NONLINEAR EVOLUTION AND SECONDARY INSTABILITIES OF MARANGONI CONVECTION IN A LIQUID-GAS SYSTEM WITH DEFORMABLE INTERFACE

The paper presents a theory of nonlinear evolution and secondary insta bilities in Marangoni (surface-tension-driven) convection in a two-lay er liquid-gas system with a deformable interface, heated from below. T he theory takes into account the motion and convective heat transfer b oth in the liquid and in the gas layers. A system of nonlinear evoluti on equations is derived that describes a general case of slow long-sca le evolution of a short-scale hexagonal Marangoni convection pattern n ear the onset of convection, coupled with a long-scale deformational M arangoni instability. Two cases are considered: (i) when interfacial d eformations are negligible; and (ii) when they lead to a specific seco ndary instability of the hexagonal convection. In case (i), the extent of the subcritical region of the hexagonal Marangoni convection, the type of the hexagonal convection cells, selection of convection patter ns - hexagons, rolls and squares - and transitions between them are st udied, and the effect of convection in the gas phase is also investiga ted. Theoretical predictions are compared with experimental observatio ns. In case (ii), the interaction between the short-scale hexagonal co nvection and the long-scale deformational instability, when both modes of Marangoni convection are excited, is studied. It is shown that the short-scale convection suppresses the deformational instability. The latter can appear as a secondary long-scale instability of the short-s cale hexagonal convection pattern. This secondary instability is shown to be either monotonic or oscillatory, the latter leading to the exci tation of deformational waves, propagating along the short-scale hexag onal convection pattern and modulating its amplitude.