Control of Marangoni convection in a variable-viscosity fluid layer with deformable surface

The effectiveness of a proportional feedback control to suppress the Marangoni instability in a variable-viscosity fluid layer with a deformable free upper surface is investigated. Viscosity variation and deformable free surface have destabilizing effects on the stability limit. The stability thresholds for the short-scale mode are strongly dependent on viscosity variation and controller gain while the stability thresholds for the long-scale mode are greatly influenced by gravity and surface deformation. The feedback control strategy through thermal perturbation in the boundary data is shown effective in suppressing the Marangoni convection and delaying the onset of instability.