Cox-Voinov theory with slip

Most of our understanding of moving contact lines relies on the limit of small capillary numbers. This means the contact line speed is small compared to the capillary speed $\gamma/\eta$, where $\gamma$ is the surface tension and $\eta$ the viscosity, so that the interface is only weakly curved. The majority of recent analytical work has assumed in addition that the angle between the free surface and the substrate is also small, so that lubrication theory can be used. Here, we calculate the shape of the interface near a slip surface for arbitrary angles, and for two phases of arbitrary viscosities, thereby removing a key restriction in being able to apply small capillary number theory.