Invariant solutions of surfactant-driven flows

Abstract

We consider a localized surfactant monolayer on the free surface of a thin viscous film. Flows generated by a gradient in surfactant concentration are described by a nonlinear system of PDE’s (Jensen’s equations). We study classical Lie symmetries of this system and discuss the classes of its invariant and partially invariant solutions. We derive corresponding reduced systems and find several classes of analytic solutions of Jensen’s equations. We discuss the properties and physical meaning of these solutions.