Thin film flow over and around surface topography: A general solver for the long-wave approximation and related equations

The three-dimensional flow of a gravity-driven continuous thin liquid film on substrates containing micro-scale features is modelled using the long-wave lubrication approximation, encompassing cases when surface topography is either engulfed by the film or extends all the way though it. The discrete analogue of the time-dependent governing equations is solved accurately using a purpose designed multigrid strategy incorporating both automatic error-controlled adaptivetime stepping and local mesh refinement/de-refinement. Central to the overall approach is a Newton globally convergent algorithm which greatly simplifies the inclusion of further physics via the solution of additional equations of the same form as the base flow lubrication equations. The range of applicability, efficiency and flexibility of the approach is demonstrated by solving a hierarchy of problems involving variations in solute concentration and solid-fluid interactions arising from flow on flexible susbtrates. © 2010 Tech Science Press.