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

publication date

  • April 2016

start page

  • 1

end page

  • 7


  • 4 (043105)


  • 93

International Standard Serial Number (ISSN)

  • 2470-0045

Electronic International Standard Serial Number (EISSN)

  • 2470-0053


  • 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.


  • buoyant-thermocapillary instabilities; horizontal temperature-gradient; liquid layers; hydrothermal waves; heat-transfer; annular pool; convection; flow