This article continues our cycle devoted to comprehensive investigation of the diatomic molecule collision process. In this paper, we focus particularly on the in-depth study of the rotational–translational (R–T) energy exchange process and Borgnakke–Larsen (BL) energy exchange model used in the direct simulation Monte Carlo method. The present study, which was performed on several levels of description (molecular, microscopic, and macroscopic), is based mainly on the highly detailed dataset (around 1011 configurations) of binary N2–N2 collisions, obtained via the classical trajectory calculation (CTC) method. This dataset, along with the explicit mathematical representation of the Borgnakke–Larsen model derived in the present paper, allowed us to obtain new results regarding the R–T energy exchange process: (1) we present an ab initio method to derive physically accurate expressions for inelastic collision probability pr in the BL model directly from CTC data; (2) we present a new two-parametric model for pr and compared it to the previously known models, including the recent nonequilibrium-direction-dependent model of Zhang et al. [“Nonequilibrium-direction-dependent rotational energy model for use in continuum and stochastic molecular simulation,” AIAA J. 52(3), 604 (2014)]; (3) it showed that apart from the well-known dependence of the rotational relaxation rate on “direction to equilibrium” (ratio between translational and rotational temperatures), on molecular scale, rotationally over-excited molecule pairs demonstrate almost zero energy transfer to the translational energy mode (even in the case of very significant discrepancies between translational and rotational energies); (4) it was also shown that the Borgnakke–Larsen approach itself may require reassessment since it fails to give a proper description of distribution of post-collision energies. Throughout this paper, we also tried to put together and analyze the existing works studying the rotational relaxation process and estimating the rotational collision number Zrot by performing reviews and assessment of (1) numerical approaches to simulate non-equilibrium problems, (2) models for inelastic collision probabilities pr, (3) approaches to estimate Zrot, and (4) intermolecular potentials used for molecular dynamics and CTC simulations. The corresponding conclusions are given in this paper.
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February 2021
Research Article|
February 22 2021
A detailed multiscale study of rotational–translational relaxation process of diatomic molecules
Special Collection:
Advances in Micro/Nano Fluid Flows: In Memory of Prof. Jason Reese
Vasily Kosyanchuk
;
Vasily Kosyanchuk
a)
1
Laboratory of Nanomechanics, Institute of Mechanics of Lomonosov Moscow State University
, Michurinskyi Avenue 1, Moscow 119192, Russia
2
Department of Mathematics and Mechanics, Lomonosov Moscow State University
, Leninskye Gory 1, Moscow 119991, Russia
3
Mechanical Engineering Research Institute of the Russian Academy of Sciences
, Maly Kharitonyevsky Pereulok 4, Moscow 101990, Russia
a)Author to whom correspondence should be addressed: [email protected]
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Artem Yakunchikov
Artem Yakunchikov
1
Laboratory of Nanomechanics, Institute of Mechanics of Lomonosov Moscow State University
, Michurinskyi Avenue 1, Moscow 119192, Russia
2
Department of Mathematics and Mechanics, Lomonosov Moscow State University
, Leninskye Gory 1, Moscow 119991, Russia
3
Mechanical Engineering Research Institute of the Russian Academy of Sciences
, Maly Kharitonyevsky Pereulok 4, Moscow 101990, Russia
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
Note: This paper is part of the Special Topic, Advances in Micro/Nano Fluid Flows: In Memory of Prof. Jason Reese.
Physics of Fluids 33, 022003 (2021)
Article history
Received:
November 13 2020
Accepted:
December 29 2020
Citation
Vasily Kosyanchuk, Artem Yakunchikov; A detailed multiscale study of rotational–translational relaxation process of diatomic molecules. Physics of Fluids 1 February 2021; 33 (2): 022003. https://doi.org/10.1063/5.0037335
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