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This is to certify that the

thesis entitled

Control of Thermal Conductivity in
Electrorheological (ER) Fluid
Composite Materials

presented by

Yinxue Su

has been accepted towards fulfillment
of the requirements for

__M..S.._degree in MechanicaLEngineering

Major professor

Date

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

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Michigan State
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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU loAn Affirmative ActiorVEquol Opportunity Institution
W

m1

CONTROL OF THERMAL CONDUCTIVITY IN
ELECTRORHEOLOGICAL (ER) FLUID
COMPOSITE MATERIALS

by

Yinxue Su

A THESIS

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

MASTER OF SCIENCE

Department of Mechanical Engineering

1997

ABSTRACT

CONTROL OF THERMAL CONDUCTIVITY IN
ELECTRORHEOLOGICAL (ER) FLUID
COMPOSITE MATERIALS

By

Yinxue Su

A theoretical model that incorporates the thermal properties and electrical
properties with the ER effect is presented. The thermal conductivity of the isotropic ER
fluid is measured and the effect of temperature on the thermal conductivity is investigated
adopting a transient method. A new approach that is defined as internal heat generation
technique has been proposed and the thermal conductivity for the chain structured ER
fluid is successfully measured using this new method. The experimental results have
demonstrated that the water content and the temperature are the dominant factors
controlling the thermal conductivity of the ER fluid exposed to electric field. A high
thermal conductivity will be resulted if strong chaining can be established at low

temperatures.

ACKNOWLEDGMENTS

I would like to express my gratitude to my advisor, Dr. John R. Lloyd for his
thoughtful and patient guidance throughout my graduate program. I am deeply impressed
by his excellent guidance and his great personality. My master’s committee members, Dr.
Andre Benard and especially Dr. Clark Radcliffe who provided me with both equipment
and patient guidance will always have my sincere thanks.

My thanks go to the other members of our team that gave me their assistance and
their friendship, especially Gloria Elliott and Omar Hayes for their help. I would also like
to thank Craig Gunn for his help with the improvement of my writing skill and with the

writing guide for this thesis.

iii

TABLE OF CONTENTS

vi

vii

1 INTRODUCTION. . ......................................................................................... 1
2 ANALYSIS. .. 5
ER FLUIDS WITH ZERO ELECTRIC FIELD 5

ER FLUIDS EXPOSED TO AN ELECTRIC FIELD ................................ 8

The Energy Distribution 8

Equations for the Electric Field. .. l 1

Temperature Field Resulted from .Ioule Heat of a Single Sphere l4

3 EXPERIMENTAL APPARATUS AND TECHNIQUE ................................ 20
HOMOGENOUS ER FLUIDS” ....... 20
Experimental Apparatus... .. 20

ER Materials and Their Properties 2l
Experimental Procedure” .. . . 22

CHAIN STRUCTURED ER FLUIDS 25

Transient Technique... .. 25

Internal Heat Generation Technique 26

Theoretical Background... 26

Experimental Procedure 29

4 RESULTS AND DISCUSSIONS" 3i
SILICONE OIL AND ZEOLITE PARTICLE CALIBRATION 31
HOMOGENOUS ER FLUIDS. .. 32
Comparison Between Prediction and Measurement 32

Temperature Effect” 34

CHAIN STRUCTURED ER FLUIDS 36

Results from Transient Technique... . . 36

Results from Internal Heat Generation Technique... 37

ER Phenomenon” 37

Thermal Conductrvuy 42

S CONCLUDING REMARKS 50

iv

APPENDIX A ........................................................................................ 56

APPENDIX B ........................................................................................ 59

LIST OF TABLES

Table 1 Characteristics of Components of the Composite Specimen

Table 2 Thermal Conductivity of ER Fluid as a Function of Applied Electric Field (fv =
35% H20 WI.8%)

Table 3 Thermal Conductivity, A of ER Fluid as a Function of Applied Electric Field (fv =
10% H20 wt.19%)

Table 4 List of Available ER Fluids

Table 5 General Characteristics of ER Fluids (Gast and Zukoski 1989)
Table 6 Data for Fig.8

Table 7 Data for Fig.9

Table 8 Data for Fig. 10

Table 9 Values of Parameters and Their Variations

vi

LIST OF FIGURES

Fig. 1. Chain Structure of Zeolite/Silicone Oil Exposed to Electric Field

Fig. 2. Effect of Ratio of Particle-Fluid Thermal Conductivity on the Temperature Field
Around a Particle

Fig. 3. Effect of Ratio of Particle-Fluid Dielectric Constant on the Temperature Field
Around a Particle

Fig. 4. Ratio of Particle-Fluid Dielectric Constant vs Temperature (Data from Conrad et
al, 1991)

Fig. 5. Experimental Setup to Measure the Thermal Conductivity of Isotropic ER Fluid

Fig. 6. Experimental Setup to Measure the Thermal Conductivity of ER Fluid With
Electric Field

Fig. 7. Schematic of Temperature Field in Half of the Symmetry ER Assembly
Fig. 8. Thermal Conductivity of Silicone Oil

Fig. 9. Thermal Conductivity of Zeolite/Silicone Oil Suspensions

Fig. 10. Temperature Effect on the Thermal Conductivity, A. of Isotropic ER Fluid

Fig. 1 1. Electric Property Response of ER Fluid with Low Electric Field and High Water
Content

Fig. 12. Electric Property Response of ER Fluid with Low Electric Field and Low Water
Content

Fig. 13. Electric Property Response of ER Fluid with High Electric Field and High Water
Content

Fig. 14. Typical Temperature Profile of ER Fluid Exposed to Electric Field
Fig. 15. Temperature Fluctuation of ER Fluid at High Electric Field

Fig. 16. Dependence of the ER Effect on the Initial States

vii

Fig. 17. Transient Temperature Profiles for T and (T'TJ) at Positions of z = O and z = L

Fig. 18. A Correction to the Thermal Conductivity of the Structured ER Fluid with
Consideration of Joule Heat

Fig. 19. Temperature Profile of ER Fluid at High Electric Field
Fig. 20. Joule Heat and Electric Conductivity of ER Fluid at High Electric Field

viii

NOMENCLATURE

Arabic Symbols

a = radius of particle

Cp 2 specific heat capacity

D = diameter of the electrode plate

D = electric induction vector

e : exponential function

E = electric field vector

E = scalar electric field, kV/mm

fv = particle volume fraction

j = current density, A/m2

K,3 = effective thermal conductivity, K, = ~3—
f

L = the thickness of ER fluid layer, mm

q = Joule heat, kW/m3

qS = surface heat flux, W/m2

m = empirical coefficient in equation (2.3)

r = radius, m

r = radius vector

R = dimensionless radius, R = L

a

ix

T = temperature (C)

 

t = time
V = voltage
X = sensitivity coefficient
2 = the coordinate along the direction of electric field in ER fluid sample
Greek Symbols
(X = thermal diffusive coefficient
[3 = dielectric mismatch parameter, ,8 = ——
8 + 28
p f
B. = ratio of dielectric constant, [31 = i
f
. . . 11,.
B2 = ratio of thermal conductmty, fl, = —
A/
y = angle between r and E
E = dielectric constant
7t = thermal conductivity, W/mK
. . T - T...
9 = d1mens1onless temperature, 0 = ,, ,
E “0' Pa ‘ / A P
p = density
0 2 electric conductivity, S/m
Subscript

P

J

particle
fluid

Joule heat

xi

1 INTRODUCTION

Electrorheological (ER) fluids, are a member of the class of smart, intelligent, or
controllable fluids, and consist of a suspension of fine dielectric particles in a liquid of
low dielectric constant. ER fluids can have variable rheological, electrical, optical,
thermal, volumetric, and acoustic properties based on the character of the microstructure
of the fluid when controlled by the application of an electric field.

Since the discovery of this ER phenomenon by Willis M. Winslow (1947),
researchers have attempted to model the properties of ER fluids and have proposed
numerous applications that attempt to utilize their special characteristics. Such
applications include the operation of active suspension systems, vibration control
systems, hydraulic valves, and transmission systems. Most of these applications are based
on utilizing the controllable rheological property of ER fluid viscosity to engineer
systems where variable viscosity is desired. Examples of these applications include
automotive engine mounts (Hartsock et al. 1991, Petek et al. 1989, Williams et al. 1993),
vibration control devices (Coulter and Duclos 1989, Hartsock et al. 1991), variable torque
transmissions (Carlson 1989), dampers (Li et al. 1995, Morishita et al. 1995), and brakes

and clutches (Carlson and Duclos 1989). And the heat transfer application of ER fluids

began with Shulman’s early work (1982) where the ER fluids were utilized as a working
medium for a heat exchanger.

Numerous papers have recently been published concerning the state of the art of
ER fluid research and application. For example, a recent review can be found in the work
of Filisko (1995) and that of Block and Rattray (1995). Recent literature indicates that
many theories have been proposed to explain the ER effect, including the classical
Maxwell-Wagner-Sillars (MWS) interfacial polarization theory, the water bridging theory
(Stangroom 1983), the electrical double layer theory (Klass and Martinek 1967a, 1967b),
and theories that focus on the intrinsic chemistry and mechanisms of the ER materials
responsible for the ER activity. All of these works are aimed at enabling the design and
improvement of ER fluid performance in regard to commercial applications.

However, the commercialization of this promising technology is still hampered by
the lack of understanding of the materials and the mechanisms responsible for the ER
effect. The application of ER fluids in heat transfer control is even more elusive, due to
the poor understanding of the heat transfer mechanism associated with the ER
phenomena. The objective of the present work is to provide some insight into the physical
mechanism from the thermal aspect associated with ER effect.

Recently, interest in the area of control of the thermal properties of ER fluids has
increased. Upon application of an electric field, the particles in ER fluids form chains
between the two electrodes along the lines of the electric field and create preferred
pathways for energy transport. The micro-structure transitions result in changes in the

macro thermal transport properties such as thermal conductivity, convective heat transfer

coefficient, and radiate heat transfer transport. ER fluids provide a novel way to control
heat transfer processes.

There has been a very limited amount of research done on this novel concept, and
that has been accomplished by Shulman and his coworkers (Shulman 1982, Shulman et
al. 1986, Korobko 1992) at the Luikov Institute of Heat and Mass Transfer in Minsk, and
by Lloyd and Radcliffe and their research group (Lloyd and Zhang 1992 a, b, 1993, 1994,
Hargrove 1997, Elliott 1997, McGregor 1997, Omar 1997) at Michigan State University.

In Shulman’s work (1982), the ER fluid was composed of diatomaceous earth and
transformer oil, which have a thermal conductivity of 0.126 and 0.144 W/mK,
respectively. It is obvious that by linearly mixing these two phases, the maximum thermal
conductivity should not be larger than 0.144 W/mK. But they found up to a three-fold
increase of the thermal conductance of this particular ER fluid over the value of 0.144
W/mK with application of a strong electric field. What is the reason behind the 300%
increase? Is this phenomenon repeatable?

Lloyd and his group are involved in an extensive research program to explore the
applications of ER fluids in thermal control areas. In one of those works, Zhang and
Lloyd (1993) have demonstrated a 55% increase in apparent thermal conductivity with
the application of a strong electric field.

In thermal control applications, it is obvious that temperature is a very important
property to take into account, especially the effect of temperature on the properties of ER
material. Nelson and Suydam (1993) have advanced to the complexity of investigating

the temperature effect on the viscosity and concluded that the viscosity decreased as the

temperature increased, characterizing the fluid as temperature thinning. And in the work
of Conrad et al. (1991) and Conrad and Chen (1995), the temperature dependence of the
electrical properties and chaining strength of electrorheological fluids have been
investigated. They found that the strength of the chaining of the ER fluid increases with
increasing temperature, and there appears to be an upper temperature limit for the
increase in strength (occurs 120 — 150°C). The electrical conductivity and dielectric
constant of the particles increase with the temperature while the dielectric constant of the
silicone oil decreases slightly with temperature. They suggested that the increase of the
conductivity and dielectric constant of the suspension stems from the diffusion of Na+
ions in the zeolite particles as well as from the mobile charge carriers whose number or
mobility are thermally activated. There is no available information about the influence of
temperature on the thermal properties of ER material.

The present work focuses on the investigation of the physical mechanisms of ER
activity, especially in the thermal aspect. Theoretical analysis of the thermal conduction
process in the ER phenomenon will be performed and a new measurement technique for
the thermal conductivity will be presented. The measured results using different

techniques will be discussed.

2 ANALYSIS

It is appropriate to discuss here the general mechanism of thermal conduction in
fluids. When a temperature gradient is applied to a liquid for which a lattice structure is
assumed, the excess energy between layers transported down the gradient is transported
by convective and vibration mechanisms. Convective transport is accomplished through
the motion of molecules. While energy transport by vibration mechanism is the
intracellular and collisional contribution with the origin in the intermolecular forces. It is
found that the convective term is negligible compared with the intermolecular force
contribution (McLaughlin 1959). A higher thermal conductivity it can be expected with
higher intermolecular forces.

The energy transport mechanism should be different for the ER fluid with
randomly distributed particles as compared to an ER fluid with chained particles. These
two states of particle organization and their effective thermal energy transport will be

analyzed in the following sections.

ER FLUIDS WITH ZERO ELECTRIC FIELD
In the absence of an electric field, the suspension is taken to be a continuous

medium with particles randomly oriented. For such a system, a statistical method for

calculating the average properties of the suspension (Khusid and Acrivos 1995, Shulman
et al. 1982) may be used.

The equation developed by Shulman (1982) for metal-filled systems will be
adopted here to predict the effective thermal conductivity of the ER suspension. He

proposed the following

(2.1)

This equation coincides with a similar equation for the derivation of the Maxwell-

Wagner expression for the permittivity of a suspension (Dukhin and Shilov 1974):

8e_8f _ 8p_8f

—- . (2.2)
£e+28f 8P+2£f

This suggests that a relationship may exist between thermal conductivity and electrical
phenomena.
Similarly, Hamilton and Crosser (1963) suggested an empirical relationship for

the thermal conductivity of the medium with randomly dispersed particles

Ae—lf Ap—Af
:fv (2‘3)
Ile+(m—l)}.f Ap+(m—1)Af

 

 

where m is an empirical coefficient accounting for the anisodiametricity of the particles.
Also more involved models have been developed for the prediction of the

effective thermal conductivity of such kinds of system. Depending on the ratio of the

individual phase conductivity, the models are based on two categories of assumptions.

One is to assume linear heat flow (for the case of fig ~1), and the other is to assume
nonlinear flow (for the case of fig >>l or [32 <<1).

Based on the linear assumption, the following equation developed by Jefferson et

a1. (1958) is selected:

7: 7r (05+n)Ka
K, = l— , + 2
4(1+2n)‘ 4(1+2n) O5+nKa

 

 

(2.4)

where

2/32 2
K = ——1 ,—
" mug—Dz "B" [3,—1

n = 0.403 ff” — 05

 

This is valid for particle volume concentration fv < 0.52.
Based on the nonlinear assumption, an expression for effective thermal

conductivity accounting for this interaction for uniform size spheres in a cubic lattice

arrangement was derived by Rayleigh (1892). He used a second - order treatment

accounting for dipoles and octupoles only and his result is shown below

2+i82 +f _0525(1—/3,)f,‘0’3
l—fi, 4/3+[32

 

 

K, =1— 3 f,[ 1" (2.5)

This equation is valid for particle volume concentrations fV < 0.5236, and it is assumed
that the particles are uniform spheres.
Prediction from these empirical equations will be compared to the measured

effective thermal conductivity of the Zeolite / Silicone Oil suspension.

ER FLUIDS EXPOSED TO AN ELECTRIC FIELD

The Energy Distribution

It is well known that upon application of an electric field, the particles align into a
chain-like or fibrous structure roughly parallel to the field. (An example of the ER effect
of Zeolite / Silicone Oil suspension with fv = 5% and E = 1.5 kV/mm is shown in Fig. 1).
This unique structure transition from isotropic to nonisotropic, referred as the “Winslow
effect”, is the key to controlling the directional thermal conductivity since it has created
preference pathways for the energy transport. From a macroscopic point of view, the

electrostatic energy of a system of charged conductor or dielectric has been defined as

1
W = EJVD- EdV (2.6)

 

Fig. 1. Chain Structure of Zeolite / Silicone Oil Exposed to Electric Field

Khusid and Acrivos (1996) concede that in the case of non-conducting particles
and liquids, the electrostatic energy of a suspension is determined completely by its
dielectric constant and the particle concentration fv. This electrostatic energy includes the
various self-energies of the suspensions and the interaction energies to bring the particles
into chaining state and to maintain the ordered structure (Reitz 1967). This highly ordered
ER fluid, which is exposed to the external electric field, has lower entropy than that
without electric field. According to the second law of thermodynamics, the decrease in
entropy of a system has to be accompanied with energy dissipation, i.e. the structured
ordering of the ER suspension occurs at a cost in the energy loss. By Joule’s law, the heat

loss in the process is

10

(2.7)

Q
ll
5..
m

The total internal energy of the system is physically meaningful associated with
the microstructure transition when the fluid is exposed to electric field. To relate the
electrostatic energy and the heat loss to the total internal energy of the system, let us look

at the first law of thermodynamics for a reversible process

dul. = Tds + dw (2.8)

where 14,- represents the change in internal energy of the system, ds represents the
change in entropy, dw is the mechanical work done on the system, T is the absolute
temperature. The quantity Tds is the heat evolved into the system during process. It is this

heat evolution that results in an increase in the entropy of the system, i.e.,

ds = (j’E/T ) dv (2.9)

Thus, the energy transfer from the external electric power source and the heat
dissipation (q) play important roles in the microstructure transition of the ER fluid. In
order to look into this phenomenon in greater detail, we shall develop a microstructure-

based model for calculating the Joule heat in the suspension.

11

Equations for the Electric Field
Consider a dielectric sphere with a permittivity of 8p surrounded by a fluid with
permittivity of 8f. If we apply an external field of E on this system and we take the origin

of spherical polar coordinates at the center of the sphere, and the direction of E as the axis
from which the polar angle is measured, then we can expect the field potential outside the

sphere in the form of

of: -E-r + A E-r/r3 (2.10)

In terms of scalar quantities of r and E and the angle between r and E, which is defined

by y, we have

 

AE
of =—Ercosy+ , cosy (2.11)
r"

The first term is the potential of the external field imposed; and the second term, which
vanishes at infinity, gives the required change in potential due to the sphere. Inside the

sphere, the field potential is in the form of

¢P = -BE.r (2.12)

12

This is the only function that satisfies Laplace’s equation, remains finite at the center of

the sphere, and depends only on the constant vector E. On the surface that separates two
substances of different dielectric constant, certain boundary conditions must be satisfied.
Assume the surface of separation is uniform as regards physical properties. One can then

follow the equations of the electrostatic field for the individual phases

curlE = 0 and divD = 0 (2.13)

(where D = EE is the electric induction). This requires the continuity of the potential and

continuity of the normal component of the induction, i.e.

¢f /sulf/ = $1) [turf

8;) V¢p ' n /Surf = 8f V¢I ' n [surf (214)

Then the constants A and B can be determined as follows:

So

13

38,
E =———E (2.15)
" 2
£p+ 8,

It is evident from equation (2.15) that the field inside the sphere has the direction
of E and is uniform. It differs only in magnitude from the applied field E by a factor
which is determined from the permittivity of the individual phases. If the dielectric
constant of the particle is larger than that of the fluid, then the electric field inside the
particle will be reduced.

In scalar format, the field outside the particle is determined from

 

 

a . 3
Ef, =——&=E(1+20,fl)cosy
. &r r-
, (2.16)
3¢f (I‘fi .
E}. =————-=—E(l— ,)s1n}/
'y rdy r'

8 — e
where [3 = ——"——1— is the dielectric mismatch parameter.

8p+2£f

These equations for electric field of the system are consistent with those of

Khusid and Acrivos ( 1995). The thermal properties will be incorporated with these results

in the next section.

14

Temperature Field Resulted from Joule Heat of a Single Sphere

From experimental observation, it is found that for the pure ER liquid when
exposed to strong electric field, there is almost no temperature increase. This indicates
that no apparent Joule heat is created by the liquid. For an ER fluid system with
considerable particle concentration, a considerable amount of Joule heating is created. In
order to further understand how the existence of a large number of particles affects the
ER fluid system from a thermal aspect, it is important to see how the Joule heat created
by one particle influences the ER fluid system.

Consider the same system of one dielectric particle in the ER fluid as for the
electric field analysis. The thermal disturbance of the particle can then be investigated
from a microscopic point of view. A clue to solving this problem is based on the fact that
the electric conductivity of the particles is orders of magnitude larger than that for the
silicone oil (Conrad and Chen 1995); and if the particles are not sufficient in number to
influence the electrical properties of the liquid, then it is found that the Joule heating is
primarily created by this particle. Then the following energy equilibrium equations can be

acquired:

div 211, .grad 7”,, +j,,-E,, = 0

div 21 grad T1: 0 (2.17)

These equations are subject to the continuous boundary conditions

15

Tp /surf= Tf /3mf: 0; A1? VT}? ' n /smff= A(f VTf ' n lsmjf (218)

where n is a unit vector normal to the surface.

Also, from the analysis of the electric field, the heating term within the particle is
uniform due to the uniform electric field. Because of the geometrical symmetry of the
sphere and the fact that temperature is a scalar quantity which is completely characterized
by its magnitude; based in a spherical coordinate system, the temperature distribution
caused by this Joule heat source is a function of the radius only. The same is true for the
temperature field in the fluid since this temperature distribution is a result of the
disturbance of the particle.

Based on the relation of 0' = j/E and upon introducing the non-dimensional

temperature and other dimensionless parameters

 

1' )
°° R=—, [3,=—”, [3,=—’— (2.19)
a 8

the following non-dimensional governing equations for the particle and fluid phases can

 

be derived:

V26] :0 (2.20)

V26 +( 3 )2-0 (221)
” l3. 2 '

16

which are subject to the boundary conditions in dimensionless form

6;) /surf : 9f /5qu = 0; 182 V6]; ' ll /surf : V9] ' n /smf (222)

From equations (2.20 ~ 2.22), it is obvious that the imposition of an electric field
makes the thermal conduction behavior more complicated and that the process is
determined by several factors including the ratio of particle-to-fluid dielectric constant

and thermal conductivity. Solving the energy equations (2.20 ~ 2.21) yields

 

1 3 7 A, B
9p:—_6_(fi +2)"R’—?'+Bo (2'23)
1
9f :_%+Co (2.24)

where C0, C1, Bo, and B, are four constants to be determined. Boundary conditions at the
interface as well as another two additional boundary conditions, i.e. the finite condition in

the center of the sphere and the zero value condition as R—>oo, are applied to determine

these constants. Then finally, we have the solutions

1 3 , [3. 3 , 1 3
” 6(fi,+2) + 3 (B,+2) +6([3,+2) ( )

17

6 ___fi7(__3__)21

—~— — 2.26
1 3 [3,+2 R ( )

It is apparent that the nondimensional temperature fields for both the particles and
the fluid are functions of the ratio of particle-fluid thermal conductivity and dielectric
constant. Fig. 2 shows the effect of the ratio of particle-fluid thermal conductivity on the
temperature field around the particle. The value of E, = 2.5 is chosen since it is atypical
value for Zeolite / Silicone Oil suspensions. From Fig. 2 it can be seen that the larger the

ratio of the particle-fluid thermal conductivity, the larger the increase of temperature in

the field.

0.4

 

0.3 ,

Cb0.2

0.1

 

 

 

 

 

 

 

Fig. 2. Effect of Ratio of Particle-Fluid Thermal
Conductivity on the Temperature Field Around a Particle

With the value of [32 = Azeome / )VSiliconc 011 = 2.5, the effect of the ratio of particle-

fluid dielectric constant, [3, , is shown in Fig. 3. In contrast to the effect of the thermal

18

 

[32:028

 

 

 

 

 

Fig. 3. Effect of the Ratio of Particle-Fluid Dielectric
Constant on the Temperature Field Around a Particle

conductivity, Fig. 3 shows that the larger the ratio, the smaller is the increase in the

temperature.

 

    

 

 

 

20 2
15 >
q; 10 --
5 o E=0
r- E=1 (kV/mm)
, E=2 (kV/mm)
O 1 1 I
0 50 100 150 200

T (°C)

Fig. 4. Ratio of Particle-Fluid Dielectric Constant vs Temperature
(Data from Conrad et al. 1991)

19

The response of the dielectric constant of the particles and that of the fluid to the

temperature can be found in the work of Conrad et al. (1991). From the data they
provided, the behavior of [3, is shown in Fig. 4. The dielectric constant of the particles

increases with the temperature. The dielectric constant of the silicone oil is not thermally
activated, it only decreases slightly with increasing temperature. This can explain the ER
fluid design recommendation of stable electric constant for the liquid phase: As

temperature increases, [3, will increase, which will suppress the further increase of the

temperature (see Fig. 3). These two factors compete against each other during the
development of the ordered structure.

From the above calculation, a variation in the temperature field in the suspension
system is found because the electric field is able to penetrate into the particle and change
the thermodynamic properties. On the other hand for a good conductor, there is no
electric field inside it; and any change in its thermodynamic properties (such as entropy)
amounts simply to an increase in its total energy by the energy of the field that it produces
in the surrounding space. This quantity is quite independent of the thermodynamic state
(and, in particular, of temperature) of the body (Landau et al. 1984), and so it does not
affect the entropy and thus the order of the structure. This may explain why good
conductors (or poor conductors) when dispersed do not induce any measurable ER effect.
There are some reports of metal particle systems being ER active, but the strengths of the

effect are quite low (Filisko 1995).

3 EXPERIMENTAL APPARATUS AND TECHNIQUE

HOMOGENOUS ER FLUIDS

Experimental Apparatus

The experimental setup for measuring thermal conductivity of the ER fluids is
shown in Fig. 5. The apparatus consisted of several layers symmetrically positioned on
both sides of an electric heater. In the center of the assembly is a Kapton resistance heater
made of a layer of etched copper between two very thin layers of electrical insulation
material. The thin layers (L: 1.6 mm) of ER fluids were vertically confined between two
stainless steel plates by using a Teflon spacer. Two thermocouples whose beads were
electrically insulated by poly vinyl chloride (PVC) electrically resistant tapes were

imbedded into two sides of the stainless steel plates as shown. A Hewlett Packard DC

 

 

 

 

 

 

 

   

 

 

 

 

 

Power Supply
Computer \
Heater
Spacer
RS-232 ,
—( Electrode (4)
//
Thermocouple /L./
Data Logger 1; " ERF Sample (2)

 

 

 

 

 

 

 

 

 

 

Fig. 5. Experimental Setup to Measure the Thermal
Conductivity of Isotropic ER Fluid

20

21

power supply (HP model 2625) was used to provide a constant heat flux to the ER fluid
samples. A Hydra Fluke 2065 data acquisition system was connected to a 486 computer
through an RS-232 interface and was used to monitor and record the transient temperature
data from the thermocouples. The sides of the assembly were insulated as much as

possible in order to minimize the heat loss through the side normal to the heat flux plane.

ER Materials and Their Properties

A knowledge of the composition of such fluids and the properties of each
individual phase is essential for any analysis of the associated heat transfer phenomena.
Generally, the ER material is composed of three parts: a dispersion phase, a dispersed
phase, and additives including surfactants and fluidizers (see table 4 for list of ER
materials).

The dispersion could be selected from any insulating or polarized liquid, such as
mineral oil or lubricant, especially silicone oil, transformer oil, cable oil, or machinery
oil. The liquid should be non—conductin g, non-aqueous, and have low and stable dielectric
constant.

The dispersed phase may be chosen from silica gel, cellulose, and especially

aluminosilicate. The size varies from 10 nm to 200nm. Typically, ER fluids consist of

fine particles that have high a dielectric constant or conductivity.
The ER fluids employed in the present experiment were made of crystalline
zeolite particles (UNION CARBIDE) suspended in phenmymethyl polysiloxane silicone

oil (DOW CORNING). The viscosity and the thermal conductivity of the silicone oil is

22

0.0953 Pa-s and 0.14 W/mK, respectively. The information provided by the supplier
indicates that the chemical composition of the zeolite particles is
Na13[(AlgO3).3(SiOg).2]ngO with a maximum of 25 wt.% H30. The main factors
contributing to the overall ER effect are the concentration and mobility of the charge
carriers within the particles.

An ER fluid is prepared by first estimating the water content of the particles. This
is done by heating the as-received zeolite particles at a temperature of 500°F for two
hours (which is proved long enough to dry out all of the water) and then weighing the dry
particles quickly. The dry particles are put into a steam chamber for several minutes, and
the wet particles are weighed again. After the water content is thus estimated, the
particles are mixed with the silicone oil to make the ER fluid with a desired particle
concentration. The suspension is then stirred by a magnetic stirrer for approximately one

half hour to make a well-mixed ER fluid.

Experimental Procedure
Using the parameter estimation method, two properties (A. and pCp) can be

obtained simultaneously from a single experiment based on the governing equation

h)

it.“ 3.
81 dz (°)

 

Ix)

with initial and boundary conditions

23

T+(Z+,0) = 0
£222 :1 (3,2,
82
dT+(1,t+) : 0
£4-

The non-dimensional transient temperature is given by (Carslaw and Jaeger 1959)

 

 

l l 7 2 °° 1 :2.
T+=t++——Z++— Z+‘—— —e"’”’cosn71:Z+ 3.3
3 2( > fig", ( > ( >
where
«1» T—Yfi +_ +__Z_
qL/A’ L“

From the above, the non-dimensional sensitivity coefficients X :2 can be

obtained. From these data we can estimate the approximate magnitude of AK~AT before

performing the real experiment

x:, = 2511 (3.4)
' d/l qL

24

Here, subscript l, 2 denotes z = 0, L, respectively. It was found (Beck and Arnold 1977)
that as t)r exceeds 1, X f , and X 2* asymptotically approach -0.333 and 0.167. This finding
helps us to determine the necessary heating time to satisfy the t+=1 condition and hence

the maximum XE, . For our experiment, 01 = 3.6><10'8 m2/ 5, L = 1.6 mm, then t = 70 sec.

Therefore, we set t = 1 10 sec. in every measurement. The difficulties involved in property
estimation for low conductivity materials such as liquids are shown through equation
(3.4). Small errors found in temperature measurement could easily distort the measured
value of the thermal conductivity, 1. Special effort must be made to minimize the
temperature measurement errors in the experiments.

A parameter estimation program PROPlD (Beck 1989) was employed to deduce
the thermal conductivity and volumetric specific heat. Parameter estimation minimizes a
least square error function, 5, with respect to the parameters to be estimated.

Mathematically. this involves the minimization of

S = [Tmea ' cal (r)]tran[T"wu ' Tall (F)]

where the subscript mea denotes measured data and col denotes calculated values
computed from a one-dimensional heat conduction equation with prescribed boundary
conditions and an estimated property value vector. The subscript tran denotes the

transposed matrix. The true value of 1" was obtained through an iteration process. An

arbitrary initial value was assumed for F, and its value was updated at each of the

subsequent iterations until convergence was obtained.

25

CHAIN STRUCTURED ER FLUIDS

Transient Technique

Traditionally, the thermal conductivity has been measured by the previously

described transient technique with the experimental setup shown in Fig. 6.

After filling the assembly with the ER fluid, the ER fluid is left for 30 minutes to

eliminate the air bubbles residing in the fluid. An electric field is then applied across the

ER sample. If the current flowing through the ER fluid is low and has leveled off, the

heater in the center of the experimental assembly is turned on; and simultaneously, the

temperature is recorded as a function of time. After 70 seconds, the heater is turned off,

and the temperature is still recorded for another 40 seconds. The thermal conductivity of

the chained ER fluid is determined by calculating the input heat flux and by using

PROP 1D. This method has been used by Zhang and Lloyd (1993), and by Elliott (1997).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NI-DAQ , .
Computer Amphfier/Supply Heater/Electrical
Insulator
RS-232 /Teflon Spacer (2)
' 1—1 Electrode (4)
//7
Th ‘ l .

Data Logger ”mom" 6 \\\ERF

fl Sample (2)

Fig. 6. Experimental Setup to Measure the Thermal
Conductivity of ER Fluid with Electric Field

26

Internal Heat Generation Technique

Theoretical Background. As the electric current passes through the ER sample,
the ER fluids rise in temperature and dissipate heat. When the ER fluids are exposed to
high electric fields and if significant current flows through the fluid, there exists a heat
source within the volume of the sample. From the open literature and from our
experimental observations, it is found that for a given electric field, the current density
increases with time at the first stage of the experiment, and then as time moves on it
levels off indicating the heat source in the ER fluid or the fluid state remains constant.
When the system reaches a steady state, the thermal conductivity of the chained structure
ER fluid can be determined. This is illustrated in more detail as follows.

The experimental setup for this volume heat source technique is the same as the
one shown in Fig. 6. Here, the heater in the center of the assembly has been replaced by
an electrical insulator. The Joule heat generated in the ER fluid is used as the heat source
to measure the thermal conductivity, and it is obtained by measuring the current density
and the applied voltage. In order to satisfy the one-dimensional conduction condition, a
value of 21 is chosen for the ratio of the diameter of the electrode to the distance between
the two electrodes. The round sides of the assembly have been insulated as much as
possible to minimize the side heat loss. The ER sample has an insulated boundary
condition on one side and a natural convection condition on the other side, which will

ensure the one-dimensional conduction process.
At the first glance at the energy equilibrium equation, it seems hard to measure 2»

without measuring the temperature distribution within the ER sample to get the value of

27

2— “5

— W. However, solving equation (3.5) with the appropriate boundary
- “Z

conditions makes this possible.

IQ

8

 

t T+j-E=0 (3.5)

If we assume that at steady state, the thermal conductivity, 2. is a constant, we can

obtain the temperature field as follows:

1'5 2
Tz—fiz +a,z+ao (3.6)

From the design of the experiment, at z = 0, an insulated boundary is imposed,
which makes (1, equal to zero. The unknowns k and a0 can then be determined by
measuring the temperatures at the boundaries of z = 0 and z = L, denoted as T0, and T),-

respectively. Thermal conductivity, 2», can then be evaluated from the equation:

.)

jEL‘

.—_————— 3.7
2(701' ‘— TLi) ( )

In the present experiment, due to the application of the high electric field, and

because of the requirement to electrically insulate the thermocouple from the fluid, the

28

thermocouple is embedded on the outer sqrface of the electrode. Therefore, the quantity
measured is To and TL (though To = To,- in our case). This is illustrated as follows in Fig. 7
by considering half geometry of the ER assembly. A correction for the evaluation is made

as follows in order to minimize the error associated with the model.

To

 

 

11']
7/1/ IZI

 

z = L z = 0 (Center Line)

Fig. 7. Schematic of Temperature Field in Half
of the Symmetry ER Assembly

Here

(113)., L2

'15 .6
2((7i) '— 72.)” _ "(J/1 )M

,1:

 

(3.8)

 

)

5166/

where the subscript st refers to the value at steady state, and 5 and Med refer to the

thickness and thermal conductivity of the stainless steel electrode. The thermal

resistances for the components used in the composite specimen of the assembly are listed

29

in Table 1. It can be seen that compared to that of the ER fluid sample the thermal

resistance of the stainless steel is negligible.

Table 1. Characteristics of Components of the Composite Specimen

 

 

 

Thickness, Thermal Thermal Resistance, 8/?»
5(mm) Conductivity, 7t (10 4 mzK/W)
(W/mK)
Stainless Steel 0.45 14.7 0.3
ER Fluid 1.6 O. l 6i0.01 106.3

 

 

 

 

 

 

Experimental Procedure. A LabVIEW VI program has been written up for the
data acquisition and processing in the measurement. The control of the applied voltage
and the data recording of the current and voltage are realized by sending commands in the
LabVIEW VI program and through the NI-DAQ interface.

An ER fluid is prepared in the same way described in the previous two sections.
About 30 minutes after the assembly is filled with the well-mixed ER fluid, an electric
field is applied across the ER sample. By using the LabView program the temperature,
the voltage across the ER fluid layer, and the current flowing through the ER fluid were
recorded simultaneously as functions of time.

When the current as well as the temperature (or temperature difference) levels off,
it is assumed that the system has reached its steady state. The Joule heat is calculated
from the product of the electric field and the current density at steady state based on

equation (2.7). The thermal conductivity is determined based on equation (3.8). This

30

procedure is repeated for the fluids with several particle concentration and at different

levels of electric field.

4 RESULTS AND DISCUSSION

SILICONE OIL AND ZEOLITE PARTICLE CALIBRATIONS

To confirm the reliability of the experimental system, the thermal conductivity of
the silicone oil was measured by both transient and steady state methods. Transient
methods allow faster determination of the thermal conductivity. The value is obtained
from the rate of the establishment of the thermal gradient in the suspending medium

system. While, in steady state methods, the value is determined from the final thermal

0.18

 

0.14 3% ......... é ........ é ......... A ......... fl:

 

 

Thermal Conductivity (W/mK)

 

 

 

 

 

0.1 0
T- u Steady State Method
0.05 A Transient Method with 95%
Confidence
------- Literature Value .
_ __1
0.02 '* ‘ '
1 2 3 4 5

Test

Fig. 8. Thermal Conductivity of Silicone Oil

31

32

gradient which takes about four hours to establish. Both of the experiments were
conducted with the same heat flux of 478 W/mz.

Fig. 8 shows the results from several experiments. It is shown that the discrepancy
between the results from PROPID and those from steady state are negligible. The
measurements exhibit very good repeatability. Furthermore, the value is close to that
given by the supplier (0.14 W/mK).

Zeolite particles exist in the form of a powder. In order to measure its thermal
conductivity the first step is to put the zeolite powder into the test assembly. After
packing the powder as much as possible the zeolite in the assembly looks like a solid. The
assembly is then closed for the measurement process. The rest of the procedure for the
measurement is very similar to the measurement of the thermal conductivity of the
silicone oil and is done by transient method and determined by PROPlD. The value

comes out to be 0.039 W/mK which is very close to the literature value, 0.04 W/mK.

HOMOGENOUS ER FLUIDS

Comparison Between Prediction and Measurement

The thermal conductivity of the ER fluids with zero electric field was measured
using the transient method. The results are shown in Fig. 9. It shows some discrepancies
between the calculated values from equations (2.1) and (2.5) and the measured values,
while the discrepancies between prediction from equation (2.4) and the measured value

are smaller. Interestingly, the prediction of equation (2.1) and that of equation (2.5)

33

 

 

 

 

 

 

 

 

 

 

3:
IE _
0 1.2 I
3 -
g I: I z
"a 0.8 \
E 32 3:
a \
F 1 Eq 21
g 0-4 mini
23 Eq. 2.5
g 1 A Measurement
LU 0 2 2
1— LD U) U)
o' 04 m V.
O O 0

Fig. 9. Thermal Conductivity of Zeolite/Silicone Oil Suspension

happens to be almost the same. It is of pragmatic importance to study the possible
reasons behind these discrepancies and coincidences.

From the agreement between the prediction of equation (2.4) and the
measurement and from the fact that equation (2.4) is based on the assumption of linear
heat flow in the fluid, we can infer that the heat flow in the ER suspension with no
electric field is linear. The model from the statistical method and the model that accounts
for only dipoles and octupoles under-estimate the thermal conductivity of the isotropic
ER fluid at the same scale. Obviously higher orders of interaction between the particles
must be considered for the isotropic ER fluid.

One of the possible reasons for the relatively high thermal conductivity of the ER
fluid is the special structure of zeolite particles as described previously. For pure
particles, the open channels of the framework are filled with air, which has a thermal

conductivity of only 0.026 W/mK. Actually, the air makes a large contribution to the low

34

thermal conductivity of the zeolite crystal (0.04 W/mK). When dispersed in the silicone
oil, the channels are occupied by the oil whose thermal conductivity is 0.14 W/mK.
Besides, when the suspension becomes dense, the particles come into close contact; and
the intermolecular forces will increase to an extent which will draw the particles together
into tighter contact and this will result in higher thermal conductivity.

Another obvious reason is the existence of water in the solution. The addition of
this third component can cause considerable change to the properties. The thermal
conductivity of water is about 0.59 W/mK, which is much larger than that of the zeolite
and of the silicone oil. Little information can be found to theoretically predict the
effective thermal conductivity for such a three-component system. As a qualitative

analysis, assume H20 wt.5% in the solution, then the effective thermal conductivity is

2., = 0.05 x 0.59+0.95 X 0.14 = 0.16 (W/mK)

which indicates that the existence of water can result in a higher thermal conductivity of

the wet fluid.

Temperature Effect
Changes in temperature due to electrical power dissipation in the fluid may
significantly change the properties of an ER fluid. Understanding the temperature effect

on ER properties is critical to further predict the ER behavior.

35

 

0.15;. E

 

 

 

 

 

 

 

i
Q i i § § $-
E 0.1
g I I
a:
0.05 .fv: 35% water wt.8°/o
.fv =5°/o water wt.9°/o
O 1 1 1
24 34 42

T (00)

Fig. 10. Temperature Effect on the Thermal Conductivity, 7»
of Isotropic ER Fluid

The temperature dependence of the thermal conductivity of a uniformly dispersed
ER fluid over the range of 24°C - 50°C is shown in Fig. 10. It shows that the thermal
conductivity decreases slightly as the temperature increases. This phenomenon is similar
to the viscosity property, which decreases as the temperature increases, and it indicates
that the fluid is temperature “thinning” (Nelson and Suydam 1993).When the temperature
increased from 24°C to 50°C, the thermal conductivity decreased from 0.13 W/mK to
about 0.08 W/mK for fluids with fv = 0.05, and from 0.15 W/mK to 0.10 W/mK for fluid
with fv = 0.35.

This result contrasts with the response of the electrical conductivity and dielectric
constant ( Conrad et a1. 1991, Conrad and Chen 1995) and is unexpected. If the electrical
conductivity and dielectric constant changes as a result of the diffusion of Na+ ions in the
zeolite particles and the mobile charge carriers whose number or mobility are thermally

activated, then a higher thermal conductivity should be expected since there are more

36

energy carriers at higher temperature. But the result suggests that prior to the application
of an electric field the isotropic ER fluid behaves like a “regular” liquid, i.e. the viscosity
as well as the thermal conductivity of the fluid decreases with increasing temperature.
Though the fluid contains ions and charge carriers, the thermal conductivity

is still different from the system with charged-particles, such as liquid metals with
abnormally high thermal conductivity. In liquid metals, according to Wiedemann-Franz-

Lorenz law, the value of NOT is almost a constant, which indicates that the current

carriers are electrons and that the current carriers must also be important in heat
conduction (Tye 1969). In a word, for the isotrOpic ER fluid, the roles of the ions and

other charge carriers are not dominant in the heat conduction process.

CHAIN STRUCTURED ER FLUIDS

Results from Transient Technique

Part of the data obtained by the transient technique is shown in Table 2. It
demonstrates a 37% increase in thermal conductivity with application of an electric field.

Zhang and Lloyd (1993) using a similar ER fluid found a 55% increase. In the application

Table 2. Thermal Conductivity, 7» , of ER Fluid as a Function
of Applied Electric Field (fV = 35% H20 wt.8%)

 

 

 

E (V/mm) Average 2» (W/mK)
Temperature (°C)

0 25 O. l 6i0.01

500 35 O. l9i0.01

 

1000 35 0.221001

 

 

 

 

 

37

of transient technique, the thermal conductivity is determined from the transient
temperature gradient and the heat flux supplied by the heater. The Joule heat, which
composes of part of the heat flux being conducted out, has been omitted. Therefore, the

transient method has under-predicted the thermal conductivity of the chained ER fluids.

Results from Internal Heat Generation Technique

ER Phenomenon. Traditionally, the ER effect was reflected by the electric
current density. For our study, when an electric field was applied to the ER fluid, three
types of current profiles (versus time) were found, as shown in Figs] 1-13. With a low
electric field, the current density increases exponentially to reach a constant (Fig.1 1), or
increase exponentially to reach a peak value then slightly drops down to reach a constant

(Fig.12). The temperature increase in the fluid caused by Joule heat is small (usually less

 

 

 

 

 

 

 

 

 

3o , 1
, 25 O
a
2? IE w
2 5‘ 8 E 20 'o'
g 2 E (7) is E
,. 2 o '2 1: E
C E 0 2 15 O \
93 “.9 V '5 i
5 T: ° 0 V
o 8 10 g
a _.._.___.._ 2-
5 L“520% H20 wt.23°/o
0 0
0 12 24 36 48

Time (min)

Fig.1 1. Electric Property Response of ER Fluid with
Low Electric Field and High Water Content

 

38

than 10°C), which is far below the boiling point of water. These two types of response are

basically stable since the water content remains approximately constant.

 

16 1

 

 

 

 

 

 

 

N
>2
23 E 12 i E 06
'2 m 8 E ' 2‘ A
a) E '0 (7) .9 E
E E 0 ° é’ 3
93 :9. 5 23 5
3 § ‘3 . 0.2 £1”
E 4 ,
f,=20% H20 wt.8%l
1
O : 1 a 1 ‘ ' - 1 ‘ ' -O.2
1 23 46 69 92 115
Time (min)

Fig. 12. Electric Property Response of ER Fluid with
Low Electric Field and Low Water Content

When the electric field is high (in Fig. 13, E = 0.75 kV/mm), the current density
shoots up sharply at the first stage of the experiment and reaches the current limit of the
amplifier (here 5.0 mA). In the meanwhile, a large amount of heat is created within the
fluid, which causes pronounced temperature increase (from 23°C to 84°C after 46 minutes
of heating , see Fig. 14). This result strongly depends on the water content.

From this experimental observation and the analysis in chapter 2, we can see that
at first, the ER effect is caused by the application of the external field. As long as the
Joule heat is created and the ER fluid is subject to a thermal disturbance, the thermal

properties and electric pr0perties of the ER material, and the water content will vary if the

39

 

 

 

 

 

 

 

 

 

 

2.5 0.8
o

- 2 ,
>2 1:3 0.6
72’ § E 1 E ‘73?

6‘1, \ .5 r v v ._

8 E g g) . ‘\ 041-:-> E
jg 3,0 '0 J '5 i
s g o 5 L”
O a)

E 05 7 0.2

' f,=20% H20 wt.23% J
o . 1 * . o
O 11 22 33 44

Time (min)

Fig. 13. Electric Property Response of ER Fluid with
High Electric Field and High Water Content

100

 

    

 

 

 

 

 

 

l
20 ' LfV=20°/o H20 wt.23%
O i 1 1 l l l J i
O N V (D (I)
v- N co v
Time (min)

Fig. 14. Typical Temperature Profile of ER Fluid Exposed to Electric Field

temperature increase is considerable, which in turn will influence the local electric field
of the ER system as well as the strength of the chaining. As the ER effect varies, the
temperature field begins to change, and a new cycle of the adjustment of all of the

parameters will start again. The cycle will continue until all of these mutual effects have

 

40

 

 

 

 

 

 

 

 

 

120
100
<29 80
'—
z = L
60 -- fv=20% H20 wt.8°/o
E=1.187kV/mm
4o . 1 . 1 1
N G) V O (D N
(‘0 V (O (1) CD :

Time (min)

Fig. 15. Temperature Fluctuation of ER Fluid

reached a compromise status where the steady state is reached. If the competition
between these parameters are comparable, it may result in a slow sine-wave like
temperature fluctuation as was measured and is shown in Fig. 15. Typically, it takes three

hours for the Zeolite/Silicone Oil ER fluid to reach steady state.

m- f. 1

 

 

 

 

 

 

 

 

 

- 120 [—f‘; 200/0 H20 Wt.23cyo
_ g E . 0.8
é‘ é A
D 2 S f,” 80 o 0.6 ‘6 A
‘E E 0 $2 . E E
93 :2 V j “- E
5 3: 5 r'—'—"'“‘—“ 04 .2 3
0 8 z 35,
_ — 0
UJ 40 r“ 2 m
0.2 L“
O L__1. . 1 __l . .1 -1- ., J_._1_4_ __L| 0
0 14 27 41 54 68 81
Time (min)

Fig. 16. Dependence of the ER Effect on the Initial States

 

41

The effect of the ER fluid strongly depends on the initial state of the fluid. This
fact is demonstrated by turning the electric field off for a minute and then turning on
again. The effect of the initial structure on the current density of the ER fluid is shown in
Fig. 16. It shows that when a same E is applied to the ER fluid, which has exposed to the
electric field previously, a lower current density results. In order to make the results
comparable, initial conditions for the measurement should be taken into account for all of
the measurement of the thermal conductivity of the ER fluid.

It can provide a useful insight into the ER phenomenon to look back to the work

of Adrian and Gast (1988) where they have introduced a parameter, C, that expresses the

ratio of polarization to thermal forces

 

(4.1)

Here a is the radius of the particles, k3 is Boltzmann’s constant. They found that
electrically determined structures were likely to occur only if the electrical forces can
overcome the thermal forces. Obviously, the ordered structure of the ER system is caused

by the external electric field. Only in the in the limit C>>1 can an effective ER effect

occur. Based on this model, when a temperature increases due to the application of an

electric field, the polarizability must also increase in order to maintain the value of l; to a

 

42

certain value. Only the material whose properties satisfy this condition can be applied as

ER materials. This can be one of the clues for the design of ER materials.

For the case where the fluid dielectric constant, 8f remains about constant during
the process, the only variables we are interested in are E2 [32/1~ . The value for the
dielectric mismatch parameter, [3, can be obtained from the work of Conrad et al. (1991)

for this particular case (temperature shown in Fig. 14). As the temperature increases from

23°C to 84°C, E2[32/I~ changes from around 5.7><10"1 to 4.1x10'4, thus indicating that the

ratio of the polarization force to the thermal force is decreased, and an electrically
induced ER fluid chain structure may not be maintained or might break down. For this

case a very low thermal conductivity (7t = 0.06 W/mK) results.

This result is in contrast with the observation by Conrad et al. (1991) where they
found that the strength of the chaining of ER fluid increased with temperature. However,
the present result is consistent with the work of Oyadiji (1995), in which he found that the

shear modulus of the ER fluid decreased with the temperature increase from 0 to 60°C.

Thermal Conductivity. There are several factors such as water content,
temperature, and ER effect that determine the thermal conductivity of an activated ER
fluid. Among those parameters, the effect of temperature together with the ER effect is
the dominant one. If strong chaining can be obtained at low temperature, then the ER
fluid at that state has a high thermal conductivity and the result will be more repeatable.
The data for the fluid of fv = 10% with H20 wt. 19% is shown in Table 3. These data have

shown a 83% increase in the thermal conductivity when an electric field of 250 V/mm is

43

Table 3. Thermal Conductivity, A , of ER Fluid as a Function
of Applied Electric Field (fV = 10% HZO wt.19%)

 

 

 

 

E (V/mm) J (mA/mz) Average 9. (W/mK)
Temperature (°C)

250 (run 1) 339.6 30 0.27:0.05

250 (run 2) 311.4 30 O.28i0.03

0 o 27 0.15:0.01

 

 

 

 

 

 

applied across the ER fluid and it has shown a good reproducibility. Note here the electric
field is very low.

Refer to the data shown in Table 2, for example, at an electric field of 1000
V/mm, the thermal conductivity enhancement is 37% based on the transient technique
without considering the Joule heat. However, for the ER fluid exposed to an electric field,
in addition to the surface heat flux, q, , supplied by the heater that has been intentionally
turned on to established a transient condition, a volumetric heat created by Joule heat

should be included in the heat equation

8T WT
”PTA?

+ q (4.2)
where q is the Joule heat. For the experimental sample in the transient technique, the
surface heat flux is supplied after the chaining is developed. If q is considered to be

constant at the time the measurement is being taken, then q represents an initial heat

44

exchange and may depend on 2, but is independent of time. Because of the linearity of the
differential equation (4.2), q and q, produce independent temperatures T1(z) and Ts(t, 2).
Therefore, the initial steady-state temperature distribution T](Z) satisfies the steady-state

equation of (3.5) which will be shown here again in the format as follows

I-J

ar,

, +q=0 (4.3)

A

 

Subtracting equation (4.3) from equation (4.2), and based on the fact that T;(z) is

independent of time, we have

flT—L):A&%T—L)

C_______
p" a: 3x2

MA)

This indicates that the actual thermal conductivity of the chained structured ER fluid
should be determined based on the transient temperature T- T;(z) if we will use transient
technique. Here T](z) is already solved in Chapter 3 and shown in Fig.7. It is possible to
make some corrections to the results from the transient technique.

It is useful to utilize a specific example in Table 2, for example with application
an electric field of 1000 V/mm, a thermal conductivity of 0.22 W/mK is determined

based on equation (3.1) which will be shown here again in the following format

 

 

45

(4.5)

Recall that the final value of the thermal conductivity was determined based on the

surface heat flux q, and from the transient temperature profiles (T in Fig. 17).

28
27
g), 26
93
3
E
m 25
Q.
E
(D
'—
24
23
22

 

Measured {at}:

Measured Tafz 77: l: i
\X . _- . -__—_.__j

    
 

 

O\

‘(T-TJ)atz =0

"(1— :T, 1 at": ; L ‘

 

 

50 70 90

Time (s)

Fig. 17. Transient Temperature Profiles for T and (T-Tg)

at Positions of 7. : 0 and 7. = L

The transient temperature of T(t,z) - T;(z) can be obtained by subtracting the

temperature value TJ(Z) at z = O and z = L (denoted as T;(O) T;(L) ) from the measured

temperatures T. Based on this corrected transient temperature gradient and using

PROPID program, the actual value of the thermal conductivity of the chained structured

ER fluid can be estimated. It is obvious that T;(0) > TJ(L) (Fig. 7). and these values are

 

46

independent of time. In the transient technique, the results are very sensitive to the value

of temperature difference between the two electrodes, AT, a decrease in AT will result in
a high value of 71... The temperature difference used in the case with consideration of Joule
heat ( A(T‘T]) in Fig. 17) is smaller than that in the case without consideration of Joule

heat (AT in Fig. 17). Therefore with the corrected temperature profiles, a higher value of

thermal conductivity is obtained.

 

032 - -

 

Corrected Thermal Conductivity

 

 

02 1 4 1 1
0 20 40 60 80 100
Joule Heat q (kW/m3)

 

Fig. 18. A Correction to the Thermal Conductivity of the Structured ER
Fluid with Consideration of Joule Heat

The calculation for consideration of several values of Joule heat in the previous
case is shown in the Fig. 18. It is seen that with consideration of Joule heat, a higher value
for the thermal conductivity can be obtained based on the level of the Joule heat. For
example, if a Joule heat of 80 kW/m3 (estimated from Table 3) is considered, a corrected
value of 0.31 W/mK can be expected, instead of a value of 0.22 W/mK which is

determined by the traditional transient technique without consideration of Joule heat. A

considerable error is involved due to the neglect of Joule heat.

 

. ‘-

-xlfll "' 'v'. .‘ 11-

 

47

In dependent of the measurement techniques, it requires that the data be
reproducible. The data in Table 3 are repeatable because the current is low; thus, the
temperature increase caused by Joule heat is under low level and the structure of the fluid
is under control. In order to obtain good and reliable data, the humidity and temperature
of the environment should be well controlled for ER fluid with water as an important
activator.

As the temperature increases to a high value, the measurement of the thermal
conductivity becomes difficult since the water in the ER fluid can evaporate off. A certain
volume of ER fluid may be boiled out depends on the temperature level. This result is not
repeatable without good control of the humidity and temperature of the environment.
Measured results from several experiments running at high temperature show a very low

thermal conductivity When the temperature is very high, the value for k at the

corresponding state is counteracted by the “thinning effect” caused by the temperature

 

 

 

 

 

 

 

120
100
a 80
a,
*' 60
"l
40 r f, = 20% H20 wt.23°/o
20 1 1 1 1 J : 1 1
O V 00 N (D O
N V 1\ O) ‘0‘.
Time (min)

Fig. 19. Temperature Profile of ER Fluid at High Electric Field

 

48

 

 

 

 

 

 

 

 

800 2
O
6‘ 1.6 ,
E 600 q 2‘
g E “J.
i 12§€%A
? 'EEEE
a 400 1,-— 8 'o .2 3
Q) C 5 x
f, 0.8 fr; 5 § V
3 E 8 L“
2 200 —‘ 1T1
0.4
X in: 20% H20 “11.23% ,
a
0 1 1 [—1 g 1 1 1 1 O
1 29 58 86 115
Time (min)

Fig. 20. Joule Heat and Electric Conductivity of ER
Fluid at High Electric Field

increase therefore its value is very low. A calculation shows )1 = 0.039 W/mK for the

fluid of fy = 20% H20 wt.23% when this fluid is exposed to high electric field (see Figs.
19 ~ 20 for temperature and electrical property response).

Similar to the discovery about the diatomaceous earth / oil suspensions (Shulman,
1982), at high temperature, the ER effect decreases due to desorption of the activator
from the particles to the continuous phase, the loss of water in the present Zeolite/
Silicone Oil suspension also cause the decrease of ER effect. This also indicates that the
current level is not the equivalent of ER effects. This is the reason for the fully chaining
ER fluid, the overall thermal conduction is enhanced to a large extent depending on the
micro structure states of the ER suspensions. With the ER fluid exposed to electric field,
the contribution of the transport of ionization energy to thermal conduction should lead to

a high value of the thermal conductivity in the ER fluid. On the other hand, as

 

49

temperature increases, the Brownian motions will prevent the energy transfer between the
particles.

When a high electric field is applied upon the wet ER fluid, the temperature of the
ER fluid is increased dramatically from 25°C to over 120°C. The particles alignment
between the two electrodes has resulted in solid-like material, while the foam-like liquid
are flowing out of the chamber, then after temperature reaches a very high level and some
of the water has been boiled off, what left on the chamber is cone-like solid. Each
experiment should start with clean apparatus using fresh fluid in order for the results to be
comparable.

Another point which deserves to be discussed is the air bubbles in the fluid. If
considerable number of air bulbs exit in the fluid, these bulbs can be a source of more
bulbs when electric field is applied, which will make the thermal conductivity reduce to a

very low value (0.02~0.06 W/mK). Therefore it is very important to make sure that the air

is dissipated out completely before application of electric field.

From the above discussion, it can be inferred that the thermal conductivity of the
chain structured ER fluid strongly depends on several factors such as water content,
temperature, electric field, and ER effect. Among these, water content and temperature
are the dominant factors controlling the thermal conductivity of the ER fluid exposed to
an electric field. The higher the temperature, the lower the thermal conductivity; the
stronger the chaining, the higher the thermal conductivity. An optimum water content
should make it possible to form strong chaining at low temperature in order to enhance

the heat conduction.

5 CONCLUDING REMARKS

The theoretical analysis about the temperature field caused by the Joule heat of the
particles and the experimental evidence that incorporate the thermal properties and
electrical properties into the ER effect have provided a good understanding of the
mechanism for the development of the chaining.

Transient method has been proved to be appropriate for the measurement of the
thermal conductivity of silicone oil and isotropic ER fluid. The investigation of the
temperature effect on the thermal conductivity of the isotropic ER fluid has shown that as
the temperature increases, the thermal conductivity of the isotropic ER fluid decreases.

A newly-proposed measurement approach - internal heat generation technique,
which uses Joule heat as the power source, has been successfully used to measure the
thermal conductivity of the chain structured ER fluid. It is found that water content and
the temperature are the dominant factors controlling the thermal conductivity of the ER
fluid exposed to an electric field. The higher the temperature, the lower the thermal
conductivity. The measured results have manifested an augmentation of heat conduction
(83% increase in the thermal conductivity when an electric field of 250 V/mm is applied

across the ER fluid) when strong chaining is formed at a low temperature.

50

51

In order to make full use of the ER fluid which uses water as an activator, further
research work is needed and should focus on the control of the water content of the ER
fluid and the control of the temperature of the ER fluid during the development of the

chaining.

BIBLIOGRAPHY

BIBLIOGRAPHY

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55

 

APPENDICES

Table 4 List of Available ER fluids

APPENDIX A

 

Particles

Corn Flour

Corn Starch

Starch

Zeolite

Zeolite

Carbon

Cellulose particles
Diatomaceous Earth

Lime

Silica

Sodium Carboxymethyl Cellulose
Gelatine

LCP solution

Glass Beads

Soft Ployurethane Particles
Poly (P—phenylene-2,
6-benzobisthiazole) [PBZ] PBZT
Aluminum dihydrogen
Copper Phthalocyanine
Iron Oxide

Piezoceramic
Sulphopropyl dextran

Suspending Fluid
Silicone oil
Corn oil
Transformer oil
Mineral Oil
Hydrocarbon oil
Transformer oil
Silicone oil
Engine oil
Mineral oil
Kerosene
Silicone oil
Olive oil

Silicone oil
Silicone oil
Mineral oil

Mineral oil

Silicone oil

Dibutyl sebacate
P-xylene

Polychlorinated biphenyls

 

56

 

Table 5 General Characteristics of ER fluids (Gast and Zukoski 1989):

 

Suspending Fluid Properties

Relative Dielectric Constant 8f 2 2-15
Low Field Strength Conductivity Of: 10'7-10'l3 mho/m
Viscosity n; = 2-15
Density pf: 10'7-10'l3 mho/m
Particle Properties
Shape close to cubic or spherical
Size a = 0.1-100um
Relative Dielectric Constant 8,, = 2-40
Suspension Properties
Zero Field Viscosity n, = 10°7-1o'l3 mho/m
Volume Fraction of Particles fv= 0.05-0.5
Electric Conductivity o, = 10'6-10‘l3 mho/m
Typical Field Strength E = 0.1-5 kV/mm

 

 

57

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6 Data for Fig.8
Test Steady State Transient Method
Method
1 0.13:0.008 0.139i0.0070
2 014350.010 01394500070
3 0.14:0.011 0.140i0.0070
4 0.143i0.0072
5 0.1 36:0.0068
Table 7 Data for Fig.9
fV Eq. (2.1) Eq. (2.4) Eq. (2.5) Measurement
0.1 0.909 1.010 0.909 07491-00374
0.2 0.824 1 .046 0.824 1 050:0.0525
0.25 0.783 1.077 0.783 1.036:0.0518
0.3 0.743 1.116 0.743 1.070i0.0535
0.35 0.667 1.167 0.704 1 .1641r0.0582
0.4 0.630 1.231 0.666 1.041 i0.0520
0.45 0.595 1.308 0.629

 

 

 

 

 

Table 8 Data for Fig. 10

 

temperature (°C)

fv = 35% water wt.8°/o

fv =5°/e water wt.9°/o

 

 

 

 

 

 

 

 

 

 

 

 

 

24 0.156i0.0078
25 0.121i0.0061
27 0.157i0.0079
34 0.1 13i0.0057
37 0.131i0.0066
40 0.1 19i0.0060 0.087i0.0044
42 0.086i0.0043
44 0.1 153500058
47 0.121i0.0061
50 0.1 17:0.0059 0.083i0.0042

 

 

58

 

APPENDIX B

Experimental Uncertainty Analysis:

The experimental determination of any parameter is based upon measurements
which by their nature contain errors. For the apparatuses considered in this study, the
uncertainty errors are due to the inability to read a measurement device exactly. Utilizing
a specific example we consider the experimental determination for the thermal

conductivity, )1. This determination is based upon measurements of j, E, L, T0,, TU. based

on equation (3.7) or the equation listed here

 

'EL"
71 z 1 1
2AT ( )
Then mathematically we have
871 871 82 31"
E = ——5' 2 + —6E 3 —-—6L 3 ——6AT 2 "2 2
"Or [((91. J) (8E ) +(8L ) +(8AT )] ()

where the 8 parameter represents the variation observed for each specific measurement,

and

59

 

 

 

 

 

                        

 

(h 2AT
a 112
3E 2AT
at 1151.2
8L AT
8/1 jEL‘
dAT 2AT
Since
E2}:
L
then
ErrorE =[(-g— 525E) ;:(%ZE 5L)2 ]”2
”2
Similarly,
. 4 I
J=— 7
7r
Error =[—5I)2 +(16D)2 ]"2
3D

_ i_2 _____ 21/2
_[(7r D2) +( :D35D)l

60

(3)

(4)

(5)

 

AT = T01: T11

 

aAT
—97111)2 +(3AT

8f. 21/2 6
an. an. L'” ”

Error” 2 [(

The variations for the data in Table 3 are shown in Table 9.

 

 

 

 

 

 

 

I.
Table 9 Values of Parameters and Their Variations '1
Parameter Value Variation _
Current (I) 0.30 (mA) 0.005 (mA)
Voltage (V) 400 (V) 0.5 (V)
Temperature (T01) 29 fiC) 0.005 (°C)
Temperature (Tu) 28.5 (°C) 0.005 (°C)
Thickness of ER 1.6 (mm) 0.05 (mm)
Fluid Layer (L)

 

 

 

 

 

Using these values and equations (1) ~ (6) the error associated with the determination of a

thermal conductivity of 0.28 W/mK can be estimated as 0.05 W/mK, which is in an error

level of i1 1%. The errors for other measurements are estimated by the similar

calculation.

61

”lillllliililillilllillf