A phase transition model for the helium supercooling

Article type: Research Article

Authors: Bonetti, Elena^; | Frémond, Michel

Affiliations: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy. E-mail: elena.bonetti@unipv.it | Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133 Roma, Italy. E-mail: michel.fremond@uniroma2.it

Note: [] Corresponding author. E-mail: elena.bonetti@unipv.it

Abstract: We build a predictive theory for the evolution of mixture of helium and supercooled helium at low temperature. The absolute temperature θ and the volume fraction β of helium, which is dominant at temperature larger than the phase change temperature, are the state quantities. The predictive theory accounts for local interactions at the microscopic level, involving the gradient of β. The nonlinear heat flux in the supercooled phase results from a Norton–Hoff potential. We prove that the resulting set of partial differential equations has solutions within a convenient analytical frame.

Keywords: supercooled helium, phase change, predictive theory, existence theorem

DOI: 10.3233/ASY-131195

Journal: Asymptotic Analysis, vol. 87, no. 1-2, pp. 29-42, 2014