Oscillatory Marangoni convection in binary mixtures in square and nearly square containers

Abstract

Three-dimensional simulations of oscillatory convection in binary mixtures driven by the Marangoni effect have been performed. The upper surface of the fluid is heated by a constant heat flux while the bottom is maintained at a constant temperature. Surface deflection is ignored. Oscillations are the result of concentration-induced changes in the surface tension due to the presence of an anomalous Soret effect. In domains with a square horizontal cross section and aspect ratio Γ=1.5 these take the form of either a standing wave with left–right reflection symmetry or a discrete rotating wave, depending on the separation ratio and the Schmidt number. Standing oscillations with reflection symmetry in a diagonal are unstable. When the cross section is slightly rectangular only the former bifurcate from the conduction state, and the transition to stable rotating waves with increasing Marangoni number proceeds via a sequence of secondary local and global bifurcations. The results are interpreted in terms of predictions from equivariant bifurcation theory.