Flow of evaporating, gravity-driven thin liquid films over topography

The effect of topography on the free surface and solvent concentration profiles of an evaporating thin film of liquid flowing down an inclined plane is considered. The liquid is assumed to be composed of a resin dissolved in a volatile solvent with the associated solvent concentration equation derived on the basis of the well-mixed approximation. The dynamics of the film is formulated as a lubrication approximation and the effect of a composition-dependent viscosity is included in the model. The resulting time-dependent, nonlinear, coupled set of governing equations is solved using a Full Approximation Storage multigrid method. The approach is first validated against a closed-form analytical solution for the case of a gravity-driven, evaporating thin film flowing down a flat substrate. Analysis of the results for a range of topography shapes reveal that while a full-width, spanwise topography such as a step-up or a step-down does not appear to affect the composition of the film, the same is no longer true for the case of localised topography, such as a peak or a trough, for which clear non-uniformities of the solvent concentration profile can be observed in the wake of the topography.