Influence of geometrical parameters on the linear stability of a Bénard-Marangoni problem

A linear stability analysis of a thin liquid film flowing over a plate is performed. The analysis is performed in an annular domain when momentum diffusivity and thermal diffusivity are comparable (relatively low Prandtl number, Pr = 1.2). The influence of the aspect ratio (Gamma) and gravity, through the Bond number (Bo), in the linear stability of the flow are analyzed together. Two different regions in the Gamma-Bo plane have been identified. In the first one the basic state presents a linear regime (in which the temperature gradient does not change sign with r). In the second one, the flow presents a nonlinear regime, also called return flow. A great diversity of bifurcations have been found just by changing the domain depth d. The results obtained in this work are in agreement with some reported experiments, and give a deeper insight into the effect of physical parameters on bifurcations.The computations shown in this work were made possible by a generous grant of computer time from the supercomputation center of the Universitat Politècnica de València