Thermodynamics and hydrodynamics of ³He-⁴He mixtures

The specific heat of liquid ³He–⁴He mixtures is usually written in terms of the sum of the specific heat of a ³He-quasiparticle gas and the specific heat of the pure ⁴He component. The thermodynamics based on this starting point is derived. Relations of important quantities and their low- and high-temperature limits are given. These are used to derive expressions for the velocity of second sound. This latter quantity is a very important source of information for the Fermi gas properties. Finally, the Fermi gas parameters are summarized in the chapter. The experimental aspects of the ³He–⁴He hydrodynamics are treated. The appearance of mutual friction that has long been neglected in this field is discussed, together with the properties of the critical velocities. The phenomenological equations of motion are given. The occurrence of mutual friction is a strong indication that ⁴He vortices play an important role in ³He–⁴He hydrodynamics. From the equation of motion of quantized ⁴He vortices, the observed cubic velocity dependence of the ⁴He chemical potential difference is explained on purely dimensional grounds. A differential equation is given from which the temperature profile in a cylindrical tube in which ³He flows through superfluid ⁴He can be calculated.