Long-wave Marangoni convection in a layer of surfactant solution

Abstract

We consider the deformational mode of Marangoni instability in a heated layer of a surfactant solution with the Soret effect and the adsorption/desorption of surfactant molecules accounted for by using a linearized model of sorption kinetics. Linear stability analysis of the layer's quiescent base state reveals a competition between monotonic and oscillatory modes of the long-wave instability, as well as a strong stabilization due to surfactant adsorption. Based on these results, we carry out the derivation of a set of long-wave nonlinear evolution equations governing the spatiotemporal dynamics of the oscillatory mode of instability. Using a weakly nonlinear analysis of the evolution equations, we study pattern selection in the case of a 2D flow near the stability threshold of the system. We validate our theoretical predictions by a numerical solution of the evolution equations.