Onset of Marangoni convection in variable-viscosity fluid layer subject to uniform heat flux from below

The onset of stationary Marangoni instabilities in a horizontal fluid layer with free surface deformation and heated from below with a uniform heat flux is considered theoretically using linear stability theory. The explicit solution is obtained and the influences of temperature-dependent viscosity, surface deformability, gravity waves and heat transfer mechanism at the free surface on the stability thresholds are investigated. Small stabilizing effect is observed in fluids with a small viscosity variation while large viscosity variation strongly destabilizes the fluid layer. The stability thresholds are critically dependent on viscosity variation, surface deformation and heat transfer mechanism.