Control of Marangoni instability in a layer of variable-viscosity fluid

The Marangoni instability in a temperature-dependent-viscosity fluid layer with deformable free surface under the influence of a linear feedback control strategy is investigated. The exact analytical solution for the stationary modes is developed and the effects of the interaction between variable viscosity, controller gains, free surface deformation, gravity waves and heat transfer mechanism on the onset of Marangoni convection are determined. The destabilizing effect of exponential viscosity variation can be effectively suppressed through small controlled perturbations in the thermal boundary data.