Hydrodynamic diffusion of a suspension of elastic capsules in bounded simple shear flow

A suspension of red blood cells in a flow undergoes hydrodynamic or shear-induced diffusion. It is known from experiments that deoxygenated or stiffer red blood cells have a lower hydrodynamic diffusion coefficient compared to oxygenated or softer red blood cells. In this paper, we numerically calculate the hydrodynamic diffusion coefficients of a suspension of elastic capsules of viscosity ratio unity and as a function of volume fraction, elastic capillary number and channel height in a bounded simple shear flow. We show that the time required for the suspension to reach the diffusive regime in the direction perpendicular to the shear plane decreases with channel height. In a narrow channel, the effect of capsule elasticity is to delay the approach to a diffusive regime. However, the motion in the direction parallel to the velocity gradient is always subdiffusive. We show that the hydrodynamic diffusion coefficient in the direction perpendicular to the shear plane varies linearly with capsule volume fraction up to about 25%. In addition, it does not increase monotonously with elastic capillary number but drops when the capsules become sufficiently soft. Finally, it displays a weak dependence on the channel height.