Radiation‐driven thermocapillary flows in optically thick liquid films

A thin liquid film on a horizontal solid surface undergoing radiative heat transfer with an external heat source and the surrounding environment is considered. Thermal gradients along the free surface give rise to a thermocapillary flow in the liquid that is opposed by a hydrostatic pressure gradient within the film. Transient and steady‐state solutions are obtained for the interfacial shape and temperature and the velocity field. These results are compared with those from another model, in which a temperature distribution is imposed on the free surface of the film. At a critical value of the dynamic Bond number, a cusp in the form of a free‐surface slope discontinuity appears in this fixed free‐surface temperature model, but not in the radiation model. When the Bond number is less than this critical value, the time required to thin the film by a significant fraction of its original thickness is much larger with the radiation model. It is shown how the thermal boundary conditions used in the models directly cause these differences.