Interfacial Instabilities, Waves and Solitons Excited by the Marangoni Effect

Abstract

For deep liquid layers we provide an extension of the Stokes- Boussinesq theory to describe (space and time modulated limit cycle) nonlinear capillary-gravity waves excited and sustained by the Marangoni effect, i.e. by the variation of surface tension with temperature or concentration of surface active material. The latter may appear as the result of chemical activity in the liquid or other processes including adsorption, etc. at the surface, coupled to the hydrodynamics in the bulk of the layer. On the other hand, in parallel with the preceding approach, for shallow liquid layers we provide an extension of the (nonlinear and dispersive) Korteweg-de Vries theory to describe the soliton excitation triggered by the same Marangoni effect and dissipation.