Relaxation of a moving contact line and the Landau-Levich effect

The dynamics of the deformations of a moving contact line is formulated. It is shown that an advancing contact line relaxes more quickly as compared to the equilibrium case, while for a receding contact line there is a corresponding slowing down. For a receding contact line on a heterogeneous solid surface, it is found that a roughening transition takes place which formally corresponds to the onset of leaving a Landau-Levich lm. We propose a phase diagram for the system in which the phase boundaries corresponding to the roughening transition and the depinning transition meet at a junction point, and suggest that for sufficiently strong disorder a receding contact line will leave a Landau-Levich lm immediately after depinning.