Gradient flow perspective on thin-film bilayer flows

We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air phase. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well-known PDE with boundary conditions. Next we propose a similar grad...

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Bibliographic Details
Published inJournal of engineering mathematics Vol. 94; no. 1; pp. 43 - 61
Main Authors Huth, R., Jachalski, S., Kitavtsev, G., Peschka, D.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 29.10.2015
Subjects
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Theoretical and Applied Mechanics
Gradient flow
Thin-film
Bilayer
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Summary:We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air phase. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well-known PDE with boundary conditions. Next we propose a similar gradient formulation for the corresponding reduced thin-film model and formally identify solutions with those of a PDE problem. A robust numerical algorithm for the thin-film gradient flow structure is then provided. Using this algorithm we compare the sharp triple-junction model with precursor models. For their stationary solutions a rigorous connection is established using Γ -convergence. For time-dependent solutions the comparison of numerical solutions shows a good agreement for small and moderate times. Finally we study spreading in the zero-contact angle case, where we compare numerical solutions with asymptotically exact source-type solutions.
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-014-9698-1