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

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.

Effect of the horizontal aspect ratio on thermocapillary convection stability in annular pool with surface heat dissipation

“…• two new kinds of hydrothermal waves recently reported by Hoyas et al [34] for deeper annular domains.…”

“…The effect of the domain depth to horizontal dimension ratio (Γ) on the onset of the flow motion and the dynamics of the different bifurcations appearing has been studied in [34,35]. However, to the knowledge of the authors, there has not been any study assessing the influence of the horizontal aspect ratio of the annular domain on the development of flow instabilities, and thus it is the main focus of the present work.…”

Inverse cascade of the vortical structures near the contact line of evaporating sessile droplets

“…Under certain conditions, the perturbations in different parameters such as the surface tension, concentration, temperature, pressure and velocity may grow into the hydrothermal instabilities 11 . Namely, the Rayleigh-Benard-Marangoni types of instabilities are found to alter the convective heat/mass transfer regimes inside the evaporating sessile droplets 18,19 .…”

Flow bifurcation routes to chaos of thermocapillary convection for low Prandtl number fluid in shallow annular pool with surface heat dissipation

“…The results showed that the interfacial evaporation has a great influence on the instability of thermocapillary convection, and the evaporation intensity is related to the non-equilibrium degree through the evaporation interface, which is dependent on the evaporation Biot (Bi) number on the free surface. Hoyas et al [28][29][30] studied the instabilities appearing in a cylindrical annulus with the heating bottom and the opening free surface to the atmosphere by linear stability analysis. After the flow destabilizes, the appearance of the various flow patterns and the flow bifurcation routes to chaos are mainly dependent on Marangoni number, Biot number and Prandtl number.…”