(123g) Particle Phase Pressure in Sheared Suspensions

Suspension pressure, denoted \Pi
and defined as minus one third the trace of the average particle contribution
to the stress, is computed for realizations of sheared suspensions of Brownian
and non-Brownian (subject to interparticle force) particles generated with the
help of Stokesian Dynamics, over a wide range of solid fraction and Peclet
number.   We will focus on the
hydrodynamic contribution to the total pressure, P.U'-Q:E, where the resistance functions P and Q
are from Jeffrey et al. (1993), U' is the deviation of particle velocities from the imposed bulk flow,
and E is the imposed rate of
strain. While \Pi has yet to be directly measured in experiment, experimental
support for existence of \Pi will be reexamined (Zarraga et al.
2000).  We will also review the use
of suspension pressure in descriptions of dispersed two-phase flow, and in
particular its association with particle migration, where the particle flux is
postulated to depend linearly on the gradient of \Pi.    The simulation results indicate that the
suspension pressure depends upon solids fraction similarly to the normal stress
differences and the connection of anisotropy of the microstructure in
developing this non-Newtonian behavior (\Pi) will be established.   At high shear rates and large
particle volume fraction close pairs of particles begin to dominate; for
suspensions of particles interacting via strong but short-ranged repulsive
forces the accurate resolution of the motion in a close pair is necessary in
order to evaluate \Pi correctly and this case often used to model non-Brownian
systems will be considered closely.

D.J. Jeffrey, J.F. Morris &
J.F. Brady Phys. Fluids A5, 2317-2325 (1993)

I.E. Zarraga, D.A. Hill &
D.T. Leighton J. Rheol. 44, 185-220 (2000)