Phase Transition In Liquid ⁴He by a Mean Field Model

Abstract

In this work the transition of ⁴He at the lambda line in presence of a Cattaneo-Maxwell heat flux is studied. A hydrodynamical model is formulated, which chooses as fundamental fields the velocity, the temperature, the heat flux and a phase field function f, for which a time dependent Ginzburg-Landau equation is proposed. Using this model we are able to describe the phase transition and to obtain the pressure-temperature phase diagram which represents the transition, the thermodynamic restrictions and a maximum theorem for the phase field.

Keywords:

• Liquid helium
• Mean phase-field model
• Phase transition

ACKNOWLEDGMENTS

MSM acknowledges the hospitality of the “Dipartimento di Matematica of the Università di Bologna” and the financial support of the “Università di Palermo,” under grant 2007.ORPA07LXEZ.

Notes

Communicated by Michele Ciarletta on 22 March 2012.