Selfsimilar solutions describing thermal capillary flows in viscous layers (Q1313985)

Thermal capillary flows in thin layers, brought about by nonuniform heating of the free boundary, are investigated at high Marangoni numbers. Selfsimilar solutions of the nonlinear boundary layer equations are constructed under conditions of axial symmetry, and asymptotic formulae for the solutions are found for small and large values of the thickness of the layer. It is shown that the selfsimilar solutions may not be unique when the parameters of the problem have certain values.