Surface force-mediated dynamics of droplets spreading over wetting films

Abstract

Despite tremendous interest in the wetting dynamics at the microscale, attention to nanodroplets has started rising only over the last two decades. In the current work, we examine the dynamics of droplets of size comparable with the range of the surface force action spreading over wetting (adsorbed) films. We show that wetting exponents are strongly affected by the ratio between the droplet height and the film thickness dictated by the surface forces, and that Cox-Voinov law is not applicable anymore for such droplets. We pay particular attention to the shape of the advancing droplet menisci and bridge our results with the Landau-Levich problem. We show both numerically and analytically that depending on the strength of the surface forces, capillary ripples of different depths can emerge in the vicinity of the advancing front. The dependence of the ripple wavelength as well the ripple amplitude on capillary number is non-monotonic. We derive the conditions at which the capillary ripples can be fully suppressed by the surface force action.