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Author: Huth, Robert × Subject: bilayer ×

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    Gradient flow perspective of thin-film bilayer flows
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Huth, Robert; Jachalski, Sebastian; Kitavtsev, Georgy; Peschka, Dirk
    We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air. 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 thin-film model and formally identify solutions with those of the corresponding free-boundary 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 [Gamma]-convergence. For time-dependentsolutions 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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    Stationary solutions for two-layer lubrication equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Jachalski, Sebastian; Huth, Robert; Kitavtsev, Georgy; Peschka, Dirk; Wagner, Barbara
    We investigate stationary solutions of flows of thin liquid bilayers in an energetic formulation which is motivated by the gradient flow structure of its lubrication approximation. The corresponding energy favors the liquid substrate to be only partially covered by the upper liquid. This is expressed by a negative spreading coefficient which arises from an intermolecular potential combining attractive and repulsive forces and leads to an ultra-thin layer of thickness e. For the corresponding lubrication models existence of stationary solutions is proven. In the limit e to 0 matched asymptotic analysis is applied to derive sharp-interface models and the corresponding contact angles, i.e. the Neumann triangle. In addition we use G-convergence and derive the equivalent sharp-interface models rigorously in this limit. For the resulting model existence and uniqueness of energetic minimizers are proven. The minimizers agree with solutions obtained by matched asymptotics.