Dewetting with Conical Tail Formation: How to Include a Line Friction of Microscopic Origin, and Possibly Evaporation?

Most studies of dewetting fronts in 3D with a “corner formation”, as happens behind a drop sliding down an incline are based on a generalisation of Voinov theory, with (at least implicitly) a slip length at small scale. I here first examine what happens, if instead of considering a free slip at small scale, one admits a non-zero additional line friction of microscopic origin. Concerning the selection of cone angles, I show that most features of the model are unchanged, except that the “slip length” must be replaced in the equations with an “effective” cut off that can become apparently unphysically small. I suggest that these results could explain problematical cut-offs in the hydrodynamical modelling observed recently by Winkels et al. on water drops [K.G. Winkels, I.R. Peters, J. Snoeijer, F. Evangelista, M. Riepen, A. Daerr, L. Limat, Eur. Phys. J. Special Topics 192, 195 (2011)]. The sole difficulty with this interpretation is the law ruling the radius of curvature of the corner tip at small scale, which remains unsatisfactory. I suggest that evaporation of the liquid should also be considered at these very small scales and propose a preliminary “toy model” to take this effect into account. The orders of magnitude are better recovered without changing the structure of the equations developed initially for “classical” wetting dynamics with silicon oil drops.