Impact of dynamic surface deformations on the flow instability in high-Prandtl-number liquid bridges

The linear stability of the axisymmetric thermocapillary flow in a in high-Prandtl-number liquid bridge is investigated numerically. We address the full two-phase problem in which both, the concentric support rods and the liquid bridge are surrounded by an annular gas duct. While many previous investigations were based on a hydrostatically determined shape of the liquid bridge assuming a vanishingly small capillary number, dynamic surface deformations caused by the axisymmetric liquid and gas flows are fully taken into account. The steady basic flow is then subjected to a linear stability analysis. Since the dynamic surface defomations are of minor importance for weak mean axial gas flow, surface deformations due to the three-dimensional perturbation flow are neglected. Critical Reynolds numbers will be presented and the effect of the dynamic surface deformations in the basic state will be assessed by comparison with the stability boundaries for statically deformed bridges. Dynamic surface deformations become more important the larger the imposed axial gas flow rate is, significantly affecting the critical Reynolds number. Different critical modes are analyzed regarding their structure and the instability mechanisms.