Thermocapillary stabilization of Liquid Space Telescopes
We investigate how spatially uniform, time-modulated heating can be used to stabilize a thin liquid mirror in microgravity. Periodic heating generates oscillatory thermocapillary flows that suppress the instability associated with sustained heating, allowing the free surface to relax through the combined effects of thermal radiation, thermocapillary transport, and capillarity. Using multiple-scale analysis of a long-wave model, we derive the coupled surface-temperature evolution over many heating cycles. A subsequent linear stability analysis yields the stability criteria and decay times of individual surface modes. Numerical simulations validate the analytical predictions and demonstrate stabilization of meter-scale surface deformations over timescales of days.