Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear

Pair-collision between viscous drops in a confined shear is numerically simulated to show that the confinement drastically alters the trajectories of the drops. In contrast to free shear, drops here move towards the centerline giving rise to a zero cross-stream separation and a net stream-wise separation. The latter varies as inverse of capillary number and the cube of the confinement (distance between the walls). The stream-wise separation does not depend on the initial positions of the drops. An analytical theory for the phenomenon is offered.