Abstract
The evolution of an advancing fluid front formed by a gravity-driven thin film flowing down a planar substrate is considered, with particular reference to the presence of Marangoni stresses and/or surface topography. The system is modelled using lubrication theory and solved via an efficient, adaptive multigrid method that incorporates automatic, error-controlled grid refinement/derefinement and time stepping. The detailed three dimensional numerical results obtained reveal that, for the problems investigated, while both of the above features affect the merger of rivulets by either delaying or promoting the same, topography influences the direction of growth.
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