Inertial two- and three-dimensional thin film flow over topography

The effect of inertia on gravity-driven thin film free-surface flow over substrates containing topography is considered. Flow is modelled using a depth-averaged form of the governing Navier-Stokes equations and the discrete analogue of the coupled equation set solved accurately using an efficient full approximation storage (FAS) and full multigrid (FMG) technique. The free-surface disturbance induced by topographic features is illustrated by considering examples of gravity-driven flow over and around peak, trench and occlusion topography. Results are presented which demonstrate how increasing Reynolds number can significantly enhance the magnitude of free-surface disturbances, a feature which may have important consequences for the wide range of coating process that aim to maximise free-surface planarity. (C) 2010 Elsevier B.V. All rights reserved.