would cause the value of Mn *’ to increase. Also, according to

published literature, temperature increases enhance ER activity. So, at larger

temperatures, one would expect a larger Mn *' . Comparison of the Mn *’ values for the

flour/oil data support these statements (Table 4.7).

K and Mn *’ , constants from Equations 2.11 and 2.12, were also calculated for

the milk chocolate data set and displayed in Table 4.7. The effects of temperature

increased the value of K; however, temperature reduced the values for Mn *' . This

corresponds to a lower shear rate requirement for the destruction of the ER response at

larger temperatures. Although temperature may enhance polarization, it may also invoke

148

 

TABLE 4.7.
COMPARISON OF ER MATERIAL CONSTANTS FOR MILK CHOCOLATE
AND FLOUR/OIL DATA.

ER Material K Mn *’
Flour/Oil

¢ = 0.2 -O.682 0.14

¢ = 0.4 -o.554 0.19
Flour/Oil

T = 25 °C -0.727 0.14

T= 50 °C -O.485 0.26
Milk Chocolate

T = 37.8 & 40.6 °C -0.472 3.46

T = 40.6 °C -O.4l6 2.69

 

1 49
effects which diminish the ER phenomenon for milk chocolate. This feature was also

observed during the ER classification of milk chocolate in Section 4.1. At larger
temperatures, peculiar and erratic results were encotmtered. It appears an apparent upper
temperature limit exists where the thermal effects lend to a diminishing ER response for

milk chocolate.

% Vs Pe' . Other dimensionless groups were compared in attempts to learn more

about interacting and competing forces among ER factors. The dimensionless viscosity
ratio was graphed against Pe' (Fig. 4.15). General trends from this figure support the
concept that temperature enhances ER activity. As the temperature effects increase,
corresponding to lower Pe' values, the apparent viscosity is larger. At large shear rates,
accompanying large Pe' numbers, the viscous effects are more pronounced and the

viscosity ratio approaches a uniform value.

Figure 4.16 depicts this comparison for milk chocolate data. Accompanying this
data, is the best-fit power law curve from Figure 4.15. The line captures the trend for
milk chocolate, except for the largest group of Pe' values. This cluster of data is

measured at the lowest temperature, 35.0 °C, for milk chocolate.

% Vs Re' . Figure 4.17 shows the log-log curve for the flour/oil data. The general

trend fiom this graph reveals a decreasing apparent viscosity with increasing Re'. The

inertial forces, comprising the numerator of Re’ , scale with the shear rate. As the shear

150

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1 53
rate increases, the ability to destroy ER microstructures is greater, as shown by the

decreasing apparent viscosity ratio with increasing Re' .

A power law relationship was applied to calculate the best-fit representation for
the milk chocolate data and placed on Figure 4.18. Once again, the best-fit line captured
the trend for milk chocolate at the highest temperature, 40.6 °C. Large deviations from
the line are experienced for the other milk chocolate experimental temperatures. For the
lowest temperature, 35 °C, it appeared that larger viscosities were achieved for the higher
shear rates. Again, the temperature dependent nature of the carrier medium may be

responsible for this unexpected behavior of ER fluids.

Re’ Vs Pe' . Figure 4.19 shows a graph portraying the ratio of inertial to viscous effects
against the ratio of viscous to thermal forces. A qualitative analysis finds the Re'
increasing linearly with Pe' . As the thermal efl‘ects become more dominant,
corresponding to lower values of Pe' , the viscous portion of Re' is more dominant.
Lower values of Re' are accompanied by either larger temperatures or a less viscous

continuum

A best-fit line was taken from Figure 4.19 and applied to milk chocolate in Figure
4.20. As observed from earlier figures, the best-fit curve represents the milk chocolate
response at the highest experimental temperature. Likewise, deviations from this curve

were seen for lower temperatures, when the continuum behaved as a shear-thinning liquid.

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1 57
4.4. Thermal Enhancement of Milk Chocolate

Equation 3.12 was programmed into an Excel spreadsheet program This
equation, along with recorded temperatures and the heat flux, allowed for estimation of
the thermal parameters. The values of k and pcp producing the lowest sum of the squares
when comparing the actual to theoretical temperatures were selected as the optimal
values. Figure 4.21 shows a typical comparison of actual and theoretical temperatures to
confirm that the predictive model accurately represented the actual time - temperature ‘

relationship found in the sample.

Figure 4.22 displays the temperature residuals at the boundaries of the chocolate
sample. When the differences are the smallest at each location, the predicted heat transfer
properties most accurately reflect the experimental values. From Figure 4.22, the

theoretical and experimental data are at the best fit between 45 and 145 seconds.

A "mirror image" concept was used to predict the thermal conductivities of milk
chocolate with and without the presence of an electric field. A total number of 18 tests
were performed (Table 4.8). Of the 18 experiments, 11 tests were run without an applied
field, yielding an average conductivity of 0. 158 W m'1K'l (standard deviation equals 0.027
W m'lK'l). Five tests were operated with 300 Volts mm'1 across the chocolate sample,
giving an average conductivity of 0. 175 W m"l('l (standard deviation equals 0.013
W m'lK'l). Further measurements were collected at 450 Volts mm'l yielding an average

conductivity of 0. 159 W m"K".

158

 

 

 

 

 

 

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2., 0 Actual (Z=0)
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a Cl Theoretical (Z=0)
.5, A Theoretical (Z=L)J
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20 T
10 ~f~
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0 50 100 150 200

Time (5)

FIG. 4.21. TRANSIENT BOUNDARY TEMPERATURES OF MILK

CHOCOLATE: COMPARISON OF ACTUAL AND THEORETICAL
TEMPERATURES.

159

 

 

 

 

 

 

 

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8
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150 180

 

FIG. 4.22. MILK CHOCOLATE BOUNDARY TEMPERATURE DIFFERENCES
BETWEEN ACTUAL AND THEORETICAL VALUES.

 

 

=

1 60
TABLE 4.8.

THERMAL CONDUCTIVITY (W m'IK'l) OF MH.K CHOCOLATE EXPOSED
TO VARYING ELECTRIC FIELDS.

 

0 Volts mm" 300 Volts mm'1 450 Volts mrn'l
0.150 0.163 0.160
0.150 0.159 0.158
0.151 0.185
0.1 18 0.185
0.127 0.182
0.194
0.184
0.177
0.185
0.180
n 11 5 2
T 0.158 0.175
S 0.027 0.013

 

161
The sample means for the conductivities at 0 and 300 volts were 0.158 and 0.175

W m’lK'l, respectively. The t distribution test statistic, with a 95% confidence interval and

14 degrees of freedom, was equal to 2.14. For our sample averages, ttest equals 1.32.
Since ttest was less than 2.14, the voltage was considered to have no significant effect on

the thermal conductivity. Therefore, the mean value of k was calculated from all 18
experiments, 0.163 W m"K'l (standard deviation equals 0.023 W m'1K"). A possible
explanation for the lack of impact an electric field has on the directional heat transfer is
that milk chocolate has a very high volume fraction of particulates. Although an electric
field affects the rheology of milk chocolate, the microstructures do not provide noticeable

increases in the rate of heat transfer.

Published values for the thermal conductivity for milk chocolate were not found.
Equation 2.26 produced a conductivity of 0. 195 W m"K". This value gives
approximately 16% error between the estimated value and the number calculated with the
compositional model Compositional and chemical variations in food systems as well as

procedural inconsistencies may be responsible for the deviation.

According to Sweat (1986), the recommended method for determining thermal
diffusivity, a, is to calculate it from experimentally derived values of conductivity (k),

specific heat (cp), and mass density (p), where

a = .13. [4.39]

1 62
According to Zhang and Lloyd (1993) the specific heat and density do not appear to be

affected by the application of an electric field. The MIM produced specific heats ranging
from 1.85 to 2.63 k] kg'l K'1 with an average value of2. 14 kJ kg'1 1('1 (standard deviation
equals 0.27 1d kg'1 [(1). Density of milk chocolate, determined as 1.24 g cm’3, lead to an
average thermal diffusivity of 6.32 x 10'8 m2 5'1 (standard deviation equals 1.46 x 10'8

m2 s") for the milk chocolate. Chocolate diffusivity data were also not available, but
comparison to known diffusivity values of other food materials (such as 7.90 x 10'8 m2 s'l
for butter between 30 and 60 °C) reported by Choi and Okos (1986) show that the

magnitude of the estimated value is reasonable.

W

Four objectivesof this research were identified in the first chapter: 1) To thoroughly
evaluate the literature in electrorheology and milk chocolate rheology; and to evaluate the
effects of shear fields and temperature on the flow behavior of milk chocolate in the
presence of an electric field. 2) To investigate the importance of six primary ER
variables, and their interactions with each other by studying model ER fluids composed of
difi‘erent flour and vegetable oil suspensions. 3) To employ dimensional analysis to
develop prediction equations for describing the ER phenomenon, linking interactions
among electrical, thermal, viscous, and hydrodynamic forces in food systems. 4) To
describe the ‘Mrror-Image—Method” for measuring thermal properties of molten milk
chocolate; and to evaluate the thermal conductivity of molten milk chocolate with and
without electric field effects. The following conclusions, addressing each objective, are

made.

5.1. Electrorheological Behavior of Milk Chocolate

This research demonstrates that milk chocolate has the unique characteristics
associated with ER fluids. The yield stress and apparent viscosity are functions of the
applied electric field, each increasing with electric field intensity. Temperature enhances

the ER response. At constant shear and electric fields, the apparent viscosity increases

163

1 64
with temperature, behavior typical of ER fluids but unexpected for milk chocolate.

However, atypical behavior was found to occur at higher temperatures and electric fields.
This deviation from a normal ER response may be attributed to the polymorphic behavior
of liquid cocoa butter. Difl‘erent factions of the cocoa butter fat are known to melt at
different temperatures. Some of the lipid components are known to consist of polar
groups, and when these fats melt and become part of the canier medium, the dielectric
constant of the liquid fat increases. This results in loss of the desirable, nonpolar liquid
phase, and consequentially, the ER response of milk chocolate. The role of cocoa butter

in the ER response needs additional research.

5.2. Investigation of Variables Influencing ER Behavior

Fractional factorial designs are useful for screening large numbers of variables

during the early stages of study. A 2"2

fractional factorial design was performed on six
ER variables: electric field, temperature, concentration, flour type, oil type, and moisture
content. Initial statistical analysis revealed that one of the variables, flour type, was
insignificant to experimental outcomes. The oil type, however, was shown to have

significance on the response. This may be due to differences between rheological

properties of canola and olive oil in the unelectrified state.

The flour type variable was removed from the analysis, and an AN OVA was
performed to demonstrate significance levels for the remaining variables and interactions.
Each of the remaining variables were ranked according to significance to the ER response

in the following order: voltage, temperature, concentration, oil type, and moisture content.

1 65
The voltage effect was wimessed to play a more dominating role in the ER response for

the lower shear rate region, while the concentration effect was more critical to the
phenomenon at higher shear rates. Temperature showed a similar importance to ER
activity regardless of the shearing speed. Multiple variable interactions, such as
temperature - concentration and electric field - temperature, also showed importance to
the ER phenomenon. Results from this statistical study effectively characterized

interactions of, and between, variables for the ER phenomenon.
5.3. Dimensional Analysis of the ER Phenomenon

After completing the statistical analysis, the flour/oil data were transformed into
ten dimensionless terms called I'I groups. These terms were regressed to develop a
relationship between the dependent group, a viscosity ratio ( 17/ 77. ), and the remaining
independent H groups, leading to development of the following equation having an r2

value of0.74:
%c = e-10.76(mc)1.38(¢)0.75(fl)-10.12(8c)-10.80(E2)0.34(nc)'/)-3.45(}',2)l.34 [5 1]

Applying a slightly modified form of this flour/oil based equation to milk chocolate data

gave:
% =e151.93(E2)o.i7(T)-26.i9(m};)-1.02(};2)o.22 [5.2]

with an r2 value of 0.99. In general, dimensional analysis proved an excellent numerical

method for developing prediction equations among ER variables.

1 66
5.4. Thermal Properties of Milk Chocolate

An electric field of up to 450 Volts mrn‘l at 60 Hz did not produce a statistically
significant enhancement of heat transfer in milk chocolate. The "Mirror Image Method"
proved to be a quick and practical technique for measuring heat transfer parameters of
fluid foods. The average thermal conductivity and thermal difiirsivity of molten milk

chocolate over a temperature range of 30 to 60 °C was 0.163 W m'1K'l and 6.32 x 10’8

m2 s", respectively.

5.5. Future Research

Future study of ER fluid foods should involve three general areas of research. The
first area should be the identification of ER food systems in addition to milk chocolate.
Food components, solid or liquid, may contribute to ER activity. However, multi-
composite food materials, such as milk chocolate, need to be identified. These systems

will be suspensions with a high fat and low moisture content.

Another area of study should be the development of analytical techniques to
separate, or identify, components based on dielectric properties. Although this technology
may not be used to difi’erentiate flour types, other applications may still exist. ER, for
example, might be used to maintain and stabilize suspensions or, to rapidly determine

moisture levels of flours.

The final area of research should be the continued research of ER in fluid milk
chocolate. This material responds as a strong ER fluid, showing dramatic increases to

yield stress and apparent viscosity with an electric field. The electrorheological response

1 67
of milk chocolate creates unique opportunities to improve product and process

development. Traditionally, the flow behavior of milk chocolate is controlled by changing
composition and temperature. Recognizing milk chocolate as an ER fluid allows for the
control of flow behavior with the application of an external voltage. For example, the ER
valve could find a home in a chocolate processing plant. A valve with no moving parts
would be beneficial to the food industry because it could be cleaned without disassembly.
The chocolate industry, having an ER material requiring no additional development, is a

prime target for ER applications.

Additional research should examine the effects of changing the protein
environment, manipulating the polar nature of the milk proteins, on the ER response of
milk chocolate. Once the primary components for ER in milk chocolate are identified,
simple model systems could be designed and studied. This system could be analyzed at
different pH levels and temperatures. Changes in pH and temperature will either increase
or decrease the polar nature of the proteins, resulting in changes in ER activity. From this
analysis, the mechanism of the ER phenomenon in milk chocolate could be better

understood.

Another idea for firture study involves the coupling of ER measurements with
analytical techniques, such as differential scanning calorimetry (DSC), to further qualify
the phenomenon. It is believed that the polymorphic behavior of cocoa butter is
responsible for the erratic ER response displayed by milk chocolate at higher
temperatures. In other words, at higher temperatures, the more polar lipid crystals of

cocoa butter are melting and contributing to the continuous phase, leading to a loss of the

 

 

|u

1 68
nonpolar requirement by the liquid phase. DSC permits one to monitor physicochemical

transitions of solid cocoa butter as the temperature is increased This technique could
assist in understanding how the polymorphic behavior of the milk chocolate continuum
influences ER activity. Through chemistry and electricity, ER technology could ultimately

permit additional control over the flow behavior of milk chocolate.

WA

Dimensional Analysis Tables.

FLOUR/OH. DIMENSIONLESS GROUPS.

169

TABLE A.1.

 

71/7]. mc ¢ 8c p 117' ns' [19' 1110'
95.1 1 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 5.77E-01 7658-1-01
173.61 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 2.89E-01 1.91E+01
350.20 1.00 0.40 3.15 0.20 1.60E-l-05 2.98E+02 1.445-01 4.7SE+00
439. 76 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 1.15E-01 3.06E-l-00
930.18 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 5.77E-02 7.645-01
1873.84 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 2.88E-02 1.9lE-01
3745.41 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 1.45E-02 4.80E-02
4615.5 8 1.00 0.40 3. 15 0.20 1.60E+05 2.98E+02 1. l6E-02 3.06E-02
9254.88 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 5.74E-03 7.57E-03
18546. 21 1.00 0.40 3. 15 0. 20 1.60E+05 2. 98E+02 2. 90E-03 1.94E-03
37044.00 1.00 0.40 3.15 0.20 1.60E+05 2.98E+02 1.455-03 4.84E-04
5.71 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 5.77E-01 7.65E+01
7.64 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 2.89E-01 1.91E+01
1 1.66 1.00 0.20 3. 15 0.20 1.00E+04 2.98E+02 1.44E-01 4755-1-00
12.97 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 1.155-01 3.06E+00
29.86 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 5.77E-02 7645-01
33.81 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 2.88E-02 1.91E-01
56.89 1.00 0.20 3.15 0.20 l.OOE+04 2.98E+02 1.4SE-02 4.80E-02
67.90 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 1.16E-02 3065-02
119.15 1.00 0.20 3. 15 0.20 1.00E+04 2.98E+02 5.74E-03 7.57E-03
192.59 1.00 0.20 3.15 0.20 1.00E+04 2.98E+02 2.9OE-03 1.945-03
403.98 1.00 0.20 3. 15 0.20 1.00E+04 2.98E+02 1.455-03 4.84E-04
36.96 1.00 0.20 2.50 0.36 1.00E+04 3.23E+02 2.015-01 7.65E+01
74.98 1.00 0.20 2.50 0.36 1.00E+04 3.23E+02 1.015-01 1.91E+01
147.67 1.00 0.20 2.50 0.36 1.00E+04 3.23E+02 5.01E-02 4.75E+00
200.15 1.00 0.20 2.50 0.36 1.00E+04 3.23E+02 4.025—02 3.06E+00
385.23 1.00 0.20 2.50 0.36 1.00E+04 3.23E+02 2.015-02 7.645-01
943.11 1.00 0.20 2.50 0.36 1.00E+04 3.23E+02 1.015-02 1.91E—01

1678.32
1981.76
3546.04
6728.04
13039.5]
3.97
5.51
9.25
10.67
13.31
38.34
51.50
58.78
106.28
161.03
345.51
4.42
6.92
10.89
9.38
16.70
20.76
32.94
63.53
119.12
173.53
353.66
44.10
87.28
172.16
221.48
455.58
943.57
1830.70
2260.10
4117.92

1.00
1.00
1.00
1.00
1.00
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20

1 70
0.36
0.36
0.36
0.36
0.36
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27

1.00E+04
LOOE+04
LO0E+04
LOOE+04
LOOE+04
LO0E+04
1.00E+04
1.00E+04
LO0E+04
LOOE+04
LO0E+04
LO0E+04
LO0E+04
1 .00E+04
LOOE+04
LO0E+04
1.60E+05
1 .60E+05
L60E+05
160E+05
1 .6OE+05
L60E+05
L60E+05
L6OE+05
L60E+05
l .60E+05
L60E+05
L60E+05
L60E+05
1 .60F.+05
1 .60E+05
L60E+05
l .60E+05
1 .60E+05
L60E+05
1 .6OE+05

3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02

5.04E-03
4.03E—03
2. DOE-03
1.01E-03
5.06E-04
5.77E-01
2. 8913-01
1.44E-01
l. lSE-Ol
5. 77E-02
2. 88E-02
1.45E-02
l. 16E-02
5. 74E-03
2. 9013-03
1 .45E—03
4.63E—01
2. 32E-01
1. l6E-01
9.27E-02
4. 63E—02
2. 32E-02
1. 16E-02
9.28E-03
4. 6 lE-03
2. 33E-03
l. l7E-O3
2. 27E-01
1. l4E-01
5. 67E-02
4.55E-02
2.27E-02
l. 14E-02
5.69E-03
4. SSE-03
2.26E-03

4.80E-02
3.0613-02
7.57E-03
1.94E-03
4. 8413-04
7.65E+01
1.91E+01
4.7SE+00
3.06E+00
7.64E-01
1.9lE-01
4.80E-02
3.06E-02
7.57E-03
1.94E-03
4. 84E-04
7.65E+01
1.91 E+01
4.75E+00
3.06E+00
7.6413-01
1.9lE-Ol
4.80E-02
3.06E-02
7.57E-03
1.94E-03
4. 8413-04
7.65E+01
1.91E+01
4.7SE+00
3.06E+00
7.64E-01
1.91E—01
4.80E-02
3.06E-02
7.57E-03

8104.32
16134.22
22.75
25.86
29.68
34.67
38.67
83.95
136.36
138.04
226.91
419.18
762.93
31.84
36.74
45.25
47.12
68.94
102.26
177.50
188.89
323.87
644.15
1331.60
22.62
42.20
84.05
107.13
212.38
460.82
965.38
1238.90
2515.42
5130.14
10813.31
53.11

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

0.20
0.20
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.20
0. 20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.40

3.15
3.15
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
3.15

1 71
0.27
0.27
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.27

L60E+05
L60E+05
LO0E+04
LOOE+04
LOOE+04
LOOE+04
1.00E+04
LO0E+04
1.00E+04
l.OOE+04
LO0E+04
1005-4-04
1.00E+04
LO0E+04
1.00E+04
LOOE+04
LO0E+04
1.00E+04
1.00E+04
1.00E+04
1 .00E+04
LO0E+04
1.00E+04
1.00E+04
1 .6OE+05
1 .6OE+05
L60E+05
l .60E+05
l .60E+05
l .6OE+05
l .GOE+05
1.60E+05
1.60E+05
1.60E+05
l .60E+05
LOOE+04

3.23E+02
3.23E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
3.22E+02
3.22E+02
3.22E+02
3.22E+02
3.225+02
3.22E+02
3.22E+02
3,225+02
3.22E+02
3.22E+02
3.22E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
29884-02
2.9SE+02
2.98E+02
2.98E+02
2.98E+02
3.23E+02

1. 14E-03
5. 72E-04
4. 63E—01
2. 325-01
1 . 16E-01
9. 27E-02
4. 63E—02
2. 32E-02
l . 16E-02
9.28E-03
4. 6 1 E-03
2. 33E—03
1 . l7E-O3
2.27E-01
l . l4E-01
5 . 67E-02
4. SSE-02
2. 27E-02
l . 14E-02
5 . 69E-O3
4. SSE-03
2. 26E-03
1 . 14E-03
5 . 72E-04
4. 63E-01
2. 32E-01
1 . 16E-01
9. 27E-02
4. 63E-02
2. 32E-02
l . 16E-02
9. 28E-03
4. 6 lE-03
2. 33E-03
l. l7E-03
2. 27E-01

1945-03

4.84E-04
7.65E+01
1.9lE+Ol
4.75E+00
3.06E+00
7 .6415—01

1.91E-01

4.80E-02
3.06E-02
7.57E-03
1.94E-03
4. 8413-04
7.65E+01
1.91E+01
4.75E+00
3.06E+00
7.6413-01

1.91E-01

4.8013-02
3061-3-02
7 .57E-03
1 9413-03
4.84E-04
7.65E+01
1.91E+01
4.75E+00
3.06E+00
7.64E-01

1.91E-01

48013-02
3.0613-02
7.57E-03
1941-3-03
4.84E-04
7 .6SE+01

63.35
79.19
92.52
104.29
147.80
207.53
247.43
395.32
665.31
1108.65
28.78
35.73
49.59
51.09
86.29
138.61
292.35
264.34
413.44
641.97
1234.13
15.76
21.90
37.44
32.66
59.47
89.52
215.80
271.95
500.66
927.08
1659.53
16.01
23.25
35.30
45.69

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50

0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20

3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
3.15
3.15
3.15
3.15

172
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.36
0.27
0.27
0.27
0.27

LOOE+04
LO0E+04
LOOE+04
LO0E+04
LO0E+04
LO0E+04
l .00E+04
LO0E+04
LO0E+04
LOOE+04
1 .60E+05
L60E+05
L608+05
L60E+05
L60E+05
L60E+05
160E+05
160E+05
160E+05
L60E+05
160E+05
LOOE+04
LO0E+04
100E+04
LOOE+04
100E+04
LO0E+04
LO0E+04
LO0E+04
100E+04
100E+04
LOOE+04
L60E+05
L60E+05
L60E+05
l .60E+05

3.23E+02
123E+02
3.23E+02
3.231902
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
123E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
123E+02
323E+02
3.23E+02
123E+02
3.23E+02
3.23E+02
123B+02
3.23E+02
3.23E+02
123E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02

1. l4E-01
5.67E-02
4.55E-02
2.27E-02
1. 14E-02
5.69E-03
4.55E-03
2.26E-03
1. l4E-03
5.72E-04
2.01E—01
1.01E-01
5.01E-02
4.02E-02
2.01E-02
1.01E-02
5.04E-03
4.03E-03
2.00E-03
1 .01E-03
5.06E-04
2.01 E-Ol
1.01E-01
5.01E-02
4.02E—02
2.01E-02
1.015-02
5.04E-03
4.03E-03
2.00E-03
1.01E-03
5.06E-04
2.27E-01
l. 14E-01
5.67E-02
4.55E-02

1.91E+01
4.75E+00
3.06E+00
7.645-01

1.91E-01

4.80E-02
30613-02
7.57E-03
1.94E-03
4.848-04
7.6SE+01
1.91E+01
4.7SE+00
3.06E+00
7.64E-01

1.91E-01

4.80E-02
3.06E-02
7.57E-03
1.94E-03

4.84E-04
7.6SE+01
1.9 l E+01
4.75E+00
3.06E+00
7.64E-01

1.9lE-Ol

4.80E-02
3.06E-02
7.57E-03
1.94E-03
4.84E-04
7.65E+01
1.91E+01
4.75E+00
3.06E+00

 

73.85
115.80
214.88
268.82
551.54

1075.38
2149.49

41.57

50.20
65.00

70.47

93.14
137.76
194.09
225.64
320.44
482.73
814.43
45.67

70.86
122.28
131.40
266.95
549.48

1203.69

1697.67

3956.43

8386.60
17010.28

53.68
69.48

91.89
97.67
136.49
204.49
382.12

0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00

0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40

3.15
3.15
3.15
3.15
3.15
3.15
3.15
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
2.50
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
2.50
2.50
2.50
2.50
2.50
2.50
2.50

173
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.29
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.36
0.36
0.36
0.36
0.36
0.36
0.36

160E+05
160E+05
L608+05
L6OE+05
L605+05
L60E+05
L605+05
LOOE+04
LOOE+04
LO0E+04
LOOE+04
LO0E+04
LO0E+04
LOOE+04
LOOE+04
100E+04
100E+04
LOOE+04
L60E+05
L60E+05
L60E+05
160E+05
160E+05
160E+05
L60E+05
L60E+05
L60E+05
L60E+05
L60E+05
LGOE+05
L60B+05
L60E+05
L60E+05
L60E+05
160E+05
L60E+05

3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
2.98E+02
2.98£+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
2.98E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02
3.23E+02

2.27E-02
l. 14E-02
5.69E-03
4.55E—03
2.26E-03
1. 14E-03
5 . 72B-04
4.63E-01
2. 32E-01
l. 16E-01
9.27E-02
4.63E-02
2. 32E-02
l. 16E-02
9.28E—03
4.61E-03
2. 33E-03
l. l7E-03
5.77E-01
2. 8913-01
1 .44E-01
1. 15E-01
5.77E-02
2. 88E—02
1 .45E-02
l. 16E-O2
5.74E—03
2. 90E-03
1 .45E-O3
2.01E-01
1.018-01
5.01E-02
4.02E-02
2.01E-02
1.01E-02
5.04E-03

7 .64E-01
1.91E-01
4.80E-02
3.06E-02
7.57E-03
1.94E-03
4.84E-04
7.65E+01
1.91E+01
4.75E+00
3.06E+00
7.64E-01
1.91E-01
4.80E-02
3.06E-02
7.57E-03
1.94E-03
4.84E-04
7.65E+01
1 .91E+01
4.75E+00
3.06E+00
7.64E-01
1.91E-01
4.80E-02
3.06E-02
7 5713-03
1.94E-03
4.84E-04
7.65E+01
1.9lE+01
4.7SE+00
3.06E+00
7.64E-01
1.91E-01
4.80E-02

354.12
439.46
584.88
897.58

1.00
1.00
1.00
1.00

0.40
0.40
0.40
0.40

2.50
2.50
2.50
2.50

174
0.36
0.36
0.36
0.36

1.60E+05 3.23E+02
1.60E+05 3.23E+02
1.60E+05 3 . 23E+02
1.60E+05 3 .23E+02

4.03E-03
2.00E-03
1.01E-03
50613-04

3.06E-02
7.57E-03
1 945-03
48413-04

 

1 75
TABLE A.2.

MILK CHOCOLATE DIMENSIONLESS GROUPS.

 

71/ 77c 117' IL' 119' II:.'
0.06 1.00E+04 3.08E+02 9.18E+01 4. 84E-04
0.09 l .00E+04 3.08E+02 9.34E+01 1.94E-03
0. 11 1.00E+04 3.08E+02 9.50E+01 7.57E-03
0. l6 1.00E+04 3.08E+02 9.67E+01 3.06E-02
0.17 1.00E+04 3.08E+02 9.72E+01 4.80E-02
0.22 1.00E+04 3.08E+02 9.89E+01 1.91E-01
0.27 1.00E+04 3.08E+02 1.01E+02 7.64E-01
0.35 1.00E+04 3 .08E+02 1.02E+02 3 .06E+00
0.39 1.00E+04 3.08E+02 1.03E+02 4.78E+00
0.53 1.00E+04 3.08E+02 1.05E+02 1.91E+01
0.78 1.00E+04 3.08E+02 1.07E+02 7.6SE+01
51.71 1.00E+04 3.11E+02 1.01E-01 4.84E-04
52.16 1.00E+04 3.1 113-+02 1.50E-01 1.94E-03
42.25 1.00E+04 3.11E+02 2.23E-01 7.57E-03
38.03 1.00E+04 3.11E+02 3.35E-01 3.06E-02
37.35 1.00E+04 3.1 lE+02 3.81E-01 4.80E-02
31.03 1.00E+04 3.11E+02 5.69E-01 1.91E-01
26.16 1.00E+04 3.11E+02 8.51E-01 7.64E-01
22.87 1.00E+04 3.1 1E+02 1.27E+00 3.06E+00
22.40 1.00E+04 3. 1 IE+02 1.4SE+00 4.78E+00
21.17 1.00E+04 3.IIE+02 2.16E+00 1.91E+01
20.89 1.00E+04 3.1 1E+02 3.24E+00 7.65E+01
1236.36 l.OOE+04 3. 14E+02 3.30E-03 4. 84E-04
869. 70 1.00E+04 3. 14E+02 6. 60E-03 1.94E-03
560.92 1.00E+04 3.14E+02 1.31E—02 7.57E-03
378. 67 1.00E+04 3.14E+02 2. 63E-02 3.06E-02
335.16 1.00E+04 3.14E+02 3.29E-02 4.80E-02
208.09 1.00E+04 3.14E+02 6.56E-02 1.91E-01

132988
86.72
76.58
54.04
40.88
0.05
0.07
0.08
0.15
0.17
0.26
0.32
0.40
0.43
0.57
0.80
48.33
41.78
43.55
39.01
42.09
42.74
35.29
29.03
27.17
24.09
22.54
1318.18
672.73
384.67
303.24
319.63
268.80
194.51
126.55
106.31

l.OOE+04
1.00E+04
1.00E+04
1.00E+04
1.00E+04
6.25E+04
6.2515+04
6.25E+04
6.253+04
6.25E+04
6.25E+04
6.25E+04
6.251-Z+04
6.25E+04
6.25E+04
6,255+04
62534-04
6.25E+04
6.ZSE+04
6.25E+04
6.25E+04
6.25E+04
6.25E+04
6.25E+04
6.25E+04
6.25E+04
6.255+04
6.25E+04
6.25E+04
6.25E+04
6.2515+04
6.25E+04
6.25E+04
6.25E+04
6.25E+04
6.25E+04

1 76
3.14E+02
3.14E+02
3.14E+02
3.14E+02
3.,14E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.1 1E+02
3. 1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3. 14E+02
3. 14E+02
3.14E+02
3. 14E+02
3.14E+02
3.14E+02
3.14E+02
3.14E+02
3.14E+02

1.3lE-01
2.62E-01
3.28E-01
6.56E—01
1.31E+00
9.18E+01
9.34E+01
9.50E+01
9.67E+01
9.72E+01
9.89E+01
1.01E+02
1.02E+02
1.03E+02
1.0SE+02
1.07E+02
1.01E-01
1.50E-01
2.23E-01
3.35E-01
3. 8 lE-Ol
5.69E-01
8.51E-01
1.27E+00
1.45E+00
2.16E+00
3.24E+00
3.30E-03
6.60E-03
1.31E-02
2.63E—02
3.29E-02
6.56E-02
1.31E-01
2.62E-01

3.28E-01 .

7.64E-01
3.06E+00
4.78E+00
1.9 lE+Ol
7.65E+01
4.84E-04
1.94E-03
7.57E-03
3.06E-02
4.80E-02
1.9 lE-Ol
7 .64E-01
3.06E+00
4.78E+00
1.91E+01
7.65E+01
4. 84E-04
1.94E-03
7.57E-03
3.06E-02
4.80E-02
1.9 l E-Ol
7 .64E-01
3.06E+00
4. 78E+00
1.91E+01
7.6SE+01
4.84E-04
1.94E-03
7 .57E-03
3.06E-02
4.80E-02
1.9lE-01
7 .64E-01
3.068+00
4.78E+00

68.33
47.27
0.09
0.09
0.12
0.15
0.16
0.21
0.32
0.46
0.50
0.60
0.75
109.30
62.20
58.60
49.05
48.26
47.26
46.43
39.95
37.55
30.92
26.98
2287.88
1692.42
963.98
713.52
585.69
436.92
316.86
204.35
176.03
111.21
72.89
0.12

6.25E+04
6.25E+04
L60E+05
160E+05
L60E+05
L6OE+05
LGOE+OS
L60E+05
L6OE+05
L60E+05
L60E+05
L6OE+05
L60E+05
L60E+05
L60E+05
L60E+05
LGOE+05
L60E+05
L60E+05
LéOE+05
L60E+05
L6OE+05
LéOE+OS
L60E+05
L60E+05
160E+05
L6OE+OS
L60E+05
L6OE+05
L60E+05
L6OE+05
L60E+05
160E+05
L6OE+05
160E+05
303E+05

1 77
3.14E+02
3.14E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
108E+02
3.0813+02
3.1 lE+02
3.1 1E+02
3JIE+02
3.1 lE+02
311E402
3.11E+02
3.1 1E+02
3.1 1E+02
3.1 lE+02
3.1 1E+02
3.1 1E+02
3J4E+02
3.14E+02
3.14E+02
3J4E+02
3.14E+02
3.14E+02
3.14E+02
3.14E+02
3.14E+02
3.14E+02
3.14E+02
3.08E+02

6.56E-01
1.31E+00
918E+01
9.34E+01
950E+01
9.67E+01
9.72E+01
9.89E+01
1.0lE+02
LOZE+02
1.03E+02
1.05E+02
1.07E+02
1.01E-01
1.50E-01
2.23E-01
3.355—01
3.81E—01
5.69E-01
8.51E-01
1.27E+00
1.45E+00
2.16E+00
3.24E+00
3.30E-03
6608-03
1.3 lE-02
2.63E-02
3.29E-02
6.56E-02
1.31E-01
2.62E-01
3.2813-01
6.56E-01
L31E+00
9.18E+01

1.91E+01
7.65E+01
4. 84E-04
1.94E-03
7.57E-03
3.06E-02
4.80E-02
1.9lE-01
7.64E-01
3.06E+00
4. 78E+00
1.91E+01
7. 6SE+01
4.84E-04
1.94E-03
7.57E-03
3.06E-02
4. 80E-02
1.91E-01
7.645-01
3.06E+00
4. 78E+00
l .91E+01
7. 65E+01
4. 84E-04
1 .94E—03
7. 57E-03
3.06E-02
4. 80E-02
l .9 1 E—Ol
7. 64E-01
3 . 06E+00
4. 78E+00
1.91E+01
7. 65E+01
4. 84E-04

0.21
0.25
0.33
0.33
0.41
0.55
0.69
0.60
0.74
0.99
170.66
87.49
76.43
75.69
86.81
84.56
69.58
56.77
43.06
34.67
26.57
1954.55
1106.06
629.12
404.95
333.03
286.19
164.38
153.31
158.10
124.15
72.55

3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.0BE+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3,035+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.0BE+05
3.03E+05
3 . 03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05
3.03E+05

1 78
3.081-:+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.08E+02
3.11E+02
3.11E+02
3.1 lE+02
3.11E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3.1 1E+02
3. 1 lE+02
3. 1 lE+02
3. 14E+02
3. 14E+02
3. l4E+02
3. 14E+02
3. 14E+02
3. 14E+02
3. l4E+OZ
3. 14E+02
3. 14E+02
3. 14E+02
3.14E+02

9.34E+01
9.SOE+01
9.67E+01
9.72E+01
9.89E+01
1.01E+02
1.02E+02
1.03E+02
LOSE-+02
1.07E+02
l.OlE-Ol
1.50E-01
2.23E-01
3355-01
3.81E—01
5.69E-01
8.51E-01
1.27E+00
1.45E+00
2. 16E+OO
3.24E+00
3.30E-03
6601-3-03
1.3 115-02
2.63E-02
3.29E-02
65613-02
1.31E-01
2.62E-01
3.28E-01
6565-01
1.3 lE+00

1.94E-03

7.57E-03

3.06E-02
4.80E-02
1.9lE-01

7 .64E-01

3.06E+00
4.78E+00
1.91E+01
7.65E+01
4.84E-04
1.94E-03
7.57E-03

3.06E-02
4.80E-02
1.91E-01

7.64E-01

3.06E+00
4.78E+00
1.9 1 5+0]
7.65E+01
4.84E-04
1 .94E-03

75713-03

3.06E-02
4.80E-02
1.91E-01

7 6413-01

3.06E+00
4.78E+00
1 .91E+01
7.65E+01

 

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