Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes

Abstract

International audienceHelium mass flow rates in a microchannel were measured, for a wide Knudsen-number range, in isothermal steady conditions. The flow Knudsen numbers, considered here, cover the range from continuum slip regime to the near free molecular regime. We used a single-channel system involved in an experimental platform more powerful than those previously used. The experimental errors and uncertainties were accurately investigated and estimated. In the continuum slip regime, it was found that the first-order approach is pertinent for Knudsen number between 0.03 and 0.3. Moreover, the slip coefficient was deduced by comparing the experiments with the theoretical first-order slip continuum approach. For Knudsen number between 0.03 and 0.7, a polynomial second-power form is proposed for the mass flow rate expression. Otherwise, the experimental results on the mass flow rate were compared with theoretical values calculated from kinetic approaches over the 0.03–50 Knudsen number range, and an overall agreement appears through the comparison. It was also found, when the Knudsen number increased, that the wall influence on measurement occurred first through the accommodation process in the transition regime followed by the wall influence through the aspect ratio in the free molecular regime

A novel experimental setup for gas microflows

“…Ewart et al studied the flow of monatomic gases through rectangular microchannels with a low-aspect ratio a* = 2% (Ewart 2007;Ewart et al 2007). With such an aspect ratio, the flow is close to a 2-D flow between parallel plates.…”

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

“…Therefore, extensive experimental and theoretical works have been conducted (see Knudsen (1909); Edmonds & Hobson (1965); Porodnov et al (1974Porodnov et al ( , 1978; Ewart et al (2007); RojasCárdenas et al (2013); Yamaguchi et al (2014Yamaguchi et al ( , 2016; Sharipov (2011) and references therein) to quantify the influence of gas-surface interaction and test the applicability of the BC: most of the time, the Maxwell model is tested (Porodnov et al 1978;Ewart et al 2007;Yamaguchi et al 2016), and the Cercignani-Lampis model is checked for a few cases (Cercignani & Lampis 1971;Sharipov 2003b). The use of the Maxwell model is not satisfactory, since in Poiseuille flow it has been seen that the TMAC has to be adjusted at different range of the rarefaction parameter (Ewart et al 2007), while in thermal transpiration flow (Yamaguchi et al 2014(Yamaguchi et al , 2016) neither the Maxwell model nor the Cercignani-Lampis model can recover the MFR and thermomolecular pressure difference (TPD, a parameter indicating the performance of the Knudsen pump) exponent simultaneously, see § 5.1 below.…”

Isothermal micro-channel gas flow using a hydrodynamic model with dissipative mass flux

“…Knudsen's experimental work in the transition flow regime [2] revealed that there is a minimum in the normalized mass flow rate G [4]. This is referred to as the Knudsen paradox in the literature, as the classical Navier-Stokes solution with no-slip boundary conditions fail to predict this phenomenon.…”

“…Behaviour of isothermal rarefied gases can be described by the Boltzmann equation [3], and the mass flow rate over the full range of Knudsen number predicted [4]. However, solution methods require an assumption on the local pressure that does not allow an investigation of the actual pressure profile [3,4].…”