Codimension-2 bifurcations for convection in binary fluid mixtures

Abstract

An amplitude equation is derived for thermal convection in a binary fluid mixture in a porous medium and in bulk, in the vicinity of the intersection point of the lines of stationary and oscillatory instabilities. Slow spatial modulations are included in the amplitude equation near this codimension-2 bifurcation. The experimental realizability in binary fluid mixtures is discussed with use of data for specific systems such as alcohol-water mixtures and normal-fluid $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures. Analogies are drawn to other physical systems which are easily accessible to experiment, such as the convective instability in nematic liquid crystals in an external magnetic field.