ABSTRACT
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 (Γ) and gravity, through the Bond number (Bo), in the linear stability of the flow are analyzed together. Two different regions in the Γ-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.
ABSTRACT
We study, from the theoretical point of view, instabilities appearing in a liquid layer, where a dynamic flow is imposed through a nonzero temperature gradient at the bottom. Experimentally many interesting dynamical behaviors have been discovered in this system. In this Brief Report we prove that the basic solution can display great richness of bifurcations which are controlled by heat related parameters. Different kinds of spatially extended and localized structures appear, which are both stationary or oscillatory. These last ones can present amazing patterns such as squares or spirals. Also competing solutions at codimension-two bifurcation points have been found: stationary radial rolls with different wave numbers, radial rolls with hydrothermal waves, and hydrothermal waves with different wave numbers. Remarkably our results recover many features of numerous reported experiments, predict new instabilities, and by giving a deeper insight into how physical parameters contribute to bifurcations, open a gateway to control those instabilities.
