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LIBRARY
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University

 

 

 

This is to certify that the
thesis entitled

CONTROL OF CONDUCTIVE HEAT TRANSFER
IN ELECTRORHEOLOGICAL FLUID
COMPOSITES

presented by

GLORIA D. ELLIOTT

has been accepted towards fulfillment
of the requirements for

M. s . degree in MECHANIQAL ENGINEERING

 
   

Major p efessor

Date APRIL 29, 1997

0-7639 MS U is an Wrrmm'w Action/Equal Opportunity Institution

PLACE It RETURN BOXtomnovethi-ehoekeuirem youneeord.

‘ TO AVOID FINES return on or before we due.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU is An Affirmative AetionEqud Opportunity Instituion‘
Wm1

 

CONTROL OF CONDUCTIVE HEAT TRANSFER
IN ELECTRORHEOLOGICAL FLUID
COMPOSITES

By

Gloria D. Elliott

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 or CONDUCTIVE HEAT TRANSFER
IN ELECTRORHEOLOGICAL FLUID
COMPOSITES
By

Gloria D. Elliott

The majority of electrorheological (ER) fluid applications are based on the
controllable viscosity changes characteristic of these suspensions. When subjected to high
voltage fields the suspended particles experience a charge separation causing them to re-
orient and to form fibrillar chain structures perpendicular to the electrodes, which in turn
induces a change in viscosity of the fluid. Controllable heat transfer is thus possible if the
heat transfer properties are similarly affected by electric field strength. A methodology
was developed to evaluate the thermal properties of chained electrorheological fluids
under such high voltage conditions. Video imaging was implemented to gain a general
understanding of the electrorheological response. Thermal conductivity (1:) and volumetric
specific heat (pCp) estimates were obtained in both zero and high DC field conditions
using a one-dimensional transient heat conduction model and Prole software. Within
the limits imposed by this technique no detectable change in thermal properties was”

observed.

To my family

Acknowledgments

I’d like to thank my advisor, Dr. John Lloyd, for supervising this work and for
allowing me the freedom to explore the aspects of this project that weren’t necessarily part
of the original strategy. I’d also like to express my appreciation to my committee
members Dr. Radcliffe and Dr. Beck, for their helpful advice and discussions during the
course of this research. I am also very grateful to Dr. John McGrath for his patience
during the completion of this work.

For guiding me in a direction that I have never once regretted, special thanks to
Kent Nielsen To Kohichiro Kawate-san I have to say arigatoa gozaimasu for inciting my
enthusiasm for research and for so positively impacting my academic pursuits.

Among my peers, I have to especially thank Mark Wilenski, who took the time to
understand my research difficulties and was a fountain of hope when things seemed
impossible, and Kevin Dowding, for his never-ending patience in discussing the details of
parameter estimation on so many an occasion. Without the support of so many of my
colleagues the completion of this thesis would have seemed an impossible task. To my
labmates P.T. Ramakrishnan, Xinsue Su, and Jeff Hargrove, I owe special thanks for their
helpful discussions and assistance. Many thanks to Heidi Relyea, Paul Hoke, Joe DeRose,
Mark Minor, and Charles Birdsong, who so graciously listened to many a monologue,

and provided a rally of support during the difficult times.

iv

Finally, I have to thank my family for instilling in me the belief that I could achieve

whatever I set out to do.

Table of Contents

LIST OFFIGURES x

1 Introductronl
2 Design and Preparation of Electrorheological Fluids .................................. 9

3 Video Imaging of Chaining Response ............................................................ 14

3.1 Imaging Apparatus and Technique .............................................................. 14
3 .2 Observations ............................................................................................... 17

3.3 Discussion .................................................................................................. 22

4 Determination of Thermal Conductivity and Volumetric
Specific Heat using a l-D Heat Conduction Model .......................................... 25

4.1 Transient MeasurementsZS

4.1.1 Overview of Method .......................................................... 25

4.1.2 Apparatus and Analytical Technique ............................................... 27

4.1.2.1 Composite Specimen ..................................................... 27

4.1.2.2 Data Acquisition System ............................................... 33
4.1.3 Governing Equations and Boundary Conditions .............................. 35
4.1.4 Data Analysis ................................................................................. 36
4.1.5 Experimental Method ..................................................................... 38
4.1.6 Results and Discussion ................................................................... 38
4.1.7 Error Analysis ................................................................................ 57

4.2 Steady-State Measurements 58

5 Conclusions and Recommendations ............................................................ 61

A thdamental Issues ........................................................................................... 65
A.l Inter-particle Forces 65
A2 Dielectric Phenomena 69

A3 InterfacialElectricDoubleLayerTheory......................................... 75

B Triple Jtmction Thermocouples ...................................................................... 78
C Q-Basic Program for Temperature Data Conversion .................................. 80
D PROP-1D Sample Data Files ........................................................................... 81

E Design of Experiment ....................................................................................... 93

El Sensitivity Analysis ............................................................................... 93
E2 Sequential Estimates ............................................................................. 96
E3 Residuals .............................................................................................. 98
EA Duration of Experiment ......................................................................... 99
F MDSC Determination of Specific Heat ......................................................... 100
El Modulated Differential Scanning Calorimetry (MDSC) ......................... 100
F.2 Results and Discussion .......................................................................... 103

F2] Cahbratron103

F.2.2 Zeolite Type 3AinSilicon 011 104

F.2.3 Error Analysis ........................................................................... 105
G An Error and Sensitivity Analysis ................................................................... 107
List of References .................................................................................................... 109

Table 2.1

Table 2.2

Table 2.3

Table 4.1

Table 4.2

Table E.1

Table F.1

Table F.2

Table F.3

Table G.1

Table G.2

List of Tables

Physical Properties of ER fluid materials ......................................... 10
Estimates of ER fluid densities ........................................................ 11
Typical ER Fluid Formulations ........................................................ 13
Material properties of components used in the composite

specimen ........................................................................................ 33
Thermal conductivity values for aluminum oxide and silicon

dioxide (Gebhart, 1993) .................................................................. 46
Optimal heating and experimental duration ...................................... 99
Calculation of MDSC cahbration constant ....................................... 103
Cahbration check with sapphire ....................................................... 104
Comparison of literature and experimental values of specific

heat of silicon oil ............................................................................. 104
Measurement error in material dimensions ....................................... 107

Sensitivity of thermal property estimation to measurement errors...

108

Figure 1.1

Figure 1.2

Figure 3.1.

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

List of Figures

Polarization of particles and subsequent chain formation along
electric field line vectors: (a) particles are electrically neutral

(b) charge separation occurs as the field is turned on (c) particles
begin to line up positive and negative ends ((1) single chains

compact into thicker columns ......................................................... 3
Two extremes of particle orientation (Furmanski and

Floryan, 1994) ................................................................................ 6
Microscopic Imaging Apparatus: acrylic base and stainless steel
electrodes ........................................................................................ l4
Elecrodes: (a)Sawtooth (b)Stepped ............................................... 15

Dynamic Imaging System comprised of high voltage
supply/amplifier, light microscope and CCD camera, video
caliper, video cassette recorder, and monitor ................................... l6

2% by volume Type 3A zeolite in silicon oil at a field strength of
(a)330 V/mm (b)1000 V/mm (c)l700 V/mm. .................................. 17

A field strength of 660V /mm had been applied for several minutes.
5 minutes after removal of the field evidence of redistribution was
observed ......................................................................................... 18

Sawtooth electrodes: The distance between tips and valleys are
1.0 mm and 2.0 mm respectively, giving rise to field strengths
between 500 V/mm and 1000 V/mm. ............................................... l9

Stepped electrodes: the separation in the upper section is 4.65 mm
and in the lower section, 2.0 mm. (a)Upper Field Strength:

215 V/mm, Lower: 475 V/mm (b) Upper Field Strength:

430 V/mm, Lowerz950V/mm. ......................................................... 20

Figure 3.8

Figure 3.9

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Figure 4.14

Figure 4.15

ER chaining response in a region of transitioning field strengths.
The chaining occurs in accordance with electric field lines ............... 21

Appearance of bubbles and/or particulate matter at the negative
electrode ......................................................................................... 21

One-half of the symmetrical composite specimen: a) Teflon air
spacer aluminum electrode c) Teflon gasket to contain the ER
fluid aluminum electrode ................................................................. 28

Triple junction T-type Copper-Constantan thermocouples attached
to aluminum electrodes with poly(viny1)chloride electrical tape

backing ........................................................................................... 30
The firlly assembled composite specimen ......................................... 31
Model for Prop-1D analysis ............................................................ 31
Data Acquisition System ................................................................ 34
Estimates of thermal conductivity of silicon oil ............................... 39
Estimates of voiumetric specific heat of silicon oil ........................... 39
Estimates of thernml conductivity of water ...................................... 41
Estimates of volumetric specific heat of water ................................. 42

Estimates of the thermal conductivity of 10% volume fiaction
Type 3A zeolite/ silicon oil .............................................................. 43

Estimates of the volumetric specific heat of 10% volume
fraction type 3A zeolite/silicon oil ................................................... 44

Estimates of thermal conductivity of a wet and dry series
of type 3A zeolite/silicon oil suspensions ......................................... 45

Thermal conductivity of f" = 5% Type 3A zeolite/silicon oil
suspension at low field strengths ...................................................... 47

Volumetric specific heat of fv = 5% Type 3A zeolite/silicon oil
suspension at low field strengths ..................................................... 48

Thermal conductivity of fv = 10% and 20% Type 3A zeolite/silicon
oil suspensions at low field strengths ............................................... 48

Figure 4.16

Figure 4.17

Figure 4.18

Figure A.1

Figure A.2

Figure A.3

Figure 13.1

Figure E]

Figure E.2

Figure E.3

Figure E.4
Figure E.5

Figure E.6

Figure 13.7

Figure F.1

Volumetric specific heat of f. = 10% and 20% Type 3A
zeolite/silicon oil suspension at low field strengths .......................... 49

Effect of electric field on the temperature distribution in the ER
fluid system ................................................................................... 51

The temperature profiles measured across the composite specimen
as the steady-state condition developed ........................................... 59

Environmental Scanning Electron Microscopy (ESEM) image
of UOP Type 3A zeolite in a minimum amount of silicon oil ............ 67

Conceptualization of a dielectric particle experiencing a charge
separation due to an applied electric field E0. (a) The centers of
positive charge in the dielectric particle (N a+ ions in zeolites) shift
towards the negative electrode, and the centers of negative charge
shift towards the positive electrode (b) The result is a net positive
surface charge on the one side of the particle and a net negative
charge on the other .......................................................................... 71

Types of polarization mechanisms observed in non-polar
molecules (von Hippel, l995):(a)e1ectronic (b)atomic
(c)orientation .................................................................................. 72

Construction of parallel 3 jtmction thermocouples:(a) typical
construction (b)—(d) electrically equivalent constructions based on

the Law of Intermediate Metals for thermocouples .......................... 79
Thermal conductivity sensitivity coefficients .................................... 95
Volumetric specific heat sensitivity coefficients ............................... 95

Comparison of measured profiles and those generated using the

parameters estimated by Prop-1D .................................................... 96
Sequential estimates of thermal conductivity .................................... 97
Sequential estimates of volumetric specific heat ............................... 97
Residual analysis for silicon oil, X=0 boundary ................................ 98
Residual analysis for silicon oil, X=L boundary ................................ 98
Values of specific heat for a series of ER fluids ................................ 105

§<wawr~fi~mmp§wm95§>£>
Q

rrfifinagrwcrna.

Nomenclature

Area

Amplitude of Kinetic Response
Amplitude of Temperature Modulation
Specific Heat

Voltage

Electric Field

Applied External Field

Induced Electric Field

Average Field

Free Energy of Attraction
Current

MDSC Cahbration Constant
Length

Period

Polarization

Resistance

Temperature

Volume

Thickness

Distance

Volume Fraction
Convection Heat Transfer Coefficient
Thermal Conductivity
Thermal Conductivity Ratio
Average Induced Moment
Heat Flux

Nuclei Separation Distance
Time

Duration of Heating
Duration of Experiment

[1112]

H
[kJ/kgK]

[V /m]
[V /mm]
[V /mm]
H

[A]

[m]
[S]

[0]
[°C
[1113]

[m]

[Angstroms]
1%]
[W/mzK]
[W/mK]

[W]
[Angstroms]
[S]

[S]

[S]

megab<txgmmp

Qumran

qm-uo—imoom

3;

ref

att
rep

Greek

Thermal Diffusivity [m2/s]
Coefficient of Expansion [m3/m3 °C]
Depth of a Potential Well

Relative Permittivity

Dielectric Constant

Dipole Moment

Characteristic Frequency

Density [kg/m3]
Conductivity

Induced Sin-face Charge Density

Modulation Frequency

Linear Heating Rate [°C/minute]

Italics

Polarizability

Constant Based on Dimensions

Planck’s Constant [Js]
Charge [e.m.u.]

Subscripts

Atomic
Composite
Electronic
Fluid
Liquid
Orientational
Particle
Solid
Total
Effective
Reference

Superscripts
Dimensionless

Attraction
Repulsion

xiv

Chapter 1

Introduction

WM. Winslow (1947) was the first to be awarded a patent for the class of fluids
he called electroviscous fluids or electro-fluids. However, theories on the viscoelectric
phenomena characteristic of these fluids date back to the 19th century (Quinke, 1897;
Duff, 1896). The distinguishing feature of electro-fluids is a viscosity controllable by the
application of a high voltage electric field. Winslow (1949) observed a marked increase in
flow resistance when these fluids were subjected to electric fields of the order 2-4 kV/mm
and attributed this response to an increase in viscosity. In static systems he observed that
the application of such fields caused solidification of the fluid, requiring a force
proportional to the square of the electric field to shear the material.

Winslow’s electroviscous fluids were later renamed electrorheological (ER) fluids
by Stangroom (1983) who felt that classifying this induced shear resistance as a viscous
response was too stringent. The non-Newtonian behavior of Winslow’s fluids could not
be explained strictly in terms of viscosity. More encompassing of this phenomena, and

better representing the fluid’s behavior, was the term ‘electrorheological’.

Electrorheological (ER) fluids are typically defined as being dispersions of finely
divided, highly polarizable, solid dielectric particles, in hydrophobic liquid carriers of
lower dielectric constant (Halsey, 1992). When subjected to a high voltage field, the
particles become polarized. The positive and negative charge densities shift to opposite
ends of the particle, resulting in a net dipole moment. Dipole-dipole attractive forces
cause the particles to rotate and translate, aligning positive and negative ends, to form
chains of single particle width oriented parallel to the electric field lines. With time, and/or
increasing field strength these single chains collapse into thicker, tighter chains, eventually
reaching what has been suggested by Tao and Sun (1991a, 1991b) to be a body-centered
tetragonal ground state lattice structure. The result is a dramatic transition fiom an
isotropic suspension to a fibrillar anisotropic material with significantly altered material

properties. These transitional stages are depicted in Figure 1.1.

 

 

7 l

[+-+-+-+-+-+-+fl [:++++++++++]

 

 

 

 

 

 

b++++++++1 +++++++++

O

 

 

(e) (4)

Figure 1.1 Polarization of particles and subsequent chain formation along electric field
line vectors: (a) particles are electrically neutral (b) charge separation occurs as the field is
turned on (c) particles begin to line up positive and negative ends ((1) single chains
compact into thicker colunms.

Typical field strengths required for activation range fi'om a few hundred volts per
mm to upwards of 10 kV/mm, depending on the application, apparatus design, and
whether or not the fluid is flowing or static. Removal of the high voltage field causes the
dipole-dipole forces to relax thus allowing fluid motion to redistribute the particles.

Several decades after this discovery researchers began to look at the fimdamental
principles behind the ER response. In 1962 Schwarz proposed an electric double layer

theory to account for the dielectric distribution occurring in colloidal dispersions as a

result of applied electric fields. Klass and Martinek (1967b) and Uejima (1972)

experimentally supported Schwarz’ theory with measurements of dielectric properties of
ER fluids, and proposed a dielectric mechanism to explain the Winslow effect.

The 197 0'5 saw a surge in application-oriented research, directed towards
harnessing this controllable change in viscosity. The devices proposed by Winslow
(1949), a soft-clutch and an electrically controlled valve with no moving parts, were
compended by dampers (Eige, 1963), and vibration and shock absorbers (Bullough and
Stringer, 1973). Also the first work was done in the area of heat transfer (Shul’man et
al., 1977{in Russian}, 1978). Shul’man (1982, 1986) was credited with the first thermal
engineering application: the utilization of ER suspensions as the working fluid in heat
exchangers. In the same work Shul’man used a transient technique to measure the thermal
conductivity of these suspensions in order to improve heat exchanger performance. He
found that specific heat (C,) was insensitive to application of electric fields but suggested
that the thermal conductivity (k) could change by upwards of 300% depending on the
volume fiaction and water-loading of the solid phase. Details of actual thermal
conductivity measurements were not included. Demchuk and Korobko (1977 {in
Russian» reported thermal conductivity changes up to 280% in suspensions of 5% silica
in transformer oil due to application of an electric field, however details of the
experimentation were not explicit.

An escalation of mathematical modeling and computational simulations pervaded
the next two decades. Adriani and Gast (1988) developed a computational microscopic
model of electrorheology, relating microscopic structural changes to macroscopic
electrorheological properties. Computer simulations were used by Klingenberg et a1.

(1989) and Hass (1993) to explore structure formation in electrorheological fluids. Davis

(1992b) was the first to use finite-element analysis to model particle-particle forces in ER
fluids.

The 1990’s saw a continuation and diversification of heat transfer research. Cha et
a1. (1990) measured ER fluid density and specific heat as functions of temperature and
field strength, observing that within the limits of the experimental technique (0.5%),
density was unaffected by field strength. They also observed that the specific heat was
insensitive to temperatures less than 100 °C. Zhang & Lloyd (1992) demonstrated that
radiation heat transfer through an ER fluid-filled composite window could be controlled
by the application of an electric field, and was sensitive to particle concentration and
electric field intensity. A 55% increase in thermal conductivity was also reported by
Zhang and Lloyd (1993). Alternating current fields were utilized in that work. Lloyd &
Zhang (1994) determined effective values of thermal conductivity for both isotropic and
chained ER fluids, and compared predicted and experimental values to elucidate the nature
of the enhanced heat transfer.

Furmanski and Floryan (1994, 1995) have also been working on adaptive heat
transfer systems. Their systems differ in terms of the micro-structural response. The
system consists of suspensions of rod-like particles in suitable carrier fluids. These
particles transition from an orientation parallel to the wall to a perpendicular orientation

when subjected to magnetic or electric fields. This response is depicted in Figure 1.2.

QC)
GOO
000
0 0
00800
0 o
00 0

000

o
000

 

 

 

 

 

 

oooooo

 

 

O
CO
000

o
0

Figure 1.2 TWo extremes of particle orientation (Furmanski et. al., 1994).

What has been learned from these systems can be utilized to improve upon the
design of electrorheological fluids for heat transfer enhancement because the underlying
principles are the same. Furmanski and Floryan (1994) have shown that the heat transfer
effects of reorientation are more pronounced when the aspect ratios (length/diameter) of
the suspended particles are high.

Concmrent with the developments in the measurement of thermal conductivity
were continued efforts to understand the nature of electrical conduction, and its influence
on properties. Conrad et a1. (1991) concluded that the temperature dependence of the
electrical conductivity in zeolite/ silicon oil suspensions reflected the diffusion of sodium
ions in the zeolite cages. This is consistent with the postulated role of proton mobility
(Makatun et al., 1983) in the polarization and conductivity of ER suspensions, based on
the results of shearing stress and conductivity experiments.

The present decade has been marked by a renewed interest in dielectric properties.
Conrad et a1. (1991) modeled mechanical response in terms of the dielectric mismatch
between particle and suspending vehicle and the local field concentration. In an

examination of polymer and cellulose derivative-based suspensions, Kordonsky et a1.

(1991) demonstrated an increase in molecular mobility and polarizability of the molecules
with increasing field intensity due to the addition of fimctional ionogenic groups (amino,
acetyl, phosphate, and others) to the base cellulose. These groups served to increase the
proton conductance and thus change the mechanism of electrical conductivity, resulting in
an increased rheological sensitivity. An increase in dielectric constant and dielectric loss
tangent were thus manifestations of this increased mobility. Conjoint with these
observations was an electrorheological dependence on the moisture content of the
filler/ salt combinations. The resulting surface charge distribution and surface structure
due to adsorbed water and its ensuing effect on the electric double layer, positively
enhanced the characteristic structure formation in the ER fluids.

As the realization is made that a comprehensive understanding of
electrorheological phenomena is only possible with a merging of such areas as physical
chemistry, colloid science, electrochemistry, dielectric physics, and interface science,
research efforts are becoming much more interdisciplinary in nature. As pointed out by
Khusid (199 6), computer simulations, which incorporate disperse phase architecture and
implement electrostatic models of dielectric property dependences, although qualitatively
correct, do not always agree with experimental data. To fully grasp the complex nature of
the structure formation in ER fluids and to be able to predict material properties and
engineer suspensions with the desired electrical, mechanical, and thermal responses, a
continued multi-disciplinary approach is imperative.

The focus of the present work was two-fold. The primary goal was to develop a
method of evaluating k and pCp of ER fluids when subjected to high voltage fields.

Conventional methods of evaluating these properties inhibit the application of high voltage

fields and as such impede property evaluation of ER Fluids in the chained state.
Knowledge of the thermal property changes as a fimction of field strength, particle
concentration, moisture content, dielectric properties, etc. provides the basis for the
development of thermally smart composites, or materials that can achieve and maintain
desired heat transfer properties via open- and clo sed-loop control. One-dimensional
transient and steady-state techniques, combined with a specially designed and modified
apparatus, were evaluated for their potential in estimating k and pCp of ER fluids in high
voltage environments.

Secondly, to be able to design ER fluids with desired controllable thermal
responses it is important to understand the frmdamental basis of ER phenomena. Thus an
equally important aspect of thermal composite design involves developing an
understanding of microscopic phenomena, and relating this knowledge to macroscopic
observations to elucidate the heat transfer characteristics of ER fluids. Efforts were thus
directed towards an investigation into the fundamental science of electrorheological

response for the purposes of designing suspensions with controllable thermal properties.

Chapter 2

Design and Preparation of
Electrorheological Fluids

The material characteristics proposed by Winslow (1949) to be most suitable for ER
activity are still quite applicable today. It was his observation that semi-conductive
particles of high dielectric constant tended to yield a strong ER response and that
hydrophilic adsorbent materials with nominal degrees of water-loading were especially
reactive. Later in his patent on ER fluid compositions (1962) he elaborated on these
qualities, indicating that the suspending vehicle should be oleagirrous (oily) in nature, have
a viscosity in the range of 2 to 20 centipoise at 25 °C, a dielectric constant between 2 and
5.5, and be stable as an electrical insulator (i.e. high dielectric strength). Khusid (1996)
has written a more current detailed review of the variety of materials that are being utilized
as ER constituents, as well as the natrn'e of their reactivity.

As previously indicated, the choice of constituents will depend on the final application
as well as the nature of the electric field being utilized. At the onset of this work the type
of field was not considered in the context of choice of materials. The constituents chosen
were done so mainly on the basis of Winslow’s (1949) observations on appropriate

materials. Enhancement of the ER response based on electrical conductivity or dielectric

10

properties was not considered to be of primary importance. The focus was more on the
thermal conductivities of the individual phases.

Type 3A Zeolite, a molecular sieve obtained from Advanced Specialty Gas Equipment,
was used as the suspended phase in the electrorheological fluid investigated in this study.
The structure of this material is discussed in Appendix A Dow Corning® Fluid 710,
poly(phenyl) siloxane oil, was chosen as the suspending medium There was convincing
evidence in the literature of strong ER response in these materials (Comad et a1, 1994).
Type 3A zeolite and silicon oil have similar densities, which aids in preventing settling, a
quality not desired in ER fluid compo site applications. The physical properties of these

materials are given below in Table 2.1.

 

 

 

 

 

 

Type 3A Zeolite Silicon Oil
Thermal Conductivity (W/mK) 0.0403‘ 0.1407
Electrical Conductivity (l/ohm-cm) (1 x 10'9 - 1x10‘I2 )2 l x 10"3
Density (37cc) dry: 1.57 wet: 2.03 1.11
Specific Heat (kl/gm - 5.99

 

 

 

 

Table 2.1 Physical Properties of ER fluid materials.

Assuming that the enhanced heat transfer previously observed for ER fluids was
directly related to the physical microstructure change as the particles chained up, it was
theorized that one phase must dominate in its contribution to the effective thermal
conductivity in the anisotropic state. Hence the change in thermal conductivity due to

application of an electric field should be Optimal when the thermal conductivity values of

 

‘ Zhang and Lloyd, 1993
2 Hao and Zn, 1996

11

the particle and suspending medium are very different. The particle to liquid thermal
conductivity ratio in this system is:

k —5—w—02864 21
T‘lt,'o.14o7" ['1

This should ensure detectable changes in thermal conductivity as the fluid transitions from
isotropic to anisotropic in character.

Samples were prepared in weight fiactions according to:
= [2.2]

where V1) and V1 are the volumes of particle and fluid, respectively, m the mass, and p the
density. The zeolite density used for these calculations was 1.80 g/cc, a value intermediate
to the wet and dry densities listed by the manufacturer.

Approximate ER fluid density measurements were made for several different volume
fractions. The mass of one cubic centimeter of zeolite suspension was measured and
recorded. This was then converted to a density reading in kg/m’. The values determined
are given below. Because of the degree of error associated with such measurements, this

information is used only in a qualitative manner.

 

 

Wet (g/cc) Dry (aloe)
5% 1.18 1.13
10% - 1.25

 

 

 

 

 

Table 2.2 Estimates of ER fluid densities.

12

The zeolite particles were shipped in an anhydrous state (< 2.5 % wt). It has been
demonstrated elsewhere that ER response in zeolite/ silicon suspensions is very dependent
on moisture content (U ejima, 1972). The laboratory environment was such that control
of moisture was very difficult. However, for the most part zeolite crystals placed in an
open container and left to equilrbrate at ambient temperature and humidity overnight,
afforded crystals with satisfactory ER behavior. The ambient relative humidity was
measured at the time of fluid preparation using an Omega sling psychrometer. Conditions
varied from extremes of 29 % to 60% relative humidity. According to manufacturer’s
specifications, water adsorption increases rapidly with relative humidity to a saturation
value equivalent to the maximum loading capacity of the particles (23% for Type 3A
zeolite powder). In the ranges given above, the zeolite particles should be firlly water
loaded at the time of preparation of the ER fluids.

In an attempt to obtain samples of the extremes of water-loading, pseudo-dry and
wet dispersion protocol development was initiated. Wet ER samples were prepared by
placing the dry zeolite crystals in a humid environment which had been created by placing
a 500 mL beaker of boiling water inside of an inverted 10 L beaker. Although normal
room humidity conditions would typically substantiate full water loading, an invariant
protocol is preferable.

The dry dispersions were much more challenging to prepare. Although the zeolite
crystals were Shipped in a dehydrated state, repeated openings of the container invalidated
the listed moisture content. The zeolite powder was placed on a watch glass and dried in
a 200°C oven for 2 hours. It is acknowledged that this does not dry the crystals

completely. The ER dispersions were prepared immediately upon removal from the oven.

13

To prepare fully anhydrous suspensions, both particle and suspending medium would have
to be dried. Also the particles would have to be dried under vacuum and immersed in an
anhydrous/hydrophobic suspending medium before removal from the oven to prevent
moisture pick-up from the atmosphere upon removal.

The ER fluid suspensions were prepared in volume fractions according to the
calculation given in equation 2.2. The appropriate amount of silicon oil was weighed into
a small plastic jar. The zeolite crystals were then weighed and transferred into this jar and
dispersed using a magnetic stirrer and stir bar. Typical ER fluid formulations are listed

below in Table 2.3.

 

 

 

 

 

ER fluid Q01. %) mass zeolite (g) mass silicon oil (gL
5 0.555 18.05
15 1.667 18.05
20 2.222 18.05

 

 

 

 

Table 2.3 Typical ER Fluid Formulations.

There are obvious drawbacks to preparation of fluids without more stringent
control, reproducibility being the most critical To prevent this fi'om causing problems in
the evaluation of the measuring technique, master batches were prepared to ensure
consistency among subsequent tests. Magnetic stirring was implemented to redistribute
particles before utilization of the fluid in the test apparatus. The apparatus was not filled

until just prior to experimentation to prevent misleading results due to particle settling.

Chapter 3

Video Imaging of Chaining Response

3.1 Imaging Apparatus and Technique
A video imaging system was constructed to record the chaining sequence in ER
fluids fi‘om initial polarization of particles to the evolution of columnar structures. The

electrode system used to induce the ER chaining is shown in Figure 3.1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.1. Microscopic Imaging Apparatus: acrylic base and stainless steel electrodes.

14

15

An acrylic base was cut to the dimensions of a typical glass microscope slide and
1.27 mm stainless steel electrodes were manufactured using wire EDM. Silicon rubber
inserts were used to contain the ER fluid between the electrodes. A glass cover slip was
placed over the fluid to prevent a meniscus from forming between the electrodes, thus
ensuring that the entire surface was in focus at a given time. A drop of Cargille certified
refractive index matching fluid with an index of refiaction of 1.530 was placed on the
cover slip to enhance the optical clarity of the images obtained. Positive and negative
leads of a Trek Model 677A supply/amplifier were attached to the electrodes. The
magnitude of the applied voltage field was controlled from the fiont panel of the
supply/amplifier. The maximum output voltage of this supply was 2000 V.

The microscopic imaging assembly was modular in design, thus allowing for easy
replacement of electrodes. Three electrode geometries were investigated to evaluate the
effects of field strength and electric field line density on the chaining mechanisms. These

are shown in Figure 3.2.

“I if

(a)

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.2 Electrodes: (a) Uniform-Gap (b)Sawtooth (b)Stepped

16

The image acquisition system is depicted schematically in Figure 3 .3. A
Panasonic WV-CD 20 Charge-Coupled Device (CCD) camera was mounted to an
Olympus BH-2 light microscope. The signal fi'om the camera was sent to an Olympus
Corp. Cue Micro 300 Video Caliper, and the output fiom the caliper was then recorded
on broadcast quality VHS tape by a Sony video cassette recorder, and displayed on a
Sony RGB monitor. Individual images were captured from the video tape for later analysis

by using a Data Translations 2625 arithmetic fiame grabber board.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LightMicroscopeand
CCDCamerafor
lnngirgERChaim
D
'2' e :30
E00
Dynamic lnngeAcquisition System: 0 U U

 

 

 

VCR, Monitor, and Video Caliper

 

 

 

 

'gh Voltage Supply/Amplifier
or Activation of ER Fluids:

 

 

 

Figure 3.3 Dynamic Imaging System comprised of high voltage supply/amplifier, light
microscope and CCD camera, video caliper, video cassette recorder, and monitor.

3.2 Observations

Suspensions of 2% by volume, roughly 1 micron diameter, type 3A zeolite powder
in silicon oil were used in the imaging work and provided the best visualization of ER
chaining activity. This particular suspension had been prepared at a relative room
humidity of 26%. Images of the chaining structure obtained at varying field strengths are
shown in Figure 3.4 (a) through (c). From left to right the fields are 330 V/mm, 1000
V/mm, and 1700 V/mm It can be seen from these images that with increasing field

strengths the chain structure becomes thicker.

The time to evolution of full chain structure was found to decrease with increasing
field strength. The chain structure at 330 V/mm (Figure 3.4(a)) took upwards of 30
seconds to establish itself whereas the structure at 100V/mm (Figure 3.4(b)) took only 5

or 6 seconds. The time to form the structure at 1700 V/mm (Figure 3.4(c)) was too short

(13)

Figure 3.4 2% by volume Type 3A zeolite in silicon oil at a field strength of (a)
330V/mm (b) lOOOV/mm (c) 1700 V/mm

to estimate by direct observation.

   

(a) (C)

18

To examine the redistribution of chain structures after field removal, a moderate
field strength of 660 V/mm was applied to the sample for several minutes, and then the
field level was manually decreased to zero by adjusting the front panel gain. This ensured
zero charge on the electrode surfaces. Redistribution occurred but was extremely slow.
Previous experiments indicated that return to the fully dispersed state required upwards of
4 to 5 hours and depended on the intensity of the field applied. Redistribution is believed
to be caused by Brownian motion. As can be seen in Figure 3.5, after 5 minutes there was
still strong evidence of the chaining structure. Sections of the chains were still intact.
Reapplication of the 660 V/mm field caused the particles to rapidly snap back into place.
Application of higher field strengths caused the chain structures to be locked ill upon

removal of the field, requiring manual deformation to cause redistribution.

Figure 3.5 A field strength of 660V /mm had been applied for several minutes. 5
minutes after removal of the field evidence of redistribution was observed.

l9

Sawtooth electrodes were used to investigate the effect of electric field line
distribution on the ER response. Application of a 1000V field between the electrodes
created field strengths between 500V/mm and 1000V/mm As shown in Figure 3.6, the
chaining occlured in a manner consistent with electric field line densities. The ER fluid
preferentially chained in the regions of higher field line density, predominantly between the
tips of the sawtooth. The chains became thinner and more disperse in the regions where

the electric field lines fanned out to areas of lower field line density.

 

Figure 3.6 Sawtooth electrodes: The distance between tips and valleys are 1.0 mm and
2.0 mm respectively, giving rise to field strengths between 500 V/mm and 1000 V/mm

Figure 3.7 shows the stepped electrode apparatus shown in Figure 3.2 (c) for
simultaneous visualization of the effects of two different field strengths. The distance
between electrodes in the upper portion is 4.65 mm, whereas in the lower portion the
separation is 2.1 mm In Figure 3.7 (a) in the lower portion of the apparatus the field

strength is 475 V/mm, and substantial chaining is observed, whereas in the upper portion

20

where the field strength is 215 V/mm, there is little evidence of chaining activity. In
Figure 3.7 (b) the applied field was increased to 2000V creating a field strength of 430
V/mm in the upper region and 950V/mm in the lower region. Definite chaining was
observed ill both the upper and lower regions of the apparatus. The field strength for
creating observable chaining of this particular fluid under the described conditions was

thus somewhere between 215 V/mm and 430 V/mm

 

(a) (b)

Figure 3.7 Stepped electrodes: The separation in the upper section is 4.65 mm and in
the lower section, 2.0 mm (a)Upper Field Strength2215 V/mm, Lower: 475 V/mm (b)
Upper Field Strengthz430 V/mm, Lower:950 V/mm

Shown ill Figure 3.8 is a close-up of the corner region shown in Figure 3.7. It
illustrates the dynamics of the chaining as it bends around the comer in accordance with

the electric field lines.

21

 

Figure 3.8 ER chaining response ill a region of transitioning field strengths. The
chaining occurs in accordance with electric field lines.

When the field strength in the straight 1.2 mm gap electrode apparatus was
increased to 1700 V/mm, small bubbles or possibly particulate matter were observed at the
site of the negative electrode. This became more pronounced the longer the duration of

the applied field.

 

Figure 3.9 Appearance of bubbles and/or particulate matter at the negative electrode.

22

It is important to note that the field strengths utilized in this work are substantially
lower than any of those reported in the literature as typical field strengths applied to

induce chaining.
3.3 Discussion

In some systems electrophoresis can be a problem (Monkman, 1991), wherein the
particles in the fluid are preferentially attracted to one electrode and repelled fi'om the
other. The appearance of this phenomenon on a microscopic level would be a coating of
particles on one electrode, with an absence of the same behavior on the other. Near-wall
effects such as these can be detrimental in various applications, and can cause
complications for most ER fluid modeling work. Such phenomena could potentially be

observed, characterized and controlled using microscopic imaging techniques.

Another phenomena that can be calamitous to ER fluid applications is the
occurrence of electrolytic reactions in the ER assemblies. Application of direct current
fields can precipitate electrolysis reactions, where non-spontaneous chemical reactions
occur due the presence of electric currents (Harris, 1987). Water is especially sensitive to

electrolysis as can be seen from its reduction and oxidation potentials (Brown et. al.,

1991)
2(2H2oa) + 2e :> H2(g) +20H(aq)) E° .... = -0.83 v
2H;O(1):>4H+(ag)+03(g)+4e' E°9L= -1.23 V

 

6H20(1) :5 4H+ (aq) + 4orr(aq) + 02(g) + 2H2(g) E° ..., = -2.06 v

23

Evidence of electrolysis has been seen for the current ER fluid within the stainless steel
electrode micro-imaging assembly. Water is the activating species in the ER fluid in this
study and is present in significant quantities. An example of this phenomenon is shown in

Figure 3.9.

A similar phenomenon was observed with aluminum electrodes as well. The
bubbles always appeared at the negative electrode. This seems to be consistent with the
reduction of water molecules to produce hydrogen gas bubbles. If the only
electrochemical reaction occurring was the electrolysis of water, with time we would
expect to see bubbles forming at the positive electrode due to the oxidation of water to
produce oxygen gas. This would occur after the reduction because of the relative
oxidation and reduction potentials of the two reactions. Instead, a silvery white deposit
was seen to accumulate on the positive electrode. It is possrble that this corresponds to
the reaction of the electrode’s aluminum oxide coating with the hydroxide ions produced
by the reduction of water at the anode (Brady and Holum, 1993). This reaction is given

by:

A1203(S) + 20H (aq) + 7H20 D 21A10120)2(0H)4]‘(aq)

Such a coating should revert back to ahrminum oxide with heating, however this was not
observed to be the case. Heating with a Meker burner flame did not disrupt the coating.
Altemately the white material could be solid sodium forming from the sodium ions in the
zeolite cages however this seems unlikely as the reduction potential for sodium ion is

greater than that for water, hence water oxidation should occur before this would occur.

24
Na+ (aq) + e' :> Na (s) E° ..d = -2.71 V
Also heating would ionize the sodium, and this was not observed.

From the video imaging it also appears that particulate matter is breaking away
fiom the surface of the electrode. This could be an electrochemical reaction in and of
itself or else a product of erosion due to the hydrogen gas generation. If this problem
persists it would be informative to further characterize the deposited material and quantify
the electrolysis to aid in the redesign of the apparatus to prevent such electrode

deterioration.

A critical field strength for this type of breakdown was observed with each
individual fluid that was manufactured. For the fluid in this particular study this critical
field strength was around 1500 V/mm In other zeolite/ silicon oil suspensions it has been
found to be as low as 500 V/mm The critical field strength appeared to decrease with
increasing water-loading of the zeolite fraction. This seems consistent with the
corresponding current increases that arise as a fimction of increasing water content. This
relationship will be discussed in later chapters. According to Faraday’s Law of
Electrolysis (Whitten et al., 1992) “the amount of substance that undergoes oxidation or
reduction at each electrode is directly proportional to the amount of electricity passing
through the cell”. This is consistent with the observation that further increasing the
voltage beyond the critical field strength elicits the first appearance of bubbles in the

system, thus rapidly increasing the deterioration process.

Chapter 4

Determination of Thermal Conductivity and
Volumetric Specific Heat using a
1-D Heat Conduction Model

4.1 Transient Measurements
4.1.1 Overview of Method

Although there exists a variety of methods for evaluation of thermal conductivity,
including absolute axial heat flow or thermal potentiometry, flash diffusivity with infi'ared
thermography, and comparative methods (Rowe, 1995), few of these lend themselves to
applicability ill high voltage environments. The current work utilized a one-dimensional
heat flow apparatus, combined with parameter estimation techniques to evaluate thermal
properties. This approach falls under the classification of inverse heat conduction
problems (IHCP), an area pioneered by Beck (1962) and Stolz (1960) wherein surface
characteristics or properties are estimated from internal temperature measurements. The
experimental apparatus typical of this method allows for the insertion of electrodes into
the composite specimen, thus permitting the application of high voltage fields necessary
for chaining activity.

The inverse heat conduction problem is analytically more difficult to solve than the

direct problem In solving the direct problem, knowledge of heat flux or temperature

25

26

histories at the surface of a sample, as well as the material’s thermal properties allow for
evaluation of internal temperature distributions. The inverse problem involves extraction
of the thermal properties, utilizing discrete measurements of the dependent variable and
knowledge of the initial and boundary conditions. The analytical solutions for these
problems are typically very detailed and typically require the use of Green’s flmctions
(Beck et al., 1985).

Parameter estimation is a multi-disciplinary field that utilizes statistical tools to
efficiemly maximize data used for the estimation of constants and functions in
mathematical models (Beck and Arnold, 1977). An evaluation of sensitivity coefficients,
residuals, and sequential estimates aid in the redesign of experiments to give optimal
precision and accuracy of estimates. Parameter estimation techniques are thus intrinsically
related to the solution of inverse heat conduction problems.

To determine thermal properties using parameter estimation techniques, a solvable
mathematical model is required, and also a well-designed experiment to extract
temperature data. Minimization of a sum of squares flmction with respect to the unknown
parameters will then elicit the desired parameters.

This work utilizes Prop-1D, a program developed by Beck (1989) for analysis of
one-dimensional heat conduction problems. The program utilizes minimum confidence
regions as the basis for the design of experiments yielding minimum variance estimators.
Information regarding variances and co-variances of error matrices are used to determine

these confidence regions.

27

4.1.2 Apparatus and Analytical Technique
4.1.2.1 Composite Specimen

The effectiveness of any parameter estilmtion program depends largely on the
associated experimental design. The physical model should be in close agreement with the
theoretical model being utilized to extract the parameters. It is desirable to keep the
physical model as simple as possrble to avoid having to model phenomena that are not
intrinsically related to elucidating the parameters of interest. Ideally the specimen would
consist only of ER fluid and electrodes. The ER fluid however, needs to be contained in a
gasket or holder. To be able to measure temperature profiles some means of attaching
these thermocouples is necessary. There is an associated contact resistance with any
attachment hence thermal pastes need to be utilized to minimize the contribution of this
contact resistance to the effective thermal conductivity. Contact resistances are especially
difficult to model Also because of the electrical conduction in the electrodes, the
thermocouples need to be electrically insulated. This requires the addition of another
material All of these materials need to be modeled in the mathematical description. With
each additional layer some accuracy is sacrificed in the final estimates due to the challenge
of finding adequate thermal property information on these materials. Contact resistances
are also a concern between each interface. Accordingly, the composite materials and
geometries were chosen so as to introduce the least possible amount of error.

Boundary conditions also need to be established. Since a constant temperature is
difficult to apply and control, a resistance heating element was utilized to apply a constant

heat flux to one side of the ER fluid. Because convection heat loss was expected fiom a

28

heater with one side exposed, a symmetrical configuration was utilized to ensure that the
heat flux delivered to the fluid was accurately known. A constant voltage was applied to
the heater, and it was assumed that the corresponding heat flux would be equally
partitioned to both sides of the heater. Thermocouple measurements made at identical
locations on either side of the heater were ill very close agreement lending credence to this
assumption. An air spacer was placed against the outer electrode of the composite
specimen using a ring of Teflon gasket material. This was modeled as an insulated
boundary condition because the thermal conductivity of air is very low and the duration of
experiment was short. Heat loss from this boundary should be negligible in that time
period. Figure 4.1 ilhlstrates the materials that make up of one-half of the symmetrical

composite specimen.

 

Figure 4.1 One-half of the symmetrical composite specimen: a) Teflon air spacer
aluminum electrode c) Teflon gasket to contain the ER fluid d) aluminum electrode.

The most challenging aspect of the experimental design was thus selection of
composite materials that were both appropriate for the experiment and had well-
characterized thermal properties (a necessity for the parameter estimation algorithm). The

choice of electrode material was flexible. The particular material chosen, McMaster-Calr

29

alloy 6061 aluminum, was done so on the basis of temper (T6) and thermal conductivity
(167.27 W/mK). The material needed to be thin and highly thermally conductive to
minimize error in the parameter estimation procedure. However to ensure that the
thickness of the fluid layer was accurately known, it was essential that this material was
very rigid. Buckling of the electrodes would cause a spatial distribution of electrode gap
widths. These circular electrodes were 0.8128 mm thick with a 3.81 cm radius. Teflon
gasket material of 3 mm thickness was used to contain the ER fluid between the
electrodes.

Triple jrmction thermocouples were attached to the aluminum disk with a very thin
layer of acrylic coating. This acrylic coating was so thin relative to the other materials it
was not included in the model Because of the voltage being applied to the aluminum
disks, direct attachment of thermocouples was not possrble. It was necessary to insulate
the thermocouples from the high voltage environment to achieve high signal-to-noise
ratios. Ideally a well-characterized, electrically insulating, thermally conducting material
would be implemented. These are difficult properties to obtain in one material
Poly(vinyl)chloride tape provided an excellent electrical insulator but a poor thermal
conductor. However its properties were known with some degree of accuracy. As such,
it was used to insulate only the areas around the junctions. Although this introduces error
into the Prop-1D estimation algorithm, it allows millivolt thermocouple measurements to
be taken without a large degree of noise from the high voltage environment. Small
sections of poly(viny1)chloride (PVC) electrically resistant tape were placed on the

electrode at the site of attachment of the thermocouple junctions. The thermocouples were

30

attached to the side of the electrode that was not in direct contact with the ER fluid. The

triple junction thermocouple was attached to each aluminum disk as shown in Figure 4.2.

 

Figure 4.2 Triple junction T-type Copper-Constantan thermocouples attached to
aluminum electrodes with poly(viny1)chloride electrical tape backing.

These thermocouples were very sensitive to mechanical damage, however the
space-averaging they provided reduced the amount of data-conditioning necessary before
nmning the Prop-1D analysis. It is common practice to average and initialize the ambient
thermocouple measurements. This feature is inherent ill the design of the triple junction
thermocouples.

To complete the construction of the composite specimen, two equivalent sets of
ER fluid material, gaskets, and electrodes were then sandwiched together with a 0.28mm
thick Kapton resistance heater at the center of the assembly. Before connecting these
components a layer of high thermal conductivity Omegabond 200 thermal paste was
affixed to each side of the heater to enhance the heat transfer and reduce the contact
resistance between the heater and the electrodes. The fully assembled composite specimen

is shown in Figure 4.3.

31

 

Figure 4.3 The fully assembled composite specimen.

The model of this composite specimen, as used for Prop-1D analysis is shown ill
Figure 4.4. Although only small sections of PVC tape were used to insulate the

thermocouples, this tape was represented as a thin 3 inch diameter layer in the Prole

 

 

 

 

 

 

 

 

 

 

 

 

 

model.

*Lineofsylnmetry
2 e
.,, -

-10 0 E E I) 9

ii E a E 2 i ‘2
u _ .—

i’g 0 E a: E 0 .‘2 3
2 K 3 “’ 2 E < 8
'— 3

TC1 TCZ
X ——>

Figure 4.4 Model for Prop 1D Analysis.

32

In the interest of understanding the relative contributions of the thermal
conductivities of the individual materials to the overall effective thermal conductivity of
the specimen, it is worthwhile to examine the steady-state response of the composite
specimen to constant temperatures imposed on either side. This abstraction permits the

consideration of these materials as thermal resistances in series via:

_ T1 - Tn _ Total Thermal Potential Difference
q (AX/M)l +'"(AX/kA)n Sum of Thermal Resistances

 

 

[4.1]

Although having no numerical Significance in the transient measurements, knowledge of
AX/k would give an indication as to its sphere of influence in the total thermal
resistance. Thus a calculation of AX/k for each of these materials is very constructive for
evaluating the effects each material has on the overall thermal conductivity, and on the
optimization of the experiment in general. The results of these computations are shown in

Table 4.1, along with the material properties utilized in the Prop-1 D algorithm.

33

 

 

 

 

 

 

 

 

 

Thickness Volumetric Thermal AX /k
(m) Specific Heat Conductivity
(10'3kJ/in’K) (W/mK)

Kapton Heaterl 0.00014 1.871 0.980 1.429x10r
Omegatherm zoo paste 0.00034 1.369 2.307 1.474x10"
PVC Tapez 0.00016 1.334 0.168 9524le
Aluminum 0.0008128 2.463 167.27 4.859x10'6
ER F1uid3 0.003 3.566 0.105 2.86 1:10-2

 

 

 

 

Table 4.1 Material properties of components used in the composite specimen.

It can be seen that km;- , the effective thermal conductivity of the composite,
depends mostly on the km; ,the effective thermal conductivity of the ER suspension. This
would imply that any inaccuracies in the thermal property information of the peripheral
materials (electrodes, PVC tape, etc.) should not have a dramatic effect on the accuracy of
the estimation of the thermal properties for the fluid. Although the model is complicated
by the presence of additional materials, the effects on the accuracy of the output should be

4.1.2.2 Data Acquisition System

The data acquisition system used for thermal property estimation is detailed in
Figure 4.5. Because of issues regarding shielding of thermocouple measurements as well
as amplification of signals, the Fluke Hydra 2065 data logger was implemented for
obtaining temperature profiles. The data logger holds information in its internal memory

which is then uploaded through an RS-232 interface to a 486 computer at the end of each

 

' Values obtainedfrommeasurementsmadebyBeck, 1996
2 Properties for PVC, Handbook of Plastics
3 Previously published work (Lloyd, 1994)

experiment. The signal-to-noise ratio of temperature measurements using the data logger
was excellent however the scan time per channel was on the order of 1 second, lengthy in
terms of ideal design of experiment criteria. This did not allow for acquisition of multiple
sensor measurements ill a reasonable time period. To circumvent this limitation, bare wire

butt-welded Copper-Constantan triple-junction thermocouples were implemented, the

34

construction of which is outlined in Appendix B.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[Z]
5
:1: 00
[E o 1:] EC] ,.
El 0 1‘;
:1 ;
r: r: g
/ / ':’°° E“
I— ? DC] Cl 1’
f y I I
4 /

   

 

    
 

T-type
thermocouples

H _h voltac leads

 

 

 

 

 

 

Components:

1) Composite specimen

2) 7100/80 PowerMacintosh with Labview software, used as a voltage controller
3) Trek 2025 high voltage DC power supply and amplifier

3) Hewlett Packard DC power supply

4) Hydra Fluke data logger equipped with T-type thermocouple sensors

5) 486 computer / RS-232 interface

Figure 4.5 Data Acquisition System

35

4.1.3 Governing Equations and Boundary Conditions:

The ratio of diameter to thickness of the plates used in the heat conduction
apparatus was quite large (~75: l ), hence heat conduction in the transverse direction was
assumed to be negligible. Convective effects in the fluid were neglected because of the
small scale involved and the associated small Raleigh number. It was also assumed that
thermal conductivity did not vary in the x-direction. In actuality the thermal conductivities
in both the chained and the randomly dispersed states are anisotropic due to the
inhomogeneous nature of the suspension. The anisotropy is more pronounced when the
particles are chained. For the purposes of these experiments however, the medium was
assumed to be homogeneous. The value of k estimated for ER suspensions is thus an
effective thermal conductivity, kfd, representing the combination of both the particles and
the carrier medium

The resulting heat transfer problem is thus represented by a l-dimensional transient

heat conduction mathematical model:

OZT 1 6T

 

where, T is temperature (K), x is distance (111), t is time(s), and or the thermal diffusivity
(mz/s).
The boundary conditions are given by:

6T

_ e55;

 

“0 = q0 constant heat flux at x=0 [4.3]

6T

0x ,2, = 0 insulated at x=L [4.4]

 

and the initial condition by:
T(x,0) = T. [4.5]

The analytical solution, using Green’s functions (Carlslaw and Jaeger, 1959), is:

 

 

L t 2 °° 1 2 2 2
T(x,t) = :0 [ii—2+ ~72 2 608(1111! {-jo —- e‘m " “"L )] [4.6]
eff

1r 1m=,rn

In dimensionless form this solution is written as:

 

2 °° 1 22+
+ + + _ + __ + _ + 2 _ _ -n711 +
r (x ,t )—t +3 x +2(x) fig“, e cos(n7tx) [4.7]
where,
T*— T'T° 48
_qL/kcfi ['1
+ or
1 :Ft [4.9]
and,
+_£ 410
x _L [- ]

4.1.4 Data Analysis

Once the appropriate mathematical model and physical experiment were
established, temperature profiles were obtained to extract the desired parameters. Data
acquisition was initiated and a constant voltage applied to the Kapton heater to deliver a
known and constant heat flux to the composite specimen. The Kapton heater was powered
by an Hewlett Packard 6024A DC. power supply. Before experimentation the resistance
of the heater was measured with a Textronix hand-held digital multi-meter, as was the

exact voltage supplied to the heater. It was assumed this output remained constant over

37

the duration of the experiment. The heat flux was applied for a pre-determined period of
time. Data acquisition was continued for a period of time after turning off the applied heat
flux.

When the test was complete the data logger memory was uploaded through the
RS-232 interface to the hard drive of the 486 computer. A temp.dat file was created by
the Starter software which stored the uploaded information. A short Quick-Basic
program was utilized to translate the data logger time stamp to seconds and to put the
temp.dat file into a text format which could be edited for input to ProplD. This program
is listed in Appendix C.

Prop-1D required two input files. The first file, the input control parameter file
(" .icp), contained the experimental design parameters such as composition of the
specimen, corresponding thermal properties and dimensions, duration of experiment and
sensor location. Initial estimates of the thermal properties of interest are also included in
this file. The second file (*.txt) contained the discrete temperature measurements at each
location, as well as the applied heat flux history. The generated output file (*.out)
included a record of the input control parameters, the temperature data, estimates of the
desired parameters and also information about 95% confidence intervals, sequential
estimates, residuals, and sensitivity coefficients, all of which gave valuable information
about the validity of results as well as insight into how the experiment Should be

redesigned. A sample of each of these files is contained in Appendix D.

38

4.1.5 Experimental Method

It was expected that the thermal properties of the ER fluids in the isotropic state
would be very similar to that of the carrier fluid alone. Silicon oil was thus utilized for the
design of experiment, as its properties were already well-established, and could better
guide the optimization process. The details of the experimental design are contained in
Appendix B. When this experiment was satisfactorily optimized, water was evaluated to
test the experiment’s reliability and accuracy for evaluating other fluids. Finally, the ER

suspensions were examined ill zero DC field and low DC field conditions.

4.1.6 Results and Discussion

Shown ill Figures 4.6 and 4.7 are the results of a series of analyses on silicon oil.
The duration of experiment was 84 seconds, with an applied heat flux of 1907 W/m2 for
48 seconds. This duration of heating and data collection was calculated fi'om the Fourier
number, which is detailed in Appendix E. It can be seen from Figure 4.6 that the values
obtained for thermal conductivity were reproducible to within 4%. When the average of
replicate measurements was compared to the literature value for silicon oil at 50°C the
agreement was within 8%. Conversely for volumetric specific heat measurements, as
shown ill Figure 4.7, the deviation fiom the mean was as much as 8 %. The reference
value for volumetric specific heat measurements was obtained by multiplying the listed
manufacturer’s value for density at 25°C by the value for specific heat as measured by
DSC at 25°C. The Cp value at this temperature was not provided by the manufacturer

however the DSC measurements at the higher temperature were in agreement with the

39

manufacturer’s listed higher temperature values, lending credence to the DSC analysis.
When this reference value for volumetric specific heat was compared to the average of

replicate measurements, the agreement was within 13%.

Estimates of Thermal Conductivity (k) of Silicon Oil
Applied Field Strength: 0 Vlmm

 

 

0.25 1’
0.2 +
0.15 "F I
g i. 1' i. i. Literature Value
.1: 0.1 «» 33d”. C
0.5 +
O i
1 2 3 4 5
Teet ’

Figure 4.6 Estimates of thermal conductivity of silicon oil.

Estimates of Volumetric Specific Heat (p43,) of Silicon Oil

 

 

3000 T Applied Field Strength: E=0

25!) ii- } }
g 2000 .. l. +_
i 1500 i l-
‘51 Literature Value
q, 1H!) '1" Em. C

m -1.
o n
1 2 3 4 5
rest:

Figure 4.7 Estimates of volumetric specific heat of silicon oil.

40

It is hard to compare these numbers precisely because the measured values
represent an average of the parameters over the temperature range that evolves due to
application of the constant heat flux. Literature values for thermal conductivity were
available only at a single temperature. In the transient experiments, the dynamic
temperature range was 23 to 40 °C. For the purposes of the optimization it was assumed
that over the 20 to 50 °C temperature range, the thermal conductivity and the volumetric
specific heat remained relatively constant.

The inability to obtain multiple data points in a relatively short period of time
prevented the measurement of the contact resistance in the system and thus complicated
the results. It was expected that this would be included in the estimate for the thermal
properties of the ER suspension. This is consistent with the slightly lower estimated
values of thermal conductivity. This however does not explain why the volumetric
specific heat estimates are consistently higher than the reference value. An examination of
the residuals indicated some correlation in errors, two-dimensional heat losses, as well as
some irregularity in the sequential estimates for volumetric specific heat, as is discussed in
Appendix E. The sequential estimates did not approach a constant value and stabilize, but
instead were somewhat erratic in nature. This indicated that the model was not in perfect
agreement with the physical experiment and that there was a possible identifiability
problem with determining both parameters simultaneously.

Despite the problems identified with the experiment, the reproducibility and
relative accuracy of the measured parameters were considered adequate from the
standpoint of evaluating thermal property changes due to electrorheological response, as

property changes of several hundred percent were expected. To ensure that the

41

experiment could perform equally well for other types of fluids and with the same level of
accuracy, water was also evaluated.

For the water analyses the duration of the experiment was 54 seconds, with an
applied heat flux of 1906 W/m2 for 30 seconds. The results of these analyses are given in
Figures 4.8 and 4.9. It can be seen that the estimates of thermal conductivity for water
are similar to those of silicon oil. When compared to the literature value at 30 °C, the
agreement is within 8%. Again the estimates are consistently lower than the reference
value, concordant with the unmodeled contact resistance. Replicate measurements agreed
to within 2%. For the volumetric specific heat measurements agreement among replicate
analyses was within 3%, however comparison of the experimental mean and the literature
value gave agreement to within 25%. Similar irregularities were. observed in the

sequential estimates, and the residuals had the same character as those obtained for the

 

 

silicon oil experiments.
Estimates of the Thermal Conductivity (It) of Water
Applied Field Strength: E=o Vlmm

0.7 1—

0.6 ~ .

O 5 ,. i. 1' i' Literature Value
* ' 30 Deg. c
E 0.4 ~»
E 0.3
8

0.2

0.1 ..

o f 41
1 2 3 4
Test a

Figure 4.8 Estimates of thermal conductivity of water.

42

Estimates of Volumetric Specific Heat (p-C,)of Water
Applied Field Strength: E= 0 Vlmm

 

 

”m 1

am «e
E 5000 1
"g 4000 «~ "
5 3000 ‘_ Literature Value
9: 30 Deg. C

211'!) ~~

1000 3r

0 e
1 2 3 4

Test!

Figure 4.9 Estimates of volumetric specific heat of water.

Based on the results of these experiments with silicon oil and water it can be
reasonably concluded that using this experimental method it is possrble to reproducrbly
generate a number that should be a sufficiently accurate measure of the thermal
conductivity of isotropic suspensions to evaluate property changes. Volumetric specific
heat measurements were not as reliable in terms of an accurate representation, and the
sequential estimates raised suspicions as to the significance of the measurement. The
parameters however were reproducible and thus can be cautiously used to evaluate
property changes. Given the limits of reproducrbility, thermophysical property changes

less than 5% could not be considered statistically significant.

43

Isotropic ER Fluid suspensions were evaluated without application of electric
fields. The experimental duration was 108 seconds with an applied heat flux of 1906.2
W/m2 for 108 seconds. Again reproducibility was within 3%. Sequential estimates and
residual analyses were consistent in character to the previously obtained results for silicon

oil and water, indicating that the non-idealities of the experiment were systematic in

 

 

nature.
Estimates of the Effective Thermal Conductivity (in...) of
fv=10% Type 3A ZeoliteISilicon Oil
0.2 .- Applied Field Strength: E= o Vlmm
0.18 ..
0.16 .. f +- +_ 1. 1.
0.14 ~~
0.12 -.
E 0.1 4»
3 0.00 «-
0.06 --
0.04 «»
0.02 ..
0 4
1 2 3 4 5
Tears

Figure 4.10 Estimates of the thermal conductivity of 10% volume fraction Type 3A
zeolite/ silicon oil

Estimates of Volumetric Heat Capacity (p6,) of

fv=10% Type 3A ZeoliteISllicon Oil
Applied Field Strength: E: o Vlmm

 

 

2500 ~—
1. l l- l- ,
2000 ..
02 13” +
i
U9 1000 i
Q
500 1»
0
1 2 3 4 5
Tears

Figure 4.11 Estimates of the volumetric specific heat of 10% volume fraction type 3A
zeolite/silicon oil

The value of thermal conductivity measured for the 10% volume fraction ER
suspension was higher than that of silicon oil alone. This was an tmexpected result. Also
a general observation was a fluctuation in the estimated properties for the same volume
fiaction fluids prepared on different days. This fluctuation was highly likely due to
moisture content variations. To further explore these observations measurements, a series
of ER suspensions of different volume fiactions were prepared on the same day and
evaluated. The results of these analyses are shown in Figure 4.12. The wet and dry

suspensions were made according to the method presented ill Chapter 2.

45

Thermal Conductivity (WImK) vs. Volume Fraction (fv)
Applied Field Strength: E=0 Vlmm

 

[11111111111111

 

Thermal Conductivity (WImK)
«taboo-smwssmalsrcnroo-smuemmsrceoo

 

. Dry LiteratureValue.
I Wet

 

 

 

411111111111

99999999999999???PPPPPPPPPPPPPP
OOOOOOSOOOdddAAdddddNNNNNNNNNNw

cameo->01

 

 

 

l T l I l l l l I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Volume Fraction (iv)

Figure 4.12 Estimates of thermal conductivity of a wet and dry series of type 3A
zeolite/ silicon oil suspensions.

It can be seen that the thermal conductivity increases with increasing volume
fraction of zeolite particles which seems counter-intuitive based on the values of thermal
conductivity for zeolite and silicon oil (0.04 and 0.1407 W/mK, respectively). As
discussed in Appendix A, zeolites are aluminosilicate cage arrays. A measurement of the

thermal conductivity of this material will necessary include the presence of large pockets

46

of air in the cavities of the sodalite cages. In its dry-packed state the zeolite will behave as
porous media, serving to reduce the heat transfer by restricting the movement of air in the
cavities (Zeng et. al., 1995). It is informative to compare the thermal conductivities of air
with the aluminum oxide and silicon dioxide that comprise the framework of zeolite
crystals (Table 4.2). It is likely that when the zeolite is suspended in the silicon oil, the air
pockets are no longer present and the contribution of the zeolite to the effective thermal
conductivity is dominated by the zeolite’s structural elements. These values are seen to be
substantially higher than those of silicon oil hence small amounts of zeolite can have

significant effects on the thermal conductivity.

aluminum ° ' 46
aluminum ' ' 36.0

Silicon ° ' ' 6.21-10.4
silicon ' ' ' 1.38
air 0.026

 

Table 4.2 Thermal conductivity values for aluminum oxide and silicon dioxide
(Gebhart, 1993).

It can be concluded that in the range of volume fiactions typical of ER fluid
applications, the zeolite serves to increase the thermal conductivity, not decrease it. In
general, the effective thermal conductivity does not decrease linearly from the value of
thermal conducitvity for pure silicon oil, 0.14 W/mK, to the value for pure zeolite, 0.04
W/mK The relationship between volume fraction zeolite and effective thermal

conductivity is thus non-linear.

47

It has been established that reproducible values are possible to obtain for water,
silicon oil and the isotropic ER suspensions via the adapted l-D transient heat conduction
apparatus. Measurements in high voltage fields were attempted next. These
measurements proved to be considerably more challenging.

Shown in Figures 4.13 and 4.14 are the results of applying low field strengths to a
5% volume fiaction of an ER fluid suspension The microscopic evaluation of the 2%
suspensions indicated that low field strengths may be adequate to ensure substantial
chaining, despite the fact that almost all applications discussed ill the literature utilized
electric fields of several thousand volts. As can be seen from the estimated results
however, no change in thermal conductivity or volumetric specific heat were observed at
these field strengths. It is possrble that chaining did indeed occur, but the effective thermal

conductivity, although different in character, was the same in measured magnitude.

Therrnai Conductivity (it) of iv=5% Type 3A
ZeoliteISilieon Oil vs. Field Strength (E)

 

 

0.2
015 L e e

E

01 ..
E
"‘ 0.05 ~

0 I Y r 1
0 100 200 300 400
E (Vlmm)

Figure 4.13 Thermal conductivity of fV = 5% Type 3A zeolite/silicon oil suspension at
low field strengths.

48

Volumetric Specific Heat (pC,) of iv=5% Type 3A
ZeolitelSlilcon 011 vs. Field Strength (E)

 

0 100 200 300 400
E (Vklln)

Figure 4.14 Volumetric specific heat of f. = 5% Type 3A zeolite/silicon oil suspension
at low field strengths.

Similarly for higher volume fractions, no significant change in properties was
evident. Shown in Figures 4.15 and 4.16 are the thermal conductivity and volumetric

specific heat estimates for f. = 10% and 20% suspensions.

Estimates of Thermal Conductivity (it)

 

 

 

 

0.22
0.21 .. $2315 if??? ‘ E= 0 Vlmm
0-2 .. 0 E= 100 Vlmm
9‘9 ‘" I E= 200 Vlmm
0.18
0.17 ‘-
E’ 0.16 «» l A 1 + + + g
0.15 v
0.14
0.13
0.12 a % T 4
1 2 3T“ ’4 5 6 7

Figure4.15 Thermal conductivity of f. = 10% and 20% Type 3A zeolite/silicon oil
suspension at low field strengths.

49

Estimates of Volumetric Specific Heat (pCp)

 

 

 

 

2800
.fl'flfi 0520112
27001752315 Tests6.7 ‘EWV/mm
250°“ eE=1OOVImm
g 350°“ .E= 200 Vlmm
" 2400»
5 m“ 1 l l +
3 mi» +
0
°- 21m1. + +
20001»
1900 ..
1&1) fit
1 2 3 4 s 6 7
roots

Figure 4.16 Volumetric specific heat of f. = 10% and 20% Type 3A zeolite/silicon oil
suspension at low field strengths.

Upon application of higher field strengths, several difficulties were encountered.
When electric fields were applied in excess of a certain field strength characteristic of each
individually prepared fluid, the electrical conductivity quickly increased to a point where
the high voltage amplifier current limited at 5 mA. This caused the voltage to drop to
maintain Ohm’s law, thus not allowing the voltages typically associated with intense
chaining activity to be applied. Significant heat generations were observed when the
current climbed to these limiting levels, sometimes as much as 10°C in a few seconds,
depending on the electric field demanded and on the particular fluid. In some cases, at
low field strengths, applying a heat flux to the system caused the current to increase to a
point where the amplifier rapidly current limited, thus filrther limiting the upper range of
field strength At lower current levels the heating was less extensive but was indeed

present. Coupled with this limiting situation was the appearance of bubbles in the system

50

and evidence of deterioration of the electrode surfaces upon disassembly of the apparatus.
The ER fluid was also observed to flow out of the apparatus indicating significant levels
of expansion.

Shown in Figure 4.17 is an example of a temperature rise in the fluid due to
application of a 500 V/mm field. In this example the temperature rises were very small
over short time periods, or the typical duration of a parameter estimation experiment. As
was oftentimes the case however, this temperature rise was not negligible in comparison
to the temperature rise due to application of the heat flux necessary to measure the
parameters. The electrical response of the manufactured ER fluids was very
unpredictable, and seemed to be heavily dependent on the ambient humidity conditions
during manufacture of the fluids. The field-dependent temperature response was
observed to qualitatively correlate with the electrical conductivity of the fluids, and
consequently with the water loading in the ER fluid. Fluid manufacture and
experimentation were not carried out under controlled humidity conditions and oftentimes
exposure to excessive levels of high temperature steam was unavoidable. The result was
greatly fluctuating responses to electric field conditions making quantification of

phenomena difficult.

51

Effect of High Voltage Field (500VImm) on the
Temperature Distribution in 5% Type 3A Zeolite
[Silicon Oil Electrorheological Fluid

 

 

 

 

 

 

700
24,4 4 Temperature at X=0
------ Temperature at X=L .. 600
24.2 ~- A I' IV ll

 

Temperature (° C)

 

 

 

Figure 4.17 Effect of electric field on the temperature distribution in the ER fluid
system

This resistance heating is not a new phenomenon. Lee et al (1993) and Nelson
and Suydam (1993) have indicated that power consumption in ER fluids increases with
increasing field strength and with increasing temperature, consistent with general electrical
theory. Before judicious modifications can be made to circumvent this problem, a means
of quantitatively characterizing this temperature response as a function of current is
necessary. This requires an analysis of the underlying mechanisms responsrble, as well as a
modeling of the response in the form of a predictive model.

Zhang and Lloyd (1993) indicated 50% change in the vahre of k with the
application of a 760 V/mm AC field. There are several reasons why this may not be
easily achievable with DC fields. It is becoming well-established (F oulc et al, 1996;

Davis, 1992a; See et al., 1996) that in high frequency AC fields, the governing parameter

52

in ER activity is the complex permmitivity mismatch, whereas the values of electrical
conductivity of the individual components of the ER fluid represent the dominant
controller in low frequency AC or DC conditions. Thus a material which is ER active
when utilized with AC fields, may not be effective in DC field conditions.

Foulc et. a1. (1996) have suggested a ratio of solid to liquid electrical
conductivities in excess of 100 to ensure significant ER effects. More specifically Boissy
et al. (1996b) have indicated that a practical conductivity guideline of 103 61. < 03 < 107,
where 0L and as are the electrical conductivities of the liquid and solid phases,
respectively, for DC fields. As seen from Table 2.1, the conductivity mismatch from
zeolites and silicon oil may or may not satisfy these criteria. As previously indicated,
somewhat crude humidity control was attempted with the zeolites to control the
conductivity of the solid phase. It was found that more sophisticated equipment was
necessary to achieve reproducrble water-loadings. Humidity control ill the liquid phase
was not given priority consideration because of its weak hydrophilicity in comparison to
the zeolite phase. Results by Wu et al (1996) have indicated that this may be a poor
assumption. Wu et al formd that the current density and electrical conductivity of Dow
Corning 200 silicone oil increased with electric field strength and water content. Control
of water content and evaluation of electrical properties of both phases are thus emerging
as essential ingredients to designing a successful ER fluid.

Qiu et. a1. (1996) in a comparison of the temperature dependence of AC and DC
conductivities, found evidence that charge carriers respond differently to AC and DC
fields. It was found that the dielectric loss could be divided into two parts, one part

originating from DC conduction and the other portion from the AC response of bound

53

charges inside the particle. When the difference between these is small, there is little
evidence of ER activity, whereas the converse is true when these components of dielectric
loss differ greatly. It was found that in an atomite ER fluid this difference was small
below 250 K but was greatly increased above 300 K In the experiments by Zhang &
Lloyd the applied heat flux resulted in a final temperature of 320 K. If the zeolite
suspension behaves similarly, this higher temperature might have favorably enhanced this
dielectric loss component difference.

The estimation routine for the sample investigated in Zhang and Lloyd (1993) was
such that the experimental duration was 600 seconds. This is not precisely in accordance
with the optimal heating time for this experimental design and, as shown by the sequential
estimates ill Appendix B, an estimate based on measurements attained over varied
experimental durations can yield dramatically different results. This may have affected the
final values and may have introduced error into the final results.

It is possible that property changes could be observed for these fluids under DC
conditions if higher field strengths could be utilized. In the interest of improving the range
of field strengths over which the property estimation could be carried out, an attempt was
made to quantify the temperature rises ill the ER fluids due to application of electric fields,
in an order-of-magnitude sense. The relationship between the suspected Joule heating and

the resulting temperature rise can be given by:

Vpc,—=12R [4.11]

54

and thus the temperature rise is by:

El
voc,

AT=

 

At [4.12]

where E is the applied field (V), I is the current (A), R is resistance ((2), V is volume (cc),
p is density (g/cc), and At is the time period of interest. The Cp data utilized in this
calculation was obtained from MDSC analysis of the zeolite suspension. These
measurements are outlined in Appendix F. Using the nominal values given by: E=485V,
I= 5mA, V=7cc, p=1.25 g/cc, Cp=1.3 J/g°C and At=605, the expected temperature rise
was determined to be on the order of 13°C. The experimentally observed vahre under
these conditions was approximately 2°C. This would seem to indicate that there were
also other interferences in the system besides pure Joule heating. Stangroom (1996) has
pointed out that the currents generated in ER fluids are non-Ohmic. He utilized a
quadratic model of current with constants characteristic of the fluid. Despite the fact that
these order-of-magnitude calculations are based on an Ohmic assumption, the results
indicate in a qualitative sense, that thermal energy dissipations are to be expected in these
high current systems.

If the temperature rises due to application of the field are comparable to those due
to the imposed heat flux, the l-D transient heat conduction model will no longer be
appropriate. A new mathematical model including a source term for Joule heating and
possibly other phenomena would be necessary to represent what is physically occurring in
the ER system This would become a very complicated problem to solve, and would

preclude the use of PROP-1 D for parameter estimation.

55

As pointed out in Chapter 2, microscopic particulate matter was observed to
dissociate from the electrode during the application of high voltage fields. Boissy et. al.
(1996a) have considered the effect of electro-chemical processes occurring at the
electrode interface on current density. It was suggested that a second component of
current density results from injection of electrode ions into the solution when high voltage
fields are applied, which could potentially control the current levels generated. This seems
consistent with the previous observations of excessive current levels, and evidence of a
chemical reaction at the electrode surface. If the particulate matter which is originating at
the surface is a charged metal ion then it is likely to be highly conductive. This has other
ramifications.

See et. al. (1996) have investigated the effect of adding small amounts of highly
conductive particles to ER fluids. A marked decrease ill the viscosity change
characteristic of the fluid was observed. If charged metal particles are entering into the
ER suspension it is likely that they will affect the structure formation This serves to
further complicate the observed results.

In terms of the ER fluid flowing from the gasket material in high current situations,
it appears as if the fluid is boiling, however the temperatures are nowhere near the levels
necessary for this to occur. Consistent with microscopic imaging observations, hydrolysis
of water and the associated evolution of hydrogen gas seems to be a likely source of the
bubbles. The expected expansion of the fluid under these temperature conditions can be

calculated from:

Ell?

[4.13]

<l~

56

where 13 is the coefficient of expansion. For Silicon oil this value is 0.00043. This yields
an expected volume change of 0.045 cc for a 15 degree temperature change, which
corresponds to a 0.6 % expansion. This would not cause the material to flow fi'om the
gasket hence the temperature rise due to heating is not the source of this phenomenon

At low field strengths, the electrical behavior was indicative of chaining activity
(McGregor, 1997), however no measurable change in thermal conductivity was measured.
Field strengths typical of ER fluid applications are upwards of several thousand volts.
These voltages would be catastrophic to the system under study. Within the limits
imposed by electrical conduction in the system, a change ill effective thermal conductivity
was not discermble at the field strengths possible.

McGregor(1997) has worked on a control algorithm which effectively controls the
electrical conductivity of a given fluid by altering the voltage applied, however the control
is limited to the ability to manipulate the moisture content, as the fluid will operate only in
a range predetermined by the inherent conductivity of the particles. The moisture content
of the zeolite affects the surface charge density on the particles, increasing the dielectric
constant, and affecting the formation of the electric double layer. Conrad et al (1994)
examined the effect of heating on the electrical an mechanical properties of zeolite/ silicone
oil suspensions. The conductivity of the suspensions increased with particle concentration
and water content heating, decreased the permittivity. The electrical conductivity of the
suspensions is directly related to this double layer development and the underlying surface

conditions.

57

To continue working with the zeolite/silicon oil systems it will first be necessary to
determine the levels of water-lo ading that yield appropriate values of effective electrical
conductivity. The mismatch between the conductivities of the suspending phase and the
dispersed phase are important to maximize the ER response ill DC field conditions.
However, to ensure the minimization of heating due to current dissipations the effective
electrical conductivity needs to be maintained below certain levels. If this can be achieved,
the current l-D transient heat conduction procedure can be utilized to measure the thermal

properties of chained ER suspensions at higher field strengths.

4.1.7 Error Analysis

There are a variety of aspects of this experiment which could be isolated as
contributing some degree of error to the experiment. Because of the time required by the
data logger to scan each channel, the time interval necessitated to ensure equal time
increments was 3 s. This is a substantial interval given that the duration of the experiment
is on the order of 1.5 minutes. Reduced intervals would be desirable however with the
current apparatus, the limit has been reached. Alternate temperature acquisition
equipment could provide reduced time intervals, however the cost to ensure quality signals
would be substantial. A data acquisition board and amplification system would be
necessary.

The timing of the heat flux application was done manually with a stop watch. A
controller online with experiment to start the heater and indicate the precise time of

application would assist in the parameter estimation routine.

58

An evaluation of the residuals revealed significant correlations indicating the
presence of systematic errors. Further optimization of the experiment in terms of the
contact resistance could possrbly reduce some of these errors. Also, the use of triple
junction thermocouples instead of multiple sensors is likely to have some adverse effect on
the correlation of errors. Alternate temperature acquisition equipment would probably
improve the situation One of the preliminary assumptions was that systematic effects
were removed from the system such that the remaining errors were considered to be
random This was not the case. The residuals also provided information about the
boundary conditions. The residuals drifted down near the end of the experiment,
indicative of heat losses at the x=L boundary.

An error and sensitivity analysis incorporating these estimated measurement errors

canbefoundinAppendixG.

4.2 Steady-State Measurements

Because of the complex nature of the electrical behavior in the ER system and the
associated temperature response of the generated current, it was difficult to model the
current behavior in the transient heat conduction model A simpler steady-state method
was evaluated for its potential for determining the thermal conductivity in high field
situations.

The apparatus used for the steady-state experiments was essentially the same as for
the transient measurements except the air spacer was removed and free convection was
allowed to occur at the x=L boundary. As ill the transient measurements a heat flux was

quantified and applied. Instead of measuring temperature profiles, the temperature

59

difference across the specimen was measured once the specimen reached steady state. The
applied heat flux had to be considerably higher to ensure that this temperature difference
was resolvable. It took approximately 2 hours for the specimen to come to steady-state
conditions when the applied heat flux was 471.6 W/mz. A sample steady-state

temperature profile is shown in Figure 4.18.

Shady Stab Temperature Profiles
f.=15% Zeolite/Silicon Oil

03
O

 

A 01
O O
1 L

 

 

 

x:

N
0

Temperature( °C)
(a)
O

x=L

 

an.

O
J
7

 

 

 

 

o
r.
1'

 

20 4O 60 80 100 120
Tbne(minutes)

0

Figure 4.18 The temperature profiles measured across the composite specimen as the
steady-state condition developed.

Because the parameter of interest is thermal conductivity and not temperature
distribution, there is no need to analytically solve the steady-state equation. The value of
thermal conductivity can be determined via knowledge of the applied heat flux, q/A, the
thickness of the components, x, the convective heat transfer coefficient, h, and the
temperature difference across the specimen, AT, through utilization of the series

resistance concept:

60

(AT)

X:in)...+(x)...+(x)...+(%)...we]

 

[4.14]

Calculation of the thermal conductivity of the ER fluid, using a value of 5 W/mzK for h,
resulted ill a reproducible value of 0.2 W/mK The limits on accuracy are related to the
lack of knowledge about the convective heat transfer coefficient. The thermal
conductivity measured was an effective value, as in the transient case. This method gave
reasonable agreement with the value of thermal conductivity obtained from the transient
measurements for isotropic suspensions. When low voltage fields were applied to the ER
sample, the amplifier current- limited almost immediately. The steady-state temperature in
the system upon application of the field was near 60°C, considerably higher than the
maximum temperature reached for the transient measurements. The current generations
were observed to increase dramatically with temperature of the composite specimen

These temperature-sensitive current generations, as monitored via the front panel of the

supply/amplifier, rendered the application of any finite amount of electric field impossrble.

 

Chapter 5

Conclusions and Recommendations

The short experimental times in the l-D transient heat conduction analyses
minimized the error due to heat losses versus typical steady-state experiments.
Information about both thermal conductivity and specific heat were extracted from a
single experiment. Extra care had to be taken in electrically insulating the thermocouples
to prevent noise in the measurements due to application of electric fields, which
complicated the Prop-1 D model. This insulation also imposed a constraint on sensor
location, in turn limiting the experimental optimization. Although some degree of
precision was sacrificed, evaluation of thermal properties in DC field environments was
possrble.

Agreement with literature values for silicon oil and water were within 8 % for
thermal conductivity and 13% for volumetric specific heat. Replicate measurements were
in agreement to within 4% and 8% for thermal conductivity and volumetric specific heat,
respectively. Replicate measurements of the thermal properties of the ER fluids prior to
application of electric fields gave estimates within 3% of one another. Evaluation of the

sensitivity coefficients and residuals for all of the materials analyzed revealed correlated

61

62

errors and indicated problems with the estimation of the volumetric specific heat.
Although the experiment was not ideal, the values obtained for thermal conductivity were
reproducrble and in reasonable agreement with literature values. The results obtained for
volumetric specific heat measurements were less reliable, but too were reproducrble.
Although there were some challenges with utilizing the 1-D transient heat conduction
experiment, the method seemed able to predict values with enough precision to be utilized
for evaluating property changes above the limit imposed by the typical spread about the
mean.

At low field strengths no statistically significant change ill thermal properties was
observed. Based on the electrical behavior during these experiments and similar
experimentation with the microscopic imaging apparatus, it seems likely that chaining is
indeed occurring at these field strengths.

The application of higher field strengths was not possrble due to the bounds
imposed by the current limit of the high voltage power supply (5 mA) and the inherent
electrical conductivity of the ER fluid compo site. Because the current levels that were
generated upon application of field strengths on the order of 500V/mm exceeded 5 mA,
high voltage levels could not be sustained. This power consumption was a problem, not
only limiting the voltage range ill which measurements could be taken but possrbly
excluding the voltage levels necessary for sufficient chaining activation Depending on the
sensitivity of the fluid (a direct consequence of its water content), the high voltage limit

before substantial heating occurred was generally in the range of 300-500 V/mm.

63

Steady-state methods proved to be equally disadvantageous. Higher temperatures
were necessitated for these experiments and thus the challenges of minimizing the current

were magnified.

There are several routes to minimizing the current generation such that this
generation term can be neglected. Precise control of the conductivity of the ER fluid via
control of the moisture content could be a viable alternative for the system explored in this
work. This would require the utilization of environmental chambers or similar equipment
to precisely and reproducibly manipulate the water content. Another route to minimize
the problems associated with high conductivities would be to select new materials which
have more stringently controlled electrical properties. The utilization of AC fields,
although proffering its own challenges ill terms of insulating thermocouples fi'om induced
noise, would likely not have the same problems with heat generation due to currents, as

the sinusoidal current density averages to zero.

From the transient measurements it was evident that the thermal conductivity of
the ER fluids increased with increasing volume concentration of fluid. The presence of the
zeolite insulating particles thus served to augment the effective thermal conductivity
instead of decrease it. This complicates the ability to predict the effect of ER fluid
chaining on the value of effective thermal conductivity.

Within the voltage limits imposed by minimal current generation, a change in
effective thermal conductivity was not be observed for the range of volume fiactions
investigated. Although the primary focus should be to isolate the conductivity regime

which allows for maximum application of voltage without substantial current generation,

64

advances towards effective heat transfer augmentation can also be made via control of
fluid design parameters. Although the transition from an isotropic to a chained structure
in ER fluids should yield changes in effective thermal conductivity, based on the results of
Furmanski and Floryan (1994) it stands to reason that utilizing particles with an aspect
ratio greater than 1.0 (spherical) should substantially increase the dynamic range over
which these particles operate.

The non-linearity of the effective thermal conductivity with particle concentration
complicates the explanation of observed results. To further optimize the methodology it
would seem desirable to utilize a disperse phase that is non-porous in nature. The simplest
choice would be a material with a thermal conductivity of several orders of magnitude
larger than the suspending medium This would serve to simplify the expression for
effective thermal conductivity and possrbly permit examination of the effect of ER
chaining on the thermal properties of the individual phases. This in turn would lead to a
greater understanding of the overall effect on the heat transfer occurring in ER fluid

composites.

APPENDICES

APPENDIX A

Appendix A
Fundamental Issues

A.1 Inter-particle Forces

To address the underlying science of ER phenomena, it is necessary to first define
the regime within which these materials lie. The term ‘suspension’ is often used
generically to descrlbe a mixture of finely divided solid particles within a gas or liquid
medium By definition, however, for such a dispersion to be deemed a suspension, the
solid phase must spontaneously settle (Brady & Hohlm, 1993). The dimensions of the
suspended phase, as well as the densities of both the suspended phase and the suspending
medium will determine the rate of this settling. A ‘solution’ differs from a suspension in
that the dispersed phase involves molecules (Everett, 1988). The molecules resist settling
because of thermal motion. Intermediate to these regimes are the colloids, wherein the
dispersed phase has dimensions in the range of l- 500 nano-meters (Weiser, 1949). The
particles in colloids do not settle, diffuse very slowly, and have very large surface areas
relative to particle volume. Although the bulk of ER fluids are technically suspensions due
to the size of the suspended particles, there are materials that push over into the colloidal

and solution regimes and still demonstrate an ER response (Filisko, 1994).

65

66

The ER fluid investigated in this work, as well as many of the ER fluids discussed
in the literature (Uejima, 1972; Conrad, 1994; Kordonsky et al, 1991), have particle
dimensions on the order of micrometers, and may border on the edge of the colloidal
domain Because the implementation of a disperse phase of colloidal dimensions would
circumvent the need to address settling issues in ER fluid-filled composites, it would seem
desirable to push this dimensional envelope. The field of colloidal science intrinsically
imparts much to the quest for an understanding of the ER fluid phenomenon.

Shown ill Figure A1 is type 3A zeolite, an open framework aluminosilicate that has
the general formula My [(8102),( (AlOz)y]. n H20. It was used as the disperse phase in the
ER fluids investigated in this study. The fi'amework is made up A104 and $104 tetrahedra,
which share apical oxygens, giving rise to a 3-dimensional crystal lattice called a sodalite
or [3 cage. When these sodalite cages are stacked together, large cavities form, and these
internal volumes are connected to one another through pores or apertures. This results in
an ordered cubic array of channels with precise diameters. These highly porous structures
yield surface areas in the range of 300-700 mz/g, with 98% of the surface area being
internal The pore size in a typical type 3A zeolite is approximately 3.5 Angstroms, which
is large enough to permit the penetration of water molecules and small ions.

The sodalite cage has a net negative charge. This negative charge is balanced by
Na+ cations. The Na+ ions in the beta cages are held by electrostatic attraction to the
oxygen anions in the framework (Dean, 1948). When the zeolite is fully water-loaded the

Na+ ion can exchange for other cations ill the water.

67

 

Figure A.1 Environmental Scanning Electron Microscopy (ESEM) image of UOP
Type 3A zeolite ill a minimum amount of silicon oil.

To formulate theoretical models to predict electrorheological response and design
materials tailored to specific applications, it is necessary to understand the long—range and
short-range inter-particle forces leading to suspension stability, and the ER effect in
general. These molecular forces can be characterized in terms of interactions between
fluctuating dipoles and motions of outer electrons, and can be calculated quantum
mechanically. A summary of these calculations as outlined by Everett (1988) follows.

Attractive forces are quantified as :

 

1"" = 7 [All

It can be seen that the attractive force increases in magnitude as the molecules approach

one another. At nuclei separation r, this force is proportional to the inverse seventh power

68

of separation. From this, the free energy of attraction between a pair of atoms or
molecules from a distance d to infinity can be found by integration, yielding:

_A'
d6

 

A6“ = [A2]

A’ can be expressed roughly in terms of experimental quantities that are related to the
nature of the individual molecules through quantum mechanical properties:

A'= (3/4)hva 2 [A3]

where,
h = Plank’s Constant (6.63 E-34 Js)
v = a characteristic frequency associated with the first ionization energy

a = polarizability

For two dissimilar molecules, 1 and 2:

 

V V
A'lz = (3 / 2)h( 1+: )aIaZ [A4]

v1 2

So, as the atoms approach, the free energy becomes increasingly negative, because of the
increasing attractive force. At close distances however, the electron clouds begin to
interact and if the electrons are ill non-bonding orbitals, repulsive forces arise. This causes
the free energy to rise. When the electron clouds interpenetrate this free energy becomes
essentially infinite. This is referred to as Born Repulsion, and gives rise to the

approximate expression for free energy of repulsion:

69

we) .5.

The total potential energy, referred to as the Lennard-Jones potential, is thus given by:

 

AG=AG‘°"+AG"‘=( % )+( 21?. )

Usually the depth of the potential well, am, is a more convenient measure of the

interaction than the constants A’ and B’. The expression thus becomes:

easier-1’21“]

where r0 is the distance at which the potential is zero.

What we have arrived at is a description of the free energy interaction of two
molecules. To determine inter-particle relationships it is necessary to find a model which
accurately accounts for the interactions between all molecules in all particles within the
limits of influence of the individual forces.

Halsey (1992) has experimentally studied the long-range, anisotropic character of
the forces attributing to electrorheological response. Ginder (1993) has also studied inter-
particle interactions using non-invasive diffuse optical probes to elucidate time scales for
structure formation. These results compared favorably with predictions based on

dielectric properties.

A.2 Dielectric Phenomenon
In Wmslow’s original work (1949) he alluded to the role of dielectric properties in
ER activity. Many researchers since have elaborated upon these precepts to generate

comprehensive models of the ER effect that detail the relationship between the dielectric

70

constants of the disperse phase and the suspending medium (Davis, 1992a; Khusid,
1996). This interplay of properties has been indicated as an important criterion in
developing materials with an ER response. In a recent finite element model by Davis
(1992b) it was shown that ER response depends on different dielectric properties
depending on the field conditions. At high fiequencies it was found that the dielectric
mismatch was the dominant parameter in determining the capacity for ER behavior,
whereas at low frequency and DC. field conditions the ratio of particle to suspending
medium electrical conductivities was a controlling factor. These results were based on a
dipole approximation.
A dielectric is an insulating material having distinct electrical properties, in that it
can carry energy by way of a charge separation. Polar molecules, which possess a
permanent charge separation, and non-polar molecules, which develop induced dipole
moments when subjected to an external electric field, are both considered dielectrics.
Polar molecules are characterized by the presence of permanent dipole moments, in
association with charges -q and +q being separated by a distance d:
u=qd [A7]
The magnitude of the dipole moment depends on the size and symmetry of the molecule
(Hill et al, 1969). Although a symmetrical molecule may have no permanent polarization,
a temporary dipole can be induced by the application of an external field, E. (Serway,
1986). This causes the centers of positive and negative charges to shift to opposite sides
of the molecule. The result is an induced surface charge density, or, on the one face of the
particle, and an equal negative surface charge density on the opposite face, as is illustrated

in Figure A.2. In Type 3A zeolite, the positive Na+ ions would migrate (within the zeolite

71

framework) towards the negative electrode, resulting in a net positive charge on one side

of the particle and a net negative charge on the other due to the anionic fiamework.

{—150

1+

 

 

 

 

 

 

 

 

 

l—l

Figure A.2 Conceptualization of a dielectric particle experiencing a charge separation
due to an applied electric field E0. (a) The centers of positive charge in the dielectric
particle (N a+ ions in zeolites) shift towards the negative electrode, and the centers of
negative charge shift towards the positive electrode (b) The result is a net positive surface
charge on the one side of the particle and a net negative charge on the other.
An opposing electric field E. is induced as a direct result of these newly developed surface
charges. The net electric field is thus given by the added effects of these opposing fields :
E = 1Eo - EI [A8]
The applied field, E0, is reduced by a factor it, in the presence of a dielectric, yielding the

net electric field E:

E=——— [A9]

1: is a property of the material and is called the dielectric constant. Related to dielectric
constant is the dielectric strength of the material. This represents the maximum electric
field that can be applied before the material breaks down electrically. The manufacturer
lists silicon oil as having a dielectric strength of 350 V/mil, and a dielectric constant of

2.95. Water has a dielectric constant of 80.

72

There are three effects giving rise to the total polarizability, an ,of a molecule and
thus we sub-classify polarization as being either electronic, ac, atomic, m or orientational,
a... In non-polar molecules the latter effect is not present. These different types of
polarization are shown below in Figure A.3. Electronic polarization, the biggest
contributor, is induced by the displacement of atoms relative to the nucleus of each atom
The displacement of the atomic nuclei relative to each other renders atomic polarization
These two types combined are called distortion polarization. Orientation polarization
occurs only ill polar molecules. In the absence of a field, the permanent dipole moments
are randomly distributed and are constantly changing direction as a result of thermal
motion. The application of a field causes alignment, giving rise to orientation polarization
This additional polarization typically gives polar molecules higher permittivities.
Orientation polarization drops off rapidly as the temperature increases and thermal motion

tends to disrupt the alignment.

E)" O'

/

_. / ./ 11/

(c) '\ /> “/fi
Nofield {-E

Figure A.3 Types of polarization mechanisms observed in non-polar molecules (von
Hippel, l995):(a)electronic (b)atomic (c)orientation

73

The permittivity of an isotropic material is given in terms of the polarization P
produced by an applied field E0:

4nP
8E o [A.IO]

 

eo=l+

where a is a constant that depends on the system of units being used. The induced surface
charge density (or induced electric moment per unit volume) can be represented by:

P = N,m [A111
where N is the number of molecules per unit volume and m is the average induced
moment due to all types of polarization. If we denote the average field acting on a
molecule as F then we may write:

in = a T F [A.12]
where 011 is given by:

atT =a°+a. +ao [A.13]
The relative permittivity can thus be written as:

+ 471N,aTF

8 :
° E03

[AM]

The three types of polarizability respond differently to the frequency of the applied
field. At low fiequencies all types of polarization can reach their corresponding steady
field value. With increasing frequency the limits of response time are reached. Orientation
polarization is the first to be affected. It contributes less and less as the frequency rises.
The fall of total polarizability from

aT=r2r¢+ag+aro [A.15]

74

to

aT = 01° + a. [A.16]
as well as the associated drop in permittivity, is referred to as the dielectric dispersion.
Because the time scale for electronic and atomic polarization is so short, ill the fiequency
range of the dielectric dispersion the distortion polarization remains unchanged. However,
at fi'equencies comparable to the natural frequencies of the Vibrations of the atoms in the
molecules, or. will fall off much more quickly than ore and another dispersion will occur.
This typically occurs in the infrared region. The electronic polarization will reach its
response limit at frequencies corresponding to the electronic transitions between different
atomic energy levels. These are typically in the visible, ultra-violet, and X-ray regions of
the spectrum

Knowledge of the dielectric dispersion can thus help to elucidate many questions
regarding the molecular mechanisms responsible for bulk properties in ER fluids. Atomic,
electronic, and orientational effects are directly attributable to molecular structure, and
thus information regarding these contributions Service the molecular design of advanced
electrorheological materials. It is also here in the realm of dielectric dispersions that
models of electrorheological based on interparticle forces coalesce with trends observed
via measurement of dielectric properties.

Investigation of measured dielectric property dependences is a very instructive
means of elucidating the nature of ER response. It is an alternative to studying inter-
particle forces but complements this body of information well Instead of dealing with the
individual forces of attraction and repulsion and from there synthesizing a net response to

externally applied fields, the ER response is tied to pr0perties such as conductivity,

75

dielectric strength, and permittivity. Inherent to both descriptions is the nature of the
polarizability of the particles in suspension Although the approaches are different they

are founded on the same phenomenon.

A.3 Interracial Electric Double Layer Theory

Although the ER response is generally attributed to the polarization of particles
under an applied electric field, this description does not account for the fact that not all
particles with a high permittivity demonstrate an ER effect (Filisko,]994), nor does it
account for the speed of the chaining response (Uejma, 1972). Klass and Martinek
(1967ab) observed ER activity at high frequency AC fields where chain reforming based
on particle polarization alone seemed kinetically rmlikely. Theories on electric double
layers for electrolytic suspensions have been around since the beginnings of colloidal
science (Graham, 1861) although Schwartz (1962) was the first to propose the electric
double layer as a mechanism for the ER response in non-conducting suspending media.
Since then, this theory has gain prominence in many theories based on dielectric
phenomena (Khusid, 1996).

Fundamental to the development of an electric double layer is the presence of
electrical charges on the surface of the suspended particles. These charges may arise from
several different mechanisms, including ionization of surface molecules, differential
solution of ions from the surface of the particle, isomorphous substitution, and preferential
ion adsorption (Everett, 1988; Weiser, 1949). Selective adsorption of H+ and OH- ions
from water may also contribute to the formation of charged surfaces. In zeolites it is

generally believed that the adsorbed layer is H20 (Uejima, 1972). The electrical charge at

76

the particle surface due to the adsorbed species attracts a layer of oppositely charged ions.
The combination of these negatively and positively charged layers is referred to as the
electric double layer. When the electric charge in one of these layers is diffusely
distributed, the assemblage is referred to as a diffuse double layer. Electric double layers
have been well characterized for aqueous electrolytic solutions however the
characterization of the nature of the double layer in nonaqeous/nonpolar systems (which
include ER systems) is complicated by the lack of a clearly identifiable ionic species
(Kitahara and Watanabe, 1984). Water is present in most ER fluids, although the amount
is small and also difficult to control Water has the potential to deplete electrons ill the
suspending hydrocarbons resulting in fiee ions which could contribute to proton
conductivity, hence it may play a key role ill the establishment of diffuse double layers.
The development of anhydrous systems by Block and Kelly (1988) has raised new
questions and perhaps closed old ones regarding the role of water in ER response. Much
is still not clearly rmderstood however.

The measurement of dielectric dispersions is becoming increasingly important in
evaluating double layer theories and understanding the molecular mechanisms associated
with this response. Although ER response is generally attributed to the polarization of
particles under an applied field, it is difficult to predict ER activity based solely on the
polarizability of the suspended phase. Polar materials possessing permanent dipoles have
high orientational polarizability and thus high permittivities, yet are not ER active.

Uejima (1972) proposed a dielectric model to explain the speed of chaining
response in ER systems. His results demonstrated the applicability of electric double layer

theory. He found the particle surface charge density to be closely related to the fraction of

77

adsorbed water in the ER system and theoried that the adsorbed water layer directly
affects the surface charge density of the electric double layers, and also increases the
dielectric constant of the ER fluid. The observed Winslow effect increased accordingly.
He also observed that when the particles were completely dried, electric double layers
never seemed to form because of the absence of dielectric dispersions at low frequencies.
There was also no evidence of an ER effect for dry fluids.

Filisko (1994), in an examination of four different types of ER fluids, found that
the presence of a unique dielectric dispersion is linked to ER activity. Although these
results do not conclusively point to a specific molecular ‘mechanism’ that can be deemed
responsible for the ER effect, they do indicate the underlying molecular ‘features’ that are
critical to the ER response. This is valuable information for designing ER fluids with
enhanced reactivity.

To bring this discussion fill] circle, the permittivity of a material is a quantification
of its polarizability with respect to a given applied field. The polarizability of a molecule
represents the interplay of molecular forces at work in the material of interest and the
dipole moments that are set up due to applied fields. Although high permittivities are
needed to manifest electrorheological behaviour, this is a necessary, but not sufficient
characterization Electric double layer theory attempts to complete this description by
bringing into play the effects of surface charge and density, and its role in the interaction

of the disperse phase and its suspending medium.

APPENDIX B

Appendix B
Triple Junction Thermocouples

The Copper-Constantan triple-junction thermocouples are parallel thermocouple
constructions, outputting the average temperature of three junctions. This type of circuit
yields a true arithmetic average of the of the individual thermocouples if all of the
thermocouple circuits are of equal resistance (ASME, 1974). In the experiments in this
work, the temperature at each of these junction locations was essentially equivalent as
heat flow in the transverse direction was negligible. This had been confirmed
experimentally via observation of a spatial distribution of thermocouples. The typical
configln'ation of parallel junction thermocouples (Beckwith et. al., 1982) is shown ill
Figure B1 (a). Based on the Law of Intermediate Metals for thermocouples, the sequence
of constructions shown in Figure B l (b) through (d), are equivalent to the configuration
shown ill Figure B1 (a), as long as T(ref.) remains constant. The configuration used in

this work is best understood in terms of Figure B1 ((1).

78

orT ff." film‘s-'1

w-“h‘ '2‘ ‘ . A.'I

79

T1 T2 r3 T2

13] i ............ .

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(T(ref)’ T(ref) T(ref) T(ref)
(a) (b) (C) (d)

 

 

 

 

 

Figure B.1 Construction of parallel 3 jrmction thermocouples: (a) typical construction
(b) - (d) electrically equivalent constructions based on the Law of Intermediate Metals for
thermocouples.

APPENDIX C

1 0
20
25
50

60
70
80
90

Appendix C
Q—Basic Program for
Temperature Data Conversion

Interval=0

Open “C:\star\test.dat” For INPUT as #1

Open “C:\elliott\Ze_15.txt” For OUTPUT as #2

IF EOF(1) THEN 80

INPUT #1, time, voltage, t2, t3, t4, t5, t6, t7, t8, t9, th, t1 1, t12, tl3, tl4,
t15, t16, t17,t18,tl9, t20, t21, t22, t23

WRITE #2, time, t2, t3

GOTO 25

Close #1, #2

End

80

APPENDIX D

 

Appendix D
PROP-1D
Sample Data Files

The sample data files that follow include an input control parameter file (‘.icp), a
data file containing the heat flux data and the experimental temperature profiles (*.txt),

and an output file (’.out) which is generated by the PROP-1D program

81

 

82

FILE: vrls_21.icp

BLOCK 1 : HEADER
15% vol fraction Zeolite/Silicon Oil/T est 2/ Aug. 14th,1996

BLOCK 2: GEO R1 NREG ITER ICONVR IPRINT ISTOR IDTAIL

.00 1.00000 7 8 0 0 0 l
BLOCK 3: INDICES FOR SIDE HEAT LOSS (I.E., FIN)

DIMENS GEOZND HSIDE DSIDE TINF
1.00000 .00000 .00000 1.00000 .00000

BLOCK 4: MAT(IA),IA=1,NREG (Material numbers for regions)
1 2 3 4 5 4 3

BLOCK 5: TL(IB),IB=1,NREG ('lhicknesses for regions)
0.00014 0.00034 0.00016 0.00075 0.003 0.00075 0.00016

BLOCK 6: MN(IC),IC=1,NREG (Number nodes for regions)
3 3 5 3 25 3 5

BLOCK 7: ICAL TI‘STAT IQINT TIMON TIMOF
4 0.0000 1 600.0000 750.0000

BLOCK 8: TIMREG(IC),IC=1,NTMREG (Time regions)
123

BLOCK 9: BOUNDARY CONDITION INDICES [T IS 1, Q IS 2]
IBCXZ IXZVAR IBCXL D(LVAR
2 l 2 0

BLOCK 10: DATA FILE INDICES
NTIM NCOLM IDATA
42 3 0

BLOCK 11: ITORQ(IQ),IQ=1,NCOLM (Temperature or heat flux index)
2 1 1

BLOCK 12: INTFAC(IQ),IQ=1,NCOLM (Interface index, 0 for x=0 surface)
0 2 7

BLOCK l3: WTINGOQ),IQ=1,NCOLM (Weights)
1.0 1.0 1.0 1.0

Trifle: 2‘3. ‘2“

 

 

83

BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho‘c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
0.000 0.980

BLOCK l6: TEMPERATURE VOL HEAT CAP.

0.000 1871000

BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho*c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
0.000 2.307

BLOCK 16: TEMPERATURE VOL HEAT CAP.
.000 1369000

BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho‘c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
0.000 0.168

BLOCK 16: TEMPERATURE VOL HEAT CAP.
.000 1 334400

BLOCK 14: NKTEMP(I) NCI'EMP(I) (No. k & rho*c s)
l 1

BLOCK 15: TEMPERATURE THERMAL COND.
0.000 1 67.27

BLOCK 16: TEMPERATURE VOL HEAT CAP.
.000 2463000

1". 3'1“.“2 . 21‘

 

BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho’c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
0.000 0.1461

BLOCK l6: TEMPERATURE VOL HEAT CAP.
.000 2345000

BLOCK l7: NUMK NUMC IWEIGH ISEQU IREGUL
1 1 0 0 0

BLOCK 18: IPK(mat.) JPK (index) (k indexes)
5 1

BLOCK 19: IPC(MAT.) JPC (INDEX)
5 1

 

FILE: vfl5_2.txt

OOOOO

1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894
1894

OOOOOOOOOOOO

24.6001
24.6046
24.6071
24.5871
24.586
26.7055
28.4887
29.98
31.06
32.0806
33.0988
34.1 1 1 1
34.937
35.8069
36.5939
37.4533
38.1444
38.864
39.5236
40.2677
40.8696
41.5245
42.1602
42.8156
43.3519
43.9475
44.5226
45.1198
45.6332
46.1356
44.944
43.4603
42.6425
41.9241
41.3102
40.7356
40.2965
39.8718
39.5289
39.1301
38.8273
38.5051

85

24.5589
24.6046
24.6071
24.5 871
24.5 86

24.6061
24.6058
24.6055
24.6261
24.6505
24.7571
24.8804
25.0628
25.2504
25.4369
25.6782
25.9129
26.1982
26.4845
26.7761
27.0455
27.3701
27.696

28.0428
28.3494
28.6766
29.024

29.3946
29.6996
30.0547
30.397

30.7682
31.0913
31.4154
31.7247
32.0339
32.2578
32.456

32.5954
32.7392
32.8384
32.9385

 

86

FILE: vf15_2_O.out

 

PROGRAM PROPlD
Version 5.31 November 1993
Written by James V. Beck
Beck Engineering Consultants Company
Ph: 517-349-6688

 

NAME OF FILE OF INPUT CONTROL PARAMETERS:
vfl5-2i.icp 1*
NAME OF FILE OF EXPERIMENTAL DATA:
vf15-2.txt .
NAME OF OUTPUT FILE: E
vfl 5-2-O.out

'._'. |‘-' ~._' ‘ ‘1’: u M ' .‘,

BLOCK 1 : HEADER

 

BLOCK 1 : HEADER

BLOCK 2: GEO R1 NREG ITER ICONVR IPRINT ISTOR IDTAIL
.00 1.00000 7 8 O 0 0 1
Since ICONVR = 0, the units must be consistent.

BLOCK 3: INDICES FOR SIDE HEAT LOSS (I.E., FIN)
DIMENS GEOZND HSIDE DSIDE TINF
1.00000 .00000 .00000 1.00000 .00000
BLOCK 4: MAT(IA),IA=1,NREG (Material numbers for regions)
1 2 3 4 5 4 3

BLOCK 5: TL(IB),IB=1,NREG (Thicknesses for regions)
.00014 .00034 .00016 .00075 .00300
.00075 .00016

BLOCK 6: MN(IC),IC=1,NREG (Number nodes for regions)
3 3 5 3 25 3 5

BLOCK 7: ICAL TI‘STAT IQINT TIMON TIMOF
4 .0000 1 600.0000 750.0000

BLOCK 8: TIMREG (End of time region)
123.00

87

BLOCK 9: BOUNDARY CONDITION INDICES [T IS 1, Q IS 2]
IBCXZ IXZVAR IBCXL IXLVAR
2 l 2 0

BLOCK 10: DATA FILE INDICES
NTIM NCOLM IDATA
42 3 0

BLOCK ll: ITORQ(IQ),IQ=1,NCOLM (Temperature or heat flux index)
2 1 l

BLOCK 12: INTFAC(IQ),IQ=1,NCOLM (Interface index, 0 for x=0 surface)
0 2 7 r

BLOCK 13: WTING(IQ),IQ=1,NCOLM (Weights)
1.0 1.0 1.0

BLOCK 14: NKTEMP(I)NCTE1VH’(I) (No. k & rho*c s)
1 1

 

BLOCK 15: TEMPERATURE THERMAL COND.
.000 .980

BLOCK l6: TEMPERATURE VOL HEAT CAP.
.000 1871000000
BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho*c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
.000 2.307

BLOCK 16: TEMPERATURE VOL HEAT CAP.
.000 1369000000
BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho*c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
.000 .168

BLOCK l6: TEMPERATURE VOL HEAT CAP.
.000 1334400000

88

BLOCK 14: NKTEMP(I) NCTEMP(I) (No. k & rho‘c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
.000 1 67.270

BLOCK 16: TEMPERATURE VOL HEAT CAP.
.000 2463000000
BLOCK 14: NKTEMP(I) NCTEMP(I) (NO. k & rho‘c s)
1 1

BLOCK 15: TEMPERATURE THERMAL COND.
.000 .146

BLOCK 16: TEMPERATURE VOL HEAT CAP.
.000 2345000000

BLOCK l7: NUMK NUMC IWEIGH ISEQU IREGUL
l l 0 0 0

BLOCK 18: IPK(mat.) JPK (index) (k indexes)

5 l
BLOCK 19: [PC JPC
5 1
END OF THE INPUTS
NNN 47

ITER RMS TH. COND. RHO SPHT. DEL-K DELCP
0 .518 .1601 .2298E+07 .lE-Ol -.5E+05
l .363 .1611 .2298E+07 .1E-02 -.2E+03
2 .362 .1611 .2298E+07 .2E-04 -.1E+03

TIME TH. COND. VOL. HEAT
3.00 .l6llE+00 .2298E+07
6.00 .l6llE+00 .2298E+07
9.00 .1611E+00 .2298E+07
12.00 .161 1E+00 .2298E+07
15.00 .1685E+00 .2375E+07
18.00 .1735E+00 .2426E+07

21.00
24.00
27.00
30.00
33.00
36.00
39.00
42.00
45.00
48.00
51.00
54.00
57.00
60.00
63.00
66.00
69.00
72.00
75.00
78.00
81.00
84.00
87.00
90.00
93.00
96.00
99.00
102.00
105.00
108.00
111.00
114.00
1 17.00
120.00
123.00

CALCULATED T(1,J) = ETEMP(I,J) - DTETC(I,J)

TIME ETEMP DTETC STRMS (k’dT/dk) (c’dT/dc)

3.00
3.00
6.00
6.00
9.00
9.00

.1636E+00
.1582E+00
.1565E+00
. 1571 E+OO
.1595E+00
.1661E+00
.171 1E+00
.1736E+00
.1743E+00
.1744E+00
.1744E+00
.1744E+00
.1738E+00
.1731E+00
.1725E+00
.1719E+00
.1713E+00
.1707E+00
.1701E+00
.1696E+00
.169OE+00
.1684E+00
.1679E+00
.1662E+00
.1654E+00
.1648E+00
.1643E+00
.1639E+00
.1636E+OO
.1632E+00
.1628E+00

.1624E+00
.1620E+00
.1615E+00
.1611E+00

.2322E+07
.2261 E+07
.2230E+07
.21 74E+07
.2081E+07
. l 985E+07
.191 0E+07
. l 8 83E+07
. l 865E+07
. l 873E+07
.1 8 84E+07
.1900E+07
. l 91 6E+07
. l 939E+07
. 1960E+07
. l 979E+07
. l 995E+07
.201 5E+07
.2034E+07
.205 3E+07
.2068E+07
.2087E+07
.21 05E+07
.2105E+07
.21 1 8E+07
.21 33E+07
.21 50E+07

.21 68E+07
.21 86E+07
.2204E+07
.2222E+07
.2241E+07
.2260E+07
.2279E+07
.2298E+07

89

 

24.605 .011 .011 -.l36E-02 -.425E-03
24.605 .039 .039 .l70E-02 .26lE-03
24.607 .014 .013 -.227E-02 -.369E-03
24.607 .040 .039 .256E-02 .353E-04
24.587 -.005 .011 -.299E-02 -.201E-03
24.587 .018 .034 .330E-02 -.28lE-03

12.00
12.00
15.00
15.00
18.00
18.00
21.00
21.00
24.00
24.00
27.00
27.00
30.00
30.00
33.00
33.00
36.00
36.00
39.00
39.00
42.00
42.00
45.00
45.00
48.00
48.00
51.00
51 .00
54.00
54.00
57.00
57.00
60.00
60.00
63.00
63.00
66.00
66.00
69.00
69.00
72.00
72.00
75.00
75.00
78.00

24.586
24.586
26.705
24.606
28.489
24.606
29.980
24.605
31.060
24.626
32.081
24.650
33.099
24.757
34.1 11
24.880
34.937
25.063
35.807
25.250
36.594
25.437
37.453
25.678
38.144
25.913
38.864
26.198
39.524
26.485
40.268
26.776
40.870
27.045
41.525
27.370
42.160
27.696
42.816
28.043
43.352
28.349
43.947
28.677
44.523

-.005
.016
-.566
.036
-.157
.034
.130
.031
.109
.041
.106
.038
.162
.097
.261
.146
.216
.227
.253
.286
.238
.316
.324
.376
.268
.406
.263
.463
.219
.500
.278
.522
.213
.505
.215
.527
.214
.534
.244
.549
.168
.510
.162
.481
.145

90

.010 -.360E-02 .120E-05
.030 .395E-02 -.625E-03
.253 -.949E-01 -.97lE-01
.032 .452E-02 -.958E-03

.240 -.321 -.325
.032 .585E-02 -.204E-02
.227 -.583 -.587
.032 .l70E-01 -.ll9E-01
.216 -.858 -.861
.033 .571E-01-.475E-01
.207 -l.l4 -l.l4
.034 .139 -.120
.203 -l.42 -1.42
.044 .266 -.233
.209 -l.70 -l.70
.061 .432 -.383
.209 -1.97 -l .97
.088 .632 -.565
.213 -2.25 -2.25
.116 .856 -.774
.215 -2.52 -2.52
.140 1.10 -l.00
.224 -2.79 -2.78
.166 1.35 -l.25
.227 -3.06 -3.04
.190 1.62 -l.52
.229 -3.32 -3.30
.216 1.88 -1.80
.229 -3.58 -3.55
.241 2.15 -2.08
.231 -3.83 -3.81
.263 2.41 -2.37
.231 —4.07 —4.06
.280 2.68 -2.67
.230 -4.31 -4.30
.297 2.93 -2.98
.229 -4.54 -4.55
.311 3.18 -3.29
.230 -4.77 -4.79
.325 3.42 -3.60
.228 -4.98 -5.04
.335 3.66 -3.91
.225 -5.19 -5.28
.342 3.88 -4.23
.223 -5.39 -5.53

91

78.00 29.024 .460 .347 4.10 -4.55
81.00 45.120 .160 .221 -5.58 -5.77
81.00 29.395 .454 .352 4.31 -4.86
84.00 45.633 .099 .218 -5.77 -6.02
84.00 29.700 .372 .353 4.51 -5.18
87.00 46.136 .035 .214 -5.94 -6.26
87.00 30.055 .333 .352 4.70 -5.50
90.00 44.944 .965 .274 -6.02 -6.41
90.00 30.397 .273 .350 4.88 -5.82
93.00 43.460 .303 .275 -5.95 -6.43
93.00 30.768 .236 .347 5.05 -6.13
96.00 42.643 .143 .272 -5.84 -6.42
96.00 31.091 .145 .342 5.21 -6.44
99.00 41.924 -.016 .268 -5.71 -6.39
99.00 31.415 .059 .337 5.32 -6.72
102.00 41.310 -.l43 .265 -5.57 -6.37
102.00 31.725 -.032 .332 5.39 -6.96
105.00 40.736 -.286 .266 -5.42 -6.34
105.00 32.034 -.107 .328 5.40 -7.16
108.00 40.297 -.341 .268 -5.26 -6.31
108.00 32.258 -.245 .326 5.37 -7.33
111.00 39.872 -.419 .273 -5.09 -6.29
111.00 32.456 -.386 .328 5.29 -7.46
114.00 39.529 -.449 .279 -4.93 -6.28
114.00 32.595 --.561 .336 5.19 -7.56
117.00 39.130 -.564 .290 -4.76 -6.27
117.00 32.739 -.709 .350 5.06 -7.64
120.00 38.827 -.608 .302 -4.58 -6.26
120.00 32.838 -.879 .373 4.91 -7.70
123.00 38.505 -.695 .318 -4.41 -6.26
123.00 32.938 -l.027 .402 4.74 -7.74
3 .362 .1611 .2298E+07 .4E-06 -3.

REG RMS TH. C VOL.
.0 .362 .1611 .2298E+07
SPATIAL CORRELATION MATRD( FOR U
.1000E+01 .4196E+00
.4196E+00 .1000E+01
PHI MATRIX = VALID(I,J)
.4646E-01 .8350E-02
.8350E-02 .8525E-02
XTWX matrix
.44731482E+05 .35581806E-03 .35581806E-03 .30787032E-09
Inverse ofXTWX matrix

92

.22563050E-04 -.26077021E+02 -.26077021E+02 .32782591E+10
COVARIANCE MATRIX OF PARAMETERS = P, B&A, page 248
.71254553E-05 -.24670656E+02 -.24670656E+02 .23883364E+10
APPROX. SQUARE REGION CONFIDENCE REGIONS
PARAMETERS plus and minus the below values
.60861290E-02
.1 1 142499E+06
INVERSE OF COV MATRDI OF PARAS = P INV, B&A, p 248
.14554735E+06 .15034518E-02 .15034518E-02 .43423160E-09
95.0 PERCENT B-MATRIX BECK AND ARNOLD (6.8.28) FOR
COORDINATES OF (B—BETA)
B11 .1887E+01 B12 .1559E+01
B21 -.1887E+01 B22 .1559E+01
SENSOR RHO SIGMAZ FOR U AND WEIGHT USED
1.0 .6950E+00 .4646E-01 1.00
2.0 .9038E+00 .8555E-02 1.00
NEW BLOCK 21: ((XTWX(I,J),I=J,N),J=1,N), INCLUDES PRIOR
INFORMATION FOR ISEQU=1
.4473E+05 .3558E-03
.3558E-03 .3079E-09
NEW BLOCK 22: ((XTPSX(I,J),I=J,N),J=1,N)
THIS IS XTWPSWX.
.1377E+05 .3217E-04
.3217E-04 .2219E-09
NORMAL TERMINATION OF PROGRAM

APPENDIX E

 

Appendix E
Design of Experiment

E1. Sensitivity Analysis

To evaluate the suitability of the mathematical model a sensitivity analysis can be
very informative. The first derivative of a dependent variable with respect to the
parameter of interest is known as the sensitivity coefficient for that parameter (Beck and
Arnold, 1977). The sensitivity coefficients of concern in this work are given by:

93 :21
5k [.1

and:

5T
5;— [13.2]

1:
If aT/ak ~ 0, then temperature is not very sensitive to a change in k, and to use
temperature profiles to estimate k would be ineffectual. It is thus desirable to choose
experimental conditions which maximize these coefficients.

Sensitivity coefficients also provide information about the linearity of the
mathematical model. If the sensitivity coefficients are not fimctions of any of the

parameters ill the model then the model is said to be linear ill the parameters. If the

93

94

mathematical model is non-linear in the parameters, the estimation algorithm becomes
more involved. This is the case for the current problem The sensitivity coefficients are
filnctions of thermal conductivity and volumetlic specific heat.

Sometimes it is not possible to uniquely estimate the desired parameters from a
given experiment, although it may be possrble to estimate a function or combination of
them This is referred to as the identifiability problem Again examination of the
sensitivity coefficients provides insight. If, over the time range of the experiment, the
sensitivity coefficients are not linearly dependent, then the parameters are uncorrelated and
can be estimated uniquely.

Shown in Figures El and E2 are plots of the thermal conductivity and specific
heat sensitivity coefficients obtained from a Prop-1D analysis of silicon oil The duration
of experiment was 147 s, with heating at 475.15 W/m2 for 90 s. From Figures El and
E2 it can be seen that the sensitivity coefficients for each of the parameters are linearly
independent over the range of the experiment indicating that both thermal conductivity
and volumetric specific heat could be estimated individually. The sensitivity coefficients
for both parameters are seen to decrease at approximately 90s, which coincides with the

heat being turned off.

 

2.0) ~-

15) +

1.00«

0.50 a

95

 

------ X=O. heated surface
X=L, insulated surface

 

 

 

 

Sensitivity Coefficients for Thermal Conductivity, Si_oil Test 30

 

 

ThennalConductivltyMlmK)
.b .o
8 8
4%

 

 

  

 

 

   

 

 

 

 

16)

4.0er - .

450+ '

-2“) __

Tine (see)
Figure E.1 Thermal conductivity sensitivity coefficients.
Sensitivity Coeffieente for Volumetric Specific Heat
SIDE-O1 - 3L0" test 30
OLDER!) . . i Te i i .
(ii ‘ 1(1) 120 14) 1G)
SIDE-01 ~>
-1 .038-(D a
ammo: - ”----
------ X=0, heated surface

-2.001=.+oo a =L, insulated surface
4.5054(1) ‘ 1'“ (NC)

 

Figure E.2

Volumetric specific heat sensitivity coefficients.

 

‘ may. u-..‘L~vr

96

Shown in Figure E.3 are the results of the Prole generated temperature profiles
based on the estimated parameters along with the initial experimental temperature

profiles. These profiles are in good agreement.

Si Oil - Test 30
Estimated Response vs. Experimental

 

 

 

 

 

 

 

 

 

Tine (s)

Figure E.3 Comparison of measured profiles and those generated using the parameters
estimated by Prop-1 D.

E.2 Sequential Estimates

Sequential estimates also provide useful information about the experiment. The
sequential estimates for thermal conductivity, Figure E.4, are seen to reach a stable value
and then drift down with time, indicating that perhaps 2-D effects are entering into the
model at extended times. Examination of the equivalent set of sequential estimates for
volumetric specific heat, Figure E.5, indicated problems with the model. Instead of
reaching a steady value with increasing information, the sequential estimates looked

erratic. This indicated that the model was not developed enough to accurately model the

physical experiment.

97

 

Sequential Estimates of Thermal Conductivity:
Si_oil 30

 

 

Thole)

 

 

 

Figure E.4 Sequential estimates of thermal conductivity.

 

 

Sequential Estimates of
Volumetric Specific Heat:
Si_oil 30

 

Voiunetric Specific
Heat (.um’ K)

 

 

 

 

 

Figure E.5 Sequential estimates of volumetric specific heat.

98

E3 Residuals

Residual analysis provides valuable information about the boundary conditions of
the physical experiment and about the errors in the experiment in general Shown in
Figures E.6 and E7 are the residuals for the x=0 and x=L temperature profiles. It can be

seen that the residuals are highly correlated, especially at the x=0 boundary, indicating the

presence of a systematic error. In both cases the residuals drift down during the last

portion of the experiment, suggesting heat loss at x=L.

Residuals at x=o Si_oil 30

 

 

 

Figure E.6 Residual analysis for silicon oil, X=0 boundary.

Residual at X=L SLOII 30

 

 

Figure E.7 Residual analysis for silicon oil, X=L boundary.

 

99

EA Duration of Experiment

The determination of the best duration of experiment was based on optimization of
the A+ criterion as outlined in Beck and Arnold (1977), for a l-D heat conduction problem
with a constant heat flux on one side and an insulated boundary condition on the other.
For this case there are two optimal times, the duration of heating (thr = 0.5) and the
duration of experiment (t: = 0.75). Depending on the thermal diflusivnies of the materials

tested, the optimal heating time would be different. These values are shown below in the

 

 

 

 

 

Table E1.
or (mz/s) t; 1;
Silicon Oil 9.3 E-08 48.05 72.08
Water 1.44 E-07 31.10 46.65
ER fluid 6.2 E-08 72.22 108.3

 

 

 

Table E.1 Optimal heating and experimental duration.

 

APPENDIX F

Appendix F
MDSC Determination
of Specific Heat

F.1 Modulated Differential Scanning Calorimetry (MDSC)

Heat capacity is an extensive property characteristic of all materials and is defined
as the amount of thermal energy required to raise the temperature of the specimen by 1
degree Celsius (Brady et. a1, 1993). Specific heat, Cp, is the heat capacity per unit mass,
and is the intensive or mass-normalized equivalent of heat capacity. It has units J/g°C Or
J/kg°K Heat capacity and thus specific heat are structure-sensitive properties.

Estimates of C, for the unchained isotropic electrorheological fluid suspensions
were obtained using Modulated Differential Scanning Calorimetry (MDSC). MDSC is a
new technique which provides the same thermal information as conventional DSC but
affords the capability to calculate a variety of other thermal transport features such as
reversing and non-reversing heat flow (TA Instruments). DSC measures the heat flow
difference between the analyzed material and an inert reference as a function of a linear
temperature change whereas MDSC measures the difference in heat flow between the two
as a simultaneous function of both a linear and a sinusoidal change in temperature. The

temperature change for MDSC is given by:

100

101

T(t) = To + Ct + AT(sincot) [F. 1]
where,

T(t) = Program Temperature

To 2 Starting Temperature

C = Linear Heating Rate (° C / minute)

t = Time (minutes)

A1 = Amplitude of Temperature Modulation (+/- °C)
0) = 21:/P, Modulation Frequency

P = Period (3)

The instantaneous heat flow rate is given by:

(1
ti? = Cp ([3 + ATro'rcosort) + f(t,T) + AAA-1111030 [F2]

where,

(B + ATco * coscot) = Measured Heating Rate (d%t)
f‘ (t,T) = Kinetic Response without Temperature Modulation
AK = Amplitude of Kinetic Response to Temperature Modulation.

The total heat flow is calculated from the average value of the modulated heat flow
signal and is qualitatively and quantitatively equivalent to the heat flow signal provided by
conventional DSC at the same average heating rate. It represents the sum of all thermal
events (melting, crystallization, etc.). CF is determined by dividing the modulated heat

flow amplitude by the modulated heating rate amplitude:

 

Heat Flow Amplitude(mW) ) [F 3]

CP : Km?) x [Heating Rate Amplitude(°C / min)
Where DSC requires a minimum of four experimental runs, MDSC requires only two, a
cahbration rim to determine the MDSC cahbration constant and then the sample analysis.

It is not necessary to rlm baseline profiles of empty pans.

 

 

102

The TA Instruments Thermal Analyzer was calibrated using a cahbration program

included with the system’s software and an indium standard, which has a well-known

melting temperature. A cell constant is calculated by the program which is used for all

subsequent tests. The MDSC cell constant was obtained using sapphire as a reference. An

MDSC run was performed using the following program:

1.

2.

Equihbriate at 5.00 °C

Data Storage: Off

Modulate +/- 1.00 °C every 60 seconds
Isothermal for 3.00 minutes

Data Storage: On

Ramp 5.00 °C/minute to 80.00 °C
Data Storage:Off

Initial Temperature: 25.00 °C

Literature values of specific heat for sapphire were divided by the experimentally

obtained values to obtain values of the cell constant. The average was then used for

subsequent analyses. A second test with sapphire was run to ensure proper cahbration.

Due to the difficulty associated with specific heat measurements of liquid samples, an

alternate callbration check with silicon oil was performed.

103

F.2 Results and Discussion
F.2.1 Calibration

The instrument’s thermocouples were cahbrated by using an indium standard to
calculate a cell constant to be used in all subsequent tests. The previously listed MDSC
program was run two times on the same 22.1 mg sapphire specimen. To determine the
MDSC cahbration constant the literature values of CI, at several temperatures were divided
by the experimental values obtained from both rims according to:

Lit. Value
Observed Value

 

K(C,) = [F.4]

Table F.l lists the results of these calculations.

 

 

 

 

 

 

 

 

 

 

Temp. (°C) Literature Experimental K(C,,) Experimental K(C,,)
Value Value Specific Run 1 Value Specific Run 2
Specific Heat Heat Heat
(Vs/°C) (Vs/°C) (Vs/°C)
Run 1 Run 2
16.85 0.7572 0.4828 1.5684 0.4933 1.5350
26.85 0.7788 0.5009 1.5548 0.5128 1.5187
36.85 0.7994 0.5188 1.5409 0.5322 1.5021
Table F.1 Calculation of MDSC cahbration constant.

The values calculated from separate nms indicated a small degree of drift. The

 

average of both runs, 1.5367 was inputted as the lVfl)SC constant and used for the
subsequent analyses. To ensure the adequacy of this average a third sapphire run was

completed. Results indicated agreement to within 2% as indicated in table F .2.

104

 

 

Temp. (°C) EXpefimental CP % Difference
(Hg/°C)

16.85 0.7590 0.2377

26.85 0.7892 1.335

36.85 0.8185 2.389

 

 

 

 

 

Table F.2 Calibration check with sapphire.

Although sapphire is used as a general wide temperature range standard, it’s
composition is significantly different than the material to be analyzed, hence a run with
silicon oil, the carrier fluid in the ER fluid suspensions, was performed. This material had
been previously analyzed by conventional DSC and as well a literature value at a specific

temperature was provided by the manufacturer. These are compared in Table F.3.

 

 

 

 

 

 

 

 

Temp. (°C) Cp-Conventional Cp-MDSC Cp-Literature
DSC (J/g/°C) (J/g/°C)
(Hg/°C)

15.00 - 1.408 -

20.00 1.417 1.420 -

25.00 - 1.43 1 -

30.00 - 1.438 -

35.00 - 1.442 -

40.00 1.470 - 1.519

 

 

 

 

 

Table F.3 Comparison of literature and experimental values of specific heat
of silicon oil.

It was found that these values were in acceptable agreement.

F.2.2 Zeolite Type 3A in Silicon Oil

The results for the ER fluids are plotted in Figure F1.

 

105

 

 

 

 

 

 

 

Cp values for a series of ER fluids with increaang weight
fraction of zeolite
1.7 ——
1.6 4» $9
epared
1.5 4. ' 5121196
.. 1.4 «~
‘2’ 1.3 4 iPl’epared f n
i 1.2 4 5’20’95 ; I
o 1.1 .. e 15 deg. c
1 «E I 25 deg c
0.9 v a 35 deg C
0.8 i i 1 1 E : 1 A
0% 2% 4% 6% 8% 10% 12% 14% 16%
Weight traction of zeolite

 

 

 

Figure F.1 Values of specific heat for a series of ER fluids.

It is interesting to note that the same fluid prepared a day later from the same base
materials, but at a lower relative room humidity, gave quite different values for C9, the
wetter fluid giving a lower value of CF. There seems to be a trend towards lower Cp
values with increasing zeolite fiaction. More tests would be required to substantiate this

claim however.

F.2.3 Error Analysis

The above results are given with 7% error bars. There were considerable
difficulties encountered when trying to obtain these measurements. The MDSC
cahbration constant was seen to shift around by as much as 30 % over the course of the
day. To avoid such a large source of error the samples were analyzed immediately after

cahbrafion. To fully quantify the magnitude of this error it would be necessary to analyze

 

106

the nature of this cahbration shift. It should be noted then that the error bars given are
estimates, and observations as to trends in the Cp data should be interpreted accordingly.
The 7 % error bars were chosen on the basis of the magnitude of drift in the cell constant
over the course of the day (typically 15-25%), and the time required to complete the tests

(roughly 3 hours). It is possrble that the error bars are substantially greater than this.

 

APPENDIX C

Appendix G
An Error and Sensitivity Analysis

The measured thicknesses of the materials used in the Prop-1D model and the

associated errors are given in Table G.1

 

 

Measured value (mm) Error (mm)
Gasket Material 3.00 i 0.05
Almninum 0.75 i 0.01
Heater 0.14 i 0.05
Thermal Paste 0.34 :l: 0.10
PVC Tape 0.16 :l: 0.02

 

 

 

 

 

Table G.1 Measurement error ill material dimensions.

The duration of the experiment was known to within i 3 seconds, as was the duration of
heating. The heat flux calculation was based on a measurement of the resistance of the
heater, which was known to i 0.5 Q, and the applied voltage which was known to i 0.05
V, and also the area of the heater which was known to 3: 0.002 cmz. These measurement
errors can change the heat flux by as much as 60 W/mz, out of 1864 W/mz.

The thermal property values used in the estimation routine were primarily literature
values and no estimate as to the degree of error can be given. The surface temper‘lfur'e as

measured by the triple junction thermocouples was known to within .1: 0.2 °C.

107

108

To evaluate the sensitivity of the Prop-1 D estimates to these measurement errors
an estimation was performed based on a worst case scenario (all errors in one direction).
The values of k and pCp were re-estimated for the same ER fluid analyzed ill Appendix D.

The results are shown ill Table G.2 along with the original estimates.

 

 

 

 

Original Estimation Worst Case
k 0.161 :1: 0.006 0.166 3: 0.027
pC, 2.3 x 106 s 0.1x 106 2.2 x106 i 0.3 x 106

 

 

 

Table G.2 Sensitivity of thermal property estimation to measurement errors.

 

The thermal property estimates were surprisingly insensitive to measurement
errors. The 95 % confidence interval was significantly larger but the generated values of k
and pCp for the two cases did not vary greatly. This information allows k and pCp to be

reported with confidence to i 0.03 and i 0.4 x 10‘, respectively.

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