Dynamics of particle settling and resuspension in viscous liquid films

We develop a dynamic model for suspensions of negatively buoyant particles on an incline. Our model includes settling due to gravity as well as resuspension of particles by shear-induced migration. We consider the case where the particles settle onto the solid substrate and two distinct fronts form, namely a faster liquid and a slower particle front. We show that the resulting transport equations for the liquid and the particles are of hyperbolic type, and study the dilute limit, for which we compute exact solutions. We also carry out systematic laboratory experiments, focusing on the motion of the liquid and the particle fronts. We show that the dynamic model predictions for small to moderate values of the particle volume fraction and the inclination angle of the solid substrate agree well with the experimental data.