Skip to main content
Article thumbnail
Location of Repository


By K. Aoki, P. Degond, L. Mieussens, S. Takata and H. Yoshida


Abstract. In this paper, we derive a one-dimensional convection-diffusion model for a rarefied gas flow in a two-dimensional curved channel on the basis of the Boltzmann (BGK) model. The flow is driven by the temperature gradient along the channel walls, which is known as the thermal creep phenomenon. This device can be used as a micro-pumping system without any moving part. Our derivation is based on the asymptotic technique of the diffusion approximation. It gives a macroscopic (fluid) approximation of the microscopic (kinetic) equation. We also derive the connection conditions at the junction where the curvature is not continuous. The pumping device is simulated by using a numerical approximation of our convection-diffusion model which turns to agree very well with full two dimensional kinetic simulations. It is then used to obtain very fast computations on long pumping devices, while the computational cost of full kinetic computations is still nowadays prohibitive for such cases. Key words. Boltzmann equation, rarefied gas flows, diffusion approximation, convectiondiffusion model, Knudsen compressor, thermal creep flow AMS subject classifications. 76P05, 82B40, 41A60, 76R05, 82C80, 65M06

Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.