Free-surface flow of confined volatile simple fluids driven by a horizontal temperature gradient: From a comprehensive numerical model to a simplified analytical description

Abstract We study the flow in a confined layer of volatile simple liquid subjected to a horizontal temperature gradient. The somewhat unusual feature of this problem is that the gas layer, which contains a mixture of vapor and air, plays a very important role. Due to phase change occurring at the free surface, the mean flow in the liquid layer and its stability are controlled almost entirely by the mass and heat transport in the gas phase. To explain why this is the case, we use numericae simulations based on a comprehensive two-sided transport model to motivate a simplified analytical description of transport in the gas phase for high-aspect-ratio geometries. This simplified description allows us to compute the interfacial temperature and hence the thermocapillary stresses at the free surface which control the flow in the central region of the cavity and to predict the net heat and mass flux in the direction of the applied gradient. The analytical solutions are found to agree quite well with the results of our numerical simulations as well as the results of relevant previous studies.