Onsager's Cross Coupling Effects in Gas Flows Confined to Micro-channels

TL;DR

This paper investigates cross coupling effects in gas flows within micro-channels using the unified gas-kinetic scheme, confirming Onsager's reciprocal relations and exploring optimal conditions for Knudsen pump design.

Contribution

It provides numerical validation of Onsager's reciprocal relations in micro-channel gas flows and explores the effects of channel geometry and Knudsen number on cross coupling effects.

Findings

Good agreement with literature for planar channels.

Confirmation of theoretical predictions in slip regime.

Maximization of off-diagonal coefficients in transition regime.

Abstract

In rarefied gases, mass and heat transport processes interfere with each other, leading to the mechano-caloric effect and thermo-osmotic effect, which are of interest to both theoretical study and practical applications. We employ the unified gas-kinetic scheme to investigate these cross coupling effects in gas flows in micro-channels. Our numerical simulations cover channels of planar surfaces and also channels of ratchet surfaces, with Onsager's reciprocal relation verified for both cases. For channels of planar surfaces, simulations are performed in a wide range of Knudsen number and our numerical results show good agreement with the literature results. For channels of ratchet surfaces, simulations are performed for both the slip and transition regimes and our numerical results not only confirm the theoretical prediction [Phys. Rev. Lett. 107, 164502 (2011)] for Knudsen number in the slip regime but also show that the off-diagonal kinetic coefficients for cross coupling effects are maximized at a Knudsen number in the transition regime. Finally, a preliminary optimization study is carried out for the geometry of Knudsen pump based on channels of ratchet surfaces.