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In order to determine the apparent viscosity, r\ aoo = —, one has to relate the shear stress r and shear
r
strain rate, y, with measured pressure drop, Ap, and volumetric flow rate, Q. If minor losses are
small, the value of r at the wall can be determined by pressure drop across the channel, as follows:
hAp f 7
r = —£- for h«w (I)
2/
It can be shown that for a one-dimensional, steady, non-Newtonian flow the shear strain rate can be
expressed as:
)=4g.
h 2 wjsri
where n = —. Equation (2) provides the relationship between t and y(r ) with the measured
dlnO
quantities Ap and 0. The term in the bracket is similar to the Rabinowitch correction used for
conventional capillary viscometer (Zaman, 1998). For a Newtonian fluid n -I. For a non-
Newtonian fluid, n can be determined from the experimental results of ln(r )V ) versus In(0//z 2 w).
For a given flow rate, n is equal to the slope of the curve at that point. Linear regression methods can
be used to obtain the best fit for \&(r w ) as a function of lu(Q/ h 2 w).
EXPERIMENTAL PROCEDURE AND DATA ANALYSIS
Experiment results are presented for three MR fluid samples that are: 1) A Hydrocarbon-based MR
fluid (MRF-132LD, Lord Corp., USA), 2) A polyalphaolefm (PAO)-based Magneto-rheological
polymer gel (MRPG) prepared by the Polymer Science Laboratory (PSL) at the University of Nevada,
Reno, and 3) A Ferro fluid-based MR fluid prepared by PSL based on information in the literature
(Ginder, 1996).
Magneto-rheological polymer gels are a type of MR material, which are prepared by suspending iron
particles in polymeric gels. These composite polymeric materials allows the control of viscosity,
provide high shear yield stress and exhibit low particle settling behavior through different
combinations of resins and crosslinkers (Wilson et al., 2002). PAO based MRPG is prepared using
polyalphaolefin as the carrier fluid with polymer/carrier fluid ratios from 10:100 to 50:100. The PAO
MRPG contains, 80% by weight, carbonyl iron particle with 99.5% purity. Ferrofluid-based MR fluid
employs a magnetizable carrier fluid, such as a ferro fluid to obtain higher shear yield stress.
All the tests were performed using INSTRON servo-hydaulic test rig Model 882IS at room
temperature. Before conducting the experiments, the accumulator was pressurized to 300-900kPa
(50~150psi) via a nitrogen tank. The displacement input was a double ramp profile to generate
constant piston velocities; hence, constant flow rates. Each set of tests included different velocities,
which covers shear strain rates from 20s" 1 to 20000s" 1 . The electromagnetic coil was energized with
current for each velocity at 0 A, 0.5A, l.OA and 2.0A, corresponding to O.OmT, 120mT, 250mT and
350mT magnetic flux densities (Bo), respectively. A ramp input displacement was used to keep the
piston moving with a constant velocity, thus, the time variations of pressure drop across the measured
channel were almost constant during each measurements.
Typical results for the input and output profiles are presented in Figure 3. As can be seen in Figure 3,
initially, an internal pressure about 300kPa (50psi) was applied by the accumulator. A pressure drop
v ;