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 $l_0=\sqrt{\xi D/V_0}$, 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.

• Received 20 July 1999

DOI:https://doi.org/10.1103/PhysRevLett.85.1686