Stationary solutions of liquid two-layer thin film models

الأصل · EN

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle conditions for such two-layer systems. We pursue this by investigating a corresponding energy that favors the upper liquid to dewet from the lower liquid substrate, leaving behind a layer of thickness h*. After proving existence of stationary solutions for the resulting system of thin-film equations we focus on the limit h*→ 0 via matched asymptotic analysis. This yields a corresponding sharp-interface model and a matched asymptotic solution that includes logarithmic switch-back terms. We compare this with results obtained using Γ-convergence, where we establish existence and uniqueness of energetic minimizers in that limit.