Onset of convection in dilute superfluid 3He-4He mixtures. I. Unbounded slab

The thermohydrodynamics of a dilute superfluid 3He-4He mixture confined between parallel horizontal planes is studied with the two-fluid equations of Landau and Khalatnikov. When heated from above, downward normal fluid flow concentrates 3He impurities near the cooler bottom plate, creating a potentially unstable density gradient. The linearized equations for the convective amplitudes contain nonclassical two-fluid terms proportional to v/sub n/0xdel-arrow-right and to del-arrow-rightxv/sub n//sup prime/, which alter the critical Rayleigh number from that for a classical one-component fluid. This shift is expected to be smaller near Troughly-equal1 K