Study of resistance of a free nonisothermal liquid film in a gravity field

In a thin-layer approximation, a problem of a free liquid film vertically bounded by solid walls and being under the influence of gravity and thermocapillary forces is considered. A solution in which the film thickness is constant and temperature is a linear function of the longitudinal coordinate is investigated analytically for stability using the matching asymptotic expansions method and numerically using the orthogonalization method for various values of gravitational acceleration. The results obtained analytically and numerically are in good agreement. It is shown that the solution is unstable, but the increment of perturbations is small even under terrestrial gravity.