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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Published in | Journal of engineering mathematics Vol. 94; no. 1; pp. 43 - 61 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
29.10.2015
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0022-0833 1573-2703 |
DOI: | 10.1007/s10665-014-9698-1 |