A Diffusion Model for Rarefied Flows in Curved Channels

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 (Bhatnagar–Gross–Krook) 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 micropumping 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 out 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 nowadays is still prohibitive for such cases.