Fokker-Planck model for binary mixtures

TL;DR

This paper extends the Fokker-Planck model to binary gas mixtures, demonstrating it satisfies conservation laws and the H-theorem, providing a new approach for modeling collision dynamics in dilute gases.

Contribution

The authors develop a binary mixture Fokker-Planck model that applies over a wide range of Schmidt numbers, extending previous single-component models.

Findings

Model satisfies conservation laws.

Model adheres to the H-theorem.

Applicable over a large range of Schmidt numbers.

Abstract

In dilute gas kinetic theory, model collision dynamics such as Bhatnagar-Gross-Krook (BGK) model is often used to get a better insight and numerical modelling. BGK model and its variants assume that highly nonlinear collision term can be replaced by a simple relaxation dynamics towards Maxwell-Boltzmann distribution. Lebowitz et al., proposed an alternative framework for the collision model, known as Fokker-Planck model, where the relaxation of an arbitrary distribution towards Maxwell-Boltzmann distribution is modelled as a drift-diffusion process in velocity space. In the present manuscript, we extend the single component Fokker-Planck model to a binary gas mixture model over a large range of Schmidt numbers. We prove that these mixture models satisfy the necessary conservation laws and the H-theorem.