The surface tension effect on viscous liquid spreading along a superhydrophobic surface

[摘要] Within the Stokes film approximation, unsteady plane-parallel spreading of a thin layer of a heavy viscous fluid along a horizontal superhydrophobic surface is studied. The forced spreading regimes induced by the mass supply are considered. Plane-parallel flow along the principal direction of the slip tensor of the superhydrophobic surface is studied in case that the corresponding slip tensor component is a power function of the spatial coordinate. An evolution equation for the film thickness is derived taking into account surface tension that is dependent on the spatial coordinate. The group classification problem is solved. Self-similar and invariant solutions are constructed for power and exponent time dependences on mass supply respectively at a special form of the surface tension coefficient. Surface tension is shown to have a significant influence on the character of the liquid spreading.

[发布机构] Lomonosov Moscow State University, Moscow, Russia^1

[效力级别] 数学

[关键词] Evolution equations;Group classification;Plane-parallel flow;Principal directions;Spatial coordinates;Super-hydrophobic surfaces;Surface tension coefficient;Surface tension effects