Nonlocal Lubrication Forces and the Sedimentary Jamming Front.

We formulate a nonlinear partial differential sedimentation equation to describe spatiotemporal changes in concentration for sedimenting particles at low Reynolds number. It is based on two fluid-mediated forces. One is the viscous interaction of a particle with the surrounding suspension, which causes the settling speed to decrease with increasing volume fraction according to an empirical hindered settling function; we constrain its form by a comprehensive data compilation. The other ingredient is a nonlocal lubrication force set by the spatial gradient in the time derivative of volume fraction. It resists change in separation between neighboring particles, and balances gravity in the accumulating sediment. These forces, plus gravity and mass conservation, lead to the sedimentation equation. We report linear response plus asymptotic analysis and numerical solution for the shape of the stationary jamming front between sediment and suspension that moves upwards at constant shape and speed. Due to the nonlocal lubrication forces, the width of the front increases with the volume fraction of the suspension. (Version dated September 12, 2017)