Abstract:
When a heat flux is switched on across a fluid binary mixture, steady state conditions for the temperature and mass concentration gradients ∇T and ∇c are reached via a diffusive transient process described by a series of terms "modes" involving characteristic times τn. These are determined by static and transport properties of the mixture, and by the boundary conditions. We present a complete mathematical solution for the relaxation process in a binary normal liquid layer of height d and infinite diameter, and discuss in particular the role of the parameter A=kT2(∂μ/∂c)T,P/TCP,c coupling the mass and thermal diffusion. Here kT is the thermal diffusion ratio, (∂μ/∂c)T,P-1 is the concentration susceptibility, μ is the chemical potential difference between the components, and CP,c is the specific heat. We present examples of special situations found in relaxation experiments. When A is small, the observable times τ(∇T) and τ(∇c) for temperature and concentration equilibration are different, but they tend to the same value as A increases. We present experimental results on four examples of liquid helium of different3He mole fraction X, and discuss these results on the basis of the preceding analysis. In the simple case for pure3He (i.e., in the absence of mass diffusion) we find the observed τ(∇T) to be in good agreement with that calculated from the thermal diffusivity. For all the investigated3He-4He mixtures, we observe τ(∇c) and τ(∇T) to be different when A is small, a situation occurring at high enough temperatures. As A increases with decreasing T, they become equal, as predicted. For the mixtures with mole fractions X(3He)=0.510 and 0.603, we derive the mass diffusion D from the analysis of τ(∇c) and demonstrate that it diverges strongly with an exponent of about 1/3 in the critical region near the superfluid transition. As the tricritical point (Tt, Xt) is approached for the mixture X=Xt0.675, D tends to zero with an exponent of roughly 0.4. These results are consistent with predictions and also with the D derived from sound attenuation data. We discuss the difficulties of the analysis in the regime close to Tλ and Tt, with special emphasis on the situation created by the onset of a superfluid film along the wall of the cell for X=0.603 and 0.675. © 1982 Plenum Publishing Corporation.