A kinetic model for rarefied flows of molecular gas with vibrational modes

TL;DR

This paper introduces a kinetic model for rarefied molecular gas flows with vibrational modes, capturing energy exchange and relaxation processes, validated by simulations, and revealing potential for micro-device applications.

Contribution

A new kinetic model that accounts for vibrational modes and intermolecular potential effects, validated against simulations, and used to study thermally-induced flows and forces.

Findings

The model accurately predicts transport coefficients and relaxation processes.

Intermolecular potential significantly affects velocity and Knudsen force.

Knudsen force can reverse direction depending on the viscosity index.

Abstract

A kinetic model is proposed for rarefied flows of molecular gas with rotational and temperature-dependent vibrational degrees of freedom. The model reduces to the Boltzmann equation for monatomic gas when the energy exchange between the translational and internal modes is absent, thus the influence of intermolecular potential can be captured. Moreover, not only the transport coefficients but also their fundamental relaxation processes are recovered. The accuracy of our kinetic model is validated by the direct simulation Monte Carlo method in several rarefied gas flows, including the shock wave, Fourier flow, Couette flow, and the creep flow driven by Maxwell's demon. Then the kinetic model is adopted to investigate thermally-induced flows. By adjusting the viscosity index in the Boltzmann collision operator, we find that the intermolecular potential significantly influences the velocity and Knudsen force. Interestingly, in the transition flow regime, the Knudsen force exerting on a heated beam could reverse the direction when the viscosity index changes from 0.5 (hard-sphere gas) to 1 (Maxwell gas). This discovery is useful in the design of micro-electromechanical systems for microstructure actuation and gas sensing.