LONGITUDINAL SHEAR-INDUCED DIFFUSION OF SPHERES IN A DILUTE SUSPENSION

We present a calculation of the hydrodynamic self-diffusion coefficient of a tagged particle in a dilute mono-dispersed suspension of small neutrally buoyant spheres undergoing a steady simple shearing motion. The displacement of the tagged particle parallel to the longitudinal or streamwise direction resulting from a 'collision' with one other particle is calculated on the assumption that inertia and Brownian motion effects are negligible. Summing over different pairs leads to a logarithmically divergent integral for the diffusivity which is rendered finite by allowing for the cut-off due to the occasional presence of another pair of particles. The longitudinal shear-induced self-diffusion coefficient is thus found to be 0.267a2-gamma{c ln c-1 + O(c)], where gamma denotes the applied shear rate, a is the radius of the spheres and c their volume concentration.