Thermocapillary-driven dynamics of a free surface in microgravity: Response to steady and oscillatory thermal excitation

Abstract

A numerical analysis of the thermocapillary-driven dynamics of a free surface in microgravity is presented for an open container of liquid subjected to steady or oscillatory thermal excitation. The response to this forcing is analyzed for parameters representative of common silicone oils. In contrast to previous investigations, we permit large-scale unconstrained motion of the contact points and deformation of the free surface, which allows us to study the interaction between free surface dynamics and thermocapillary flow. First, the response of the free surface to steady thermal excitation is considered and characterized by the asymmetry of the contact points. Linear dependence of this asymmetry on the applied Marangoni number is found, which is amplified by the vibroequilibria effect when supplemental (high-frequency) vibrations are introduced. In low-viscosity liquids, the transient dynamics of the free surface includes sloshing modes, suggesting that thermal modulation may be used to excite them. The free surface response to oscillatory thermal excitation is then studied for a wide range of parameters, including variations in contact angle β, viscosity ν, container length L, and fluid height H. We perform a frequency analysis and obtain Bode-type diagrams for the contact point oscillations, characterizing the low-frequency response by its amplitude and phase with respect to the thermal forcing, and demonstrate a resonance peak corresponding to the principal sloshing mode. Overall, these results indicate the potential of oscillatory thermal excitation for fluid control in microgravity.