Steady pattern formation and film rupture in a two-dimensional thermocapillary thin-film model of the Bénard–Marangoni problem
We study two-dimensional, stationary square and hexagonal patterns in the thermocapillary deformational thin-film model for the fluid height h [Formula presented] that can be formally derived from the Bénard–Marangoni problem via a long-wave approximation. Using a linear stability analysis, we show that the flat surface profile corresponding to the pure conduction state destabilises at a critical
