Studies in Thermocapillary Convection of the Marangoni-Benard Type

A nonlinear feedback control strategy for delaying the onset and eliminating the subcritical nature of long-wavelength Marangoni-Benard convection is investigated based on an evolution equation. A control temperature is applied to the lower wall in a gas-liquid layer otherwise heated uniformly from below. It is shown that, if the interface deflection is assumed to be known via sensing as a function of both horizontal coordinates and time, a control temperature with a cubic-order polynomial dependence on the deflection is capable of delaying the onset as well as eliminating the subcritical instability altogether, at least on the basis of a weakly nonlinear analysis. The control coefficients required for stabilization are O(1) for both delaying onset indefinitely and eliminating subcritical instability.