Marangoni patterns on a rhombic lattice in a thin film heated from below

Pattern formation due to oscillatory Marangoni instability in a thin film heated from below is studied. We focus on the stability of patterns that are produced by nonlinear interaction of two standing waves propagating at the angle ϕ between the wave vectors. We provide weakly nonlinear analysis within the amplitude equations, which govern the evolution of the layer thickness and the characteristic temperature. This leads to a set of four complex Landau equations that govern the evolution of wave amplitudes. The coefficients of Landau equations, which define pattern formation, have been calculated in a wide range of governing parameters. Stable traveling rectangles and alternating rolls on a rhombic lattice are detected.