Motion of a spherical liquid drop in simple shear flow next to an infinite plane wall or fluid interface

Abstract

The velocity of translation of a spherical liquid drop under the influence of simple shear flow near an infinite plane wall or fluid interface is computed with high accuracy using a boundary-integral method for Stokes flow based on Fourier decomposition in the absence of significant gravitational effects. Accurate results are obtained for very small gaps between the drop surface and the wall or interface, several orders of magnitude smaller than the drop diameter. As the gap decreases, a liquid drop tends to stick to a solid wall but is able to slide over an interface irrespective of the drop and ambient fluid viscosities. In the case of flow near an interface, the dependence of the drop velocity on the drop position and viscosity ratio is not necessarily monotonic. The interfacial deformation is computed to leading order with respect to the capillary number and is shown to exhibit an asymmetry due to the presence of the wall or interface. The predictions of the asymptotic analysis for nearly spherical drops are in agreement with boundary-element simulations of three-dimensional flow.