Marangoni Instability in a Fluid Layer with Insoluble Surfactant

The effect of linear proportional feedback thermal controller on the onset of steady Marangoni instability in a horizontal fluid layer with insoluble surfactants is studied theoretically by using linear stability analysis. The exact analytical solution for the stationary modes is obtained and the effects of elasticity number, thermal controller gain, surface deformation, Galileo number, Lewis number and Biot number on the onset of Marangoni convection are determined.The elasticity number, Biot number, Galileo number and small controller gain are found to have stabilizing effects on the fluid layer but the Lewis number and large controller gain are destabilizing factors. The heat transfer mechanism and the presence of insoluble surfactant at the free surface significantly stabilize the fluid system.