Thermocapillary instability and rivulet structure formation in uniformly heated falling liquid film

A system of equations is derived to describe the nonstationary three-dimensional flow of non-isothermal liquid film in the presence of thermocapillary effect in long-wave approximation. The developed model is applicable for moderate Reynolds numbers and does not imply an a priori temperature profile in the film. Based on the derived equations the stability of a uniformly heated vertically falling liquid film is considered relative to spanwise perturbations. The linear analysis of the flow stability is carried out, and the dispersion dependences are obtained. A numerical method is used to study the nonlinear development of instabilities in 2D and 3D statements. It is shown that in a 3D statement, a small transverse perturbation evolves into the time-independent rivulet structure. The influence of dimensionless criteria of the problem on characteristic time and spatial scales of instability development and parameters of rivulet structures has been revealed. (C) 2019 Elsevier Ltd. All rights reserved.