A MECHANISM FOR SLIP BETWEEN A LIQUID AND A RANDOM SURFACE WITH TRAPPED GAS DUE TO A TEMPERATURE-GRADIENT

The motivating example for this study is the flow of a viscous liquid over a hairy surface, with gas trapped in the hairs. This sort of boun ding surface is found on the surfaces of many partly submerged river p lants, for example. Thus, on a microscopic scale, the boundary conditi on between the viscous liquid and the bounding surface is almost entir ely that for a liquid-gas interface, except on the protruding hair tip s. For simplicity we assume that the liquid-gas part of the bounding s urface is planar, which clearly can occur if the pressure jump across the interface is negligible on roughness dimensions and the contact an gles on the hairs have the right values. The macroscopic slip length f or a viscous how over the surface can be determined by using the resul ts of an earlier study. However, in this study, the author also includ es the effect of a temperature gradient, and obtains a generalized bou ndary condition.