A.A. Golovin, B.Y. Ruinstein, and L.M. Pismen

Technion

Abstract

The effect of Van Der Waals forces on the fingering instability of a wetting horizontal liquid film driven by thermocapillary stresses induced by a longitudinal thermal gradient is considered. The film dynamics is described by evolution equation in the long-wave approximation. Stationary wave solution corresponding to a uniformly spreading liquid film is found numerically. The solution has three regions: rear region with nearly planar interface, narrow "contact one" region with a capillary ridge and a sharp decrease of the film thickness, and the front region of a thin precursor film, governed by viscous and Van Der Walls forces. Linear stability analysis of this solution is performed numerically. It is found that Van Der Waals forces suppress the fingering instability. It is shown that for physically realistic conditions the fingering instability is governed by a single dimensionless parameter characterizing the competition between the capillary and Van Der Waals forces. The threshold value of this parameter corresponding to the onset of the fingering instability is found,. Nonlinear analysis of the fingering instability is performed. It is shown that near the threshold the "contact line" spatio-temporal dynamics can be described by a Kuramoto-Sivashinsky equation. The effects of heat transfer to the surrounding gas phase, as well as temperature dependence of Van Der Waals forces are currently under investigation.