Dissipation in Dynamics of a Moving Contact Line

The dynamics of the deformations of a moving contact line is studied assuming two different dissipation mechanisms. It is shown that the characteristic relaxation time for a deformation of wavelength $2\pi/|k|$ of a contact line moving with velocity $v$ is given as $\tau^{-1}(k)=c(v) |k|$. The velocity dependence of $c(v)$ is shown to drastically depend on the dissipation mechanism: we find $c(v)=c(v=0)-2 v$ for the case when the dynamics is governed by microscopic jumps of single molecules at the tip (Blake mechanism), and $c(v)\simeq c(v=0)-4 v$ when viscous hydrodynamic losses inside the moving liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated dominant dissipation mechanism can be experimentally determined using relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T. Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].