Gradient flow perspective on thin-film bilayer flows
Abstract
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.
- Publication:
-
Journal of Engineering Mathematics
- Pub Date:
- October 2015
- DOI:
- 10.1007/s10665-014-9698-1
- Bibcode:
- 2015JEnMa..94...43H
- Keywords:
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- Bilayer;
- Contact line;
- Gradient flow;
- Thin-film