The Mathematical Institute, University of Oxford, Eprints Archive

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

Yatim, Y. M. and Duffy, B. R. and Wilson, S. K. (2013) Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film. Physics of Fluids . (Submitted)

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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 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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1713
Deposited By: Peter Hudston
Deposited On:30 Jul 2013 13:18
Last Modified:29 May 2015 19:24

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