A model of film deformation and rupture under the action of thermo-capillary forces

A model of the deformation of a free weightless liquid film with rims fixed at a plane contour and subject to the action of thermocapillary forces is investigated. The film free-surface temperature is assumed to be a known function of the coordinates and time. The equation describing the film thickness evolution in the long-wave approximation is of the second order with respect to time and of the fourth order with respect to the longitudinal coordinates. A model plane nonstationary problem is calculated, making it possible to estimate the lifetime of the film as a function of the rate of variation of the temperature profile curvature on the free boundary. If the characteristic time of the temperature variation is large as compared with the film's natural oscillation period, the problem can be considered in the quasi-steady approximation, which is studied in detail for the plane and axisymmetric cases. The critical values of the temperature profile curvature, for which the film thickness on the symmetry axis vanishes, resulting in the rupture of the film, are calculated.