A phase transition model for the helium supercooling

TL;DR

This paper develops a predictive phase transition model for helium and supercooled helium, incorporating microscopic interactions and nonlinear heat flux, with proven existence of solutions to the governing PDEs.

Contribution

It introduces a novel mathematical framework for modeling helium supercooling, including microscopic interactions and nonlinear heat flux, with analytical proof of solution existence.

Findings

The model accurately predicts the evolution of helium mixtures at low temperatures.

Mathematical analysis confirms the well-posedness of the PDE system.

The theory captures local microscopic interactions affecting phase transition dynamics.

Abstract

We build a predictive theory for the evolution of mixture of helium and supercooled helium at low temperature. The absolute temperature and the volume fraction 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 $\beta$. 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.