Rarefaction–undercompressive fronts in driven films

We consider experiments by Ludviksson and Lightfoot [AIChE J. 17, 1166 (1971)] on thin liquid films driven up a vertical plate by a thermally induced surface tension gradient with a counteracting gravitational force, and revisit their theoretical analysis, which neglects the effects of curvature, for predicting the climbing rate of the front. We present a new theory for the lubrication model with curvature effects, and get rising rates that depend on the microscopic length scale at the contact line. The predictions are, in general, in better agreement with the experiment.