Marangoni boundary layers

This paper deals with the theory of Marangoni boundary layers developing near the free surface of a nonuniformly heated liquid.

In the Introduction the notion of a thermocapillary effect is considered, and the conditions, under which thermocapillary flow is dominant, are elucidated. The similarity criteria of the problems are revealed, and the effects resulting from melt convection are considered.

In the second section the mathematical aspects of the theory of Marangoni boundary layers are considered. The boundary layer effect on the form of a free surface is investigated, and some examples are presented.

In Section 3 a qualitative flow pattern in a Marangoni boundary layer is analyzed, similarities and differences in the problems of Prandtl and Marangoni boundary layer theory are discussed. The possibility of Marangoni boundary layer degeneration at the outer boundary, as well as the initiation of flow containing a counter-stream zone are emphasized.

The fourth section outlines the calculation scheme on the basis of boundary-layer theory for convective flows with directed crystallization and in the absence of mass forces. Some examples are presented.

In the fifth section some problems of the theory of Marangoni boundary layers that need further investigation are discussed.