Exact Non-Local Hydrodynamics Predict Rarefaction Effects

TL;DR

This paper develops an exact non-local hydrodynamic model derived from kinetic theory, accurately predicting rarefaction effects like Couette flow and thermal creep, by combining spectral closure with Maxwell boundary conditions.

Contribution

It introduces a novel non-local hydrodynamics framework that incorporates arbitrary accommodation, providing explicit solutions and accurately capturing rarefaction phenomena.

Findings

Accurately predicts Couette flow and thermal creep effects.

Provides explicit steady state solutions for shear-mode dynamics.

Demonstrates the model's effectiveness in capturing rarefaction effects.

Abstract

We combine the theory of slow spectral closure for linearized Boltzmann equations with Maxwell's kinetic boundary conditions to derive non-local hydrodynamics with arbitrary accommodation. Focusing on shear-mode dynamics, we obtain explicit steady state solutions in terms of Fourier integrals and closed-form expressions for the mean flow and the stress. We demonstrate that the exact non-local fluid model correctly predicts several rarefaction effects with accommodation, including the Couette flow and thermal creep in a plane channel.