Side wall effects in thin gravity-driven film flow – steady and draining flow

Abstract

The increasing demand for thinner films in scientific and technological applications requires a better knowledge of the effect of side walls on such flows, especially as far as the formation of a capillary boundary layer is concerned. In this paper gravity-driven thin film flow in an open channel is investigated, highlighting the competing effects of the no-slip condition and velocity overshoot due to capillary elevation at the bounding side walls. Their influence on the flow rate, the velocity field, the Reynolds number, and the free surface shape is studied for two flow types: (i) the case with vanishingly small capillary elevation at the side walls compared to the film thickness at the center of the channel; (ii) the situation when capillary elevation at the side walls dominates over the film thickness at the center of the channel. For both, large deviations from the two-dimensional reference system occur. The theoretical predictions are compared to experimental observations, for the case of side walls with different wetting properties defined in terms of the static contact angle there.