Travelling-wave similarity solution for unsteady flow around a dry patch driven by gravity and constant surface shear stress

Mohd Yatim, Yazariah and Duffy, Brian and Wilson, Stephen (2012) Travelling-wave similarity solution for unsteady flow around a dry patch driven by gravity and constant surface shear stress. In: Proceedings of the 2nd International Symposium on Frontiers of Computational Sciences 2012. AIP, pp. 88-98. ISBN 9789698453022

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    Abstract

    In this paper we use the lubrication approximation to analyse three-dimensional unsteady flow of a thin film of Newtonian fluid around a symmetric slender moving dry patch on an inclined planar substrate. The flow being driven by gravity and a prescribed constant shear stress at the free surface. We obtain a novel unsteady travelling-wave similarity solution for the dry patch of uniform thickness, in which the dry patch travels at constant speed. This solution predicts that the dry patch has a parabolic shape which may be concave up or concave down the substrate. In all cases investigated numerically the film thickness is found to increase monotonically away from the contact line.