Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film - Yazariah M. Yatim,; Duffy, Brian R.; Wilson, Stephen K. (Universiti Kebangsaan Malaysia, 2013)
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.