Journal
JOURNAL OF ENGINEERING MATHEMATICS
Volume 94, Issue 1, Pages 43-61Publisher
SPRINGER
DOI: 10.1007/s10665-014-9698-1
Keywords
Bilayer; Contact line; Gradient flow; Thin-film
Funding
- German Research Foundation DFG [SPP 1506]
- DFG Research Center MATHEON
- Max-Planck-Institute for Mathematics in the Sciences in Leipzig
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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 -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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