najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-422Research ArticlePHYSICSФИЗИКАStochastic molecular modeling the transport coefficients of rarefied gas and gas nanosuspensionsRudyakV. Ya.

Leningradskaya, 113, Novosibirsk

Pirogova, 1, Novosibirsk

valery.rudyak@mail.ruLezhnevE. V.

Leningradskaya, 113, Novosibirsk

lionlev@yandex.ruNovosibirsk State University of Architecture and Civil Engineering; Novosibirsk State UniversityRussian FederationNovosibirsk State University of Architecture and Civil EngineeringRussian Federation202030072025113285–293Copyright © Rudyak V.Y., Lezhnev E.V., 20252025Rudyak V.Y., Lezhnev E.V.Rudyak V.Y., Lezhnev E.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/422

The subject of this paper is the stochastic molecular modelling of the transport coefficients for rarefied gases and gas nanosuspensions. The proposed method is an alternative one to the molecular dynamics method. However, unlike the latter, the phase trajectories of the molecular system are simulated stochastically. Adequate integral characteristics of the studied system are obtained by averaging the calculated data over independent phase trajectories. The efficiency of the proposed algorithm is demonstrated by calculation of the diffusion and viscosity coefficients of several noble and polyatomic gases and rarefied gas nanosuspensions. The modeling accuracy increases when a greater number of molecules and phase trajectories are employed.

diffusiongas nanosuspensionrarefied gasstochastic molecular simulationtransport processestransport coefficientsviscosityThis work is partially supported by the Russian Foundation for Basic Research (grant No. 20-01-00041).ReferencesChapman S., Cowling T.G. The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, Cambridge, 1990, 423 p.Chapman S., Cowling T.G. The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, Cambridge, 1990, 423 p.Hirschfelder J.O., Curtiss Ch.F., Bird R. B. Molecular Theory of Gases and Liquids, John Wiley and Sons, Inc. Chapman and Hall, Lim., 1954, 1219 p.Hirschfelder J.O., Curtiss Ch.F., Bird R. B. Molecular Theory of Gases and Liquids, John Wiley and Sons, Inc. Chapman and Hall, Lim., 1954, 1219 p.Ferziger J., Kaper H. Mathematical Theory of Transport Processes in Gases, North-Holland Publishing Company, Amsterdam–London, 1972, 546 p.Ferziger J., Kaper H. Mathematical Theory of Transport Processes in Gases, North-Holland Publishing Company, Amsterdam–London, 1972, 546 p.Rudyak V.Ya. Statistical Aerohydromechanics of Homogeneous and Heterogeneous Media. Vol. 2. Hydromechanics, NSUACE, Novosibirsk, 2005, 468 p.Rudyak V.Ya. Statistical Aerohydromechanics of Homogeneous and Heterogeneous Media. Vol. 2. Hydromechanics, NSUACE, Novosibirsk, 2005, 468 p.Norman G.E., Stegailov V.V. The stochastic properties of a molecular dynamical Lennard-Jones system in equilibrium and nonequilibrium states. J. Exp. Theor. Phys., 2001, 92, P. 879–886.Norman G.E., Stegailov V.V. The stochastic properties of a molecular dynamical Lennard-Jones system in equilibrium and nonequilibrium states. J. Exp. Theor. Phys., 2001, 92, P. 879–886.Norman G.E., Stegailov V.V. Stochastic and dynamic properties of molecular dynamics systems: simple liquids, plasma and electrolytes, polymers. Comput. Phys. Commun., 2002, 147, P. 678–683.Norman G.E., Stegailov V.V. Stochastic and dynamic properties of molecular dynamics systems: simple liquids, plasma and electrolytes, polymers. Comput. Phys. Commun., 2002, 147, P. 678–683.Rudyak V.Ya., Lezhnev E.V. Stochastic method of the simulation of the rarefied gas transport coefficients. Math. Mod., 2017, 29, P. 113–122.Rudyak V.Ya., Lezhnev E.V. Stochastic method of the simulation of the rarefied gas transport coefficients. Math. Mod., 2017, 29, P. 113–122.Rudyak V.Ya., Lezhnev E.V. Stochastic algorithm for simulating gas transport coefficients. J. Computational Physics, 2018, 355, P. 95–103.Rudyak V.Ya., Lezhnev E.V. Stochastic algorithm for simulating gas transport coefficients. J. Computational Physics, 2018, 355, P. 95–103.Klimontovich Y. Kinetic Theory of Non-Ideal Gases and Non-Ideal Plasmas, Pergamon Press, Oxford, 1982, 314 p.Klimontovich Y. Kinetic Theory of Non-Ideal Gases and Non-Ideal Plasmas, Pergamon Press, Oxford, 1982, 314 p.Rudyak V.Ya. Statistical Theory of Dissipative Processes in Gases and Liquids, Science, Novosibirsk, 1987, 287 p.Rudyak V.Ya. Statistical Theory of Dissipative Processes in Gases and Liquids, Science, Novosibirsk, 1987, 287 p.Zubarev D.N. Nonequilibrium Statistical Thermodynamics, Consultants Bureau, New York, 1974, 371 p.Zubarev D.N. Nonequilibrium Statistical Thermodynamics, Consultants Bureau, New York, 1974, 371 p.Hoover W.G. Computational Statistical Mechanics, Elsevier, Amsterdam, 1991, 324 p.Hoover W.G. Computational Statistical Mechanics, Elsevier, Amsterdam, 1991, 324 p.Ernst M.H. Formal theory of transport coefficients to general order in the density. Physica, 1966, 32, P. 209–243.Ernst M.H. Formal theory of transport coefficients to general order in the density. Physica, 1966, 32, P. 209–243.Khon’kin A.D. Equations for space-time and time correlation functions and proof of the equivalence of results of the Chapman-Enskog and time correlation methods. Theoretical and Mathematical Phys., 1970, 5, P. 1029–1037.Khon’kin A.D. Equations for space-time and time correlation functions and proof of the equivalence of results of the Chapman-Enskog and time correlation methods. Theoretical and Mathematical Phys., 1970, 5, P. 1029–1037.Krishna R., Wesselingh J.A. The Maxwell-Stefan approach to mass transfer. Chemical Engineering Science, 1997, 52, 1997, P. 861–911.Krishna R., Wesselingh J.A. The Maxwell-Stefan approach to mass transfer. Chemical Engineering Science, 1997, 52, 1997, P. 861–911.Rudyak V.Ya., Belkin A.A., Ivanov D.A., Egorov V.V. The simulation of transport processes using the method of molecular dynamics. Selfdiffusion coefficient. High Temperature, 2008, 46(1), P. 30–39.Rudyak V.Ya., Belkin A.A., Ivanov D.A., Egorov V.V. The simulation of transport processes using the method of molecular dynamics. Selfdiffusion coefficient. High Temperature, 2008, 46(1), P. 30–39.Van Heijningen R.J.J., Harpe J.P., Beenakker J.M. Determination of the diffusion coefficients of binary mixtures of the noble gases as a function of temperature and concentration. Physica, 1968, 38, P. 1-34.Van Heijningen R.J.J., Harpe J.P., Beenakker J.M. Determination of the diffusion coefficients of binary mixtures of the noble gases as a function of temperature and concentration. Physica, 1968, 38, P. 1-34.Valander S.V., Nagnibeda E.A., Ridalevskaya M.A. Some Questions of the Kineticic Theory of Chemical Reacting Gas Mixure, LSU, Leningrad, 1977, 289 p.Valander S.V., Nagnibeda E.A., Ridalevskaya M.A. Some Questions of the Kineticic Theory of Chemical Reacting Gas Mixure, LSU, Leningrad, 1977, 289 p.Zhdanov V.M., Alievskii M.Ya. Transport Processes and Relaxation in Molecular Gases, Science, Moscow, 1989, 335 p.Zhdanov V.M., Alievskii M.Ya. Transport Processes and Relaxation in Molecular Gases, Science, Moscow, 1989, 335 p.Grigoriev I.S., Meilihova E.Z. Physical values. Handbook, Energoatomizdat, Moscow, 1991, 978 p.Grigoriev I.S., Meilihova E.Z. Physical values. Handbook, Energoatomizdat, Moscow, 1991, 978 p.Helfand E. Theory of molecular friction. Phys. Fluids, 1961, 4, P. 681–691.Helfand E. Theory of molecular friction. Phys. Fluids, 1961, 4, P. 681–691.Suddaby A., Gray P. Relation between the friction constant and the force correlation integral in Brownian movement theory. Proc. Phys. Soc., 1960, 75, P. 109–118.Suddaby A., Gray P. Relation between the friction constant and the force correlation integral in Brownian movement theory. Proc. Phys. Soc., 1960, 75, P. 109–118.Rudyak V. Basic kinetic equation of a rarefied gas. Fluid Dynamics, 1989, 24, 954-959.Rudyak V. Basic kinetic equation of a rarefied gas. Fluid Dynamics, 1989, 24, 954-959.Rudyak V. Correlations in a finite number of particles system simulating a rarefied gas. Fluid Dynamics, 1991, 26, P. 909–914.Rudyak V. Correlations in a finite number of particles system simulating a rarefied gas. Fluid Dynamics, 1991, 26, P. 909–914.Bird G., Molecular Gas Dynamics, Clarendon Press, 1976, Oxford. 302 p.Bird G., Molecular Gas Dynamics, Clarendon Press, 1976, Oxford. 302 p.Gimelshtein S.F., Rudyak V.Ya. Simulation of rarefied gas by the small number particles system. Sov. Tech.-Phys. Letters, 1991, 17, P. 74–77.Gimelshtein S.F., Rudyak V.Ya. Simulation of rarefied gas by the small number particles system. Sov. Tech.-Phys. Letters, 1991, 17, P. 74–77.Jabbari F., Rajabpour A., Saedodin S. Thermal conductivity and viscosity of nanofluids: a review of recent molecular dynamics studies. Chemical Engineering Sci, 2017, 17, P. 67–81.Jabbari F., Rajabpour A., Saedodin S. Thermal conductivity and viscosity of nanofluids: a review of recent molecular dynamics studies. Chemical Engineering Sci, 2017, 17, P. 67–81.Rudyak V.Ya., Krasnolutskii S.L. Diffusion of nanoparticles in a rarefied gas. Technical Physics, 2002, 47, P. 807–813.Rudyak V.Ya., Krasnolutskii S.L. Diffusion of nanoparticles in a rarefied gas. Technical Physics, 2002, 47, P. 807–813.Rudyak V.Ya., Krasnolutskii S.L. Kinetic description of nanoparticle diffusion in rarefied gas. Doklady Physics, 2001, 46, P. 897–899.Rudyak V.Ya., Krasnolutskii S.L. Kinetic description of nanoparticle diffusion in rarefied gas. Doklady Physics, 2001, 46, P. 897–899.Rudyak V.Ya., Krasnolutskii S.L., Nasibulin A.G., Kauppinen E.I. Methods of measuring the diffusion coefficient and sizes of nanoparticles in rarefied gas. Doklady Physics 2002, 47, P. 758–761.Rudyak V.Ya., Krasnolutskii S.L., Nasibulin A.G., Kauppinen E.I. Methods of measuring the diffusion coefficient and sizes of nanoparticles in rarefied gas. Doklady Physics 2002, 47, P. 758–761.Rudyak V.Ya., Krasnolutskii S.L., Ivanov D.A. The interaction potential of nanoparticles Doklady Physics, 2012, 57, P. 3335.Rudyak V.Ya., Krasnolutskii S.L., Ivanov D.A. The interaction potential of nanoparticles Doklady Physics, 2012, 57, P. 3335.Wang X-Q., Mujumdar A.S. A review on nanofluids – Part II: experiments and applications. Brazilian J. Chem. Eng., 2008, 25(4), P. 631–648.Wang X-Q., Mujumdar A.S. A review on nanofluids – Part II: experiments and applications. Brazilian J. Chem. Eng., 2008, 25(4), P. 631–648.Wong K.V., De Leon O. Applications of nanofluids: Current and future. Advances in Mech. Eng., 2010, 2, Article ID 519659.Wong K.V., De Leon O. Applications of nanofluids: Current and future. Advances in Mech. Eng., 2010, 2, Article ID 519659.Usoltseva L.O., Volkov D.S., Avramenko N.V., Korobov M.V., Proskurnin M.A. Nanodiamond aqueous dispersions as potential nanofluids: the determination of properties by thermal lensing and other techniques. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9(1), P. 17–20.Usoltseva L.O., Volkov D.S., Avramenko N.V., Korobov M.V., Proskurnin M.A. Nanodiamond aqueous dispersions as potential nanofluids: the determination of properties by thermal lensing and other techniques. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9(1), P. 17–20.Lari H., Morsali A., Heravi M.M. The prediction of COOH functionalized carbon nanotube application in melphalan drug delivery. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10(4), P. 438–446.Lari H., Morsali A., Heravi M.M. The prediction of COOH functionalized carbon nanotube application in melphalan drug delivery. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10(4), P. 438–446.Einstein A. Eine neue Bestimmung der Molekiildimensionen. Annalen der Physik, 1906, 19, P. 289–306.Einstein A. Eine neue Bestimmung der Molekiildimensionen. Annalen der Physik, 1906, 19, P. 289–306.Batchelor G.K. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 1977, 83, P. 97–117.Batchelor G.K. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 1977, 83, P. 97–117.Acrivos A. Chang E.Y. A model for estimating transport quantities in two-phase materials Phys. Fluids, 29 P. 459-464.Acrivos A. Chang E.Y. A model for estimating transport quantities in two-phase materials Phys. Fluids, 29 P. 459-464.Mooney M. The viscosity of a concentrated suspension of spherical particles J. Colloid Sci, 1951, 6-8, P. 162170.Mooney M. The viscosity of a concentrated suspension of spherical particles J. Colloid Sci, 1951, 6-8, P. 162170.Frankel N.A., Acrivos A. On the viscosity of a concentrated suspension of solid spheres Chem. Eng. Sci, 1967, 22, P. 847853.Frankel N.A., Acrivos A. On the viscosity of a concentrated suspension of solid spheres Chem. Eng. Sci, 1967, 22, P. 847853.Rudyak V.Ya., Minakov A.V. Thermophysical properties of nanofluids Eur. Phys. J. E, 2018, 41, P. 15.Rudyak V.Ya., Minakov A.V. Thermophysical properties of nanofluids Eur. Phys. J. E, 2018, 41, P. 15.Rudyak V.Ya. Thermophysical characteristics of nanofluids and transport process mechanisms. J. of Nanofluids, 2019, 8(1), P. 1-16.Rudyak V.Ya. Thermophysical characteristics of nanofluids and transport process mechanisms. J. of Nanofluids, 2019, 8(1), P. 1-16.Rudyak V.Ya., Krasnolutskii S.L. About viscosity of rarefied gas suspensions with nanoparticles. Doklady Physics, 2003, 48, P. 583–586.Rudyak V.Ya., Krasnolutskii S.L. About viscosity of rarefied gas suspensions with nanoparticles. Doklady Physics, 2003, 48, P. 583–586.Rudyak V.Ya., Krasnolutskii S.L. Effective viscosity coefficient for rarefied nano gas suspensions. Atmosphere and Ocean Optics, 2004, 17, P. 468–475.Rudyak V.Ya., Krasnolutskii S.L. Effective viscosity coefficient for rarefied nano gas suspensions. Atmosphere and Ocean Optics, 2004, 17, P. 468–475.

The authors declare that there are no conflicts of interest present.