Modeling Gaseous Flows Through Micro- and Nano-Channels

The overall object of this paper is a systematic study of gaseous flows in two-dimensional micro- and nano-channels in terms of the effects of compressibility, rarefaction, and surface roughness which are usually neglected in conventional flow analysis, using direct simulation Monte Carlo (DSMC) method. The flows are mainly in slip and transition regimes that are often encountered in Microelectromechanical Systems (MEMS), Nanoelectromechanical Systems (NEMS), and other microscale devices in diverse fields like molecular biology, space propulsion, and particle physics. For the effect of compressibility, two flows with same outlet Knudsen number (Kn) but different pressure drop ratios (case1:1.3, case2: 4.5) were simulated. It was found that high pressure drop flow (case2) show a 15% higher friction coefficient than that of a fully developed flow while the low pressure drop flow (case1) is consistent with incompressible flow prediction. The inspection for the velocity profile development shows that when pressures drop increase along the channel, the center-line velocity become flatten and the velocity gradients near the wall are higher compared with parabolic velocity profile. The effect of rarefaction was studied by simulating two nitrogen flows with low-pressure drop ratio (= 1.9) but different Kn numbers. (case3: 0.043, case4: 0.083). The pressure distribution, velocity profile, local friction coefficient are checked. The comparison with continuum flow theory (fRe = 24.0) shows that the rarefactions reduce the friction coefficient by 22% and 36% for case3 and case4, respectively. Apparent velocity slips along the channel wall exist for these flows. A locally fully developed model based on local velocity slip and fully developed assumptions predicts the friction coefficient accurately but fails in transition region where the Kn is over 0.1. Two important ratios are investigated for surface roughness effect in micro- and nano-channel flows: relative roughness and distribution of roughness. The DSMC results show that the surface roughness has more profound effect for a lower Kn number microchannel flow. The roughness distribution also plays a very important role in microchannel flows. The denser the roughness distribution, the higher friction coefficient. The future work will focus on flows in free-molecular flow regime and three-dimension geometries.