Effect of surface tension on convection in a binary fluid layer under a zero gravity environment

The Marangoni flows in a horizontal layer of a binary mixture with an undeformable free upper surface are studied analytically and numerically. The system is heated and cooled by constant heat fluxes. The surface tension is assumed to vary linearly with temperature and solute concentration. Both double diffusive convection and Soret induced convection, in a zero gravity level, are considered. The governing parameters of the problem are the thermal Marangoni number MaT, the solutal Marangoni number MaS, the Prandtl and the Lewis numbers Pr and Le, the aspect ratio A and the parameter a defining the mechanism responsible for the occurrence of the solutal gradients (double diffusion or Soret effect). An approximate analytical solution, based on the parallel flow approximation, is proposed. Bifurcation diagrams are presented for the cases in which the solutal Marangoni effect acts in the same direction or competes with the thermal Marangoni effect. The stability of the parallel flow solution is studied numerically and the threshold for Hopf bifurcation determined. The validity of the analytical model is tested against the results obtained by solving numerically the full governing equations.