  A coarse grained description of a two phase fluid is used to study the steady
state configuration of the interface separating the coexisting phases, and the
motion of the contact line at which the interface intersects a solid boundary.
The fluid is set in motion by displacing two parallel, infinite solid
boundaries along their own plane. Dissipative relaxation of the order parameter
leads to interfacial slip at the contact line, even when no-slip boundary
conditions for the fluid velocity are considered. This relaxation occurs within
a characteristic length scale l that depends on the order parameter mobility,
the equilibrium interfacial tension, the imposed wall velocity, the thermal
correlation length, the equilibrium miscibility gap, and the mutual diffusion
coefficient. Steady-state interface equations which describe the system on a
length scale large compared to the correlation length are derived. Scaling
forms which involve the ratio l/L, where L is the width of the fluid layer, and
the capillary number follow from the interface equations. The scaling results
are verified by direct numerical solution of the governing equations.
