INTERACTION OF ADVANCING FRONTS AND MENISCUS PROFILES FORMED BY SURFACE-TENSION-GRADIENT-DRIVEN LIQUID FILMS ∗

Abstract. On a tilted heated substrate, surface tension gradients can draw liquid up out of a reservoir. The resulting film thickness profile is controlled by two parameters, which depend on the tilt of the substrate, the imposed temperature gradient, and the thickness of a postulated thin precursor layer. The evolution of this film in time is studied using a lubrication model. A number of distinct behaviors are possible as the substrate tilt angle and other parameters are varied. Recent results for the multiple stationary profiles possible near the meniscus are used, and the interaction of these profiles with the advancing front is examined. We demonstrate how to systematically determine the evolution of the entire film profile from the meniscus to the apparent contact line. This allows a categorization of the range of behaviors for a transversely uniform profile in a two-dimensional parameter space. In addition to capillary fronts and double shock structures, new combinations that arise for certain ranges of large substrate tilt and precursor thickness are described. These include profiles involving rarefaction fans, connecting to either an undercompressive or a classical wave at the advancing front