Feedback control of oscillatory thermocapillary convection in a half-zone liquid bridge

Active feedback control was applied to suppress oscillations in thermocapillary convection in a half-zone liquid bridge. The experiment is on a unit-aspect-ratio liquid bridge where the most unstable azimuthal mode has wavenumber 2 when control is absent. Active control was realized by locally modifying the surface temperature using the local temperature measured at different locations fed back through a simple control law. The performance of the control process was quantified by analysing local temperature signals, and the flow structure was simultaneously identified by flow visualization. With optimal placement of sensors and heaters, proportional control can raise the critical Marangoni number by more than 40%. The amplitude of the oscillation can be suppressed to less than 30% of the initial value for a wide range of Marangoni number, up to 90% of the critical value. The proportional control was tested for a period-doubling state and it stabilized the oscillation to a periodic state. Weakly nonlinear control was applied by adding a cubic term to the control law to improve the performance of the control and alter the bifurcation characteristics.