Fast relaxation phenomena and slow mode in extended thermodynamics of superfluids

A macroscopic monofluid model of liquid helium II which is based on extended thermodynamics was formulated in previous works, both in the presence and in the absence of dissipative phenomena. In all these studies, the time evolution of the nonequilibrium stress tensor was neglected, putting the relaxation times τ0 and τ2 of the nonequilibrium pressure and of the stress deviator equal to zero. In this work, the time evolution of these fields is not neglected and the complete model with 14 fields is studied, in the linear approximation. The propagation of waves is studied and a dispersion relation of degree 14 is obtained. The solutions of this equation are carried out, perturbing the solutions obtained in the limiting case τ0 = 0 = τ2. The corresponding modes are also investigated. Two vector fields, having the dimension of velocity, arise in the theory and they are interpreted as the velocities of the normal and the superfluid component in helium II, allowing the connection between this macroscopic model and the microscopic one.