Abstract
The gravity-driven flow of a liquid film down an inclined plane wall with small-amplitude two-dimensional oblique or three-dimensional doubly periodic corrugations is investigated for finite Reynolds numbers. The film surface may exhibit constant or variable surface tension due to an insoluble surfactant. The key idea is to express the wall geometry as a Fourier series, and then reconstruct the three-dimensional flow in terms of the individual two-dimensional transverse and unidirectional flows over the constituent oblique two-dimensional corrugations. Three-dimensional corrugations may either reduce or amplify the surface deformation with respect to their two-dimensional counterparts due to the simultaneous effect of the constituent oblique components on the effective wave number, capillary number, and Reynolds number.
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