Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium

TL;DR

This paper extends a simple kinetic model for phase transition to analyze the stability of uniform states and investigates transition processes, revealing that incomplete transitions can occur alongside clear phase transitions.

Contribution

It clarifies the stability of equilibrium states in kinetic regimes and explores transition dynamics using linear stability analysis and numerical simulations.

Findings

Neutral stability curve is invariant with respect to Knudsen number

Transition process depends on Knudsen number

Incomplete transitions can occur alongside clear phase transitions

Abstract

This is a continuation of the previous work (Takata & Noguchi, J. Stat. Phys., 2018) that introduces the presumably simplest model of kinetic theory for phase transition. Here, main concern is to clarify the stability of uniform equilibrium states in the kinetic regime, rather than that in the continuum limit. It is found by the linear stability analysis that the linear neutral curve is invariant with respect to the Knudsen number, though the transition process is dependent on the Knudsen number. In addition, numerical computations of the (nonlinear) kinetic model are performed to investigate the transition processes in detail. Numerical results show that (unexpected) incomplete transitions may happen as well as clear phase transitions.