Influence of the dynamical free surface deformation on the stability of thermal convection in high-Prandtl-number liquid bridges

Abstract

We analyze theoretically the stability of the thermal convection in high-Prandtl-number liquid bridges. The steady axisymmetric base flow, as well as its corresponding linear non-axisymmetric eigenmodes, are calculated taking into account the free surface deformation caused by both that flow and the perturbations. The stability limits and the oscillation frequencies obtained from the linear stability analysis satisfactorily agree with previous experimental data. The dynamical free surface deformation produced by the base flow approximately coincides with that measured in the experiments. When the deformations are normalized with their corresponding values of the Capillary number, they collapse onto a single curve. The dependence of the free surface oscillation amplitude with respect to the axial coordinate approximately coincides with that measured in previous experiments. Our results show that the dynamical free surface deformation has very little effect on the eigenvalues characterizing the linear modes, and, therefore, on the stability limits.