Thermophoresis and uniform flow in rarefied polyatomic gases: The role of constitutive relations and boundary conditions

Abstract

Recently, Rana and Barve [“A second-order constitutive theory for polyatomic gases: Theory and applications,” J. Fluid Mech. 958, A23 (2023)] developed a second-order coupled constitutive relations (CCR) for polyatomic gases that include quadratic nonlinearities in the entropy flux and apply the second law. However, in that work, the boundary conditions were heuristically obtained to match the drag coefficient on a sphere and may not be accurate in situations where thermal transpiration and thermal stress are significant factors, as indicated by their asymptotic analysis. This article presents a systematic approach for deriving thermodynamically admissible boundary conditions for the CCR model. We also propose a set of higher-order boundary conditions based on an asymptotic analysis of the solutions for drag on flow past a sphere and thermophoretic drag. The goal of deriving these boundary conditions is to improve the accuracy of the CCR model when applied to external flows, such as slow flow past particles and thermophoretic motion of a spherical particle and doublet. The results of the study demonstrate that the combination of the newly derived boundary conditions in conjunction with the CCR equations shows excellent agreement with both theoretical predictions and experimental data over a wide range of Knudsen numbers. The study suggests that the approach presented in this article can be used to improve the accuracy of the CCR model in a variety of external flow applications.