Longwave Stability of Two Liquid Layers Coating Both Sides of a Thick Wall in the Absence of Gravity

A system of two coupled nonlinear equations was calculated to describe the thermocapillary evolution of the free surface deformations of two liquid layers coating both sides of a wall of finite thickness and thermal conductivity in the absence of gravity. The equations were obtained under the small wavenumber approximation. A temperature gradient appears perpendicular to the liquid-wall-liquid system due to the temperature difference between the atmospheres outside the free surfaces of both fluid layers. The linear growth rate of the system was investigated with respect to a variety of parameters. Under some conditions, two stationary modes and one oscillatory mode between them were found. The second stationary mode was concluded to be always stable. It was also found that under different conditions only stationary convection is possible. These results depended on the relative thickness of the two fluid films. It is of interest to know if the coupled free surface perturbations presented a nonlinear sinuous or varicose mode. Thus, a two-dimensional numerical analysis was performed to find out which conditions lead to the sinuous or to the varicose mode of instability.