Thermocapillary structures in a heated liquid film

The system of the equations which in long-wave approach describes a non-stationary 3D non-isothermal film flow in the presence of thermocapillarity is derived. The used model, unlike lubrication theory, is applicable not only for small, but also for a moderate Reynolds number in a wide range of hydrodynamic and thermal parameters of a flow and does not assume a priori set a temperature profile in a film. Based on the derived equations the numerical simulation of stationary 3D thermocapillary rivulets in a liquid film flowing over a "semi-infinite" heater is executed.