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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.

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Numerical simulations are used to analyze the dynamics of a free surface excited by thermal modulations at the lateral boundaries that generate a time-dependent thermocapillary flow. Fluid parameters are selected to be representative of 5 cSt silicone oil. Following the work of Gligor et al. [“Thermocapillary-driven dynamics of a free surface in microgravity: Response to steady and oscillatory thermal excitation,” Phys. Fluids 34, 042116 (2022)], the response of the free surface to oscillatory thermal excitation is characterized by the displacement of the contact points, and a frequency sweep is used to obtain a Bode-type diagram that reveals a resonance peak in the vicinity of the first sloshing mode. The ability of the thermocapillary flow to excite this sloshing mode suggests a control strategy that uses thermal modulations to dampen sloshing motion. After the response of the isothermal surface to a generic pulse-like inertial perturbation is measured, a classical proportional integral derivative control is implemented and the effect of its gains is considered separately. The efficacy of the controller is characterized by the decay time of the contact point oscillations and by a cost function. The effect of possible delays in the control loop is accounted for. Finally, a controller with a derivative gain is selected and used to dampen the motion induced by a reboosting maneuver of the International Space Station.