Contents lists available at ScienceDirect Vacuum journal homepage: www.elsevier.com/locate/vacuum Inﬂuence of quantum intermolecular interaction on internal ﬂows of rareﬁed gases Felix Sharipov Departamento de Física, Universidade Federal do Paraná, Curitiba, 81531-980, Brazil ARTICLE INFO Keywords: Quantum scattering Oriﬁce ﬂow Direct simulation Monte Carlo ab initio potential ABSTRACT In order to model gaseous ﬂows over the whole temperature range beginning from 1 K, the intermolecular interaction should be considered on the basis of quantum approach. Such a consideration becomes important in case of light gases like helium and hydrogen. Recently, the direct simulation Monte Carlo (DSMC) method widely used to calculate ﬂows of gases has been generalized to implement the quantum approach to intermolecular collisions. To evaluate the inﬂuence of the quantum scattering on typical ﬂows of light gases, a benchmark problem has been solved for two helium isotopes 3 He and 4 He using an ab initio potential. More speciﬁcally, the ﬂow-rate and ﬂow-ﬁeld of helium ﬂowing through an oriﬁce have been calculated over the temperature range from 1 K to 300 K for various values of the pressure ratio with the numerical error of 0.5%. As expected, no inﬂuence of the quantum eﬀects on the ﬂow-rate has been detected for the temperature 300 K. Though, the quantum approach requires less computational eﬀort than the classical one at this temperature. For temperatures lower than 300 K, the inﬂuence of the quantum eﬀects exceed the numerical error and reaches 41% at the temperature of 3 K. In this case, the quantum interaction is the only approach to model gas ﬂows. 1. Introduction The direct simulation Monte Carlo (DSMC) method [1] is widely used to calculate rareﬁed gas ﬂows in vacuum systems, microsystems, around space vehicles, etc. The open codes SPARTA [2] and FOAM [3] based on this method became a widespread tool used in many tech- nological ﬁelds. An essential part of this method is a simulation of in- termolecular collisions that requires a physical potential in order to obtain reliable results. Recently, the DSMC method has been general- ized to an arbitrary potential [4] using the phenomenological Lennard- Jones potential as an example. Along with phenomenological potentials containing some adjustable parameters, the generalization of the DSMC method allowed us to apply ab initio (AI) potentials [5], which are free from such parameters. Nowadays, the ab initio potentials are available in the open literature, see e.g. Refs. [6–13], practically for all noble gases and their mixtures Thus, the DSMC method based on AI potential [5] became free from adjustable parameters and was used to study the inﬂuence of the interatomic potential on various phenomena in rareﬁed gases [14–18]. In all these works, the intermolecular interaction was considered basing on the classical mechanics which is well justiﬁed at high temperatures for heavy gases. As is known [19–25], the interaction of light gases, e.g. helium, hydrogen, at low relative velocity is not classical any more so that the quantum eﬀects must be considered. In the previous paper [26], it was shown that the classical interaction applied to transport phenomena through helium at low temperatures leads to a signiﬁcant error of heat ﬂux and shear stress. The aim of the present paper is to evaluate the inﬂuence of quantum eﬀects in a benchmark problem of vacuum gas dynamics [27]. More speciﬁcally, we are interested in quantum eﬀects only in interatomic iterations. Other eﬀects, like high densities at low temperatures when the interatomic distance is comparable to the de Broglie wavelength, are disregarded here. The benchmark problem considered here is a rareﬁed gas ﬂow through a thin oriﬁce [28], which is solved for both quantum and classical approaches to intermolecular collisions. It is pointed out the temperature range where the classical approach fails and the quantum theory becomes an unique alternative to calculate gas ﬂows. This is important in many technologies such as cryogenic pumps [29,30], cryogenic systems used in the huge fusion reactor ITER [31,32], monochromatic beams of helium [33,34], acoustic thermo- metry at a low temperature [35,36], experimental set-up to measure the neutrino mass [37,38], etc. A comparison of computational eﬀort of both approaches shows that the quantum scattering requires less computational time in comparison with the classical approach at high temperatures. Thus, it is suggested to apply the quantum scattering for the whole range of the temperature. https://doi.org/10.1016/j.vacuum.2018.07.022 Received 28 May 2018; Received in revised form 27 June 2018; Accepted 15 July 2018 E-mail address: sharipov@ﬁsica.ufpr.br. URL: http://ﬁsica.ufpr.br/sharipov. Vacuum 156 (2018) 146–153 Available online 18 July 2018 0042-207X/ © 2018 Elsevier Ltd. All rights reserved. T