Hydrodynamic interactions between a particle and two rigid walls: Effect of surface roughness and many-body hydrodynamic interactions

The sedimentation of a particle trapped between two rigid walls allow us to demonstrate the effect of many-body hydrodynamic effects arising in a confined geometry. A theoretical treatment of this problem is presented together with an experimental investigation of the sedimentation of a macroscopic particle by image analysis which allows us to directly obtain the trajectory of the particle. Theoretical drag force in the presence of the two planes is shown to be in good agreement with the experimental results. The determination of the sedimentation of a particle, initially applied on the upper plate by a magnetic field gradient, is shown to provide a relevant information on the average surface roughness.