Benard-Marangoni convection within isotropic droplets in overheated free standing smectic films

We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions.