Thermocapillary rivulets in a locally heated falling liquid film

Abstract

The formation of a three-dimensional rivulet structure in a heated falling liquid film is investigated theoretically. For a description of the dynamics of a non-isothermal film, the theoretical model is developed taking into account the thermocapillary force. Within the framework of the spatial approach, a linear analysis of the stability of the heated film relative to perturbations in the spanwise direction to the flow is performed for the first time. A spatial growth rate of these perturbations down-stream is obtained. Analysis of experimental data for different liquids and different Reynolds numbers has shown that the distance between the rivulets corresponds well to the wavelength of most amplified perturbation. The stationary rivulet structure in the film is simulated by numerical method for two types of heating conditions implemented in our previous experiments: with constant wall temperature and heat flux on the wall. Calculations show, that on a heater with constant temperature of a wall the developed rivulet structure has a quasistationary character and very slightly changes downstream. The development of rivulets on a heater with a constant heat flux on the wall has been calculated for the first time. The good agreement between calculations and our experimental data is found for both types of heating conditions implemented in the experiments.