Longitudinal Shear-Induced Gradient Diffusion in a Dilute Suspension of Spheres

We present the calculation of the particle drift velocity for a dilute, neutrally buoyant suspension of spheres under the action of shear when inertia and Brownian e ects are negligible, resulting from the e ect of an imposed concentration gradient. Using a renormalization technique employed previously, we found that the particle drift velocity is proportional to the concentration gradient through a proportionality term depending on the square of the sphere radius, the rate of strain, and an O(1) constant, b, that depends on the angular velocity of the fluid flow. In particular, b=2.40 for simple shear flow, and b=3.12 for pure straining flow. Finally, combining the expression of the drift velocity with that of the self-di ffusivity, we determined the shear-induced particle volumetric flux and cross gradient di ffusivity for the case of simple shear flow