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This is to certify that the

dissertation entitled

ANALYSIS AND EXPERIMENTAL STUDY OF RADIATIVE HEAT
TRANSFER THROUGH ELECTRORHEOLOGICAL FLUIDS

presented by

Jeffrey B. Hargrove

has been accepted towards fulfillment
of the requirements for

Ph .D . degree in Mechanical Engineer ing

 

 

 

MS U is an Affirmative Action/Equal Opportunity Institution DJ 2771

 

 

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Michigan State
Unlverslty

 

 

 

PLACE IN RETURN BOX
to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

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DATE DUE

 

M‘-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1m WWpGS-p.“

 

ANALYSIS AND EXPERIMENTAL STUDY OF
RADIATIVE HEAT TRANSFER THROUGH
ELECTRORHEOLOGICAL FLUIDS
By

Jemey B. Hargrove

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

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

1997

ABSTRACT
ANALYSIS AND EXPERIMENTAL STUDY OF
RADIATIVE HEAT TRANSFER THROUGH
ELECTRORHEOLOGICAL FLUIDS
By

J effi‘ey B. Hargrove

Radiation heat transfer control utilizing the unique properties of electrorheological
(ER) fluids has recently been the subject of considerable interest as an innovative new
area of research. While some work has been done to demonstrate the concept and to
show the potential for radiation transmittance control, little has been done to Specifically
characterize the ftmdamental radiation transport mechanisms involved. This work seeks
to identify the dominant modes for attenuation of radiant energy incident upon a typical
ER fluid. Models are developed to predict radiation heat transfer through a composite
window featuring a central layer of ER fluid while the particles are in a randomly
dispersed state. A model for prediction of the enhanced levels of energy transport in the
electric field-induced chained particle state was then developed by taking into account
particle chain geometries. Additionally, the effect of radiation wavelength was studied
for incident light beams ranging fiom 500 nm to 800 nm. Furthermore, the eflect of the
angle of incidence of the striking beam onto the composite window was studied, and a
model is proposed to predict the change in transmittance associated with the angle of
incidence. The levels of transmittance predicted by these models were compared to data
obtained by experimental measurement, and excellent agreement was shown. The result

of this work is a set of models for radiative heat transfer in ER fluid-based composite

windows, both in the particle-dispersed and particle-chained states for cases when the
plane of the window is held normal to the path of the incident light beam and when it is
off normal by some angle, for wavelengths of incident light ranging from 500 nm to 800
nm. Clearly, an understanding of the physical mechanisms involved will provide insight
into understanding heat transfer augmentation in the other primary modes. The models
developed can be used to develop sensors used for optimal control strategies to manage
the response of ER fluids for reliable use in commercial and industrial applications.
Furthermore, with reliable control of the heat transfer properties of ER fluids will come
the opportunity to develop thermally “smart” materials that will provide solutions to
advanced heat transfer problems encountered in next generation technologies and

applications.

This work is dedicated to my wife
Laurie

whose patience exceeds words of admiration

iv

ACKNOWLEDGMENTS

I would like to express my gratitude for the faithful guidance of my
advisor and friend, Dr. John R. Lloyd. Throughout my entire graduate program he
has served to guide not only my academic development, but also my professional
development from a philosophical standpoint that can only be thought of in terms
of legacies and excellence in commitment to developing students. I hope that I
may someday reflect his distinct qualifications to those that I mentor.

The assistance of my doctoral committee members, Dr. Clark Radcliffe,
Dr. James Beck, Dr. Craig Somerton, Dr. Henry Kowalski and Dr. Roger
Callantone is also gratefully acknowledged. The collective insight that each of
these individuals gave me played a critical role in the shaping of this work.

A fond note of thanks is also given to a number of my fellow graduate
students for their support and assistance in this endeavor. Thanks to Gloria Elliot,
Ruth Andersland and Stefan Tabatabi, just to name a few.

For all of the members of my families, especially my parents, I offer my
most sincere words of gratitude.

Great appreciation is given to my colleagues at GMI Engineering &
Management Institute in Flint, Michigan. I’m especially grateful to the persistent

encouragement of my long-time mentor and friend, Professor Gary Hammond.

 

Finally, a fond note of thanks is due to all of my dear friends for their
endless support and encouragement. For all who listened and understood,
although far removed from the intricacies of the problem at hand, you are

beautiful people.

vi

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
NOMENCLATURE

CHAPTER 1 - INTRODUCTION

1.1 BR Fluid Fundamentals

1.2 Objectives and Scope of This Work
1.3 Overview of ER Fluid Technology

CHAPTER 2 - EXPERIMENTAL APPARATUS AND METHODS
2.1 Experimental Apparatus
2.2 Experimental Methods

CHAPTER 3 - RADIATIVE TRANSFER THROUGH RANDOMLY
ORIENTED PARTICLES

3.1 Extinction of Radiant Energy
3.2 Experimental Results & Discussion

CHAPTER 4 - RADIATIVE TRANSFER THROUGH PARTICLES IN THE
FIELD-INDUCED CHAINED STATE

4.1 Additional Experimental Apparatus
4.2 Analysis of Particle Chain Geometry
4.3 Experimental Results and Discussion

CHAPTER 5 - ANGULAR TRANSMITTANCE ANALYSIS
5.1 Additional Experimental Apparatus
5.2 Analysis of Particle Chain Geometry at Oblique Angles

vii

ix

xii

Ox-hsr—v—

l4
l4
19

25

26
32

41

41
42
46

58
59
61

5.3 Experimental Results and Discussion

CHAPTER 6 - OPTICAL SENSORS FOR STATE CLASSIFICATION

CHAPTER 7 - CONCLUSIONS AND RECOMMENDATIONS FOR
FURTHER STUDY

APPENDIX A - AN OVERVIEW OF RECENT DEVELOPMENTS IN ER
FLUID TECHNOLOGY

APPENDD( B - EXPERIMENTAL DATA FROM AN GULAR
TRANSMITTANCE MEASUREMENTS

APPENDD( C - EXPERIMENTAL UNCERTAINTY ANALYSIS

C.l Sources of Error

C.2 Error in the Dispersed Particles Model

C.3 Error in the Chained Particle Model

C.4 Error in the Chained Particle Model With Field Strength as a Parameter
C.5 Error in the Angular Transmittance Model

BIBLIOGRAPHY

viii

71

78

82

85

93

96
96
100
101
103
105

109

LIST OF TABLES

Table 3-1 Experimental vs. Calculated Extinction Coefficients (Dispersed
Particles, 2a = 11pm, L = 1.9 mm)

Table 3-2 Experimental vs. Calculated Extinction Coefficients (Dispersed
Particles, fv = 0.005, L = 1.9 mm)

Table 4-1 Experimental vs. Calculated Transnrittance Levels (V; = I 6 0 Vrms/mm,
L = 1.9mm, 20 = 11 pm)

ix

37

38

54

 

LIST OF FIGURES

Figure 1-1 Conceptual Schematic of ER Fluid Particle Dispersion Under No Field 3
and Chain Structure with a Sufliciently Large Field Applied

Figure 2-1 Schematic of Experimental Apparatus 14
Figure 2-2 Photograph and Schematic of the ER Fluid Window Showing the 16
Components Held in Place by the Holding Fixture

Figure 2-3 Photograph of the Experimental Apparatus 17
Figure 2-4 Transmittance Through a 50-50 Beam Splitter and a 10 Percent 18
Transmitting Neutral Density Filter

Figure 2-5a Zeolite Particles, Average Diameter 11 Microns 20
Figure 2-5b Zeolite Particles, Average Diameter 25 Microns 21
Figure 2-5c Zeolite Particles, Average Diameter 40 Microns 21

Figure 3-1 Cross Section of Zeolite Particle Showing Radiation Absorbing Cavities 29
Figure 3-2 Normal Transmittance Through ER Fluids of Different Volume Fractions 33
with Fully Dispersed Particles (L = 1.9 mm, 2a = 11 ,um)

Figure 3-3 Transmittance as a Function of Sensor Position Transverse to the Axial 34
Direction of the Incident Beam

Figure 3-4 Transmittance in the Dispersed State for Varying Volume Fractions as a 36
Function of Pathlength (Za = I 1 pm)

Figure 3-5 Transmittance in the Dispersed State for Varying Particle Sizes as a 38
Function of Pathlength (fv = 0.005)

Figure 3-6 Comparison of Experimental Transmittance to the Fundamental Beer’s 39
Law (2a = 11pm)

Figure 4-1 Microscope Electrode Apparatus 42
Figure 4-2 Uniformly Spaced Single-Particle Chains for the Ideal Case of F ield- 43
Induced Chaining

Figure 4-3a Stacking Effect of Particles at the Electrode 47
Figure 4-3b Microscopic Video Still Showing Stacking Effect 48
Figure 4-4a Early Stages of Chain Bending 49
Figure 4-4b Early Stages of Chain Bending 49
Figure 4—4c Initial Contact Between Chains 50
Figure 4-4d Initial Contact Between Chains 50
Figure 4-4e Single Column of Multiple Chains 51
Figure 4-4f Single Column of Multiple Chains 51
Figure 4-5 Transnrittance in the Chained Particle State as a Function of Volume 54

Fraction (V;= 160 Vrms/mm, L = 1.9 mm, 2a =11,um)

X

Figure 4-6 Effect of Field Strength on Transmittance (fv = 0.0075, L = 1.9 mm, 2a =
11 .10")

Figure 4-7 Efl‘ect of Field Strength on Transmittance - Linearized Model

(fl, = 0.0075, L = 1.9 mm, 2a = 11 ,um)

Figure 5-1 ER Fluid Window with Normal Energy Incidence, Viewed from the Top
Figure 5-2 Rotation of ER Fluid Window About a Vertical Axis

Figure 5-3 Experimental Apparatus for Angular Transmittance Measurements
Figure 5-4 Particle Chains Parallel to the Path of Incident Energy

Figure 5-5 Particle Chain Profile in a Rotated ER Fluid Window

Figure 5-6 Blocking Area of Particles That are Exposed to Incident Energy

Figure 5-7 Conceptualization of a Rotated Particle Chain in 3d

Figure 5—8 Effective Blocking Area

Figure 5-9 Overlapped Columns Extending Across the Entire Area of Irradiation
Figure 5-10 Angular Transmittance: Experimental Data Versus Model Predictions
(L = 1.9 mm, Za = 11 gm, Vf= I60 Vrms/mm)

Figure 5-11 Transmission Intensity of Energy Through Glass as a Function of Angle
Figure 5-12 Transmission Intensity of Energy Through Glass as a Function of Angle
Figure 5-13 Sampled Transmitted Energy Data Points Against a Model of the
Waveform of Incident Energy

xi

55

56

58
60
61
62
63
65
66
68
69
73

74
75
76

AB
Cabs

C ext

NOMENCLATURE

mean particle radius

particle volume fraction

absorptive index

index of refraction

pathlength variable

direction unit vector

particle size parameter

total blocking area of all particle chains

area of blocking particle-chain face

absorption cross section

extinction cross section

volume fraction dependent total number of columns
scattering cross section

number of chains per volume of ER fluid

incident energy

incident energy absorbed

incident energy transmitted through an empty window

incident energy scattered

xii

Qext

Vf

0).
Ta

Tc

9:

calculated average extinction coeflicient

the extinction pathlength of ER fluid

effective pathlength

number of particles per unit volume

total number of particles per volume of ER fluid
extinction efficiency

volume of ER fluid

RMS voltage field strength per millimeter
volume of an individual particle
extinction coeficient

absorption coefficient

incident radiation wavelength

scattering coeflicient

transmittance in the dispersed state
transmittance in the chained state
azimuthal angle

angle of transmission through glass

xiii

CHAPTER 1 - INTRODUCTION

1.1 ER Fluid Fundamentals

In 1947, Willis M. Winslow introduced the concept of changing the rheological
properties of certain suspensions of particles by subjecting them to an electric field of
sufficient strength (Winslow, 1947). These substances have since been termed
“electrorheological (ER) fluids”, and since the time of the very earliest descriptions of the
phenomena associated with them, the scientific community has actively sought to find
ways to capitalize on them.

Over the years, countless numbers of researchers have studied the phenomena of
ER fluids. From their foundational work, many theories have emerged and have been
refined that have helped to shape our understanding of the fundamental physical
mechanisms behind these responses. Along the way numerous devices and commercial
applications have been proposed. Yet, for all of the potential held by devices that would
employ ER fluids, engineering and design limitations continue to persist that have kept
applications elusive for the most part.

There is a specific void in understanding the response of ER fluids to an applied
electric field and in achieving enough repeatability and reliability in that response to

confidently utilize them in applications. This work will seek to further that

2

understanding, and to provide for a unique way to provide a measure of the geometric
micro-state of the ER fluid’s particles by quantifying the level radiative of energy
transmittance through it. As this is achieved, the development of optical sensors will
enable development of optimized feedback control systems, as a key to managing the
response of an ER fluid, can proceed. Therefore, this work will have far reaching
ramifications on the future of ER fluid-based applications, and is critical to progress in a
number of ER fluid related fields.

Electrorheological fluids are suspensions of highly polarizable, micron sized
particles suspended in a suitable carrier fluid. Typically, the particulate medium is
hydrophilic, whereas the carrier fluid is hydrophobic. Ideally, the Specific gravity of the
particulate would match that of the carrier fluid, so that maintenance of long term
dispersion is ensured.

When placed in an electric field of sufficient strength, the otherwise randomly
dispersed particles form particle chains that are aligned with the field, thus giving rise to a
complex “fibrous”, or chained, structure as illustrated in Figure 1-1. Depending upon the
strength of the field, this chaining structure will advance toward a body centered cubic
orientation, which represents the lowest possible energy state (Tao and Sun, 1991).

Additionally, upon removal of the electric field there is a tendency for thermally
induced motion to overcome the weak colloidal forces holding the chains together, thus
allowing the particles resume their random distribution. Hence, the process of
electrically-induced chaining is reversible without need of an external stimulus, but as we

will find out, not necessarily fast.

 

 

 

 

 

 

 

 

 

Figure l-1 Conceptual Schematic of ER Fluid Particle Dispersion Under No Field and
Chain Structure with a Sufficiently Large Field Applied

The immediately obvious areas of application are those that capitalize on the
mechanical properties of ER fluids, such as viscosity. When the particles are in the field-
induced chained state, the apparent viscosity of the ER fluid is dramatically increased,
suggesting use in hydraulic valves, mechanical transmissions, and active suspension
systems (Morishita and Ura, 1993).

But more recent work has suggested an entirely new and revolutionary area of
application for ER fluids in the realm of augmenting and controlling heat transfer in
thermal processes (Shul’man, 1982). Zhang and Lloyd (1992, 1994) have shown that
radiative transmittance in ER fluids is significantly increased when the particles are in the
field-induced chained state. Their work, along with supporting work by Andersland

(1996), has also shown that transmittance levels can be managed by controlling the

4
electric field strength. Both studies have demonstrated these concepts with strongly

supportive experimental data, but have only suggested a theoretical basis for

understanding the physical processes affecting radiative transfer.

1.2 Objectives and Scope of This Work

In the introductory statement, it was observed that commercially successful ER
fluid-based applications have been elusive. This may be due, in part, to the extremely
interdisciplinary nature of ER fluid technology. To fully understand the nature and flow
properties of ER fluids will require an understanding of the physics of fluids, particulate
systems and solids, colloid and surface chemistry, electrochemistry, mechanical
engineering, electrical engineering, mathematics, polymer and material science, just to
name a few. Only recently have trends in engineering research been such as to bring
together individuals of diverse expertise with a singular outcome objective.

Naturally, increased fundamental knowledge of the physical mechanisms of ER
fluid response to applied fields is a necessary forerunner to applications. In order to
determine the feasibility of any device utilizing ER fluids, many key parameters must be
known for a wide variety of operating conditions and parameters. This includes, but is
certainly not limited to, thermal conditions, aging considerations and moisture content of
the particles of the ER fluid, and a wide array of applied voltage waveforms and
parameters that the ER fluids may be subjected to. Furthermore, this entire process is

complicated by the vast number of physical parameters associated with the ER fluid itself.

5
Varying particle properties and carrier fluid properties must be accounted for and then

related to all other system parameters before optimal responses may even conceivably be
achieved.

The overall objective of this work is to further advance ER fluid related
technology toward applications. Specifically, this work will entail three interrelated
studies that contribute to providing an understanding of radiative heat transfer through a
composite window featuring a layer of ER fluid made of silicone oil and Zeolite particles.
The first study focuses on the modeling of radiative heat transfer through the condition
where the ER fluid’s particulate medium is in a fully dispersed state. The second study
then considers radiative heat transfer for the condition where the particles are in an
electric field-induced chained state. In each of these first two studies, the beam of
incident radiation is applied to the window normal to the plane of the window. In the
third study the window is rotated about a vertical axis passing through the mass center of
the ER fluid so that off-normal transmittances may be quantified. In all of the studies, a
sequence of experiments was conducted in which transmittance measurements were taken
over a range of volume fractions, particle sizes, extinction pathlengths and electric field
strengths. The experimental data collected were used to make comparisons to levels of
transmittance predicted by the newly developed models, and hence provide a measure of

the validity of the models.

1.3 Overview of ER Fluid Technology

To review the history of progress and advancement of ER fluid technology, one
could easily examine the past half-century of research and published findings and gain a
thorough understanding of the phenomenon. There has been a tremendous amount of
research on the subject since the findings of Winslow (1947), and acknowledgment of the
contributions of many investigators should be made.

However, to exhaustively survey the past work would not necessarily provide any
insight or contribution to this thesis. Instead, this section will focus on providing an
overview of recent work that has a more direct significance to the scope of this
investigation. Altemately, to provide the reader with the opportunity to review the most
recent developments in ER fluids research, Appendix A is provided. A more complete
survey of the past few year’s research in all areas of ER fluids technology is found there.
Within these works one can also gain a general overview of the full field of ER fluid
technology, and gain reference to the earlier pioneering works of those who have brought
this field of technology to where it is today.

An overview of recent progress in the field of ER fluid research should begin with
acknowledgment of the great deal of effort that continues to be applied toward
understanding the basic mechanism of the phenomenon of ER fluids. The advancement
of ER fluid technology of this investigation, as any other, critically depends on good

firndamental knowledge of the physics behind ER fluids as its basis.

7
One such study to understand the fundamentals of ER fluids (Kita et a1, 1993)

cites that although numerous theoretical and experimental studies have been conducted at
many laboratories and institutions, there is still a controversy regarding the fundamental
mechanism involved in the ER efl‘ect. In this investigation, the effects of electric fields,
shear rates, and particle concentration on shear stress acting in the ER fluid were studied.
This led to classification of fluid flow between electrodes as either (1) an almost-solid-
state-layer, (2) a two-phase layer, or (3) a pure-liquid layer.

In a study regarding the role of water capillary forces in ER fluids (See et al,
1993), the authors point out that many researchers have noted that the viscosity of ER
fluids under electric fields increases through a maximum as water content of the particles
is increased. The authors explain this by suggesting that the particles are held together by
the capillary force of water trapped in their contact area. A model is proposed that
equates cohesive force between particles to numerous microscopic water bridges created
by electric field. The number of these water bridges depends on field strength and
amount of adhered water. Experimental confirmation of the model, along with estimation
of time scales for formation and relaxation of bridges is presented, along with comparable
experimental results.

The effect of electrical field characteristics on static shear stresses in ER fluids has
also been the subject of a recent study (Ginder and Ceccio, 1995). Here, the authors
investigate the effect of time-varying electric fields on the stresses in a variety of ER
fluids in steady shear. By studying the dependence of the time-averaged shear stress on

the frequency of the applied field, two classes of ER fluids were realized: (1) those that

8
exhibit considerable ER shear stresses with DC and low frequency AC fields, and (2) ER

fluids that perform poorly in DC fields but show considerable electrorheological activity
in AC fields. The authors fruther point out that these behaviors are consistent with the
existence of two separate means of producing ER activity, that is, mismatches of
conductivities and dielectric constants, respectively, between the suspended particles and
the suspending fluids. In this study, it was further noted that the characteristic times for
the growth and decay of induced stresses varied only weakly with strength of the applied
field. It was also shown that response times were shortened with increased shear rates.

In yet another study on the effects of AC and DC electric fields, the dynamic shear
response of ER fluids consisting of rod-like particles was investigated (Kanu and Shaw,
1994). Here, the authors propose that particle geometries should be considered to
enhance the particle-particle interactions that are typically accepted as being solely
responsible for the rheological properties of ER fluids. Experimental evidence shows that
the dynamic modulus increased with increased particle aspect ratio.

The influence of the orientation of the electric field on shear flow of ER fluids has
also been studied (Ceccio and Wineman, 1994). This work considered the possibility of
electric fields with components both normal and parallel to the direction of fluid velocity.
The analysis done included the effects of the electric field on (1) the material parameters
and (2) the contribution to stress components because of the interaction of the electric
field vector and the shearing.

There has also been a recent study on the eflect of prior heating of Zeolite/silicone

oil ER fluids on their subsequent electrorheology (Conrad et al, 1994). BR fluids were

9
heated to 80 degrees Celsius and then cooled to 25 degrees Celsius. Results showed that

heating generally produced a decrease in permittivity and current density. Furthermore, it
was shown that an increase in shear resistance after being heated to up to 80 degrees
Celsius could be expected, but at higher temperatures a decrease in shear resistance
occurs. It was concluded that both a decrease in water content and a rearrangement of
water remaining in the Zeolite cages was the cause of the mechanical changes
experienced.

Another broadly studied area related to the basic understanding of the ER fluids
phenomenon was that of sensing the structure of the field-induced particle chains. This is
of particular interest to this investigation. A study of permittivity of ER fluids under
steady and oscillatory shear (Adolf et a1, 1995) was used to show a relationship between
viscosity of the ER fluid suspensions and permittivity for a variety of volume fiactions
and applied fields. This work showed that the highest permittivities coincide with the
lowest levels of strain under high fields and low strain amplitudes, while coinciding with
the minimum strain rate under low fields and high strain amplitudes.

In the time dependent dielectric response of quiescent ER fluids (Adolf and
Garino, 1995), which was a follow-up study to the one above, the evolution of particle
structure was monitored by following the increase in perrrrittivity after an electric field
was applied. Measured permittivity agreed well with predictions for dense columnar
aggregates for low particle volume fractions and high fields. However, the authors point
out that for higher concentrations of particles or lower fields the measured perrrrittivities

were lower than expected because final particle chain structures were less compact. In

10

another work with similar objectives, normal stress measurements have been used to
indicate the induced chain network structure (Kimura et a1, 1994).

Ginder (1993) has used diffuse optical probes to measure transmittance through a
commercial ER fluid in an effort to observe particle motion and structural formation.
This work has successfully provided a measure of the time scale for field-induced
structure formation, by measuring the temporal variation in diffuse transmittance, that is
consistent with the induced-dipole attraction between particles. The dependency of
response times on field strength is studied in this work as well.

As indicated in Appendix A, there continues to be tremendous effort and resulting
strides being made in applied research that seek to capitalize on the unique mechanical
properties of ER fluids. However, a noticeable level of research focused on taking
advantage of the equally unique thermal properties of ER fluids is starting to emerge.

Beginning with a pioneering study by Shul’man (1982), and subsequent works, an
overview of enhancements in therrnophysical properties by applying electric fields to ER
fluids has been attained. For example, it has been conclusively shown that increases in
heat conduction by as much as 55 percent are achievable (Zhang and Lloyd, 1993) while
the Specific heat of the ER fluid remains unchanged. Further studies have quantified the
characteristics of ER fluids flowing in an axial direction between concentric cylinders
(Tsukiji and Furuse, 1994). Here, pressure drop and flow rate were measured under
application of electric field.

In work of a similar nature to that presented in this thesis, the optical effects of ER

fluids were studied by Hunter et a1 (1993). The authors reported a transmission drop

1 1
when fields were applied perpendicular to the light path. Furthermore, the authors report

no drop in transmission for fields parallel to light path, which would otherwise contradict
the reportings of other investigators who have shown increases in transmission for such
fields. The authors also report that they were unable to resolve the dependence on the
electric field.

Several studies have been carried out that treat light transmission through ER
fluids as a scattering phenomenon. Martin et a1 (1993), Halsey (1993) and Martin and
Odinek (1995) have performed a comprehensive study of light scattering through the
evolving ER fluid particle structure during transition upon application of an electric field.
Some results of these studies include prediction of increasing column width with time,
where the time constant decreases with increased field strength. Another result was the
development of a theoretical model describing the dynamics of field-induced structures in
oscillatory shear based on light scattering observations and by considering the efi‘ects of
hydrodynamic and electrostatic forces on a fragmenting / aggregating particle chain.

Finally, in a study that used a technique that proved critical to the work presented
in this thesis, Fisher et al (1993), used optical microscopy and statistical analysis to
quantitatively determine the structure of glass bead ER fluids as a fimction of electric
field strength and concentration of beads. The authors note that the initial structure was
of single particle (bead) chains, and that increased fields caused only slight changes in the
structure. These observations parallel those made in this work. In the previous study, the

authors note that no clear effect of bead size on chain structure was observed.

12

The work of this thesis is an extension of recent work that has suggested an
entirely new and revolutionary area of application for ER fluids in the realm of
augmenting and controlling heat transfer in radiative processes. Zhang and Lloyd (1992,
1994) have shown that radiative transmittance in ER fluids is significantly increased
when the particles are in the field-induced chained state. In their work, a monochromatic
beam of radiation energy was transmitted through a composite window cell containing a
layer of ER fluid. Radiation heat transfer was studied under various physical conditions
that included particle volume fraction, electric field strength and extinction pathlength. In
addition to measuring significant increases in transmitted energy upon application of an
electric field, the authors were able to identify the primary controlling parameters in the
response of the ER fluid.

More recently, supporting work (Andersland, 1996 and Radcliffe et al, 1996) has
shown that transmittance levels can be managed by controlling the electric field strength
through the uses of sensory feedback. By employing feedback control, response times of
particle alignment upon application of an electric field were shown to be 35 times faster
than those achieved by direct application of the electric field without any form of
feedback. In addition, it was shown that desired transmittance levels could be achieved
using feedback control with dramatically accurate results. Both studies have
demonstrated these concepts with strongly supportive experimental data, but have only
suggested a theoretical basis for understanding the physical processes affecting radiative

transfer. As stated earlier in the scope of this work, a primary objective of this work is to

13
establish the underlying mechanisms behind radiative heat transfer, and to provide

models to describe such processes.

To do so, this work will focus specifically on identifying the fundamental modes
for attenuation of radiant energy through a typical ER fluid. As this is completed, the
focus will shift to (1) development of a model to describe transmittance through an ER
fluid-based composite window in which the particles are in a randomly dispersed state,
(2) development of a similar transmittance model for the chained-particle state, and (3)
development of a transmittance model for the case where the path of incident radiation is

not parallel, or at an oblique angle, to the direction of particle chains.

CHAPTER 2 - EXPERINIENTAL APPARATUS AND METHODS

2.1 Experimental Apparatus

A schematic diagram of the apparatus used to take all experimental data is seen in
Figure 2-1. Note that the apparatus as shown shows the plane of the window being held
normal to the path of the incident beam of radiation energy. A variation to this was done
for the third study, where the window was rotated about an axis through the mass center

of the ER fluid (perpendicular to the page) to provide off-normal transmission of energy.

ER Fl 'd
Light Beam Wind;

  
  
 
 
 

 

 

SPEC T ROME T ER

3 LIGHT
SOURCE

PC - BASED J

 

 

   

Beam Shown Passing
Through ER Fluid
Window at Normal

Incidence

- HIGH VOL TA GE
GENERA TOR

FUNCTION I

   

 

 

 
 

 

 
 

 

 

GENERA TOR

 

Figure 2-1 Schematic of Experimental Apparatus

14

15

The window consisted of two pieces of glass separated by a gasket, as illustrated
in Figure 2-2. The center of the gasket was cut out to form a chamber into which the ER
fluid could be injected. The glass used was 1 mm thick soda lime glass coated with a 900
angstrom thick layer of indium-tin oxide (ITO). The gasket material was sulfur-cured
styrene butadiene, which served two distinct purposes: (1) to create a seal around the
glass so that the ER fluid did not leak out, and (2) to act as an electrical insulator capable
of withstanding the typically high field strengths associated with ER fluid use. All of this
was mounted in a steel holding fixture that was designed specifically to hold the window
at a desired orientation to the incident energy beam.

Because of the nature of the experimentation, where the ER fluid window was
repeatedly removed from the holding fixture and replaced with another experimental
window, the holding fixture was designed for extreme precision and repeatability of
window location. This was accomplished by implementing rigid stops at all points where
variation of window location could occur. Furthermore, the holding fixture was
electrically insulated from the window by a layer of silicon rubber placed between the
glass and the steel. For the transmittance experiments, it was desired to measure
transmittance through a window in which the beam of energy’s incidence angle was
normal to the plane of the window. The holding fixture was also used for mounting the
optics to present the incident radiation, as is described in greater detail below, and was
therefore designed so that the incident radiation beam was always oriented normal to the

composite window.

16

Steel "

 

Insulator

   

 

 

Insulator l” l l“ 7.2.,
,; l 1 )l
,, «Iii 'i .. r
Actual Photograph 1 .‘l '7' H" ‘ ,_ '11:} is“ G ass
ofthe Holder ,aj-li i ii...) liiri’Gasket
Assembly [11‘ ‘ . W allfTLGlass
// "\j l i
‘ ‘l
‘ I” g 1 Steel

Figure 2-2 Photograph and Schematic of the ER Fluid Window Showing the
Components Held in Place by the Holding Fixture

The electrically conducting ITO coating served as an electrode to distribute the
electric field uniformly across the window glass and through the ER fluid. The coating,
which had a thickness of about 900 angstroms, was thin enough so that the amount of
beam energy lost to absorption by the coating was minimal. Normal transmittance
through glass alone (no coating, two pieces) was measured to be 96.5 percent. The
addition of the coating on the two pieces reduced the transmittance to 93.5 percent,
meaning that on an individual piece of glass the coating reduces transmittance by 1.5
percent. Regardless, the overall reduction in transmittance was mathematically
eliminated from measurements involving the ER fluid, as described at the end of this
section and in section 2.2.

Figure 2-3 shows a photographic layout of the entire experimental apparatus.

 

Figure 2-3 Photograph of Experimental Apparatus

The major components include a PC-based spectrometer. The PC1000
manufactured by Ocean Optics was used for taking transmittance data. This was
connected to an 80486 nricroprocessor based PC. SpectraScopeGD version 2.3 software
from Ocean Optics was used to process the spectral data, including radiant intensity, from
the spectrometer. A trmgsten-halogen lamp served as the light source, providing useful
light in the wavelength range of 500 nm to 800 nm. This incident radiation was
transnritted to the ER fluid-based composite window via a 400m fiber optic cable with a
3 millimeter diameter collimating lens attached to its end. Radiation transmitted through
the window was collected by an identical collimating lens, which was aligned to the path
of the incident energy beam, and focused on another 400nm fiber optic cable that was

connected to the input of the spectrometer. Both collimating lenses, the temrinal ends of

18

the fiber optic cables, and the composite window were affixed to rigid steel holders that
were designed so that their location and orientation could be maintained for repeatability.

Before shipment fiom its manufacturer, the PC 1 000 spectrometer was calibrated
to a standard low pressure mercury-argon light. Calibration coefficients were provided
for a regression fit that the software uses to determine the true spectral nature of the
incident light. After installation in the PC, and before using the instrument for
measurements, calibration was verified. This was done by observing the transmittance of
light passing through a 50-50 beam splitter and a 90 percent attenuating (10 percent
transmitting) neutral density filter. It should be noted at this point that these levels of
attenuation (50% and 90%) should only be treated as average values. Figure 2-4 shows
the actual transmittance of the tungsten-halogen light source over the observable

wavelength range.

 

1

0'9 1” [Wavelength (A) - nmJ
0.8 +

 

 

 

0.7 ~- 50-50 Beam splitter

§ 0.3 ..

E 05 1M """"""""""""""""""" W'
0.4 «» X

*- 0.3 T Expmm' ental Values

02 >A
Q1 W - ............................ q

0

 

 

 

agezgaraaagsagtgaas
§a§3$§§§§§ §§~33§E§

mutton Vthvelength

Figure 2-4 Transmittance Through a 50-50 Beam Splitter and a 10 Percent Transmitting
Neutral Density Filter.

19

The dashed horizontal lines indicate 50 and 10 percent transmission. The upward
drift observed is due to the slight decrease in absorptance in the filter expected with larger
wavelengths (Modest, 1993). The average value of transmittance is 8.8 percent (12%
error) through the neutral density filter and 48.6 percent (2.8% error) through the beam
splitter. As a further check, other devices used for light transmittance measurement, as
described by (Zhang and Lloyd, 1992 & 1994) and (Andersland, 1995) were used to
independently verify transmittance levels as determined from the spectrometer data.

Prior to all transmittance experiments with ER fluids, transmitted intensity levels
through the glass windows filled with carrier fluid only were measured and recorded by
the Spectrometer. This was done to isolate the effect of the carrier fluid and window

coating on transmittance, and focus attention on the particles as the cause of extinction.

2.2 Experimental Methods

The electrorheological fluids used in this study consisted of particles of anhydrous
crystalline Zeolite. The average particle sizes (diameters) used were about 11, 25 and 40
microns respectively, as shown in Figures 2-5a, 2-5b and 2-5c. As can be seen best in
Figure 2-5b, which is an electron-micrograph of the 25 micron diameter Zeolite, the
particles are made up of conglomerations of crystals, with individual crystal sizes
typically 1-3 microns. To insure minimal water adsorption, and repeatability of
experiments, the particles were baked at 300°F for a period of time sufficient to vaporize

any attached water. Monitoring of particle weight was used while the baking process was

 

20
done to insure that no significant water remained, as indicated by a stabilization in
weight.

These particles were mixed with phenylmentlryl polysiloxane silicone oil in
varying volume fractions to create the ER fluid. To insure good random dispersion of the
particulate, the suspension was stirred prior to each experiment for 10 minutes by a
magnetic stirrer, and was then allowed to set for 10 minutes to allow air bubbles created

by the stirring process to rise to the surface and dissipate.

ISKU 82.090

 

Figure 2-5a Zeolite Particles, Average Diameter 11 Microns

188“» 682205

 

Figure 2-50 Zeolite Particles, Average Diameter 40 Microns

22

A syringe was then used to inject ER fluid into the cavity. Once the cavity was
filled with ER fluid, transmitted intensity was measured while the particles were in their
randomly dispersed state.

Transnrittance levels were calculated from the data by simply dividing transmitted
energy through the ER fluid by the transrrritted energy through the window filled only
with silicone oil at the same wavelengths. All transmittance levels presented were taken
from data at 684 nm, which was representative of the location of average transmittance
levels over the entire spectrum.

In addition to the particle sizes already mentioned, experiments were canied out
for a range of particle volume fractions for the fluids that varied from 0.0025 (0.25
percent) to 0.0150 (1.5 percent). Pathlengths were also varied between values of 0.7 mm
and 2.2 mm, giving a comprehensive set of data for a wide variety of transnrittances as a
fimction of pathlength, particle size and volume fraction for both the dispersed state and
the field-induced chained state.

For the field-induced chained state, field strengths were varied from less than 100
RMS (root-mean-square) volts per millimeter (V rmsImm) to about 500 Vans/mm. This AC
signal had a fi'equency of 60 Hz. The electric fields were provided by amplifying the
signal from a Goldstar model FG-2002C function generator by a Trek model 609C-6 high
voltage amplifier that had a fixed gain of 1000. Signal amplitudes and frequencies were
verified by a Hewlett Packard model 1222A oscilloscope prior to each experiment. When
a voltage field was applied to the ER fluid window, a period of time of 30 minutes was

allowed to transpire before transmittance data was taken. This was to allow ample time

23
for a steady state condition of particle chaining to be achieved. It should be pointed out at
this time that heating of the ER fluid, both from the incident energy beam and fiom
resistive heating upon application of the electric field, was negligible. A thermocouple
applied to the ER fluid window’s surface took continuous measurements of temperature
over the span of time that the experiments were in progress. At no time was an increase
in temperature greater than 0.1 degree Celsius observed.

For the third study, the window was rotated about a vertical axis through the mass
center of the ER fluid held in the window. This is described in greater detail in chapter
five. For this study, the ER fluid window assembly and holding fixture were mounted to
a Zeiss model 6334 rotary indexing table. Again, to insure precision and repeatability,
the holding fixture was mounted to the indexing table with rigidly mounted locating pins.
In this experiment, transmittance through the window that was rotated as much as - 12.0 to
+120 degrees away fiom normal was measured.

In all experiments a set of standard or control parameters were used. The
standards used were a volume fraction of 0.005, particle diameter of 11 microns,
pathlength of 1.9 millimeters, field strength of 160 Vrms / millimeter. Furthermore, with
the exception of the angular transmittance study, the energy beam was held at a 90 i 0.5
degree angle of incidence (normal) to the plane of the ER fluid window. This level of
repeatability of the angle of incidence was determined by measuring the variation in
location of the reflection of a laser beam aimed at the window.

The overall accuracy of the measured transnrittances in the described experiments

is estimated and comprehensively presented in Appendix C. This estimation of

24
uncertainty includes various error sources introduced in the experiments such as variation
in volume fractions, measured pathlengths, particle diameters, field strength and initial

transmission of light energy on an empty window.

CHAPTER 3 - RADIATIVE TRANSFER THROUGH RANDOMLY ORIENTED
PARTICLES

As already noted, radiation heat transfer control utilizing the unique properties of
electrorheological (ER) fluids has recently been a subject of interest as an innovative new
area of research. While much work has been done to demonstrate the concept and show
the potential for radiation transmittance control, little has been done however to
specifically identify the fundamental radiation transport mechanism involved. This
chapter seeks to determine the dominant modes for attenuation of radiant energy incident
upon an ER fluid made of Zeolite particles. Specifically, the focus of this chapter will be
on the case where the particles are in a fully-dispersed, or randomly oriented, state. Such
would be the case in the ER fluid prior to application of the electric field.

Once the dominant modes of attenuation are established, appropriate models will
be developed to predict radiation heat transfer through a composite window featuring a
layer of ER fluid. Later on in the chapter, a comparison will be made between the levels
of extinction predicted by these models and data obtained by experimental measurement.

It is known that when the particles of an ER fluid are in the fully dispersed state
under a zero-voltage condition, each particle acts to attenuate incident radiation. Upon

field-induced chaining (see Figure 1-1), small trmnel-like regions form that are void of

25

26
particles. This allows a greater amount of radiant energy to pass unimpeded, hence
increasing transmittance (Tabatabai, 1993).

In attempting to quantify attenuation, it has been frequently stated that each
particle may be treated as a point scatterer. Assuming that the multiple scattering regime
has not been entered, the classic Mie solution for light scattering (van de Hulst, 1957;
Kerker, 1969; Brewster and Tien, 1982; Buckius, 1986) could be employed to define
radiative properties for transfer through an ER fluid. Yet, the distinctly different
mechanisms of scattering and absorption have often been lumped under the singular term
extinction, and little has been done to differentiate between the true cause of attenuation
for ER fluids.

The obvious benefit of doing such a study is understood when one considers the
inherent mathematical difficulties involved with determining scattering parameters.
Scattering is the result of mutual enhancement and cancellation of reflected wavelets of
energy (Bohren and Huffman, 1983). Modeling the attenuation of incident energy
transport would be greatly simplified if the particles involved could be treated as point
absorbers that Simply remove energy from the beam with no further inter-particle

interaction.

3.1 Extinction of Radiant Energy

Radiant thermal energy transport in an absorbing, emitting, and/or scattering

medium is described by a radiative energy balance. It may be stated that “the change in

27
radiation intensity along a path defined by a vector «3 through a medium is due to a
positive contribution fi'om emission and fiom radiation scattered into a“, minus
contributions fiom absorption and scattering away from the a‘ direction. ” (Modest,
1993). This energy balance leads to various forms of the equation of radiative heat
transfer.

Since operating temperatures involved with ER fluids are typically low, the
contribution due to emission may be neglected. Absolute absorption is proportional to
the magnitude of incident energy and the distance the beam travels along a pathlength 0 _<_
s S L through the medium. The change in intensity of an incident beam in the distance ds

is thus written as

d] =—K,Ids (3.1)

abs

where the negative Sign denotes a decrease in intensity, and K), is the absorption
coefficient. Similarly, the portion of the energy traveling through the medium that is
redirected or scattered is given as

d] = - 0,1ds (3.2)

SCG

where or is the scattering coefficient for all directions. Since both absorption and
scattering coefficients are linear, they may be combined and the resulting equation

integrated once to yield the familiar Beer’s Law:

28

I(s)=I(0)e—‘6t’ (3.3)

where

,6; = K; + 0'1 (3.4)

is defrned as the extinction coefficient for the medium. For a particulate medium, this

may be further expanded to

fll = N (Csca + Cabs) (35)

where N is the number of particles per unit volume; Cm and Cab, are the absorption and
scattering cross sections which are a measure of the amount of extinction by a particle
defined in terms of the ratio of the energy extinction rate to the incident irradiance.

Beer’s Law gives an expression for the intensity of radiation at any points along
the pathlength as a fraction of the intensity entering the medium at s = 0. The ratio
I(s)/I(0) is the transmittance, and will be denoted here by the symbol :3. The subscript
represents the case of transmittance for the particles-dispersed state.

It is now left, before further development of a model to describe transmittance, to
determine which mode of attenuation, if any, is dominant. In any medium, a beam of
light is attenuated by both absorption and by scattering. Although absorption may be the
dominant mode of attenuation, scattering is never entirely absent (Bohren and Huffman,

1983). Measurement of transmitted energy will therefore be influenced by a combination

29

of the effects of absorption and scattering. However if the efl‘ect of scattering is minimal,
the medium can be modeled as one in which absorption is the sole cause of attenuation.

For collections of particles, whether attenuation is dominated by absorption or not
depends upon the size and optical properties of the particles. For the Zeolite particles, we
first turn to a qualitative analysis. In the typical scattering analysis based on
electromagnetic wave theory, particle surfaces are always assumed to be optically
smooth. However, referring back to the electron-micrograph of Zeolites in Figures 2-5
will quickly show that such assumptions are strictly invalid since surface roughness
levels, with voids on the order of microns, are large compared to the wavelengths of
incident radiation studied here. Looking at a cross-section of the structure of a Zeolite
particle, conceptually shown in Figure 3-1, one sees a network of grooves and cavities
and is immediately reminded of surfaces that are designed to enhance absorption

(Modest, 1993) by multiple reflections within the geometric boundaries of the surface.

 

 

   

Zeolite Particle

 

 

Figure 3-1 Cross Section of Zeolite Particle Showing Radiation Absorbing Cavities

30
Further observation of the Zeolite particles reveals yet another insight into their
radiative properties. Since the surface characteristics indicate that absorption will be
strong, we may be able to assume that the absorptive index k is reasonably large and is on
the order of one.
Considering the range of radiation wavelengths under study (500 nm S ,u S 800
nm), the particles being studied are of size (11 jam 5 2a 5 40 pm) that the particle size

parameter used for scattering analysis

x = 27mm (3.6)

yields values that range from about 43 to 251. Since 10: >> 1, we may treat the particles
as large opaque spheres and invoke the extinction paradox (van de Hulst, 1957), which
states that a large particle will remove exactly twice the amount of light from an incident

beam as it can intercept. Hence, the extinction efficiency, defined as

Qext = Cext/ 7w) (3.7)

where

Cart = Cabs + Csca (38)

will be always have a value of exactly two.
Since particles of this size are described well by geometric optics, where the
projected area of a particle for absorption and reflection is 71212 , half of this extinction

efficiency is due to diffraction. Exactly how much of the other half is due to absorption,

31
and how much is due to reflection, will depend upon the reflectivity of the particle
surface. This issue will be dealt with later.
Working from the basic Beer’s Law and the definition of transmittance, equation

(3.3) may be rewritten as

rd =e'fl‘1‘ (39)

where the pathlength variable s has been replaced with the total pathlength L of ER fluid,
which is defined by the distance between the inner surfaces of the glass windows.
Combining equations (3.5), (3.7), and (3.8) yields an expression for the extinction

coemcient

)6). = mzNQext (310)

The number of particles per unit volume may be determined fiom the expression

(3.11)

2
ll
5b

where Vp is the volume of a single particle. If the particles can be modeled as spheres,

this equation becomes

N _ 3f, (3.12)

47ta3

 

32
Substituting into equations (3.9) and (3.10) yields a simple model for transmittance in

terms of the ER fluid volume fraction, pathlength and particle size

-3 L
rd :8 ”/2. (3.13)

The extinction coefficient may now be written as

-211 (3.14)
— 2a

.51

Note here that the value of Qext = 2 has been substituted and that the denominator of the

exponent is merely the particle diameter.
3.2 Experimental Results and Discussion

Before analyzing transmittances for the purpose of making comparisons to the
proposed model, we will return briefly to the issue of absorption as the dominant mode of
attenuation.

A clear indicator that absorption dominates the extinction process is a noticeable
absence of the interference structure and the ripple structure in the extinction efliciency
over a range of wavelengths (Bohren and Hufl'man, 1983). When this is the case,
extinction and transmittance over that spectral range will be relatively constant and will

not exhibit oscillations. This supports the most fundamental assumption for a perfectly

33
absorbing surface, that is, a black surface. In this idealized case, then there will be no
wavelength dependence on transmittance. Figure 3-2 shows normal transmittance levels
for ER fluids of different volume fractions in the particle-dispersed state, and clearly
demonstrates the absence of large-scale oscillations as a function of wavelength (the
visible variation in the plot is due to signal noise in the Spectrometer’s measurement).
There is, however, a wavelength dependence for transmittance. As expected (Modest,

1993), we see that transmittance will increase with increasing wavelengths.

 

0.05

 

0-045 .- Dispersed particles -
0.04 .. zero field strength
0.035 c
0.03 0
0.025 ~~
0.02 «L
0.015 -*

°-°‘ ‘* fv = 0.0075 fv = 0.010

 

 

 

fv = 0.005

Transmittance

 

 

   

§§§§§§§§§§§§§§§§
Radiation Wavelength

Figure 3-2 Normal Transmittance Through ER Fluids
of Different Volmne Fractions with Fully Dispersed Particles
(L = 1.9mm, 2a = 11 um)
Yet another indicator that scattering is less important can be made by the

qualitative observation that scattering is a process that augments radiative intensity in

directions other than that along the path of the incident beam. If scattering is to make a

34

significant contribution to the transfer process in the ER fluids studied, then transmittance
should increase in directions away fiom that of the incident beam path. To test this, the
light sensor was moved in small increments along a direction transverse to the incident
beam and transmittance levels measured. The result is shown in the curve of Figure 3-3.
After recalling that the diameter of the beam and sensor is 3 mm, and realizing that the
total travel of the light sensor will be twice the diameter of the beam in order to travel the
distance needed to fully cross the light beam, it is clearly seen that there is no
transmittance in directions other than that of the beam. In this figure, the sensor position
of zero represents perfect alignment with the source beam.

CO CD 0 CID 00
W “Source-sensor

0'9 1 alignment ‘5

1 4- ->
0.8. Two Beam [j]

. Diameters , - .
0-7 T .——Theoretical‘i

0'64; i :1 Measured I

0.5 ' _
0.4 l
0.3 l

 

 

 

  
 

Normallzed Transmittance

 

 

“t-irr-i-i-H—t-Hrri-rfi- .
'0. ‘9. “'2 “l ". “9 0’. ‘9. F.
v.- 9 O x- N ('0 V’ II)

Sensor Poeltlon (mm)

Figure 3-3 Transnrittance as a Function of Sensor Position Transverse to the Axial
Direction of the Incident Beam

35
Hence, from all of the evidence stated, our assertion is made that the dominant
mode of attenuation in these ER fluids is absorption and that the model proposed
(equation 3.13) will predict transmittance in the dispersed state.
Prior to the presentation of transmittance data, uncertainty of measurements is
addressed by considering equation (3.13) and rewriting transmittance in terms of
transmitted energy through the ER fluid (0 divided by transmitted energy through an

empty window (10). Measured energy transmitted through the ER fluid can be modeled as

_3va (3.15)
I = Ioe 2"

 

For the PC 1000 spectrometer, intensity is measured as a voltage across an internal CCD
camera in terms of analog-to-digital converter counts. Measurement error was then

calculated by the formula:

2 2

2
+

0”]
5L 6L

0"!
do 60

31
31,

,2
5f.

 

+

 

 

 

 

 

 

 

51,

 

2 ”2 (3.16a)
5fv :l

ERROR = [

Appendix C provides a detailed analysis of the sources of error. With reference to that

analysis, it is seen that the error of equation (3.16a) is determined to be:

ERROR = (o. 7 + 165.5 + 25.8 + 1231.2)”2 ~38 counts (3.16b)

36
We see here that the leading causes of error are the components due to measurement of
volume fraction and particle size. The summation equation (3.16b) is divided by the
initial, unattenuated incident radiation intensity of 1210 counts to obtain a 3% error.
Again, this is detailed in Appendix C.

Transmittance as a function of beam pathlength for ER fluids with volume
fractions of 0.0025, 0.0050 and 0.0100 was first measured. Each of these fluids used
particles that had an average diameter of 11 microns. From these measured
transmittances for each volume fraction, equation (3.9) was used to determine
corresponding extinction coefficients, and these coefficients were then averaged. Figure
3-4 shows the measured transmittance data points plotted on a natural logarithm scale

with linear extinction lines drawn using the average extinction coefficients.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9 I—WL
V”- -___ K a .33 l l l l l l l l
.L. _ - _LAL. -1 a .._L..,L -.IL__
8 _-~-——..--1<=1.30 Zerofield T f
7 «~ K323 r- strength ~—~- «e—T- — AA edeafleee—tfi
’5 a .L l "2.0025 . t. n3.-. Lajje A -_. AL
‘ 1v=.005
g 5.- 1. o1 .. +fma- v- - __
O =- i ‘ 1 . . 1 +
a 4 .AV I : 7—5-19 1 ; .L a“ A$-A + A J_‘.- an .__ LIA
£3 1 l l I eI : i . Fl L
L. 1 t Ff -r-- ~~~~ ~—*---‘—+-- t—+ f—Tf 3' + ffiytr r. ”4.x, -%H T
I 2 i ii. V 9' ' -‘t i l l i
T . ‘7 T - T'FT ‘ T: g1: - T- T
1 _T _ I“; i i. 1A A .—_.—-_~_-:::f"f __,__,.. .L;L_.___. ._i.-:._,.e.-ea
. TA; .1, -11, 1: 11
o N x. o. m. .- 01 v 0. «1 N 01 x. 0. «a n
O O O O v- s- ‘- 1- N N N N
Pathlengthtmm)

Figure 3-4 Transnrittance in the Dispersed State for Varying Volume Fractions
as a F rmction of Pathlength (2a = 11pm)

37
The experimental extinction coemcients of Figure 3-4 were determined by
application of Beer’s Law (equation 3.3) to measured transmittances. Coefficients from
multiple experiments were mathematically averaged to determine the reported
coefficients. These were then compared to expected coefficients calculated directly from

equation (3.14). The results are tabulated in Table 3-1.

 

 

 

 

Volume fraction K [mm'l] [3 [mm'l]
(experimental) (eq. 3.14)
0.0025 0.66 :l: 0.03 0.68
0.0050 1.39 :t 0.07 1.37
0.0100 2.80 :l: 0.38 2.73

 

 

 

 

 

Table 3-1 Experimental vs. Calculated Extinction Coefficients
(Dispersed Particles, 2a = 11pm, L = 1.9 mm)

Note that the largest error between experimental and calculated values is 2.6%.

In further experimental work, transmittance through ER fluids made with particles
of varying size was measured. As stated earlier, these particle diameters (2a) were 1 1, 25
and 40 microns respectively. The volume fraction for each of these fluids was held at a
constant value of 0.005. Again using equation (3.9), average extinction coefficients are
calculated based on these measurements. Figure 3-5 shows the measured transmittance
data points with extinction lines drawn using the average extinction coefficients, much in

the same way as Figure 3-4.

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

4511111141er “‘fll'l
K-.37 l J i I I l
“ r Zerofield 4 4e 4 l
3,5 4 ——————————— K859 ~ strength 44.-__4. .. .- -44 . 7.- ._ l
A 4 K-1.42 I I A 4 4
3 3 4| . 4 . 4 4— -1.. _4_-_!4_._.l_.. _ 4 __
r: | ‘ 2831111!" I i i 1 E 4
g 2-5 *1 . 2a=25um g 4 tr f“: + {1+4 * rfl—H
| 4 , ! 4 4
2 2 «4 . 2a=40um 4 ‘5 % vi -‘ l7 - ‘-
E ‘T ‘T 4 [ T‘T"“ ' ' l 4 4 _4
t 1.5 ~ + 4 e+ ; , 4 4 +4 . _._ a. '_____,_-.4~, 4
c 4 4 i 4 I ' ..-~TI" I
.4 4 . 4 4 4 4 44 4 4 I
1 ..__._,_+._ .1... ‘ +_ in ..,... __i_ _.,_ if A __ l fi+i¥ 71‘- J” --:;:._l _.
s . 4 .. l 41* flwrwfi’” TT | A 4 '
0.5 9* ’ :_ %i,;:_.;;f “W -: 1
0 r4 4 4 . 4 i , ; ,
o N. V. «a «a v- N V. 0. 0°. N N V. «9. «a n
O O O O '- F '- P N N N N

Pathlength (mm)

Figure 3-5 Transmittance in the Dispersed State for Varying Particle Sizes
as a Function of Pathlength (f; = 0. 005)
Note here that the largest error between experimental and calculated values is 3.7%.
Once again, these average extinction coefficients are compared to theoretical

values calculated directly from equation (3.14), with these results tabulated in Table 3-2.

 

 

 

 

Particle Diameter K [mm'l] [3 [mm'l]
(experimental) (eq. 3.14)

11 um 1.42 :t 0.04 1.36

25 um 0.59 :l: 0.02 0.60

40 um 0.37 :t 0.05 0.38

 

 

 

 

 

Table 3-2 Experimental vs. Calculated Extinction Coefficients
(Dispersed Particles, j; = 0. 005, L = 1.9 mm)

All transmittance data is now collected and presented in Figure 3-6 for

comparison to the fundamental Beer’s Law model of equation (3.9), confirming with

39
conclusive evidence that this basic model is highly capable of predicting radiative

attenuation under the conditions of the investigation.

 

 

 

 

 

 

7T *4“ 4‘ 4‘ 4 4 4 4 T7
. . 4 4 .
6 ‘4‘ ‘T‘ Zero field “"1 4 fr 4 A ‘4 —~ -+:—,:4
I strength 4 4 I ' ~‘4 ’ 4 .
5 4‘ ——- —— 4 4 4 ._ - 4 .1-" .44

 

 

 

 

 

 

 

-In('l'ransmittance)

 

 

 

 

 

 

 

 

 

 

 

 

Extlnctlon Coefflcle nt x Pathlength

Figure 3-6 Comparison of Measured Transmittance
to the Fundamental Beer’s Law (2a = 1 1m)
Thus, we have established in this chapter that the dominant mode of radiant
energy attenuation in an ER fluid made of Zeolite particles is absorption. A simple
empirical model has been developed that describes attenuation of transmitted radiation

energy while the particles are in a fully dispersed state.

As can clearly be seen, the experimental data that was taken shows excellent
agreement (errors less than 4%) between experimental levels of transmittance and those
predicted fiom calculated extinction coefiicients using the absorption theory. This
confirms that attenuation of radiant energy can be predicted by treating the dominant

mode of extinction as absorption.

40
With this foundational work, it remains now to translate the same concept of
attenuation by absorption to describe the effect of electric field-induced particle chaining,

and its influence on the radiation transport properties.

CHAPTER 4 - RADIATIVE TRANSFER THROUGH PARTICLES IN THE

FIELD-INDUCED CHAINED STATE

Since the Zeolite particles have been shown to be dominantly absorbing, it stands
to reason that the cross-sectional area of the particle chains is the key to describing
overall thermal energy attenuation for a beam of light of parallel incidence to the axis of
the chains. Hence, the geometry of the particles at the interface between the glass
electrode and the ER fluid (at the side of the window fi'om which radiation emanates)
creates a series of “energy blockers”. It is left, therefore, to develop a simple model that
quantifies the shape, area, and number of these blocking surfaces to provide for a way to

model transmittance.

4.1 Additional Experimental Apparatus

For this segment of the study it was desirable to observe chaining at a microscopic
level in a direction transverse to the field lines. To accomplish this, an apparatus was
devised in which two flat aluminum plates 0.25 millimeters thick were rigidly mounted
with epoxy to a glass slide, as shown in Figure 4-1. These plates had progressive steps

ground away from one edge, and were mounted so that a variety of distances (0.7 - 5.0

41

42

mm) separated them. Furthermore, provision was made on the aluminum plates for
attaching wires from the high voltage amplifier, thus making them act as electrodes. ER
fluid was placed in the gap separating the plates, and an electric field was applied to
induce particle chaining. This apparatus was placed under an Olympus model BH-2
microscope with a Sony model XC-7ll CCD camera (pixel resolution 768 x 493)
attached. Videotaped footage was obtained showing the transition of particles from the
fully dispersed state to the field-induced chained state. The stepped-edge geometry of the
aluminum plates allowed for simultaneous observation of the particle chains over

multiple field strengths.

,—~— GLASS SLIP

 

Gap Distances
0.7 - 5.0 mm

 

 

 

 

 

 

 

 

v . ,_ ALUMINUM
ELECTRODE

Figure 4-1 Microscope Electrode Apparatus

4.2 Analysis of Particle Chain Geometry

In the most ideal arrangement for the development of chains, all of the particles in

the ER fluid will come together to form a series of uniformly spaced chains of single

43
particle width. This ideal line of single particles would stretch from one electrode surface

to the other, as illustrated in Figure 4-2.

Since the assumption is made that the spacing of these chains would be uniform,
the total number of chains would then depend upon the total number of particles present
and the number of particles needed to make one chain. That number is, of course,
dependent upon the total pathlength or spacing between electrodes. In an idealized case,
we also assume that all particles present in the ER fluid move to form chains. The total
number of particles per unit volume (N) is given in terms of the volume fraction ([4,) and

the volume of a single particle (VP) as

(4.1)

2
ll
4‘3 Its

\

  

 

 

 

 

 

 

\

ELECTRODES

Figure 4-2 Uniformly Spaced Single-Particle Chains for the Ideal Case
of Field-Induced Chaining

44

If the particles can be assumed to be modeled as spheres, then the total number of

particles per unit volume is given by

N 3 fv (4.2)

47:03

 

where a is the particle radius. The total number of particles (NT) in a given volume of ER
fluid would then be found by simply multiplying the total number of particles per unit
volume by the volume under consideration.

To determine an expression for the volume of ER fluid, V, we consider a
cylindrical beam of radiant energy that has unity cross-sectional area. As this beam
passes through a slab of ER fluid, such as would be presented in the ER fluid filled
window cavity, the total volume of ER fluid illuminated by this beam would be given in
terms of the area of the cylinder face multiplied by the pathlength (L), or the distance
separating the electrodes.

The total number of particles present in this volume is now given by simple

modification of equation (4.2):

 

3f.L (4.3)
N, = 3
47m

In a chain formed by single particles stretching over the entire pathlength, the total

number of particles per chain is found by simply dividing the pathlength (L) by the

 

45
diameter of particles (20). Therefore, the total number of single particle chains possible

in the cylindrical volume (C y) of irradiated ER fluid of unity cross-sectional area and
pathlength L is determined by dividing the total number of particles in the volume (N T) by

the number of particles per chain, which yields the expression:

 

CV _ 6f‘, (4.4)

47m2

Now, in the ideal case, if each particle forming the single particle chain were perfectly

aligned, the blocking area (A B) of each chain would simply be

AB = m2 (4.5)

With this, we have an expression for the total blocking area (A) of the ER fluid chains in
the irradiated volume which is simply the blocking area of each chain (A B) multiplied by
the total number of chains (Cy). Combining equations (4.4) and (4.5) yields the

expression:

A = 1.51:, (4.6)

From this, it stands to reason that the energy transmitted through the volume of
irradiated ER fluid (11.) will be attenuated by an amount that will be a function of this
blocking area of the ER fluid chains. It was essentially this exact same concept that led to

the basic model for transmittance for the dispersed-particle state (equation 3.13). The

46

model for chained-particle transmittance should therefore follow the same format, that is,

an exponentially decaying function of blocking area and pathlength:

—AL : 64.5va (4.7)

We note at this point that particle size does not appear explicitly in this model.
This is reconciled by realizing that volume fraction is a function of particle size. Also,
the thesis behind development of this model was to compare the number of structures
(particle chains) in a cross-sectional area to the amount of area void of structures. This,

of course, is directly attributable to volume fraction.

4.3 Experimental Results and Discussion

A careful study of the microscopic video footage taken of the chaining process
revealed that the idealization of single particle chains, even in the earliest stages of chain
formation, is far from reality. In fact, higher electrostatic forces at the electrode tend to
pull particles from the chains to the interface, thus causing a “stacking” of particles into a
conical geometry and widening the blocking area of each particle chain, as shown in
Figure 4-3a. Figure 4-3b shows an actual microscopic video still showing this stacking
effect. Visual analysis shows that this blocking area becomes as much as five particle
diameters (10a) at the interface. This leads to a new expression for blocking area, similar

to equation (4.5), where

 

47
AB = n(5a)2 = 2574442 (4-8)

Multiplying this by the total number of chains per volume (equation 4.4) yields a new

expression for total blocking area

A = 37.5f. (4.9)

and a new model for chained-particle transmittance

= e—37.5f,L (4.10)

   
 

\

STACKED
PARTICLES

 

ELECTRODE

Figure 4-3a Stacking Effect of Particles at the Electrode

Stacked Particles

Electrode Surface

 

Figure 4-3b Microscopic Video Still Showing Stacking Effect

It has been shown in previous studies that transmittance through the field-induced
particle chains of ER fluids increases as field strength increases (Zhang and Lloyd, 1992).
Further analysis of video footage provides insight into the mechanism behind this
phenomenon also. In this it was observed that particle chains that begin as typically
uniformly spaced, single particle diameter structures begin to bend toward each other
when field snengths are increased (conceptually shown in Figure 4-4a, video stills of
actual phenomenon in Figure 4-4b). We note that as many as eight neighboring chains
may be involved in this bending action around a single, central chain. This continues
until the field is strong enough to make two or more of the particle chains connect,
typically somewhere near their geometric middle at first (Figures 4-40 and 4-4d). But as
time progresses, and/or field strengths increase, the connected region of the chains begins
to increase (Figure 4-4c) until a new, single chain of multiple particle diameters is

formed.

49

M

\ ELECTRODES /

 

 

 

 

Figure 4-4a Early Stages of Chain Bending

 

Figure 4-4b Early Stages of Chain Bending

 

 

50

\ ELECTRODES /

Figure 4-4c Initial Contact Between Chains

 

Figure 4-4d Initial Contact Between Chains

 

 

\ ELECTRODES

 

 

Figure 4-4e Single Column of Multiple Chains

 

Figure 4-4f Single Column of Multiple Chains

52
This suggests that a simple geometric model for transmittance as a function of

field strength is appropriate, similar to that already developed in equation (4.10). Such a
model would be constructed under the same assumptions as before, that is, transmittance
would be determined by finding the total facial area blocked by particle structures. From
that, it seems reasonable that by simply moving existing structures about within the same
volume one would not expect very dramatic changes in transmittance, if any at all. The
level of enhancement that does materialize may be a result of the tightening of particles
held in the structure of the chain due to increased forces holding them together.

All of this leads to the idea that the model already proposed (equation 4.10) may
be sufficient to fully describe chained particle transmittance with the addition of an
empirical modification, which is a function of field strength. Of course, the video footage
can only provide evidence to support this contention. The validity of the argument will
be determined from experimental data, and therefore determination of the empirical
constant will be reserved until that time.

Prior to presenting experimental results, uncertainty of measurements is addressed
by considering equation (4.10) and rewriting transmittance in terms of transmitted energy
through the ER fluid (1) divided by transmitted energy through a window filled only with

silicone oil (1,). Measured energy can then be written as

I ___ I e-37.5f,L (4.11)

0

with experimental uncertainty calculated by the formula:

53

2
+

2
+

d
35L

0'! or
0761’ a:

0

 

 

2 )2
6f, ] (4.123)

 

 

 

 

 

 

ERROR = [

Appendix C provides a detailed analysis of the sources of error. With reference to that

analysis, it is seen that the error of equation (4. 12a) is determined to be:
ERROR = (384.8 + 7150.4 + 495.2)”: z90 counts (4.12b)

The magnitude of this level of error is in terms of the units of intensity as measured by the
PC 1 000 spectrometer. We see here that the leading source of error is the component due
to measurement of volume fraction. The summation equation (4. 12b) is divided by the
initial, unattenuated incident radiation intensity of 1210 to obtain a percent error of 7.4%.

In Figure 4-5 we see experimental transmittance data taken at Vf = 160 rms
volts/mm for three difi‘erent sets of experiments with a variety of fluids of varying volume
fraction. Superimposed against this is a line drawn to represent the model of equation
(4.10).

Table 4-1 summarizes comparisons of transmittance from experimental results to
model prediction values. Note that the largest error between experimental and calculated

values is 7.2%.

54

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0'49 TT TT T T T‘ T 4»!
_ LT; i 4 L; f ////
0.7 L ' LLL “
§ 0 6 L .L L. L L L L //
c o 4 r— 4 4 —— 4 [v 4//
g 0 5 ' L—L »« - 4» L PJL—L . _4__a
E I l f f—AL if ' LI L-——-—- Model
b 03 L L . I” WM'T'I'L 9 #44 Ex erimental
5:- 02 L—L L L L44 L L l - p
°‘ 4.2/”L *4 4 T ‘ 4 4
0 LLLLT444, ;; LLL
O ‘- N ('3 If) h F ‘— N
888§8§8§§355
o o o o o c o o o o 0
Volume Fraction

Figure 4-5 Transmittance in the Chained Particle State as a Function of Volume Fraction
(Vf= I60 Vrms/mm, L = 1.9mm, 2a = 11 pm)

 

 

 

 

 

 

Volume T (average 1, (eq. 4.10)
fraction experimental)

0.0025 0.77 i 0.04 0.83

0.0050 0.69 :t 0.05 0.70

0.0075 0.59 :l: 0.07 0.59

0.0100 0.49 :t 0.08 0.53

0.0125 0.41 :t 0.03 0.43

 

 

 

 

 

Table 4-1 Experimental vs. Calculated Transmittance Levels
(Vf= 160 Vrms/mm, L = 1.9 mm, 2a =11,um)
Experimental evidence of the effect of field strength is shown in Figure 4-6. In
this graphic, an ER fluid of volume fraction 0.0075 was subjected to increasing field

strengths until arcing across the electrodes occurred. We observe that as field strengths

55

increase, the experimental variation tends to decrease. This supports the concept that
greater order of the chain structure is achieved with greater field strengths. It also
suggests that much more predictable transmittance levels will be obtainable with higher
field strengths. Note that these voltage levels reported are RMS volts.

It is also apparent that the relationship between field strength and transmittance is
non-linear. However, the basic chained-particle model of equation (4.10) can easily be
modified with a field strength based factor to accommodate changes in voltage levels and

hence increase the robustness of the model.

°'7"‘-" w ‘TT"4
I

4 l
4 l
0.5 .L . L . ,-L. t L. 4 . . L_T-;;:#IM91L.

‘ ' i "”7 4

0,5- 7. *’~- — , —— -

i 4
0.4 .- __4 - 14-44;. 4—4 44—4 L44 4+ 4 -4 -

. l

4 l L a 4
. I . 4

5 0.3 «-44-; 44; .41--. w L- .4444 “fi—e AL :7- _4.4

‘ 4 _--—tlodol
‘ - ExportnontSott L

4‘f—‘T——fl
‘ Exporlmnt Set 2

4 w T 4'44
_ - -LJ- LU -. L

200 250 300 350 400 450 500 550

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.
4
.

 

 

 

 

 

 

 

 

Hold Strength (Vrm I I III III)

Figure 4-6 Effect of Field Strength on Transmittance
(I; = 0.0075, L = 1.9 mm, 20 =11 m)
Figure 4-7 is provided to demonstrate the data correlation to a linearized model. Here,
the natural logarithm of transmittance is plotted as a function of the inverse of the cube-

root of field strength.

 

 

 

 

 

 

 

 

 

 

 

-|n('|'ransml&ance)
—t N
-l 01 N at (a)

 

 

.0
or

 

 

 

 

 

 

 

 

 

 

 

 

[x
F

o‘ o‘ o' o‘ o‘ o‘ 6
Field Strength as a Function of tho Cube-root of Vrms/mm

u—' s-' 0'

Figure 4-7 Effect of Field Strength on Transmittance - Linearized Model
([1, = 0.0075, L = 1.9mm, 2a = 11 ,um)

Based on the above data, an empirical model is proposed. First, two very broad
assumptions: (1) At fields below 100 ms volts/mm the ability to drive particle chaining
significantly drops off. This is evidenced in the significant drop in transmittance at that
voltage level as seen in Figure 4-6, and (2) that no dramatic changes in the chaining
process take place at fields higher than Vf = 500 rms volts/mm. The model proposed
accounts for these assumptions very well. Also, when application of a higher field level
was attempted, the insulating properties of the fluid broke down, causing arcing across
the ER fluid, and the experiment was terminated.

Regardless, based on the data taken, an enhancement to equation (4. 10) is

proposed:

~37.5f,L46-253,——V 0 625]
2' = e / f+ ' (100 Vm/mmSVfSSOO Vrms/mm) (4.13)

C

57

This model accounts for the effect of various field strengths on transmittance.
Note that this model predicts that as field strengths approach zero the transmittance will

decrease to that predicted by the dispersed-particle model.

CHAPTER 5 - AN GULAR TRANSMITTAN CE ANALYSIS

Until this point, all models have treated the problem of energy transmittance
through an ER fluid composite window that is oriented so that its plane is held normal to
the incident light beam (see Figure 5-1). As a result, in all cases of transmittance through
particles held in the field-induced chained state, the particle chains have been aligned

parallel to the energy path.

 

Light Sensor

 

 

 

 

 

 

 

 

 

Light Source

 

 

Figure 5-1 ER Fluid Window with Normal Energy Incidence, Viewed fi'om the Top

58

59

In this chapter, we explore the case where the window is rotated about a vertical
axis, as shown in Figure 5-2, thus presenting an oblique angle of incidence for the energy
beam. The Zeolite particles are dominantly absorbing, which led us in Chapter four to the
concept that the ends of the particle chains are the key to describing overall thermal
energy attenuation for a beam of light of parallel incidence to the axis of the chains. In
this case, however, the geometry of the entire particle chain, especially at the interface
between both glass electrodes and the ER fluid will be responsible for creating the energy
blocking objects within the medium. To quantify the level of transmittance will require
only a modification to the existing model of Chapter four to provide for the angle

dependent blocking area and pathlength.

5.1 Additional Experimental Apparatus

Because of the angle sensitivity to transmittance measurements, it was clear that a
very high degree of collimation of the energy source would be critical. As a result, the
tungsten-halogen source used for the experiments in Chapters two and three was replaced
with a helium-neon laser that not only provided collimated light, but was monochromatic
at 632.8 nanometers.

However, this created a problem in that the spectrometer became saturated with
the higher intensity of light from the laser. To accommodate this, the spectrometer was
replaced with an Oriel model 7070 photomultiplier tube (PM'I) and amplifier as the light

sensor unit.

 

60
Additionally, the ER fluid window assembly and holder was mounted to a Zeiss
Model 6334 rotary indexing table which allowed for precision control of rotation of the
window about a vertical axis through the mass center of the ER fluid held in the orifice of
the window. To insure precision and repeatability of mounting, locating pins were
mounted on the Zeiss table and mating holes provided on the window mounting fixture.
The result was provision for rotation of the window that would enable measurement of

transmitted radiation as avfunction of azimuthal angle as is defined in Figure 5-2.

 

Light Sensor

 

 

 

 

 

 

 

 

\4 Light Source

Figure 5-2 Rotation of ER Fluid Window About a Vertical Axis

 

 

61
A photograph of the experimental apparatus with the new light source / sensor
equipment is given in Figure 5-3. Note that this is basically the same schematic of the
apparatus shown in Figure 2-1.
Prior to conducting experiments with the new light source / sensor equipment,
calibration transmittances were measured through a sample of ER fluid and compared to
levels measured with the spectrometer. Equivalent levels of measurement were achieved

in all cases.

 

Figure 5-3 Experimental Apparatus for Angular Transmittance Measurements

5.2 Analysis of Particle Chain Geometry at Oblique Angles

In Chapter four, the incident light was held perpendicular to the plane of the ER

fluid composite window. Because the electric field lines are also perpendicular to this

plane, and the particles form chains that align with the field lines, the particle chains were

62
parallel to the incident energy’s path. This is shown schematically in Figure 5-4. As a
result, based on the hypothesis of Chapter two in which the particles were found to be
strong absorbers, and hence absorption was the dominant mode of energy attenuation, we
needed only to consider the area of the ends of the particle chains to describe energy

attenuation.

 

 

4
1
4

e
{on
¢>
e
. 0 .
’fk.%’¢®96 @flflmefiw 5$$@03.%
an

9..

 

Chain End Geometry

 

 

 

 

 

 

Incident Energy

 

 

 

 

 

 

Figure 5—4 Particle Chains Parallel to the Path of Incident Energy

However, if the window is rotated about the vertical axis identified in Figure 5-2,

two significant changes in the extinction problem occur. First, the profile of the blocking

63
area of the particle chain changes, as is shown in Figure 5-5. Secondly, the total
pathlength of radiation travel through the ER fluid changes, which is also depicted in

Figure 5-5. Both of these changes are of course directly attributable to the angle 0.

 

 

 

Figure 5-5 Particle Chain Profile in a Rotated ER Fluid Window

According to experimental evidence, the previously proposed models are accurate
predictors of energy attenuation based on total blocking area due to particle geometries.
Therefore, if modifications can be made that provide for the changes in pathlength and

blocking area due to angle 6?, then the new models should provide satisfactory results for

64
transmittance through ER fluid windows held at oblique angles to the incident energy

beam.

With this, we begin development by first considering the change in pathlength.
For an angle 0, there will be an obvious change in L associated with the cosine of 6. It
can easily be seen that the efl‘ective pathlength of a particle chain presented to a beam of

incident radiation at an oblique angle Bwill be given by the formula:

Lefl=L/COSQ (5.1)

We now consider the profile of the blocking area of the particle chain. As a chain
is rotated some angle 0 about the vertical axis suggested in Figure 5-2, a significantly
larger blocking area is presented. This area is composed of the particles forming the
chain and the conical formation of particles on the window / particle interface opposite
the direction of radiation incidence. This is illustrated conceptually in Figure 5-6, where
the white particles represent those that are illuminated by, and hence absorbing, the

incident radiation.

65

 

Figure 5-6 Blocking Area of Particles That are Exposed to Incident Energy

It remains, therefore, to model the enhancement of blocking area presented by the
additionally irradiated particles in order to model angle dependent transmittance. We
begin to accomplish this by realizing that in three dimensions the rotated particle chain
will present two distinct elliptical shapes that are connected by a line of particles. A
conceptual representation of this is presented in Figure 5-7. Here, the primary ellipse
represents the blocking area of the conical formation of particles closer to the source of
incident radiation, and the secondary ellipse is associated with the particle formation
farther away from the source. Between these two formations is a line of particles.
However, for very small angles the line of particles will simply cast a shadow on the

secondary ellipse, and will have no net effect on the overall blocking area. Another way

66
to think of this is to realize that whatever particles are in front of the elliptical blocking
area will remove the same amount of radiation as the particles that their shadow covers

on the conical formation.

Secondary Ellipse

   

'\ . .
anaryEllrpse
Incident Energy / / /

Figure 5-7 Conceptualization of a Rotated Particle Chain in 3-d

Consider now the aspect ratio between the effective diameter of the conical face

(10 particle radii) and the pathlength. For the experiments reported here, this ratio is

approximately 0.05. This leads to the conclusion that for angles greater than about three

degrees the particle chains (between the conical particle formations) could add significant

blocking surface to the secondary elliptical surface mentioned above. '
To further complicate the matter, we consider the formula for the number of

chains per unit volume which was presented in Chapter four:

6f v (52)

 

67

For an ER fluid with a volume fraction of 0.0075, which was the average volume fraction
used for this particular study’s experimental phase, this relationship provides for a
maximum of about 118 single particle chains per square millimeter. It should be noted
that a particle diameter of 11 microns is used here as well.

Let’s assume then that there exists then about 118 columns per square millimeter.
This means that there will be about 11 columns per linear millimeter, leading to the idea
that the center-to-center distance between columns will be about 0.09 millimeters. Based
on this, we consider the effect of turning the window and at what level we can expect
columns to begin to “overlap” each other. Using a simple trigonometric analysis with a
pathlength of 1.9 millimeters, it is found that overlap will start to occur at angles greater
than about 2.75 degrees. This leads to the idea that since multiple overlaps will occur
almost immediately upon turning the window we may model the blocking area presented
by the rotated chains as a function of the effective diameters of the conical face.

It has been previously shown that single particle chains are not necessarily what
form upon introduction of an electric field. Indeed, with the fact that the particles form
the conical geometries at the window interfaces and that particle columns may be
composed of at least two single particle chains combined, a relationship between the true
number of columns as a function of particle volume fraction must exist. However,
prediction of this relationship analytically will be complicated by the fact that at lower
volume fractions a larger number of “fewer particle chains ” may exist than at larger

volume fractions. Similarly, for those larger volume fractions, where there are obviously

68
more particles available for development of multiple-chain columns, we may expect to
find fewer total columns composed of very large numbers of particles. Therefore,
treatment of this effect will be done empirically after experimental data has been
collected.

Based on these concepts, a model is proposed for blocking surface area. As noted
above, the overlap of columns begins to occur at about the same angle that the chains
between the conical formations begin to add blocking area to a single column. Therefore,
we will combine these effects to model an angle dependent geometric blocking area as

shown in Figure 5-8.

 

 

   

 

 

 

A
V

Angle Sensitive Region

Figure 5-8 Effective Blocking Area

Thus, the particle columns now become modeled as cylindrical shapes as viewed
from an oblique angle. After column overlap, these shapes will appear to extend across
the entire area of irradiance on the window, and will be represented as a series of lines

across the region (see Figure 5-9).

69

 

Figure 5-9 Overlapped Columns Extending Across the Entire Area of Irradiation

The blocking area of this geometry is specified by the area presented by the ends
of the conical faces at the glass interface, as has been previously developed, and an
angular dependent component. The angular dependent portion will be composed of three
terms. The first is a term describing the projected length of a single chain, which is
simply the pathlength multiplied by the sine of the angle 0. The second term is the
effective width of the chain, which is given by ten particle radii. Finally, the third term is
the volmne fraction dependent total number of columns Cfl which will be determined
empirically later. The product of these three terms provides the angle dependent
component of blocking area, and for the proposed geometry the total blocking surface is

given by

A = 37541+ Cf" ~10a-1.9sin64 (5-3)

70

There remains still one more consideration before presenting a transmittance
model. So far it has been assumed that the blocking area will be a function of the angle
of incidence of the radiation beam with respect to the window. However, since the glass
of the window and the air that the radiation travels through to reach it are different
mediums with respect to their index of refraction, the angle of incidence and the angle of

transmission are not the same. To determine this, we turn to Snell’s law which states

sine, _1 (5.4)
sinfl _ "2

where the subscripts represent the two different mediums and n is the index of refraction.
For soda-lime glass and air, the indices of refraction are approximately 1.5 and 1,

respectively. Ifwe treat 6?,- as the angle of transmission through glass, then it is related to

the angle of incidence 0by:

Q = Sin-1(sin&%2) (5.5) 4 f

where, in this case n; is again the refractive index for air and n 2 is the refiactive index for

‘.‘-—-
4

the glass. This angle should be used for the blocking area model of equation (5.3), so that

it becomes

A = 375{1+ C, .10a -1.9sina} (5-6)

71

Similarly, equation (5.1) should be modified to utilize 6,- as well.

With this we now provide a transmittance model that follows the same pattern as
previously proposed models. In those models (see for example equation 4.7)
transmittance was modeled as an exponentially decaying function of blocking area,
volume fraction and pathlength. We may now combine equations (5.1) and (5.6) to

propose a model for transmittance:

2' = e-4f.{37.5(1+C,v -10a-1.9sinq)}-%o s 62] (5.7)

Here again, Cf, will be determined empirically after analysis of experimental data.
5.3 Experimental Results and Discussion

Prior to the presentation of experimental results, uncertainty of measurements is
addressed by considering equation (5.7) and rewriting transmittance in terms of
transmitted energy through the ER fluid (0 divided by transmitted energy through an
empty window (1,), as has been done in all previous analyses of measurement error.

Measured energy transmitted through the ER fluid can now be modeled as

I _ I e‘4fv {37.541+Cfv.10a-1.9sin6,)}.%080i] (5.8)

0

72

Measurement error was then calculated by the formula:

2 2

2
+

2
+

07
dado

0‘!
397““

a
07.

d a
a 670 +Z5L

0

 

 

+

2 R
4’. 4 (5.9a)

 

 

 

 

 

 

 

 

 

ERROR = 4

 

Appendix C provides a detailed analysis of the sources of error. With reference to that

analysis, it is seen that the error of equation (5.9a) is determined to be:

ERROR = (858.6 + 508.4 + 79.2 + o + 18. 7)”? z38 counts (5.9b)

The magnitude of this level of error is in terms of the units of intensity as measured by the
Oriel PMT tube. We see here that the leading sources of error are the components due to
measurement of incident energy intensity and volume fraction. The large variation in
incident energy intensity is addressed later in this chapter. The summation of equation
(5.9b) is divided by the initial, unattenuated incident radiation intensity which was 540 to
obtain an uncertainty error of 7. 1%. Again, this is detailed in Appendix C.

Transmittance as a function of window angle (off normal) for ER fluids with
volume fractions of 0.0025, 0.0050, 0.0075, 0.0100 and 0.0125 was measured. Each of
these fluids used particles that had an average diameter of 11 microns. From these
measured transmittances for each volume fraction, an empirical relationship for ny was
determined that provided for the best fit to data. Noting the similarity to the empirically

determined field-strength term of equation (4.13), we have:

 

73

5 (5.10)

Ur

 

CI. =

3

>8

so that the transmittance equation becomes

(5.11)

-4}. {37541345745} .100.1_9sm014 4%05944

r=e

Experimental data is shown graphically against model predictions in Figure 5-10.
In this figure, note that the model lines represent different volume fractions, beginning
with 0.0025 at the top and increasing in the order 0.0050, 0.0075, 0.0100 and 0.0125 as
the lines progress downward. Furthermore, it should be noted that transmittance at 9 = 0

degrees has been adjusted to fit the normal transmittance model. This was done for two

reasons.

4 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Transmittance

 

 

 

 

 

 

 

 

 

 

 

 
 
 

.-.-L-L- £,= 0.0100
Oflhcgk=piogshtfl°l~

oooooooooooooooooooooooo

 

 

 

 

 

4...
TEL
4
4

 

 

 

 

 

Figure 5-10 Angular Transmittance: Experimental Data Versus Model Predictions
(L = 1.9 mm, 2a =11,um, Vf=160 Vrms/mm)

74

First, during this phase of the investigation it was discovered that at ofi-normal
angles (6 ¢ 0) there is an extremely strong dependence on angle for transmitted energy
through an empty glass window (10). Consider for example Figure 5-11. Here we see an
apparently periodic function for transmission of energy through glass only. Further, we
see that the period seems to be on the order of about 0.3 degrees. Over the span of just a
few one-hundredths of a degree, the level of transmission intensity can change as much as
approximately 15 percent.

Now this may initially suggest that intensity can be modeled as a sinusoidal
firnction of angle and incident energy wavelength, since the apparent period is known
fi'om data. But in another series of measurements, as shown in Figure 5-12, the apparent
period has changed now to about 0.4 degrees, or about 33 percent from previous
measurements given in Figure 5-11. Instead, this second set of data leads to another

conclusion.

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5‘
5
E
i
s .
480 4’“ T ’ 4 T T'T4T 4% TT- -,L 4‘4
460«~— 4 4L _' L- 4 . L4-
8. 53. 8. 8. 9. 3. . E 8
to no to ID to ID ID ID ID

Degree. from Normal

Figure 5-11 Transmission Intensity of Energy Through Glass as a Function of Angle

75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Transmission Intensity

 

 

 

 

 

 

 

 

 

Figure 5-12 Transmission Intensity of Energy Through Glass as a Function of Angie

It is readily apparent that the data points collected may be samples of a much
smaller wavelength signal. Indeed, using a simple math model that predicts the repeating
of the incident energy signal’s intensity (wavelength = 632.8 run) every few thousandths
of a degree, the data points collected and presented in Figure 5-12 are plotted against the
incident energy waveform in Figure 5-13. From this, it is obvious that although the data
points could be construed as representative of the incident energy waveform, they are
more likely to be aliasing the true waveform.

Now, to reverse this logic, we must consider what we have when we take data
points of energy intensity without particles, which will be used in transmittance

calculations. In essence, we have a level of energy that can change dramatically with the

Pa... .;. .fl

fun .In.

76
slightest change in angle (less than a few hundred-thousandths). It is not predictable,
because we cannot be sure of the actual waveform it represents (equipment limitations
prohibit further resolution of angle). Therefore, we must use a level of transmission that

will be representative of all levels of possible intensities, that is, an average value.

380

360
340

320
300
280
260
240

Transmitted Intensity

 

mvmmmnmvmmmom
Qai'fiui‘fleiQm'YdQco'.
co co co co co m e)

N. ‘9 0’.
to co co

3.75
3.85
3.95

Angle (degrees)
Figure 5-13 Sampled Transmitted Energy Data Points Against
a Model of the Waveform of Incident Energy
Secondly, averaging the values of 1., provided for a more consistent form of
transmittance in the data representation. Yet, it also provided a significant source of error
in transmittance levels. However, the objective of this study was to identify and model
the angular dependence on transmittance as previously defined. Therefore, to further
negate the error from the uncertainty in 10 and shift the focus of the data more to the
angular effects, the level of transmittance was adjusted to fit the model for normal
transmittance by simply modifying 10 for each volume fraction. This modified 1., was
then used to calculate transmittances for all data points at off-normal angles, providing

the results shown previously in Figure 5-10. In essence, the data is forced to be correct to

77
the normal transmittance model so that the true profile of the angular effect can be
considered.
Because of the large amount of data, the results of the modified data values to the
levels predicted by the model (equation 5.12) are presented in Appendix B.
Corresponding measurement errors are presented there as well. Note that the average

error is 3.44 percent, with the greatest error being 9.76 percent.

 

CHAPTER 6 - OPTICAL SENSORS FOR STATE CLASSIFICATION

The work of this investigation has demonstrated that ordered arrangements of the
particulate in an ER fluid made of Zeolite particles causes significant and measureable
changes in the level of radiation energy transmitted through a composite window. The
levels of transmittance have been modeled for the cases of randomly dispersed particles
(chapter 3), particles chained by application of an external electrical field (chapter 4), and
for transmittance through chained particles at ofllnormal angles of incident radiation
(chapter 5). During this study, it has been shown that transmittance is consistently
predictable with less than ten percent error, and that these levels are functions of physical
parameters of the ER fluid such as particle size, volume fraction, radiation pathlength and
voltage field strength.

A natural corollary to the results of this investigation is to consider the use of
measured transmittance of radiant energy as a reliable means of qualifying the state of
particle chaining. Clearly, a much broader ramification of this study lies in the idea that
radiative transmittance may be used as a sensory quantity for use in control systems that
can manage the level of particle chaining, and hence the unique properties of the ER
fluid, for engineering applications.

Consider the work of Radcliffe et al (1996) in which feedback control as an

entirely new approach to ER fluid response management was investigated. The traditional

78

79
method of controlling ER fluids has been to simply apply an electric field and “see what

you get” (that is, use open-loop control). If a precise relationship between a controlled
system and a stimulus is known, this method of control can produce results that compare
well to those desired. However, for an ER fluid, this relationship has yet to be fully
established, especially in the case of repeated applications of an electric field.

The use of feedback, or “closed-loop”, control overcomes the difficulties of open-
loop control for systems such as ER fluids. Here, some form of measured system output
is utilized by a controller to drive the system to a desired output. With this, the precise
relationship between a controlled system and a stimulus is no longer needed, provided
some form of accurate system state indication can be achieved. However, Andersland
(1996) was quick to point out that “the missing element in previous work has been an
accurate and precise sensor of ER fluid state”.

Yet, in this foundational study, an optical sensor was used to indicate the state of
the ER fluid and to provide feedback to a controller. The controller was intrinsically
linked to the ER fluid stimulus, that is, the applied electric field. By defining a system
error as the difference between an actual level of energy transmittance (the level of light
illuminating the optical sensor) and a desired level of transmittance, the electric field was
controlled to drive the ER fluid system toward some objective state.

The results of this work were astounding. Experimental work showed that the use
of the most simple proportional feedback control system yielded ER fluid response times
(between a dispersed-particles to a chained-particles steady state) that were 35 times

faster than those possible with open-loop control. Furthermore, the precision of actual

 

 

80

levels of transmittance as compared to desired levels was improved by a factor of 21
times. Hence, it was shown conclusively that simple feedback control systems could be
employed to greatly enhance the management of an ER fluid system by overcoming slow,
non-linear and non-repeatable ER fluid response. As an added benefit, this enhancement
is achieved with an applied electric field that is more optimized, thus conserving system
energy. This, of course, can become extremely important when considering remote
applications.

We now know that the objective state achieved by Andersland (1996) was an
indicator of the particle chain geometry. Furthermore, as a result of the present work,
mathematical models have been developed that link those geometries to levels of
transmittance, as a function of the physical parameters of the ER fluid and the applied
voltage field. Also, the models presented provide a way of predicting the level of
transmittance enhancement expected with changes in the system. Specifically, knowing
the efi‘ect of changes in field strength on transmittance, when giving consideration to the
type of feedback control used by Andersland (1996), will provide for optimal control
algorithms and hence optimal ER fluid systems.

However, in the work of Andersland (1996) the optical sensor was not optimized.
A silicon solar cell was used, along with a laser diode light source. This is not to suggest
that this energy source / sensor pair was in any way inadequate, for it certainly achieved
the results necessary to prove the concept. Yet, when considering ER fluid applications

that are an integral part of some larger mechanical or thermal system, a significant level

L.

81
of attention should be given to the sensor. The results of the present study provide some

fundamental guidelines for this.

In the present study energy transmittance models have been developed based on
particle geometries, after showing that energy is removed by an irradiated particle by
absorption. We have visually confirmed these geometries using a microscope, and have
confirmed the validity of the models with experimental data. Integral to the development
of these models has been the ability to quantify such parameters as the number of particle
chains per unit area and the geometry of particle groupings at the electrode / particle chain
interface. Linking these parameters to the physical parameters of the ER fluid particles
(i.e. particle size, volume fraction, pathlength and angle of incidence) provides the
foundation for the development of optical source / sensor pairs for such design constraints

as size and functionality.

4:
4
41
ll

 

CHAPTER 7 - CONCLUSIONS AND RECOMMENDATIONS

FOR FURTHER STUDY

This work has served to provide a comprehensive understanding of the physical
problem of radiative heat transfer through an electrorheological fluid-based composite
window. The underlying foundation of this work has been the assertion that for an ER
fluid made from Zeolite particles, the dominant mode of energy attenuation is absorption.

From this, analytical and empirical models have been derived that permit
quantification of the levels of transmittance of incident energy through the ER fluids for a
variety of particle states and physical parameters. These include analytical models for the
case of transmittance through an ER fluid with its particles in a randomly dispersed state,
and for transmittance through an ER fluid with its particles in an electric field-induced
chained state. Also, an empirical enhancement to the chained-particle model was made to
quantify the change in transmittance with changes in the level of applied electric field,
and a semi-analytical / empirical model to determine the change in transmittance for the
case of off-normal energy incidence was developed.

Although the mode of heat transfer studied here was that of radiation, the physical
understanding of the particle-particle interactions, for both a dispersed state and a field-
induced chained state, will provide a foundation for studies that address conductive and

convective heat transfer. In these future studies, the energy transport phenomena should

82

83
be readily quantifiable by considering once again the geometric forms of the particle

structures within the ER fluid suspension.

But a much broader ramification of this study, and hence the potential for a much
greater contribution, lies in the area of utilizing radiative energy transmittance as a
sensory quantity for determination of particle state. It is now well known that the particle
chains are responsible for both changes in mechanical and thermal properties in ER
fluids. Having the ability to simply and precisely sense the level of particle chaining with
optical sensors will therefore have far reaching application in the control of both
mechanical and thermal systems involving ER fluids.

It takes little to imagine the possibilities of minimizing the size of optical source /
sensor pairs. Sub-millimeter size light beams can encompass a number of particle chains
to provide indication of the overall state of the ER fluid, and drive control systems that
make applications viable and reliable. Of course, in the present study a “through-beam”
source / sensor arrangement was utilized because of the availability of transparent
electrodes. However, the use of reflective source / sensor pairs can open a wide variety of
non-invasive sensing possibilities in systems where through-beam sensing is not possible.

And then there is the potential for micron-sized source / sensors. As development
of specific components progresses, such as micron-sized lasers, the feasibility exists to
develop methods of classifying the activity of even smaller groups of particles yet, or
perhaps even single particles. Future work may lead to understanding the dynamic
response of particles as electric fields are being applied. That will allow prediction of

upcoming particle geometries - before they even exist - and provide for the creation of

 

84
ultra-fast and ultra-precise control systems. We can hardly imagine what possibilities

exist if we have the capability of literally tracking a single particle with a micron-sized

source / sensor pair. Nor can we wait to find out.

APPENDICES

 

84
ultra-fast and ultra-precise control systems. We can hardly imagine what possibilities

exist if we have the capability of literally tracking a single particle with a micron-sized

source / sensor pair. Nor can we wait to find out.

a.

a l
I‘ i'ilil. 4|“.

APPENDICES

APPENDIX A

AN OVERVIEW OF RECENT DEVELOPMENTS IN ER FLUID TECHNOLOGY

The logical progression of ER fluids basic understanding, as outlined in Chapter
1, leads to new models of the behavior encountered. Many of these models came as a
result of attempts to introduce ER fluids to commercial application. An example of this
is the modeling of ER fluids when used in the oscillating squeeze-flow mode for a
prototype automotive engine mount (Williams et al, 1993). Here, the authors report a
solution for modeling the non-Newtonian behavior of ER fluids by introducing a “bi-
viscous” characteristic.

Another example of this was a study that considered distributed vibration control
using ER fluids (Mahjoob et al, 1993). This work explored shortcomings in models for
predicting mechanical properties of composite structural members filled with ER fluids.
The authors present a method of extracting the “complex modules” of the ER fluids layer
from modal parameters of the beam, and propose a modal modification scheme based on
the discrete dynamic model of the composite beam.

A study of ER non-Newtonian flow (Korobko and Mokeev, 1994) expanded
existing models for mechanical behavior in low concentration suspensions to include ER

fluids of high volume fiaction. The physical-mathematical model described here takes

85

if
t
.4 .
4
.13

 

86

into consideration the competition between the Maxwell tension in a disperse medium
and the Maxwell pressure in a micro-nonuniform electric field between solid particles.
Experimental data was presented that compares well to model predictions.

An experimental investigation into the electrical modeling of ER fluids in the
shear mode (I-Iosseini-Sianaki et al, 1994) studied the efl'ects of electrode separation and
surface area, as well as fluid temperature, and the effect of these physical considerations
on shear. This work also considered electrical characteristics of the ER fluids system,
showing that capacitance does not vary significantly with field strength, shear rate or
temperature, but does increase with increasing electrode surface area and reduces with
increasing electrode separation. This study further showed that system resistance exhibits
no reliable dependency on shear rate, but does indeed reduce with increasing field
strength, temperature, and electrode surface area, while increasing with increased
electrode separation.

Historically there has always been an emphasis on potential applications for ER
fluids that capitalize on the changes in mechanical properties associated with the ER
effect. Recent work has included several studies that further the understanding of this
mechanical behavior. For example, a recent theoretical and experimental study of ER
fluids yield stress (Miyamoto and Ota, 1993) produced a calculation of static yield stress
using a particle chain model. In this study, the Maxwell stress was calculated by direct
solution of the Maxwell equation using a finite difi‘erential method.

Creep behavior of ER fluids has also been the subject of a recent study (Otsubo

and Edamura, 1994), which showed that creep recovery is purely plastic and the critical

‘1
t
t
.4
‘1
l

 

87
stress corresponds to the static yield value. The authors of this work point out that

although yield stress in steady shear can be predicted with the ideal chain model,
instantaneous deformation without recovery below the yield stress cannot be predicted by
this model. Further work has focused on creep and stress relaxation of ER fluids (Fisher,
1994). This investigation focused on characterizing the solid state properties of ER fluids
in the pre-yield to post-yield stress region through dynamic mechanical analysis, stress
relaxation and creep testing. Results showed that a range of viscoelastic properties exist,
with dependence on temperature, applied stress mode, and the applied strain amplitude.
Explanation of these results focused on the rearrangement of the particle structure
induced by applied fields.

As noted, with the evolution of the understanding of the fundamental mechanisms
behind the ER fluid phenomenon, more and more effort is turned to the potential for
commercial applications. A large portion of this work has been devoted to applications
that seek to exploit the rheological properties of ER fluids for active vibration damping
and control.

A prime example of this was a study that dealt with vibration control of hollow
cantilevered beams containing ER fluids (Choi et al, 1993). Here, a proof-of-concept
experimental evaluation of the vibration properties of a hollow cantilevered beam filled
with ER fluids was studied. The result was the development of an empirical model to
predict field-dependent vibration characteristics. This was done by treating the beams as
uniform viscoelastic materials and modeling as viscously-damped harmonic oscillators.

In another vibration study on the effect of an ER fluids layer on a cantilevered beam

7:]

ll
4
ll

 

88
(Haiquing et al, 1993), it was suggested that improved vibration control is gained by local

application of ER fluids over that of a sandwich beam.

In a similar study, the modeling and control of an ER fluids sandwich beam (Rahn
and J oshi, 1994) was presented with advanced models for ER fluids structures based on
viscoelasticity and sandwich beam theory. Simulations of a cantilevered ER fluids beam
showed improved response stability and transient decay.

A discussion of several applications for vibration control was provided by
Morishita and Ura (1993). This work described four applications of active vibration
control actuators and an adaptive neural-net control system suitable for controlling the
actuators. Included were (1) an automotive shock absorber system, (2) a squeeze film
damper bearing for rotational machines, (3) a dynamic damper for multi-degree-of-
freedom structures and (4) a vibration isolator. Experimental support for vibrating beam
control by a dynamic damper was provided.

A further analysis of a short squeeze-film damper operating with ER fluids was
provided by Jung and Choi (1995). From this work, a lubrication analysis of a short
squeeze-film damper is carried out. The ER fluids were modeled as Bingham fluids for
the development of the governing lubrication equation. With this, the authors reported a
“significant increase in damping capability”.

Another study involving the squeeze film damper for semi-active vibration control
devices (Morishita et al, 1995), reported successful application of ER fluids to a squeeze
film damper enabling a reduction in “whirling amplitude” in a flexible rotor. The model

used in this study was based on the short bearing approximation of a journal bearing with

89
a Bingham plastic fluid being used. This work showed that the natural frequency of a

flexible shaft was increased continuously as the applied electric field was strengthened,
and that optimum damping for the flexible rotor for various rotating speeds could be
achieved by controlling the field strength.

In a similar study focusing on distributed damping of rotorcraft flexbeams using
ER fluids (Kamath and Wereley, 1995), a model was developed to simulate the dynamic
characteristics of ER fluids. The model uses two linear models for viscous and
viscoelastic damping in combination with non-linear shape functions of strain rate.
Model pararrreters are estimated for difi‘erent values of field strength using least squares.

Damping and stiffness control in a mount structure using ER fluids (Kudallur et
al, 1994) has also been studied. This work specifically addresses the design, construction
and characterization of a mount structure for precision applications. Based on a one
degree-of-fieedom system, the authors have shown that the ability to switch from an
under-damped to an over-damped system at an appropriate switching time is better than
critical damping in a situation where a mass is displaced fiom equilibrium and then
released. The ER fluids in this work were modeled as a simple linear viscoelastic model
(V oigt model with variable viscosity). Another damper study (Brennan et al, 1995)
compared two types of ER fluids dampers. The findings of this work were that a damper
using the shear mode of the fluid has a much greater range of damping than a damper
operating in the valve mode. Again, the Bingham plastic model was used. The resulting
non-linear damping model consisted of an off-field viscous damping component and an

on-field Coulomb damping component.

90

In other works related to vibration damping and control, a proof-of-concept
investigation on vibration control of a single-link flexible manipulator incorporating
embedded ER fluids was carried out (Choi et al, 1995) This work placed an emphasis on
simplified models and increased robustness in feedback control system. Also, an ER
fluids damper for robots (Li et al, 1995) has been proposed and studied to control the
elastic vibrations of robotics mechanisms. In this investigation, a device is described that
works like a normal fluid damper when the ER fluids are not subjected to an electric
field, yet provides great counter-torques when the field is applied.

Several areas of applied research have been carried out that focus on the potential
for automotive applications. As an example, a treatise on automotive engine mounts
(Sproston et al, 1994) discusses a recently filed patent and highlights the potential
advantages of using ER fluids in tension and compression rather than in shear. This
followed a previous study on the potential for automotive engine mounts (Sproston et al,
1993), where a tenfold reduction in transmitted vibrations near resonance (4.25 Hz) was
shown with fields of lOkV. Furthermore, an investigation into an anti-vibration mount
utilizing ER fluids (Spurk and Muenzing, 1994), provided a theoretical description of the
dynamic behavior of an ER fluids based engine mount under steady state harmonic
excitation, with good experimental versus theoretical results shown.

Another area of automotive application is that of enhanced suspension systems.
An actively damped passenger car suspension system utilizing a low-voltage ER magnetic
fluid has been described by Pinkos et a1 (1993). ER magnetic fluid technology is applied

to a rotary shock absorber system with a control algorithm. Actual vehicle installation

91

with extensive testing was carried out, showing this to be a practical alternative to the
currently used multi-damping shock absorbers. A similar study on the application of ER
fluids to vibration control (Wei and Fu, 1994), discussed the potential for ER fluid-based
shock absorbers. A new type of shock absorber. and control system was presented with
test results.

Finally, in an effort to expand ER fluid application beyond the confines of earth, a
study on ER fluids for smart space materials was carried out (Lee et al, 1993). This work
addresses the need for vibrational damping on large space systems characterized by
lightly damped, large dimensional structures linked together at several joints, such as the
multi-body truss structures used in space cranes. This work studied the use of ER fluid as
a distributed actuator in flexible beam structures. In a similar work, a variable structure
controller for a tentacle manipulator (Ivanescu and Stoian, 1995), suggested a new class
of tentacle arms based on the use of flexible composite materials in conjunction with ER
fluids. A model was proposed using Lagrange’s principle for infinite-dimensional
systems, and was represented by a set of integral-difl‘erential equations.

There has also been an abundance of non-vibrational control related applications
studies performed in recent years. For example, a new type of linear piezoelectric stepper
motor has been described (Dong et al, 1995) that combines the piezoelectric effect with
the electrorheological effect. Here, the ER fluids act as a clamp while the piezoelectric
actuator indexes the motor along a grid base. The authors cite advantages such as no

vibration noise, zero wear, and high mechanical resolution.

92
ER fluids flow in journal bearings (Kollias and Dimarogonas, 1994) has also been

studied to determine the effects of using ER fluids as lubricants in journal bearings.
Here, the authors used the lubrication approximation of the equations of motion and
conservation of mass. With this, a generalized non-linear Reynolds equation model based
on the experimentally verified Bingham stress model was derived and solved by
numerical techniques. Results showed an increased load capacity for journal bearings
with increased electric field strength.

A novel application of ER fluids for the dynamic performance enhancement of
machine tool table systems has been described by Ishiyama et al, (1994). In this work, a
method of reducing chatter vibration in rolling guideways during machining operations
using an ER fluids-based variable damping mechanism was discussed.

In a study of electrorheologically controlled landing gear, Lou et al (1993)
discussed the application of ER fluids in aircraft landing gear. This work showed that
energy absorption efficiency can reach almost 100% at various sink rates.

And then a most interesting study on the development of ER fluids actuators for
driving artificial muscles was performed by Tanaka and Tsuboe (1994). Here the authors
described a method for obtaining an arbitral pressure and driving artificial muscle by
controlling the electric field applied to an ER fluids. In an experimental apparatus
described, it was confirmed that the artificial muscle can be driven smoothly for a variety

of applied electric field types.

APPENDIX B

EXPERIMENTAL DATA
FROM AN GULAR TRANSMITT AN CE MEASUREMENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 Volume 4 4 Data . Model 4 4 Percent.

3 auction Angle , (9 (9 ’ Error. . 9

0.0025 -12 0.712 0.754 5.57

-10 0.733 0.767 4.43

-8 0.718 0.780 7.95

-6 0.762 0.794 4.03

.4 0.749 0.808 7.30

-2 0.764 0.822 7.06

2 0.767 0.822 6.69

4 0.788 0.808 2.48

6 0.788 0.794 0.76

8 0.764 0.780 2.05

10 0.733 0.767 4.43

12 0.728 0.754 3.45

0.0050 -12 0.597 0.595 0.34

-10 0.620 0.611 1.47

-8 0.631 0.627 0.63

-6 0.641 0.641 0.00

 

93

 

 

 

 

94

 

 

_ Volume ' : Data _ Model “:‘szmem.
fiction ,. 441131.85 3 (9 * (9 - Err"
0.0050 .4 0.651 0.651 0.00

-2 0.654 0.681 3.97
2 0.690 0.681 1.32
4 0.677 0.662 2.27
6 0.672 0.645 4.19
8 0.612 0.627 2.39
10 0.605 0.611 0.98
12 0.613 0.595 3.03

0.0075 -12 0.489 0.474 3.17
-10 0.504 0.490 2.86
-8 0.518 0.507 2.17
-6 0.542 0.526 3.04
.4 0.569 0.545 4.40
-2 0.579 0.565 2.48
2 0.547 0.565 3.19
4 0.576 0.545 5.69
6 0.559 0.526 6.27
8 0.530 0.507 4.54
10 0.509 0.490 3.88
12 0.489 0.474 3.17
0.0100 -12 0.402 0.379 6.07
-10 0.418 0.395 5.82
-8 0.432 0.412 4.85
-6 0.429 0.430 0.23
.4 0.450 0.449 0.22

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

95

Percent
Error

5.12
2.13
1.78
6.74
9.22
8.61
9.76
5.94
0.63

0.60

1.14

 

APPENDIX C

EXPERINIENT AL UNCERTAINTY ANALYSIS

Each segment of the investigation into radiative heat transfer through ER fluid
windows has involved the development of models to predict the level of energy that is
absorbed by the particulate medium in the ER fluid. The validity of these models was
tested by gathering experimental data and making comparisons. In any experimental
endeavor consideration must be given to measurement errors, those sources of variation
that naturally skew the accuracy of experimental data. The effects of measurement error
have been eluded to in each chapter, but are expanded upon and discussed in detail here.
The methodology employed follows the guidelines set forth by Moflat (1988) for single-

sample uncertainty analysis of experimental results.

C.l Sources of Error

There are many possible sources of error in an experimental system. For the
apparatuses considered in this study, these included a series of measurement errors and
bias errors. This includes inherent variations in the measurement devices, such as the

spectrometer itself, which we had little control of. Along with this, we found that the

96

_ “1‘51

 

 

97

spectrometer itself, which we had little control of. Along with this, we found that the
spectrometer had a problem in that it appeared to integrate a static signal over time. This
caused the magnitude of the intensity of measurements to appear to drop, where in reality
it was nearly a constant. Attempts to discover the source of this proved futile, and the
manufacturer was unable to isolate this problem as well. As a result, this change in
intensity proved to be one of the greatest sources of measurement error for the
experiments.

Other possible sources of error, that were beyond control, include fluctuations in
the intensity of the light source resulting from changes in line voltage, and variations in
the properties of the ITO coated glass used as electrodes. In the case of the glass, changes
in the thickness of coating may cause a change in its reflectivity / transrnissivity
characteristics. Changes in the thickness of the glass itself may also contribute to changes
in these characteristics as well. Although no significant change in measured transmitted
intensity was ever observed, this is nonetheless a possible source of error and should be
noted.

The most significant, and fortunately determinable, sources of error came from

errors in making measurements of system parameters. These are summarized below:

Variations in the measurement of ER fluid pathlength. As was noted in the chapter on
experimental apparatus, the gasket material separating the glass electrodes was sulfur-
cured styrene butadiene, which has rubber-like properties. As each window was placed in

the window holding apparatus, the entire window assembly was sandwiched and held

98

together by tightening four finger screws. Changes in applied pressure against the gasket
material created slight changes in its thickness, and thus the pathlength, and therefore are
accounted for.

Variations in the particle radius. The electron-photomicrographs of the Zeolite particles
(reference Figures 2-5) clearly show that they are irregular in shape. Our approach to
modeling these was to treat them as spheres of an average diameter. Determination of
that average diameter came fiom measurement of the major and minor axes
(perpendicular to each other) across a number of particles shown in each electron-
photomicrograph. This was done by hand and compared to the scale printed on each
picture by the electron microscope itself. Simple mathematical averages of these
diameters (and corresponding radii) led to the determination of the average values used.
Variations in particle volume fraction. Particle volume fraction was actually determined
by creating ER fluids of known weight fiactions. Since the specific gravities of the
Zeolite particles (1.10) and the silicone oil (1.11) are very nearly the same, the weight
fi'action of particles to carrier fluid will effectively be the same as the volume fi'action,
provided that no contaminating substances were present. Of these possible contaminants,
only water was considered significant, especially since Zeolites are natural desiccants and
adsorb water molecules immediately upon exposure to them. To eliminate adsorbed
water molecules, the Zeolite particles were baked in an oven at 300°F for a period of time
sufficient to “boil off” any attached water molecules. To create the desired weight
fraction, exact amounts of silicone oil and Zeolite particles (measured with a Mettler

electronic scale) were mixed immediately upon removal of the baked Zeolite particles

99

from the oven. However, it must be remembered that the Zeolites again began adsorbing
water at the instant of exposure. In this case, the transfer from oven to silicone oil meant
exposure to air. Although the ambient humidity was low, some water did indeed reattach
in this brief period of time, causing the weight of the Zeolite to increase, and hence
imparting error on the volume fi'action measurement.

Variations in field strength. Field strength was determined by setting the output of a
function generator to a voltage level between 0 and 2000 millivolts, and then inputting
that signal to a high voltage amplifier that had a fixed gain of 1000. The amplitude of the
function generator’s output was determined by visually measuring the signal on an
oscilloscope, which imparted a certain level of error.

Variations in window angle. As was discussed thoroughly in chapter 5, a slight change
in window angle caused considerably different levels of transmitted intensity to be
measured. A micrometer scale on the Zeiss rotary table was used to provide positioning
with accuracy to the nearest 1/60th of a degree. However, as was demonstrated, much
smaller variations in angle resulted in difl‘erent transmitted energy measurements.
Therefore, a significant source of error was presented. Furthermore, because the window
holding apparatus was designed so that the window could be removed for experiment
preparation, a certain level of positioning variation existed, especially as bearing

materials began to wear over time.

 

lOO

C.2 Error in the Dispersed Particles Model

Recall from chapter 3 the dispersed particles model:

_344 (3.15)
I=Ioe 2"

 

Using the chain rule of differentiation leads to

1 2

+

07
E6“

 

07
E51.

 

 

 

2
0'!
+—v+
it?

 

076%

0

d
ERROR = I:

 

 

,.8
] (3.16a)

 

 

where the 5 parameter represents the variation observed for each specific measurement,

and:

 

 

 

 

 

J _3ivL (C.l)
_ = e a
5?;
3f,L _ C2
1: I e— 2a ( 3L) ( )
2. ° 2a
3va .
51:] e_ 20 (_3fVJ (C3)
OI ° 2a

101

 

o7 -ifv—L (- 3 f, L) (CA)

2a2

For the series of experiments carried out to measure transmitted intensity in an ER
fluid with its particles in a randomly dispersed state, the following parameter values and

variations may be considered to be typical:

 

 

 

 

 

 

 

 

 

Parameter Value Variation
Initial Intensity (10) 1210 40
Volume Fraction (fv) 0.0075 0.001
Pathlength (L) 1.9 (mm) 0.1
Particle Radius (a) 5.5 x 10'3 (mm) 2 x 10'3

 

Using these, and applying to equations (C.l) - (C4) and (3.16a) yields an expected error
level in measured intensity of 37.7 analog-to-digital converter counts. In terms of

transmittance, after dividing by I, = 1210, this leads to an expected error level of i 3%.

C3 Error in the Chained Particle Model

Recall from chapter 4 the chained particles model:

I = I e-mm (4.11)

0

Again using the chain rule of differentiation leads to a statement of the expected error,

which is given as the change in measured intensity I, or

102

2
+

2
+

07
Z90

a a
21—51, 56L

T (4.12a)

The 6 parameter, as before, represents the variation observed for each specific

 

 

 

 

 

 

ERROR = I:

measurement, and:

1: €37.5va (C.5)
07..
(C.6)
g = [Gem's/"L (_ 37.51.)
(0.7)

37 5

_fl _ — . f, L

_ Ice (— 37.5 f,)
For the series of experiments carried out to measure transmitted intensity in an ER

fluid with its particles in a field-induced chained state, the following parameter values

and variations may be considered to be typical:

 

 

 

 

 

 

 

 

Parameter Value Variation
Initial Intensity (10) 1210 40
Volume Fraction (fv) 0.0100 0.002
Pathlength (L) 1.9 (mm) 0.1

 

103

Using these, and applying to equations (C.5) - (C7) and (4.12a) yields an expected error
level in measured intensity of 89.6 counts. In terms of transmittance, afler dividing by I,

= 1210, this translates to an expected error level of i 7.4%.
C.4 Error in the Chained Particle Model With Field Strength as a Parameter

The chained particle model of chapter 4 was modified to include an empirical
term to account for the change in transmittance as a function of field strength. A model

was proposed with field strength as a parameter:

(4.13)

-37.5 1,497 ]
s/V, +0.625

r=e

C

which is rewritten here in terms of measured intensity:

I = I e-375 1.49% V, +0625] (Q8)

0

From this, an equation for error can be written:

2
+

2
+

2

l
W!

1
41

a a
d 07, Ea.

 

.1}.

<7. 5";

2 a
] (C.9)

 

 

 

 

 

 

 

ERROR = [

 

104

where, as before, the 6' parameter represents the variation observed for each specific

measurement, and:

a -37.5f,L[6-7W+0‘625] (C. 10)

at"

 

, 925,, (C11)
51 =Ie 3 5fL[ /l/+0.625] '[-375L[ 6.25 ]]

 

9‘. ° {/2 + 0.625
07 "37'sf'L[6'% V, +0.62 J l: [ 625 II (C' 12)
—=I,e - —375f, —
01 3M + 0.625
(0.13)
’37" 'L 625w +0625
1:10,, ’1/J7 1.137% 625 2
5V! 3 (fo + 0.625) V25

For the series of experiments carried out to measure the effect of field strength on
transmitted intensity in an ER fluid with its particles in a field-induced chained state, the

following parameter values and variations may be considered to be typical:

 

 

 

 

 

 

 

 

 

Parameter Value Variation
Initial Intensity ([0) 1210 40
Volume Fraction (fv) 0.0100 0.002
Pathlength (L) 1.9 (mm) 0.1
Field Strength (V f) 200 (V rmts/mm) 20

 

 

105

Using these, and applying to equations (C.10) - (C.13) and (Q8) yields an expected error

level in measured intensity of 89.6 counts. In terms of transmittance, after dividing by I,

= 1210, this translates to an expected error level of i 7.4%.
C.5 Error in the Angular Transmittance Model

The angular transmittance model of chapter 5 was developed to quantify
transmittance of chained particles when the ER fluid window is rotated some angle off
normal about a vertical axis through the ER fluid mass center. A model was proposed
that included an empirical term to provide for a volume fraction dependent total number

of particle columns:

(5.11)

—[f, {37.5[1+5%/—£-106-1.9sina) }%osa]

r=e

It should also be noted again that 6) is the transmittance angle of light through the
soda-lime glass. It is determined fiom Snell’s Law (equation 5.4), and is a fimction of the

measured incidence angle 6?. From this, an equation for error can be written:

2

+

2 2

d
506a

or
9‘.

o”!
0161.

 

 

+

2
a
+550,

 

 

 

 

 

 

 

 

+

a O a;

O

a 2 % (5.9a)
Em=[ a ]

 

106

where once again the 6 parameter represents the variation observed for each specific
measurement. To perform the necessary partial differentiations, the exponential term is
written out in a full term-by-term expansion (note that the transmittance equation is also

written now in terms of intensities):

2
{37.5 f,L/coso,. +3918.75 Manna/66319] (C-14)

I=Ie

0

We may also write equation (C. 14) as:

I = I e-fl (C.15)

where

,B = 375va/cosfl, + 3918.75 flame, (016)
From this we can now write the partial derivatives:
0‘1 _fi (019)
2,70- = e
(021)

g = Ioe’” -[375L /cos€,. +26125f;%aLtan9,]

V

107

c.22
% = Ice—p '[375f, /cos6l, +3918.75f,%atan6,] ( )
a ‘ (C23)
—_ 5 2/3
a: —1,e -[3918.75f, LtanQ]
fl _ -3 375/,Lsino/ % , ] ((3.24)
50f!” .[ icoszgi+391875fv aLsec o,

For the series of experiments carried out to measure the effect of off-normal
incidence on transmitted intensity in an ER fluid with its particles in a field-induced

chained state, the following parameter values and variations may be considered to be

typical:

 

 

 

 

 

 

 

 

 

 

Parameter Value Variation
Initial Intensity (lo) 540 50
Volume Fraction (fv) 0.0075 0.001
Pathlength (L) 1.9 (mm) 0.1
Particle Radius (a) 5.5 x 10'3 (mm) 2 x 10'3
Off-normal Angle (9,) 0 (degrees) 0.0167

 

Using these, and applying to equations (C.20) - (C.24) and (C.14) yields an expected error
level in measured intensity of 38.3 counts. In terms of transmittance, after dividing by I,
= 540, this translates to an expected error level of :l: 7.1%.

In addition to the estimation of uncertainty in the overall result, confidence
intervals around the mean extinction coeficients of chapter three are considered as a final

indicator of the integrity of these parameters. For example, Table 3-1 reports an

«I—

108

extinction coefficient calculated from equation (3. 14) of ,B = 0.68 for a volume fraction of
0.0025. Data points collected at this volume fraction yielded experimental extinction
coeflicients of 0.64, 0.64, 0.65 and 0.69. Based on these, a confidence interval is
constructed using the t-distribution with three degrees of freedom and an estimate of the

standard deviation based on the equation:

2 n§Xi2_(;XJZ (C22)
S = n(n-1)

 

In this case, a 95% confidence interval for the true value of the coefficient is found to be:

06zsps070

Computations for the remaining extinction coemcients produce similar results, which
leads to the conclusion that the reported values are indeed the best estimate for the result,
and, with 95% confidence, the true value is believed to be within the limitations set forth

by the percent error for each experiment.

BIBLIOGRAPHY

BIBLIOGRAPHY

Adolf, D., and Garino, T., 1995, “Time Dependent Dielectric Response of Quiescent
Electrorheological Fluids,” Langmuir, Vol. 11, No. 1, pp. 307-312.

Adolf, D., Garino, T., and Hance, B., 1995, “Permittivity of Electrorheological Fluids
Under Steady and Oscillatory Shear,” Langmuir, Vol. 11, No. 1, pp. 313-317.

Andersland, R. M., 1996, “Feedback Control of Electrorheological Fluids,” Master ’s
Thesis, Michigan State University, East Lansing, Michigan.

Bohren, C. F., and Huffman, D. R., 1983, “A bsorption and Scattering of Light by Small
Particles. ”

Brennan, M. J., Day, M. J., and Randall, R. J., 1995, “Electrorheological Fluid Vibration
Damper,” Smart Materials and Structures, Vol. 4, No. 2, pp. 83-92.

Brewster, M. Q., and Tien, C. L., 1982, “Radiative Transfer in Packed Fluidized Beds:
Dependent Versus Independent Scattering,” J. of Heat Transfer 104, 573.

Buckius, R. 0., 1986, “Radiative Heat Transfer in Scattering Media: Real Property
Considerations,” Proc. of Eighth International Heat Transfer Conf., Vol. 1, 141.

Ceccio, S. L., and Wineman, A. S., 1994, “Influence of Orientation of Electric Field on
Shear Flow of Electrorheological Fluids”, Journal of Rheology, Vol. 38, No. 3, pp. 453-
463..

Choi, S., Park, Y., and J ., 1993, “Vibration Characteristics of Hollow Cantilevered
Beams Containing an Electrorheological Fluid,” International Journal of Mechanical
Sciences, Vol. 35, No. 9, pp. 757-768.

Choi, S., Thompson, B. S., and Gandhi, M. V., 1995, “Experimental Control of a Single-
Link Flexible Arm Incorporating Electrorheological Fluids,” Journal of Guidance,
Control and Dynamics, Vol. 18, No. 4, pp. 916-919.

Conrad, H., Shih, Y., Chen, Y., 1994, “Effect of Prior Heating Zeolite / Silicone Oil
Suspensions on Their Subsequent Electrorheology at 25 Degrees C,” Developments in

109

110

Electrorheological F lows and Measurement Uncertainty - 1994 American Society of
Mechanical Engineers Fluids Engineering Division, Vol. 205, pp. 83-87.

Dong, S., Li, L., Gui, Z., Zhou, T., and Zhang, X., 1995, “New Type of Linear
Piezoelectric Stepper Motor,” IEEE Transactions on Components, Packaging and
Manufacturing Technology - Part A, Vol. 18, No. 2, pp. 257-260.

Fisher, M. D., Sprecher, A. F ., and Conrad, H., 1993, “Metallography Applied to the
Structure of Electrorheological (ER) Fluids,” Metallography: Past, Present and Future
ASTM Special Technical Publication, No. 1165, pp. 372-3 89.

Fisher, M. D., 1994, “Creep and Stress Relaxation of ER Fluids,” Developments in
Electrorheological F lows and Measurement Uncertainty - 1994 American Society of
Mechanical Engineers Fluids Engineering Division, Vol. 205, pp. 89-98.

Ginder, J. M., 1993, “Difliuse Optical Probes of Particle Motion and Structure Formation
in an Electrorheological Fluid,” Physical Review, Vol. 47, No. 5, pp. 3418-3429.

Ginder, J. M., and Ceccio, S. L., 1995, “Effect of Electrical Transients on the Shear
Stresses in Electrorheological Fluids,” Journal of Rheology, Vol. 39, No. 1, pp. 211-234.

Haiquing, G., King, L. M., and Cher, T. B.,1993, “Influence of Locally Applied
Electrorheological Fluid Layer on Vibration of a Simple Cantilever Beam,” Journal of
Intelligent Material Systems and Structures, Vol. 4, No. 3, pp. 379-3 84.

Halsey, T. C., 1993, “Coarsening of a Quiescent Electrorheological Fluid 11: Theory,”
Materials Research Society Symposium Proceedings, Vol. 289, pp. 57-61.

Hosseini-Sianaki, A., Bullough, W. A., Tozer, R. C., Whittle, M., and Makin, J., 1994,
“Experimental Investigation into the electrical modeling of Electrorheological Fluids in
the Shear Mode,” IEEE Proceedings: Science, Measurement and Technology, Vol. 141,
pp. 531-537.

Hunter, L. W., Mark, F. F., Kitchin, D. A., Feinstein, M. R., Blum, N. A., Platte, B. R.,
Arcella, F. G., Kuespert, D. R., and Donohue, M. D., 1993, “Optical Effects of
Electrorheological Fluids,” Journal of Intelligent Material Systems and Structures, Vol.
4, No. 3, pp. 415-418.

Ishiyama, M., Aoyama, T., and Edamura, K., 1994, “Application of Electrorheological
Fluid for the Dynamic Performance Enhancement of Machine Tool Table Systems
(Analysis of the Dynamic Characteristicsof a Simple Table System),” Transactions of
the Japan Society of Mechanical Engineers - Part C, Vol. 60, No. 577, pp. 2964-2970.

 

111

Ivanescu, M., and Stoian, V., 1995, “Variable Structure Controller for a Tentacle
Manipulator,” Proceedings - IEEE International Conference on Robotics and
Automation, Vol. 3, pp. 3155-3160.

Jung, S. Y., and Choi, S., 1995, “Analysis of a Short Squeeze-film Damper Operating
with Electrorheological Fluids,” T ribology Transactions, Vol. 38, No. 4, pp. 857-862.

Kamath, G. M., and Wereley, N. M., 1995, “Distributed Damping of Rotorcrafi
F lexbeams Using Electrorheological Fluids,” AIAA / ASME / ASCE / AHS Structures -
Structural Dynamics & Materials Conference - Collection of Technical Papers, Vol. 4,
pp. 2297-2307.

Kanu, R. C., and Shaw, M. T., 1994, “Eflects of AC and DC Electric Fields on the
Dynamic Shear Response of Electrorheological Fluids Consisting of Rod-like Particles,”
Developments in Electrorheological F lows and Measurement Uncertainty - I 994
American Society of Mechanical Engineers Fluids Engineering Division, Vol. 205, pp.
1 17-124.

Kerker, M., 1969, “The Scattering of Light and Other Electromagnetic Radiation, ”
Academic Press, New York.

Kimura, H., Minagawa, K., and Koyama, K., 1994, “Induced Network Structure in
Liquid Crystalline Polymer Evidenced from Electrorheological Normal Stress
Measurements,” Polymer Journal, Vol.26, No. 12, pp. 1402-1404.

Kita, Y., Ohshima, T., Takase, H., Kondoo, I., and Fujisawa, S., 1993, “Fundamental
Study of Electrorheological Fluids,” Transactions of the Japan Society of Mechanical
Engineers, Part B, Vol. 59, No. 562, pp. 1816-1821.

Klingenberg, D. J., van Swol, F. and Zukoski, C. F., 1989, “Dynamic Simulation of
Electrorheological Suspensions,” Proceedings of the ACS Division of Polymeric
Materials Science and Engineering, Vol. 61, pp. 154-155.

Kollias, A., and Dimarogonas, A. D., 1994, “Electrorheological Fluid Flow in Partial
Journal Bearings,” Developments in Electrorheological Flows and Measurement
Uncertainty - I 994 American Society of Mechanical Engineers Fluids Engineering
Division, Vol. 205, pp. 69-81.

Korobko, E. V., and Mokeev, A. A., 1994, “Study of Electrorheological Non-Newtonian
Flow,” Developments in Electrorheological F lows and Measurement Uncertainty - 1994
American Society of Mechanical Engineers Fluids Engineering Division, Vol. 205, pp.
147-154.

Kudallur, S. B., Conners, G. H., and Bufl'mgton, K. W., 1994, “Damping and Stifiiress
Control in a Mount Using Electrorheological (ER) Fluids,” Developments in

112

Electrorheological F lows and Measurement Uncertainty - 1994 American Society of
Mechanical Engineers Fluids Engineering Division, Vol. 205, pp. 57-61.

Lee, G. K., Yuan, F., and Conrad, H., 1993, “On the Use of Electrorheological Fluids for
Smart Space Materials,” Space Exploration Science and Technologies Research -
American Society of Mechanical Engineers Aeorspace Division, Vol. 31, pp. 107-115.

Li, J ., Jin, D., Zhang, X., Zhang, J ., and Gruver, W. A., 1995, “Electrorheological Fluid
Damper for Robots,” Proceedings - IEEE International Conference on Robotics and
Automation, Vol. 3, pp. 2631-2636.

Lou, Z., Ervin, R. D., Filisko, F. B., and Winkler, C. B., 1993, “Electrorheologically
Controlled Landing Gear,” Aerospace Engineering, Vol. 13, No. 6, pp. 17-22.

Mahjoob, M. J ., Martin, H. R., and Ismail, F., 1993, “Distributed Vibration Control
Using Electrorheological Fluids,” Proceedings of SPIE - The International Society for
Optical Engineering, Vol. 1923, part 1, pp. 768-774..

Martin, J. E., Odinek, J., and Halsey, T. C., 1993, “Coarsening of a Quiescent
Electrorheological Fluid 1: Experiment,” Materials Research Society Symposium
Proceedings, Vol. 289, pp. 49-56.

Martin, J. B., and Odinek, J ., 1995, “Light Scattering Studies of an Electrorheological
Fluid in Oscillatory Shear,” Dynamics in Small Confining Systems 11 - Materials
Research Society Symposium Proceedings, Vol. 366, pp. 155-162.

Miyamoto, T., and Ota, M., 1993, “Theoretical and Experimental Study on ERF ’s Yield
Stress”, Transactions of the Japan Society of Mechanical Engineers, Part B, Vol. 59, No.
562, pp. 1822-1828.

Modest, M. F ., 1993, “Radiative Heat Transfer, ” McGraw-Hill, New York.

Mofi‘at, R. J., 1988, “Describing the Uncertainties in Experimental Results,”
Experimental Thermal and Fluid Science, Vol. 1, pp. 3-17.

Morishita, S., and Ura, T., 1993, “BR Fluid Applications to Vibration Control Devices
and an Adaptive Neural-Net Controller,” Journal of Intelligent Material Systems and
Structures, Vol. 4, No. 3, pp. 366-372.

Mosishita, S., An, Y. K., and Mitsui, J., 1995, “ ER Fluid Squeeze Damper for Semi-
active Vibration Control Devices: A Parametric Study,” ASME Paper 95-GT-251.

Otsubo, Y., and Edamura, K., 1994, “ Creep Behavior of Electrorheological Fluids,”
Journal of Rheology, Vol. 38, No. 6, pp. 1721-1733.

 

113

Pinkos, A., Shtarkman, E., and Fitzgerald, T., 1993, “Actively Damped Passenger Car
Suspension System with Low Voltage Electrorheological Magnetic Fluid,” Vehicle
Suspension and Steering Systems - SAE Special Publications, No. 952, pp. 87-93.

Radcliffe, C. J., Lloyd, J. R., Andersland, R. M., and Hargrove, J. B., 1996, “State
Feedback Control of Electrorheological Fluids”, ASME International Mechanical

Engineering Congress and Exhibition and ASME J. Dynamic Systems - Measurement
and Control, Atlanta, GA, November 1996.

Rahn, C. D., and Joshi, S., 1994, “Modeling and Control of an Electrorheological
Sandwich Beam,” Active Control of Vibration and Noise - American Society of
Mechanical Engineers Design Engineering Division, Vol. 75, pp. 159-167.

See, H., Tamura, H., Doi, M., 1993, “Role of Capillary Forces in Electrorheological
Fluids,” Journal of Physics D: Applied Physics, Vol. 26, No. 5, pp. 746-752.

Shu’lman, Z. P., 1982, “Utilization of Electric and Magnetic Fields for Control of Heat
and Mass Transfer in Dispersed Systems (Suspensions),” Heat Transfer - Soviet
Research 14(5), 1, September - October.

Sproston, J. L., Stanway, R., Prendergast, M. J., Case, J. R., and Wilne, C. B., 1993,
“Prototype Automotive Engine Mount Using Electrorheological Fluids,” Journal of
Intelligent Material Systems and Structures, Vol. 4, No. 3, pp. 418-419.

Sproston, J. L., Stanway, R., Williams, E. W., and Rigby, S., 1994, “Electrorheological
Automotive Engine Mount,” Journal of Electrostatics, Vol. 32, No. 3, pp. 253-259.

Spurk, J. H., and Muenzing, R., 1994, “Anti-vibration Mount with ER-fluid,”
Developments in Electrorheological F lows and Measurement Uncertainty - I 994
American Society of Mechanical Engineers Fluids Engineering Division, Vol. 205, pp.
51-56.

Tabatabai, S., 1993, “Aspects of Radiation Heat Transfer in ER Fluid Based Composite
Windows,” Studienarheit, Rheinisch-Westfalrsche Technische Hochschule Aachen /
Michigan State University, 84 pages.

Tanaka, Y., and Tsuboe, H., 1994, “Development of ERF-actuator for Driving Artificial
Muscle,” Transactions of the Japan Society of Mechanical Engineers - Part C, Vol. 60,
No. 579, pp. 3882-3887.

Tao, R., and Sun, J. M., 1991, “Three-Dimensional Structure of Induced
Electrorheological Solid,” Physical Review Letters, July 15, Vol. 67, No. 3, pp. 398-401.

Tsukiji, T., and Furuse, N., 1994, “Flow Characteristics of ER Fluids Between
Concentric Cylinders,” Developments in Electrorheological F lows and Measurement

114

Uncertainty - 1994 American Society of Mechanical Engineers Fluids Engineering
Division, Vol. 205, pp. 7-14.

van de Hulst, H. C., 1957, “Light Scattering by Small Particles, ” Wiley.

Wei, C., and Fu, Z.., 1994, “Electrorheological Fluid and Its Application in Vibration
Control,” Journal of Beijing Institute of Technology, Vol. 3, No. 1, pp. 91-98.

Williams, E. W., Rigby, S. G., Sproston, J. L., and Stanway, R., 1993,
“Electrorheological Fluids Applied to an Automotive Engine Mount,” Journal of Non-
Newtonian Fluid Mechanics, Vol. 47, pp. 221-238.

Winslow, W. M., 1947, U. S. Patent 2,417,850.

Zhang, C., and Lloyd, J. R., 1992, “Measurements of Radiation Heat Transfer in
Electrorheological Fluid Based Composite Materials,” Developments in Radiative Heat
Transfer, HT D, Vol. 20, 1992 National Heat Transfer Conference, San Diego, CA, Aug.
8-11, pp. 55-62.

Zhang, C., and Lloyd, J. R., 1993, “Enhancement of Conductive Heat Transfer Through
an Electrorheological Fluid Based Composite Medium,” Fundamentals of Heat Transfer
in Electromagnetic, Electrostatic and Acoustic Fields, HTD, Vol. 248, pp. 75-82.

Zhang, C., and Lloyd, J. R., 1994, “Control of Radiation Heat Transfer Through 8
Composite Window Featuring ER Fluid: A Conceptual Investigation,” Inzhenerno-
F izichoskii Zhurnal, Vol. 6, No. 2, pp. 131-142.

 

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