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Publication 16-CNA-032

Dynamics And Stability Of Surface Waves With Surfactants

Chanwoo Kim
Department of Mathematics
University of Wisconsin
Madison, Madison, WI 53706 USA

Ian Tice
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Abstract: In this paper we consider a layer of incompressible viscous fluid lying above a at periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and evolves in time. We assume that a mass of surfactants resides on the free surface and evolves in time with the fluid. The surfactants dynamics couple to the fluid dynamics by adjusting the surface tension coefficient on the interface and also through tangential Marangoni stresses caused by gradients in surfactant concentration. We prove that small perturbations of equilibria give rise to global-in-time solutions in an appropriate functional space, and we prove that the solutions return to equilibrium exponentially fast. In particular this proves the asymptotic stability of equilibria.

Get the paper in its entirety as  16-CNA-032.pdf

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