Thermocapillary modulation of self-rewetting films

Abstract

Whereas surface tension decreases linearly with temperature for most fluids, here we consider those that exhibit a well-defined minimum. Specifically, our study is motivated by dilute aqueous mixtures of long-chain alcohols, for which surface tension is typically assumed to be a quadratic function of temperature. Utilization of these so-called ‘self-rewetting fluids’ has grown significantly in the past decade, due to observations that heat transfer is enhanced in applications such as film boiling and pulsating heat pipes. With similar applications in mind, we investigate the dynamics of a thin film with quadratic surface tension which is subjected to a temperature modulation in the bounding gas. A model is developed within the framework of the long-wave approximation, and a time-averaged thermocapillary driving force for destabilization is uncovered that results from the nonlinear surface tension. Linear stability analysis of the nonlinear partial differential equation for the film thickness is used to determine the critical conditions at which this driving force destabilizes the film and numerical investigation of this evolution equation reveals that linearly unstable perturbations saturate to regular periodic solutions (when the modulational frequency is set properly). Properties of these flows such as bifurcation at critical points and long-domain flows, where multiple unstable linear modes interact, are also discussed.