Effect of Shear Flow on the Self-diffusion of Microorganisms in a Semi-dilute Suspension

Abstract

In this paper, the effect of the imposed shear flow on the diffusion of swimming model micro-organisms in a semi-dilute suspension is investigated. A swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity. Effects of inertia and Brownian motion are neglected. The three-dimensional movement of 27 identical squirmers in a simple shear flow, contained in a cube with periodic boundary conditions, is computed, for random initial positions and orientations, by the Stokesian-dynamics method. When a shear flow is induced in the suspension, the diffusion tensor is no longer isotropic. We investigated the effect of the shear rate, squirming velocity, squirming mode and volume fraction on the unisotropic property of the diffusion tensor. The results show that the diffusivity, when it exists, is strongly dependent on the direction relative to the shear flow, the squirming velocity and the volume fraction.