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.