A Potential Field Description for Gravity-Driven Film Flow over Piece-Wise Planar Topography

Scholle, Markus; Gaskell, Philip H.; Marner, Florian

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.

Citation

Scholle, M., Gaskell, P. H., & Marner, F. (2019). A Potential Field Description for Gravity-Driven Film Flow over Piece-Wise Planar Topography. Fluids, 4(2), Article 82. https://doi.org/10.3390/fluids4020082

• Journal Article Type: Article
• Acceptance Date: Apr 16, 2019
• Online Publication Date: May 2, 2019
• Publication Date: Jun 30, 2019
• Deposit Date: May 2, 2019
• Publicly Available Date: May 2, 2019
• Journal: Fluids
• Electronic ISSN: 2311-5521
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 2
• Article Number: 82
• DOI: https://doi.org/10.3390/fluids4020082
• Public URL: https://durham-repository.worktribe.com/output/1331862