Mass flow rate measurement of thermal creep flow from transitional to slip flow regime

Abstract

The measurements of the thermal creep flow through a single rectangular micro channel connected to two tanks maintained initially at the same pressure, but at different temperatures, is carried out for five noble gas species, in a large pressure variation range and for two temperature differences between the tanks. The time dependent pressure variations in both cold and hot tanks are investigated, and the temperature driven (thermal creep) mass flow rate between two tanks is calculated from these data for the rarefaction parameter ranging from the transitional to slip flow regime. The measured mass flow rate is compared with the numerical solution of the S-model kinetic equation, showing good agreement with each other. A novel approximative expression to calculate the temperature driven mass flow rate in the transitional and slip flow regimes is proposed. This expression provides the results in good agreement with the measured values of the mass flow rate. In the slip flow regime, the thermal slip coefficient is calculated by employing the previously reported methodology, and the influence of the gas nature on this coefficient is investigated. The measured values of the thermal slip coefficient agree well with the values available in the literature, indicating that this coefficient is independent of the shape of a channel.

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

“…The performance of various gas-surface BCs are compared for Poiseuille and thermal transpiration flows between two infinite parallel plates, and for flows through pipes with rectangular or circular cross sections, where several experimental data are available (Yamaguchi et al 2014(Yamaguchi et al , 2016Ewart et al 2007;Rojas-Cárdenas et al 2013). We emphasis that the MFR in both Poiseuille and thermal transpiration flows are measured for the same gas and solid surface interactions simultaneously, which provide ideal and strict test cases to the kinetic BCs.…”

“…Consider the thermal transpiration of helium through a long rectangular channel made of polyether ether ketone (Yamaguchi et al 2014(Yamaguchi et al , 2016, where the aspect ratio of the rectangular cross section is 27.27. For such a large aspect ratio, the numerical simulation based on the Shakhov kinetic model revealed that, when δ 0.5, there is no difference in the dimensionless flow rates for flows through two infinite parallel plates and rectangular cross sections (Graur & Ho 2014).…”

“…The Epstein BC allows more flexibility to choose the velocity slip coefficients and should be able to give better agreement to the experiment. To demonstrate this, we choose the effective thermal slip coefficient ω to be the experimental measured value (Yamaguchi et al 2016). To achieve this, we choose α = β in (2.10) for simplicity.…”

“…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.…”

“…It is the purpose of this paper to assess the accuracy of various gas-surface BCs, in particular the overlooked Epstein model, and develop a new BC if necessary, by comparing the numerical solution of the Boltzmann equation to recent sound and reliable experiments of Poiseuille and thermal transpiration flows (Ewart et al 2007;Rojas-Cárdenas et al 2013;Yamaguchi et al 2014Yamaguchi et al , 2016. Especially, in thermal transpiration flows, the MFR and TPD exponent have been measured using the same gas and solid surface, which provides an ideal and strict case to test the BCs.…”