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A potential field description for gravity-driven film flow over piece-wise planar topography.

Scholle, Markus and Gaskell, Philip H. and Marner, Florian (2019) 'A potential field description for gravity-driven film flow over piece-wise planar topography.', Fluids., 4 (2). p. 82.

Abstract

Models based on a potential field description and corresponding first integral formulation, embodying a reduction of the associated dynamic boundary condition at a free surface to one of a standard Dirichlet-Neumann type, are used to explore the problem of continuous gravity-driven film flow down an inclined piece-wise planar substrate in the absence of inertia. Numerical solutions of the first integral equations are compared with analytical ones from a linearised form of a reduced equation set resulting from application of the long-wave approximation. The results obtained are shown to: (i) be in very close agreement with existing, comparable experimental data and complementary numerical predictions for isolated step-like topography available in the open literature; (ii) exhibit the same qualitative behaviour for a range of Capillary numbers and step heights/depths, becoming quantitively similar when both are small. A novel outcome of the formulation adopted is identification of an analytic criteria enabling a simple classification procedure for specifying the characteristic nature of the free surface disturbance formed; leading subsequently to the generation of a related, practically relevant, characteristic parameter map in terms of the substrate inclination angle and the Capillary number of the associated flow.

Item Type:Article
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Available under License - Creative Commons Attribution.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.3390/fluids4020082
Publisher statement:This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Date accepted:16 April 2019
Date deposited:02 May 2019
Date of first online publication:02 May 2019
Date first made open access:02 May 2019

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