Journal of Fluid Mechanics



Self-diffusion in sheared suspensions by dynamic simulation


DAVID R. FOSS a1 and JOHN F. BRADY a1
a1 Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

The behaviour of the long-time self-diffusion tensor in concentrated colloidal dispersions is studied using dynamic simulation. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces, and the volume fraction, φ. Here, Pe = &γdot;a2/D0, where &γdot; is the shear rate, a the particle size and D0 = kT/6πηa is the Stokes–Einstein diffusivity of an isolated particle of size a with thermal energy kT in a solvent of viscosity η. Two simulations algorithms are used: Stokesian Dynamics for inclusion of the many-body hydrodynamic interactions, and Brownian Dynamics for suspensions without hydrodynamic interactions. A new procedure for obtaining high-quality diffusion data based on averaging the results of many short simulations is presented and utilized. At low shear rates, low Pe, Brownian diffusion due to a random walk process dominates and the characteristic scale for diffusion is the Stokes–Einstein diffusivity, D0. At zero Pe the diffusivity is found to be a decreasing function of φ. As Pe is slowly increased, O(Pe) and O(Pe3/2) corrections to the diffusivity due to the flow are clearly seen in the Brownian Dynamics system in agreement with the theoretical results of Morris & Brady (1996). At large shear rates, large Pe, both systems exhibit diffusivities that grow linearly with the shear rate by the non-Brownian mechanism of shear-induced diffusion. In contrast to the behaviour at low Pe, this shear-induced diffusion mode is an increasing function of φ. Long-time rotational self-diffusivities are of interest in the Stokesian Dynamics system and show similar behaviour to their translational analogues. An off-diagonal long-time self-diffusivity, Dxy, is reported for both systems. Results for both the translational and rotational Dxy show a sign change from low Pe to high Pe due to different mechanisms in the two regimes. A physical explanation for the off-diagonal diffusivities is proposed.

(Received February 2 1999)
(Revised July 26 1999)



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