Matvey Morozov (Israel Institute of Technology): Long-wave Marangoni Convection in a Binary-Liquid Layer with Soret effect and Surfactant Adsorption/Desorption
We consider a heated binary-liquid layer lying on a solid horizontal substrate; free surface deformations and the Soret effect are taken into account. In the previous studies of this model system, surface tension was assumed to be a function of the temperature and the bulk concentration of the solution near the free surface. In reality, surface tension depends on the concentration of the solute molecules adsorbed at the interface. Thus, we also take into consideration the adsorption/desorption kinetics and advection of the adsorbed molecules along the interface. Linear stability analysis of the quiescent state of the layer reveals a competition between monotonic and oscillatory modes of instability; and nonlinear analysis yields the set of long-wave nonlinear evolution equations governing the dynamics of the local layer thickness and local solute concentration. We use the evolution equations to study pattern selection in the case of a 2D flow. Finally, we check our theoretical predictions numerically by solving the evolution equations using the method of lines.