Effect of volume ratio on thermocapillary convection in annular liquid pools in space

In systems with liquid/liquid or liquid/gas interface under microgravity, and even in shallow liquid layers in the terrestrial conditions, thermocapillary force takes the principal role to drive natural convections. A series of numerical simulations are conducted to investigate the stability limit of axisymmetric steady thermocapillary flow in annular liquid pools with curved and adiabatic liquid surface for eight volume ratios 0.809 <= Vr <= 1.173, where Vr is defined as (liquid vol/vol of the annular gap). Simulations provide the critical temperature difference Delta T-c, frequency f(c), and azimuthal wave number mc for each liquid pool. At the critical condition, oscillations start in form of standing wave. At the slightly supercritical condition (Delta T*), the standing waves turn to traveling oscillations. The calculated Delta T-c values decrease with the increase of Vr. A simulation code with a convective thermal boundary condition in the liquid surface suggests that heat transfer through the liquid surface significantly increases the Delta T-c value.