Self-diffusion of Brownian particles in concentrated suspensions under shear

TLDR

The study considers Brownian hard spheres in shear flow, where γ̇ is the shear rate, a the particle radius, and D0 the single‑sphere diffusion coefficient at infinite dilution. The authors investigate the self‑diffusivity of Brownian hard spheres in a simple shear flow using numerical simulation. They simulate a monolayer of identical hard spheres with Stokesian dynamics that incorporates many‑body hydrodynamics and lubrication, computing short‑ and long‑time self‑diffusivities across a range of Péclet numbers. The simulations reproduce the hard‑disk pair distribution without shear and reveal a transition from Brownian‑dominated (Pe < 1) to hydrodynamically dominated (Pe > 10) behavior, marked by a dramatic change in long‑time self‑diffusivity.

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 (Pe&amp;lt;1) to a hydrodynamically dominated regime (Pe&amp;gt;10) with a dramatic change in the behavior of the long-time self-diffusivity.