Interface and contact line motion in a two phase fluid under shear flow

We use a coarse grained description to study the steady state interfacial configuration of a two phase fluid under steady shear. Dissipative relaxation of the order parameter leads to interfacial slip at the contact line, even with no-slip boundary conditions on the fluid velocity. This relaxation occurs within a characteristic length scale l(0) = root xi D/V-0, with xi the (microscopic) interfacial thickness, D an order parameter diffusivity, and V-0 the boundary velocity. The steady state interfacial configuration is shown to satisfy a scaling form involving the ratio l(0)/L, where L is the width of the fluid layer, for a passive interface, and the capillary number as well for an active interface.