Stationary convective instability in a superfluidHe3-He4mixture

Abstract

The stationary convection instability of a superfluid mixture is considered. The criteria for the instability onset in a superfluid region of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ phase diagram and in different limiting cases are obtained. It is shown that in different regions of the phase diagram, depending on the magnitude of the kinetic coefficients, the stationary-instability criterion is similar to that of either the regular binary mixture with abnormal thermal diffusion, to the pure liquid, or to the compressible pure liquid. The stability is also strongly dependent on concentration and temperature, and the critical temperature gradient rises sharply with decreasing temperature and concentration. At very low temperature (below 0.5 K) and concentration (dilute solution) the superfluid solution becomes stable with respect to stationary convection. Asymptotic behavior of the criterion in the vicinity of the $\lambda$ line, the tricritical point and for infinitely dilute solutions is also estimated.