Self-diffusion of Brownian particles in concentrated suspensions under shear

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Abstract
The self‐diffusivity of Brownian hard spheres in a simple shear flow is studied by numerical simulation. Particle trajectories are calculated by Stokesian dynamics, with an accurate representation of the suspension hydrodynamics that includes both many‐body interactions and lubrication. The simulations are of a monolayer of identical spheres as a function of the Péclet number: Pe =γ̇a2/D0, which measures the relative importance of shear and Brownian forces. Here γ̇ is the shear rate, a the particle radius, and D0 the diffusion coefficient of a single sphere at infinite dilution. In the absence of shear, using only hydrodynamic interactions, the simulations reproduce the pair‐distribution function of the equivalent hard‐disk system. Both short‐ and long‐time self‐diffusivities are determined as a function of the Péclet number. The results show a clear transition from a Brownian motion dominated regime (Pe10) with a dramatic change in the behavior of the long‐time self‐diffusivity.

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