Inertial and viscous effects on dynamic contact angles

An investigation is made into the dynamics involved in the movement of the contact line when a single liquid with an interface moves into a vacuum over a smooth solid surface. In order to remove the stress singularity at the contact line, it is postulated that slip between the liquid and the solid or some other mechanism occurs very close to the contact line. It is assumed that the flow produced is inertia dominated with the Reynolds number based on the slip length being very large, Following a procedure similar to that used by Cox (1986) for the viscous-dominated situation (in which the Reynolds number based on the macroscopic length scale was assumed very small) using matched asymptotic expansions, we obtain the dependence of the macroscopic dynamic contact angle on the contact line velocity over the solid surface for small capillary number and small slip length to macroscopic lengthscale ratio. These results for the inertia-dominated situation are then extended (at the lowest order in capillary number) to an intermediate Reynolds number situation with the Reynolds number based on the slip length being very small and that based on the macroscopic lengthscale being very large.