Viscous film flow down corrugated surfaces

A theoretical analysis of a downward viscous film flow on corrugated surfaces is reported. The study is based on Navier–Stokes equations (for one- and two-dimensional surfaces) and on an integral model (for a three-dimensional surface with double corrugation). The calculations were carried out in a wide range of Reynolds numbers and geometric characteristics of the surface with due allowance for the surface-tension force. The shape of the free surface of the liquid film and other characteristics of the flow are calculated. It is shown that, in the case of a one-dimensional surface, there exists a range of parameters where the flow is predominantly governed by surface-tension forces; this flow can be adequately treated with the integral approach. In this range of parameters, on the surface with double corrugation, the average quantities of the downward flow in wide corrugation valleys are determined by the fine-texture geometry.