Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film

Yatim, Y.M. and Duffy, Brian and Wilson, Stephen (2013) Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film. Physics of Fluids, 25 (5). ISSN 1070-6631

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    Abstract

    A novel family of three-dimensional travelling-wave similarity solutions describing a steadily translating slender dry patch in an infinitely wide thin fluid film on an inclined planar substrate when surface-tension effects are negligible is obtained, the flow being driven by gravity and/or a prescribed constant shear stress on the free surface of the film. For both driving mechanisms, the dry patch has a parabolic shape (which may be concave up or concave down the substrate), and the film thickness increases monotonically away from the contact lines to its uniform far-field value. The two most practically important cases of purely gravity-driven flow and of purely surface-shear-stress-driven flow are analysed separately.