A Simple Kinetic Model for the Phase Transition of the van der Waals Fluid

作者：Takata Shigeru^*; Noguchi Takashi

来源：Journal of Statistical Physics, 2018, 172(3): 880-903.

DOI：10.1007/s10955-018-2068-z

• Boltzmann equation
• Kinetic theory for non-ideal gases
• Phase transitions
• Nonlinear dynamics

A simple kinetic model, which is presumably minimum, for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas has not been treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined from the equation of state for the van der Waals fluid, with the aid of the balance equation of momentum, (ii) a functional which monotonically decreases in time is identified by the H theorem and is found to have a close relation to the Helmholtz free energy in thermodynamics, and (iii) the Cahn-Hilliard type equation is obtained in the continuum limit of the present kinetic model. Numerical simulations based on the Cahn-Hilliard type equation are also performed.

• 出版日期2018-8