Drag, deformation and lateral migration of a buoyant drop moving near a wall

Abstract

The problem of a drop of arbitrary density and viscosity moving close to a vertical wall under the effect of buoyancy is analysed theoretically. The case where the suspending fluid is at rest far from the drop and that of a linear shear flow are both considered. Effects of inertia and deformation are assumed to be small but of comparable magnitude, so that both of them contribute to the lateral migration of the drop. Expressions for the drag, deformation and migration valid down to separation distances from the wall of a few drop radii are established and discussed. Inertial and deformation-induced corrections to the drag force and slip velocity of a buoyant drop moving in a linear shear flow near a horizontal wall are also derived.