HYDRODYNAMIC DIFFUSION IN A SUSPENSION OF SEDIMENTING POINT PARTICLES WITH PERIODIC BOUNDARY-CONDITIONS

The hydrodynamic diffusivity tenser is determined for a monodisperse suspension of non-Brownian sedimenting particles in the point-particle approximation using both theoretical and simulation approaches. The diffusion is dominated by convective motions occurring on the length scale of the box size H. The diffusivity is proportional to the product of the root-mean-square velocity and H or to fN(1/2), where N is the number of particles in the unit cell and f is the ratio of the magnitude of the buoyancy force acting on a particle to the fluid viscosity. The ratio of the diffusivity in the vertical to that in the horizontal direction is a strong function of the shape of the periodic box and becomes smaller as the aspect ratio (vertical over horizontal length) is increased.