Open Access

Peter L. Evans, Andreas Münch

• On a tilted heated substrate, surface tension gradients can draw liquid up out of a reservoir. The resulting film thickness profile is controlled by 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 behaviours 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. It is shown how to systematically determine the evolution of the entire film profile from the meniscus to the apparent contact line. This allows a categorisation of the range of behaviours for a transversely ­uniform profile, in a two­dimensional parameter space. In addition to capillary fronts, and double shock structures, a new combination of a Type I meniscus with a rarefaction fan, and either an undercompressive or a classical wave at the advancing front, that arises for certain ranges of large substrate tilt and precursor thickness is described.