Chapter 2 - Single-Phase Gas Flow in Microchannels

Abstract

This chapter gives an overview of the specific properties of gas flows at microscale. In microchannels, the Knudsen number, which represents the ratio of the mean free path of gas molecules over the hydraulic diameter, is non-negligible and leads to rarefaction effects. The increase in the Knudsen number results in a local thermodynamic disequilibrium, first encountered close to the walls. In the so-called Knudsen layer, nonlinear phenomena occur: a velocity slip and a temperature jump are observed between the wall and the gas. In addition, for the smallest microchannels, the continuum approach becomes inappropriate, and a molecular approach can be necessary, as introduced in Section 2.1. When dimensions decrease, rarefaction effects increase and different flow regimes (slip flow, transition, and free molecular regimes) should be considered. These regimes are detailed in Section 2.2, with the main approaches and numerical tools available for their description. The models for pressure-driven steady gas flows in microchannels are then developed in Section 2.3, considering different possible cross-sections, with a focus on the slip flow regime, which is the most frequent regime in microchannels. Unsteady gas flows aspects in this regime are also briefly described in Section 2.4. Thermally driven gas microflows and their promising applications for vacuum generation are discussed in Section 2.5, and an introduction to convective heat transfer is proposed in Section 2.6, showing the antagonist roles played by the velocity slip and the temperature jump at the wall. A few practical exercises and problems conclude the chapter and help the reader to familiarize with the modeling of heat transfer and fluid flow in rarefied gas microflows.