Self-diffusion in sheared suspensions by dynamic simulation

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 Peclet number, Pe, which measures the relative importance of shear and Brownian forces, and the volume fraction, phi. Here, Pe = (y) over dot a(2)/D-0, where (y) over dot is the shear rate, a the particle size and D-0 = kT/6 pi eta a is the Stokes-Einstein diffusivity of an isolated particle of size a with thermal energy kT in a solvent of viscosity eta. 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, D-0. At zero Pe the diffusivity is found to be a decreasing function of phi. As Pe is slowly increased, O(Pe) and O(Pe(3/2)) 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 phi. 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, D-xy, is reported for both systems. Results for both the translational and rotational D-xy 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.