A slip boundary condition for an unsteady moving contact line

Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems, such as that of a moving contact line. The Navier and Maxwell slip boundary condition which is widely used to alleviate the singularity at the moving contact line are derived with the implicit assumptions of the flow being steady and having a velocity variation only in the wall-normal direction. Both of these assumptions are invalid in the case of an unsteady moving contact line. Here, by relaxing these assumptions we re-derive the slip boundary condition that shows that slip velocity is dependent on the acceleration and linear strain rate, in addition to its dependence on shear rate. This new finding is validated using molecular dynamics simulations.