title: 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.
authors.affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, València, Spain.
authors.forename: S
authors.initials: S
authors.lastname: Hoyas
authors.affiliation: Aerospace Engineering Group, Universidad Carlos III de Madrid, Leganés 28911, Spain.
authors.forename: P
authors.initials: P
authors.lastname: Fajardo
authors.affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, València, Spain.
authors.forename: M J
authors.initials: MJ
authors.lastname: Pérez-Quiles