Prof Michele Sciacca (Palermo University) gives a webinar on ‘The one-fluid extended model of superfluid helium: a complementary model’ (4PM UK time)

Liquid helium-4 becomes superfluid at very low temperatures (below the threshold temperature T = 2.17 K). Among the most important peculiarities, it flows without friction, at least in very narrow channels, and its thermal conductivity, which can be extremely high, depends on the boundary conditions. The aim of the webinar is to introduce the one-fluid extended model, as complementary model of the well-known two-fluid model for describing superfluid helium [1, 2].

The one-fluid extended model, with heat flux as an additional independent variable, is able to describe, among the others, some heat transport properties of superfluid helium such as second sound and nonlocal transport. Important features arise in the presence of superfluid turbulence, characterized by a tangle of quantized vortices, which leads to strong nonlinearities between heat flux and temperature gradient.

The dynamics of vortex lines and their interaction with heat dynamics, a central topic in superfluid turbulence, is dealt with by introducing the vortex line density as an independent variable and writing its dynamical equations, considering the transitions from laminar to turbulent flows and from diffusive to ballistic regimes.

It is worth noting the appearance of an extended two-fluid model in the one-fluid model, which may be directly compared to the classical two-fluid one. For this purpose, we have recently performed some numerical comparison between these two models of superfluid helium in a 2D counterflow channel [3].

References

[1] M.S. Mongiovì, D. Jou, M. Sciacca, Non-equilibrium thermodynamics of superfluid helium and quantum turbulence Springer (in press) 2025.

[2] M.S. Mongiovì, D. Jou, M. Sciacca, “Non-equilibrium thermodynamics, heat transport and thermal waves in laminar and turbulent superfluid helium” Physics Reports 726 (2018): 1-71.

[3] L. Galantucci, M. Sciacca, “The wall effect in a plane counterflow channel” Journal of Non-Equilibrium Thermodynamics 49 (2024): 205-214.