Back to Departmental Colloquium: Spring 2000
Departmental Colloquium
Date: Tuesday, Feb 22, 2000
Time: 4:15PM
Location: JWB 335
Anette Hosoi
MIT
Title |
Wine tears and other instabilities in climbing films |
Abstract |
We consider the flow in a thin film generated by partially submerging a rigid plate into a reservoir of ethanol- or methanol-water solutions and wetting its surface. Evaporation leads to concentration and surface tension gradients that drive flow up the plate. An experimental study indicates that the thin film is subject to two distinct instabilities. The first is a convective instability characterized by flattened (wide) rolls aligned in the direction of flow and accompanied by free surface deformations; in the meniscus region, this instability gives rise to pronounced ridge structures. The second instability was evident only when the plate was nearly vertical, and was characterized by transverse waves propagating up the plate. We demonstrate that the observed longitudinal rolls are driven by the combined influence of surface deformations and alcohol concentration gradients. Guided by the observation that the rolls are flat, we develop a quasi-two-dimensional theoretical model for the instability of the film based on lubrication theory which includes the effects of gravity, capillarity and Marangoni stresses at the surface. We develop stability criteria for the film 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 experimental flows, including the slow lateral drift and merger of the ridges. |
Mathematical Biology
Computational Mathematics
Applied Mathematics