Interdisciplinary Applied Mathematics

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carbon dioxide in contact with prime silicon crystal in the slip and early transitional flow regime (0 < Kn < 0.4). It is observed that av is less than unity, and independent of Kn in that range (Arkilic, 1997; Arkilic et al., 2001). Lower accommodation coefficients are possible due to the low surface roughness of prime silicon crystal.


(Maurer et al., 2003) presented experimental results for helium and nitrogen flow in 1.14 pm deep 200 pm wide glass channel covered by an atomically flat silicon surface. Flow behavior in the slip and early transition regimes was investigated for channel-averaged Knudsen numbers of 0.8 and 0.6 for helium and nitrogen flows, respectively. Using the flowrate data and a second-order slip model represented by equation (2.42), TMAC values of 0.91±0.03 for helium, and 0.87±0.06 for nitrogen were obtained. The authors also estimated the upper limit of slip flow regime as Kn = 0.3±0.1, where Kn is based on the channel height. In a separate study, (Colin et al., 2004) presented experimental results for nitrogen and helium flow in a series of silicon microchannels fabricated using deep reactive ion etching (DRIE). Using mass flowrate and the corresponding pressure drop data, and the second-order slip model by (Deissler, 1964), they reported TMAC values of 0.93 for both helium and nitrogen. These authors reported breakdown of the first-order slip model for Kn > 0.05, and of the second-order theory of Deissler for Kn > 0.25, where Kn was based on the channel depth. These limits are unusually low compared to the values commonly accepted in the literature. A comparison between the experiments of (Colin et al., 2004) and (Maurer et al., 2003) shows that the uncertainty in the channel depth was ±0.1 pm for Colin’s channels, where it was 0.02 pm for Maurer’s channels. In addition, the fabrication methods and the channel aspect ratios in these studies were different. These are certainly some of the reasons for the differences between the measurements of TMAC values by these two groups.

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