Extended irreversible thermodynamics of liquid helium II: boundary condition and propagation of fourth sound

The work deals with further developments of a study previously initiated, in which a macroscopic monofluid model of liquid helium II, based on extended irreversible thermodynamics, has been formulated. The transversal modes are investigated and a boundary condition, suggested in the natural way by their analysis, is formulated; the existence of the fourth sound is demonstrated too. A possible experimental determination of the coefficients appearing in the theory is proposed: it is shown that the model is able to express the velocities and the attenuations of the two sounds in bulk helium II, in accord with the experimental data, using a number of parameters smaller than those introduced in the two-fluid model. Further, in the work, the theoretical values for the velocity of the fourth sound are determined at various pressures and at the temperature of 1.2 K, starting from experimental data on velocity and attenuation of the first and second sound in bulk liquid helium II, under the simplifying assumption that helium flows inside a superleak in the complete absence of dissipation: such theoretical values are in good agreement with experimental data