Onset of surface driven convection in selfrewetting fluid layer overlying a porous medium

The onset of thermocapillary convective motion in a self-rewetting fluid layer overlying a porous medium with thermally dependent surface tension is studied analytically. Surface tension is assumed to be a quadratic function of temperature. The top surface of a fluid layer is deformably free and the bottom is rigid. We considered boundaries to be insulating to temperature perturbations. The governing equation that satisfies the composite system is analyzed by the normal mode approach and solved by the regular perturbation technique for linear stability. A mathematical expression is derived for the critical Marangoni number by solving coupled equations. The influence of crispation number, thermal diffusivity ratio, and other physical parameters involved therein are analyzed for the convective stability of the bilayer system. It has been found that the start of convection is delayed when the crispation number goes down and the thermal diffusivity ratio goes up. Also, the impact of the ratio of the thickness of the fluid to the thickness of the porous matrix and the other physical parameters on controlling the convective motion of the configuration is examined in detail.