Planform selection in two-layer Bénard-Marangoni convection

Bénard-Marangoni convection in a system of two superimposed liquids is investigated theoretically. Extending previous studies, the complete hydrodynamics of both layers is treated and buoyancy is consistently taken into account. The planform selection problem between rolls, squares, and hexagons is investigated by explicitly calculating the coefficients of an appropriate amplitude equation from the parameters of the fluids. The results are compared with recent experiments on two-layer systems in which squares at onset have been reported.