BENARD CONVECTION IN A BINARY MIXTURE WITH A NONLINEAR DENSITY-TEMPERATURE RELATION

Benard convection of a two-component liquid in a porous medium is cons idered. The mixture displays Soret effects and shows a nonlinear densi ty-temperature relation, i.e., non-Boussinesq properties. A two-parame ter perturbation analysis is used to determine the effects on the stab ility of the basic state and the finite-amplitude convection. Linear t heory demonstrates the nonlinear density-temperature relation to have a destabilizing effect; the critical Rayleigh numbers for the onset of oscillatory and steady-state convection are decreased. For the case o f two-dimensional convection, traveling waves and steady-state solutio ns are considered. They are determined up to fifth order of the amplit ude parameter. In the vicinity of the codimension-two point, a stable branch of traveling wave solutions exists near the onset. If the Rayle igh number is increased the wave motion vanishes and a transition to s teady-state convection occurs. Due to the symmetry of the two-dimensio nal solutions this bifurcation is not affected by the non-Boussinesq p roperties of the mixture. However, for the case of three-dimensional c onvection the nonlinear density-temperature relation leads to an unfol ding of the bifurcation of steady-state hexagonal solutions. As a cons equence the branch of the oscillatory solution terminates at an isolat ed point in the parameter plane.