Fluctuation dynamics of a single magnetic chain
Adriana S. Silva,
1
Robert Bond,
1
Franck Plouraboue
´
,
2
and Denis Wirtz
1,
*
1
Department of Chemical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218
2
Ecole Supe ´rieure de Physique et Chimie Industrielle de la Ville de Paris, Laboratoire PMMH, 10 rue Vauquelin,
F-75231 Paris Cedex, France
Received 27 March 1996
‘‘Tunable’’ fluids such as magnetorheological MR and electrorheological ER fluids are comprised of
paramagnetic or dielectric particles suspended in a low-viscosity liquid. Upon the application of a magnetic or
electric field, these fluids display a dramatic, reversible, and rapid increase of the viscosity. This change in
viscosity can, in fact, be tuned by varying the applied field, hence the name ‘‘tunable fluids.’’ This effect is due
to longitudinal aggregation of the particles into chains in the direction of the applied field and the subsequent
lateral aggregation into larger semisolid domains. A recent theoretical model by Halsey and Toor HT ex-
plains chain aggregation in dipolar fluids by a fluctuation-mediated long-range interaction between chains and
predicts that this interaction will be equally efficient at all applied fields. This paper describes video-
microscopy observations of long, isolated magnetic chains that test HT theory. The measurements show that,
in contrast to the HT theory, chain aggregation occurs more efficiently at higher magnetic field strength ( H
0
)
and that this efficiency scales as H
0
1/2
. Our experiments also yield the steady-state and time-dependent fluc-
tuation spectra C ( x , x ' ) [ h ( x ) -h ( x ' )]
2
1/2
and C ( x , x ' , t , t ' ) [ h ( x , t ) -h ( x ' , t ' )]
2
1/2
for the instanta-
neous deviation h ( x , t ) from an axis parallel to the field direction to a point x on the chain. Results show that
the steady-state fluctuation growth is similar to a biased random walk with respect to the interspacing | x -x ' |
along the chain, C ( x , x ' ) | x -x ' |
, with a roughness exponent =0.530.02. This result is partially con-
firmed by Monte Carlo simulations. Time-dependent results also show that chain relaxation is slowed down
with respect to classical Brownian diffusion due to the magnetic chain connectivity, C ( x , x ' , t , t ' ) | t -t ' |
,
with a growth exponent =0.350.05
1
2
. All data can be collapsed onto a single curve according to
C ( x , x ' , t , t ' ) | x -x ' |
( | t -t ' | / | x -x ' |
z
), with a dynamic exponent z = / 1.42.
S1063-651X9613911-8
PACS numbers: 47.50.+d, 83.80.Gv, 83.20.Jp
I. INTRODUCTION
Over the past decade, a great deal of attention has been
focused on the development of a new class of fluids, termed
‘‘tunable’’ fluids 1,2. Electrorheological ER and magne-
torheological MR fluids belong to this class. These fluids
offer the promise of fast-response devices, which would ef-
ficiently interface mechanical components with electronic
controls. Advantages of such devices include fast switching
speed, miniaturization, and continuously variable control.
The inherent value of these materials lies in their ability to
quickly and reversibly change from a liquidlike state to a
semisolid state when subjected to an electric or magnetic
field, with a response time on the order of a few milliseconds
3. This rapid ‘‘tunable’’ phase transition induces a rapid
and drastic increase of the fluid viscosity 4.
ER fluids are comprised of fine dielectric particles im-
mersed in a medium of different dielectric constant i.e., sili-
cone oil, water3. Due to particle chaining in the direction
of the applied electric field, the fluid undergoes a change in
viscosity 3,4. The development of ER fluids dates back to
the 1940s, with the original work by Winslow 5. The sys-
tem used was comprised of an ER fluid based on dispersed,
moist silica gel. Winslow observed that, upon application of
an electric field, particles suspended in oil formed fibrous
structures aligned with the field. In addition, working with
field strengths on the order of 3 kV/mm, he determined that
the shear stress [ ( E ) - (0)] was dependent on the square
of the applied voltage. Winslow postulated many applica-
tions of ER fluids and described their use in clutches, brakes,
and valves 3.
After a brief period of intense interest, work in the field
dwindled for almost 30 years. The next extensive work was
carried out by Klass and Martinek 6,7, who reported their
results from ER fluids comprised of silica and calcium titan-
ate. In two landmark papers 6,7, these authors described the
( E ) - interdependence and how shear stress is ef-
fected by several variables such as electric field strength ( E ),
frequency ( f ), fluid composition , temperature ( T ), and
shear rate
˙
. Klass and Martinek 7 also presented bulk
conductance measurements of the fluid as a whole and
the consequent power demand of these typical ER systems
under use.
Our work focuses on the magnetic analogs of ER fluids,
which are termed magnetorheological fluids MR fluids.
Similar to ER fluids in many respects, MR fluids exhibit
several key differences, among which are the absence of
charge, higher strength, better stability over broader tempera-
ture range, and less stringent manufacturing requirements
1. In addition, MR fluids are experimentally easier to work
with as several potential difficulties are avoided such as elec-
trode polarization and direct contact with the fluid. MR flu-
ids, therefore, constitute model ‘‘tunable’’ fluids with prop- *Author to whom correspondence should be addressed.
PHYSICAL REVIEW E NOVEMBER 1996 VOLUME 54, NUMBER 5
54 1063-651X/96/545/55029/$10.00 5502 © 1996 The American Physical Society