Thermal Segregation Beyond Navier-Stokes

TL;DR

This paper develops an exact kinetic theory framework for dilute impurity suspensions in gases, revealing conditions for thermal segregation beyond traditional Navier-Stokes predictions.

Contribution

It introduces a scaling form for distribution functions enabling exact hydrodynamic field determination without small gradient restrictions.

Findings

Identifies thermal diffusion factors as functions of particle properties and temperature gradients.

Derives conditions for impurity segregation along and opposite the temperature gradient.

Shows segregation occurs beyond Navier-Stokes hydrodynamics, which predicts none.

Abstract

A dilute suspension of impurities in a low density gas is described by the Boltzmann and Boltzman-Lorentz kinetic theory. Scaling forms for the species distribution functions allow an exact determination of the hydrodynamic fields, without restriction to small thermal gradients or Navier-Stokes hydrodynamics. The thermal diffusion factor characterizing sedimentation is identified in terms of collision integrals as functions of the mechanical properties of the particles and the temperature gradient. An evaluation of the collision integrals using Sonine polynomial approximations is discussed. Conditions for segregation both along and opposite the temperature gradient are found, in contrast to the Navier-Stokes description for which no segregation occurs.