Stationary Solutions of Liquid Two-Layer Thin-Film Models

• Autores: S. Jachalski, Robert Huth, Georgy Kitavtsev, Dirk Peschka, Barbara Wagner
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 3, 2013, págs. 1183-1202
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 $h_*\to 0$ 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 $\Gamma$-convergence, where we establish existence and uniqueness of energetic minimizers in that limit