Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
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