New SFB 1313 publication, published in the scientific journal SIAM Journal on Applied Mathematics. The work has been developed in the context of the SFB 1313 research project C02.
"A Hyperbolic Model for Two-Layer Thin Film Flow with a Perfectly Soluble Anti-Surfactant"
Authors
Abstract
We consider the motion of a two-layer thin film that consists of two immiscible viscous fluids and is endowed with an anti-surfactant solute. The presence of such solute particles induces variations of the surface tension and interfacial stress driving a Marangoni-type flow. We first analyze a lubrication limit and derive one-dimensional evolution equations for film heights and solute concentrations. Then, under the assumption that the capillarity and diffusion effects are negligible and the solute is perfectly soluble, we obtain a conservative first-order system in terms of film heights and concentration gradients. This reduced system is found to be strictly hyperbolic for a certain set of states and to admit an entire class of entropy/entropy-flux pairs. We also provide a strictly convex entropy for the hyperbolic system. Thus, the well-posedness for the Cauchy problem is given. Moreover, the system is almost a Temple-class system, which allows one to compute explicit solutions of the Riemann problem. The paper concludes with numerical experiments using a Godunov-type finite volume method, which relies on the exact Riemann solver.