A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures

TL;DR

This paper formally derives a coupled Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures, providing a simplified model for steady spray dynamics.

Contribution

It introduces a derivation of the thin spray equation coupling a kinetic Vlasov type equation with a steady Stokes equation from Boltzmann equations.

Findings

Derivation of the coupled Vlasov-Stokes system from Boltzmann equations.

Formal connection between kinetic theory and fluid dynamics for aerosols.

Extension of previous methods to steady gas flow scenarios.

Abstract

In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.