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 2π/|k| of a contact line moving with velocity v is given as τ^-1(k)=c(v)|k|. The velocity dependence of c(v) is shown to depend drastically on the dissipation mechanism: we find c(v)=c(v=0)-2v for the case in which the dynamics is governed by microscopic jumps of single molecules at the tip (Blake mechanism), and c(v)≃c(v=0)-4v 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 352, 418 (1991)].