Korteweg–de Vries soliton excitation in Bénard-Marangoni convection

Abstract

For a two-dimensional shallow liquid layer open to air and subjected to a thermal gradient (Bénard problem), the threshold condition is given for the onset of a Korteweg–de Vries soliton as the result of an instability triggered by the Marangoni effect, i.e., by the variation of the interfacial tension with temperature or concentration of a surfactant. In the absence of buoyancy, in contrast with Bénard convection, the heating for standard liquids must be done from the air side. However, for liquids exhibiting a minimum in surface tension with temperature the heating can also be done from the liquid side when operating past the minimum where the surface-tension coefficient increases with temperature.