Pattern selection for thermocapillary flow in rectangular containers in microgravity

Resumen

A detailed numerical investigation of pattern selection for thermocapillary flow in rectangular containers in microgravity is presented. These dynamics are studied for liquid n-octadecane, an alkane with high Prandtl number (Pr = 52.53), due to its relevance to recent microgravity experiments. Pattern selection is analyzed in terms of the aspect ratio, I', and the applied Marangoni number, Ma. In short containers, the bifurcation picture is characterized by a transition from steady thermocapillary flow to a standing wave (SW) oscillatory mode as Ma is varied. This transition takes the form of a primary subcritical Hopf bifurcation accompanied by a secondary saddle node; these two bifurcations delimit a region of bistability. In large containers, the dynamics is characterized by a supercritical Hopf bifurcation that marks the transition from steady flow to a traveling wave (TW) mode. The critical Ma for this transition increases with I'. In intermediate containers, a complex pattern selection scenario is found, where both steady and oscillatory convection, in the form of either TWs or SWs, can appear depending on I' and Ma. Finally, we apply this bifurcation analysis to help explain recent results on thermocapillary flows during the melting of phase change materials in microgravity [Salgado S??nchez et al., A20 (2021)]. The temporal evolution of the phase change is characterized by an effective I' and Ma in the liquid phase. We find very good agreement between the flow transitions observed during melting and those predicted for the equivalent rectangular containers over the explored range of 1.5 I' 16.