Evaporative instabilities in climbing lmsBy

We consider ow in a thin lm generated by partially submerging a rigid plate in a reservoir of ethanol-or methanol-water solutions and wetting its surface. Evaporation leads to concentration and surface tension gradients that drive ow up the plate. An experimental study indicates that the climbing lm is subject to two distinct instabilities. The rst is a convective instability characterized by attened convection rolls aligned in the direction of ow and accompanied by free-surface deformations; in the meniscus region, this instability gives rise to pronounced ridge structures aligned with the ow. The second instability, evident when the plate is nearly vertical, takes the form of transverse surface waves propagating up the plate. We demonstrate that the observed longitudinal rolls are driven by the combined in-uence of surface deformations and alcohol concentration gradients. Guided by the observation that the rolls are at, we develop a quasi-two-dimensional theoretical model for the instability of the lm, based on lubrication theory, which includes the eeects of gravity, capillarity and Marangoni stresses at the surface. We develop stability criteria for the lm which are in qualitative agreement with our experimental observations. Our analysis yields an equation for the shape of the interface which is solved numerically and reproduces the salient features of the observed ows, including the slow lateral drift and merging of the ridges.