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

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...

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Bibliographic Details
Published in:Fluids (Basel) 2019-06, Vol.4 (2), p.82
Main Authors: Scholle, Markus, Gaskell, Philip H., Marner, Florian
Format: Article
Language:English
Subjects:
analytic solutions
Approximation
Boundary conditions
Dirichlet problem
FE solutions
film flows
first integrals
Free surfaces
Inclination angle
Integral equations
Kinematics
lubrication theory
Numerical prediction
Potential fields
Reynolds number
Substrates
Topography
Velocity
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Summary: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.
ISSN:2311-5521
2311-5521
DOI:10.3390/fluids4020082