Kinetic calculation of rarefied gaseous flows in long tapered rectangular microchannels

Abstract

Gaseous flows in microsystems have attracted considerable attention in fluid dynamic communities over the last few years. When the size of the device is in the range of microns, the molecular mean free path becomes comparable with the device size, and the details of the molecular interactions need to be taken into account. The proper description of such microflows requires the consideration of the velocity distribution function of the molecules and kinetic equations. The scope of the present paper is to discuss the determination of the behavior of pressure driven rarefied gas flows in microchannels at the kinetic level. As a new application of the methodology, preliminary results are presented for pressure driven flows of single gases through long rectangular tapered microchannels, which have constant widths but varying depths along the axis of the channel. The kinetic calculation is based on the solution of the linearized Bhatnagar-Gross- Krook (BGK) equation and refers to the determination of the mass flow rate through the channel and the axial distribution of the pressure. The BGK equation is solved by the discrete velocity method. It is shown that the mass flow rate exhibits the diodicity effect, which means that the flow rate depends on the orientation of the channel. If the gas flows from the larger cross section towards the smaller one, the flow rate is larger than in the opposite situation. The pressure profile strongly varies near the small cross section, and it has a quite different character than in the case of channels with uniform cross sections. The tapered microchannel might be useful for separating the different gaseous components in engineering applications.