Distortion of capillary interfaces exposed to external heating is analyzed. This problem is of interest in material processing under zero gravity conditions and in thermal management of spacecrafts. The analysis is focused on a model problem where thermocapillary effect is the dominant driving force. Flow response to an external heating consists of convection in the liquid and interface deformation, with both effects being strongly coupled. Detailed results are presented in the case of cavity with a free upper surface. It is demonstrated that large interface deformation and rupture represent the dominant response of such dynamical system if the interface is sufficiently long. Flow conditions corresponding to the limits points have been identified. Limit points identify extreme values of flow parameters that guarantee the existence of steady continuous interface. It is shown that rupture can be delayed by changing the mass of the fluid, i.e., changing the initial shape of the interface.

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