Transverse shear-induced gradient diffusion in a dilute suspension of spheres

Abstract

We study the shear-induced gradient diffusion of particles in an inhomogeneous dilute suspension of neutrally buoyant spherical particles undergoing a simple shearing motion, with all inertia and Brownian motion effects assumed negligible. An expansion is derived for the flux of particles due to a concentration gradient along the directions perpendicular to the ambient flow. This expression involves the average velocity of the particles, which in turn is expressed as an integral over contributions from all possible configurations. The integral is divergent when expressed in terms of three-particle interactions and must be renormalized. For the monolayer case, such a renormalization is achieved by imposing the condition of zero total macroscopic flux in the transverse direction whereas, for the three-dimensional case, the additional constraint of zero total macroscopic pressure gradient is required. Following the scheme of Wang, Mauri & Acrivos (1996), the renormalized integral is evaluated numerically for the case of a monolayer of particles, giving for the gradient diffusion coefficient 0.077γa2c¯2, where is the applied shear rate, a the radius of the spheres and c¯ their areal fraction.