Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film

Yatim, Y.M. and Duffy, B.R. and Wilson, Stephen (2013) Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film. Sains Malaysina, 42 (7). pp. 975-980. ISSN 0126-6039

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Abstract

We investigate unsteady flow of a thin film of Newtonian fluid around a symmetric slender dry patch moving with constant velocity on an inclined planar substrate, the flow being driven by a prescribed constant shear stress at the free surface of the film (which would be of uniform thickness in the absence of the dry patch). We obtain a novel unsteady travelling-wave similarity solution which predicts that the dry patch has a parabolic shape and that the film thickness increases monotonically away from the dry patch.