Nonlinear theory of traveling wave convection in binary mixtures

Traveling wave (TW) convection in binary mixtures is studied by an expansion in the séparation ratio (|ψ| ⪡ 1) around the pure fluid convective state (ψ = 0 ). For free-freepermeable boundary conditions the bifurcation from the conducting state to TW convection is critical. For the experimentally relevant rigid-rigid-impervious boundary conditions with ψ ⪡ — L 2, the sub-critical bifurcation curve from the conducting state to TW convection is obtained and the concentration profiles are evaluated. The transition from traveling waves to steady convection is predicted to be critical and the value of the Rayleigh number at which it happens is calculated analytically and numerically. Comparison with available data and suggestion for further experiments are discussed.