Non-Newtonian Couette-Poiseuille flow of a dilute gas

TL;DR

This paper analytically investigates the non-Newtonian behavior of dilute gas Couette-Poiseuille flow under external forces using the BGK model, revealing transitional temperature profiles and comparing with classical Navier-Stokes solutions.

Contribution

It provides an analytical solution to the BGK kinetic equation for Couette-Poiseuille flow, exploring effects of external forces and transition of temperature profiles beyond Navier-Stokes predictions.

Findings

Transition from bimodal to parabolic temperature profiles

Analytical solutions up to second order in force

Comparison with Navier-Stokes highlights non-Newtonian effects

Abstract

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.