Theory of hydrodynamic interaction of two spheres in wall-bounded shear flow

Abstract

It is shown theoretically that the presence of a wall induces qualitative and quantitative changes in the hydrodynamic interaction between two particles in a shear flow. The phase portrait of particles' relative motion is rather different from the classical Batchelor and Green's theory corresponding to an unbounded shear flow. It has the same topology upon varying the distance between the particle pair and the wall and contains new, previously overlooked, regions of closed trajectories. The theory is able to explain the origin of open swapping trajectories found earlier in numerical simulations.