Competition between roll and square convection patterns in binary mixtures.

Abstract

We present a few-mode Galerkin model for convection in binary fluid layers subject to impermeable horizontal boundary conditions at positive separation ratios. It describes convection in the form of rolls in x direction, y direction, and squares. To incorporate symmetry-breaking sidewall forces selecting the spatial phase of the patterns relative to the walls we introduce into the model equations a single small inhomogeneity that favors the experimentally realized phase. Then squares are stabilized shortly above onset of convection where the amplitudes are very small. Far above onset, the amplitudes strongly increase, nonlinear mode coupling dominates, and causes rolls to be stable. In an intermediate regime, there are oscillations between the three competing patterns of rolls in x direction, squares, and rolls in y direction. Heat transport, spatial, and temporal behavior of the various convective states are in good agreement with recent experiments.