PATTERN-FORMATION IN LARGE-SCALE MARANGONI CONVECTION WITH DEFORMABLE INTERFACE

We derive a nonlinear evolution equation describing the evolution of large-scale patterns in Marangoni convection in thermally insulated two-layer liquid-gas system with deformable interface, and generalizing equations obtained previously by Knobloch and Shtilman and Sivashinsky. Both surface deformation and inertial effects contribute to the diversity of long-scale Marangoni convective patterns. In the space of parameters - Galileo and capillary numbers - different regions are found where not only hexagonal, but also roll and square patterns are subcritical. Stability regions for various patterns are found, as well as regions of multistability. It is shown that competition between squares and hexagons leads to formation of a stable quasicrystalline dodecagonal convective structure.