Abstract
Formal asymptotic expansions of the solution of the stationary problem of the thermocapillary flow of fluid in an unbounded region, with the free boundary unevenly heated, are constructed for large values of the Marangoni number. A non-linear boundary layer is formed near the free surface, and selfmodelling solutions are found for this layer near the critical point. A slow flow outside the boundary layer satisfies the equations of an ideal fluid. An equation describing the free boundary is obtained. When the temperature gradient vanishes, this equation becomes the well-known equation of the equilibrium of the free boundary of a capillary fluid. Numerical computations are carried out to determine the form of the meniscus at the vertical solid wall, the free boundary of the fluid poured onto a horizontal surface for the plane and axisymmetric case, and the surface of a gas bubble adjacent to the wall in a heated fluid.
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