Particle pressure in sheared Brownian suspensions

Abstract

The isotropic contribution of the particle phase to the bulk stress, or the particle pressure, is studied for Brownian hard sphere suspensions in computationally simulated shear flow. The particle pressure is mechanically defined as the negative mean normal stress exerted by the particles, i.e., Π=−(1∕3)[Σ11+Σ22+Σ33] for a viscometric flow where 1, 2, and 3 refer to the flow, velocity gradient, and vorticity directions, respectively. Analysis is provided to relate the particle pressure to the equilibrium osmotic pressure and to show the relation of Π to particle migration phenomena. Utilizing existing hydrodynamic functions and simulating the flow by the Stokesian Dynamics technique, the particle pressure is evaluated for particle volume fractions in the range 0.1⩽ϕ⩽0.52 for monodisperse spherical particles. The relative strength of Brownian to shearing motion is given by the Peclet number Pe=γa2∕D0, where γ is the shear rate of a simple shear flow, a is the spherical particle radius, and D0=kT∕6πηa wit...