An experimental study of pressure distribution nonlinearity in a circular micro-tube

Abstract

This paper presents an optical absorption method for determining the magnitude of pressure distribution nonlinearity in gas flowing through a circular micro-tube, based on the technique of tunable diode laser absorption spectroscopy (TDLAS), and its application to quantify the dependence on pressure ratio and rarefaction of the nonlinearity of such pressure distributions. This technique has the advantages of straightforward deployment and non-intrusive measurement, avoiding the complex fabrication of embedded mechanical sensors inside microfluidic devices used in previous studies. A dimensionless nonlinearity quantity is defined to examine the deviation of the pressure profile from a linear profile. The nonlinearity is measured for different pressure ratios between inlet and outlet. We also operate the system in a regime where the influence of pressure ratio on the nonlinearity is constant, in order to unambiguously quantify the nonlinearity as a function of mean Knudsen number (Kn). It is found that increased rarefaction changes the pressure profile from convex to linear. Our measurements were conducted over a range of mean Kn of gas flow from 0.02 to 6.6, covering the slip flow regime (0.01 < Kn < 0.1) and the bulk of the transition flow regime (0.1 < Kn < 10), extending the lower limit of pressure compared with previous investigations of pressure profiles in micron-scale channels. Furthermore, it is shown that existing theoretical models provide differing predictions of the spatial pressure profile, and this disagreement becomes significant in the transition and free molecule regimes. In particular, except for the continuum regime and the early slip regime, the existing models have not been experimentally verified, due to the lack of available experimental data. In this paper, the existing models are examined based on our experiments from the slip regime (Kn = 0.02) to the near free molecule regime (Kn = 6.6), with detailed discussions provided. Moreover, an empirical correlation is proposed that characterizes the nonlinearity as a function of both Knudsen number and pressure ratio. With this correlation, one can predict the nonlinearity of the pressure profile at a given inlet/outlet pressure condition.