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)