Dynamics of a suspension confined in a thin cell

Abstract

A suspension confined between two close parallel plates is studied in the Stokesian regime. The use of boundary integral equations and the lubrication approximation allows computation of the hydrodynamic forces acting on the particles. The forces are long ranged (decaying as R−2) and depend on the orientation of the relative position and velocity of particles. This tensorial character predicts an “antidrag” that is observed in experiments. Also, the far-field forces vanish when a particle is surrounded by an homogeneous suspension, but net forces appear in the presence of abrupt discontinuities of the suspension. The effect of the computed hydrodynamic forces is studied in the dynamics of a cluster of particles falling in a gravitational field, where the different features of the hydrodynamic forces are present. The cluster spreads and deforms from the initial circular shape due to the action of the hydrodynamic forces in the presence of the cluster boundary. The expression for the hydrodynamic forces at long distances allows application of a mean-field approximation, where the forces on a particle can be computed in terms of the particle current field. This approximation gives an excellent numerical agreement with the direct computation of all the hydrodynamic forces, being numerically much faster, yet preserving the accuracy.