Marangoni convection induced by a nonlinear temperature-dependent surface tension

2014 Marangoni instability in a thin horizontal fluid layer exhibiting a nonlinear dependence of the surfacetension with respect to the temperature is studied. This behaviour is typical of some aqueous long chain alcohol solutions. The band of allowed steady convective solutions is determined as a function of the wavenumber and a new dimensionless number, called the second order Marangoni number. We show that the cells which take the shape of rolls and rectangles are unstable while hexagonal planforms remain allowed The field equations are expressed as Euler-Lagrange equations of a variational principle which serves as the starting point of the numerical procedure, based on the Rayleigh-Ritz method. J. Physique 47 (1986) 23-29 JANVIER 1986,