Thermocapillary rivulets in the uniformly heated liquid film

The set of equations which describes a non-steady 3D flow of non-isothermal liquid film in the presence of thermocapillary effect is deduced in the long-wave approach. The used model is applicable for moderate Reynolds's numbers Re∼10 and does not imply in advance set the profile of temperature in a film. The linear analysis of a stability of a film in relation to perturbations in spanwise direction is carried out and dispersion relations are gained. Nonlinear development of instability is investigated numerically in cases of 2D and 3D flow and appearance of quasistationary rivulet structure. Influence of dimensionless parameteres on characteristic scales of rivulet structures is revealed.