Pair-particle dynamics and microstructure in sheared colloidal suspensions:Simulation and Smoluchowski theory

Abstract

The Smoluchowski equation (SE) approach reduced to pair level provides an accepted method for analysis of the pair microstructure, i.e., the pair distribution functiong(r), in sheared colloidal suspensions. Under dilute conditions, the resulting problem is well-defined, but for concentrated suspensions the coefficients of the pair SE are unclear. This work outlines a recently developed theoretical approach for analytical and numerical study of the pair SE for concentrated colloidal suspensions of spheres in shear flow, and then focuses upon evaluation of coefficients and related properties of the problem from Stokesian Dynamics simulation, over a wide range of particle volume fraction, ϕ, and Péclet number (ratio of shear to Brownian motion). The pair distribution functiondetermined from the SE theory is in generally good agreement with Stokesian Dynamics, as are the computed viscosity and normal stresses of the material. The primary focus of the work is to consider the pair relative velocity predicted by the theoryin comparison to Stokesian Dynamics simulations, as well as to evaluate quantities related to the hydrodynamic dispersion needed in the theoretical approach. The pair dynamics for moderate particle volume fraction, 0.20 ⩽ ϕ ⩽ 0.35, are found to be remarkably different from the form for an isolated pair of spheres, and at ϕ ⩾ 0.40 a qualitative change is again seen. Agreement of the theory and simulation on the primary features of the particle motion and structure is good, and discrepancies are clearly delineated.