Modeling dissipative processes in open and closed hydrodynamic systems
- Authors: Rudyak V.Y.1,2
-
Affiliations:
- Novosibirsk State University of Architecture and Civil Engineering
- Siberian Federal University
- Issue: Vol 89, No 5 (2025)
- Pages: 825-842
- Section: Articles
- URL: https://rjsocmed.com/0032-8235/article/view/696416
- DOI: https://doi.org/10.7868/S3034575825050091
- ID: 696416
Cite item
Abstract
In this paper, the modeling of transport processes in both closed and open hydrodynamic systems is discussed. The main focus is on reviewing the relevant mechanisms. It is shown that in weakly nonequilibrium systems, dissipative processes are caused by microscopic thermal molecular fluctuations, and their irreversibility is associated with the non-potential nature of intermolecular interactions. In open hydrodynamic systems the rheology of the fluid changes at sufficiently high shear rates. The nature of these changes is demonstrated using molecular dynamics simulations. It is established that with increasing shear rate, both simple liquid and nanofluids become pseudoplastic. In the latter case, the critical shear rate of rheology change depends on the concentration of nanoparticles and their size. However, at sufficiently high shear rates, dissipative processes cease to depend on the sizes of the internal structural elements of the medium. Its viscosity drops sharply. In all cases, the change in the rheology of the medium is associated with the transformation of its structure. In particular, with the degradation of the short-range order.
About the authors
V. Ya. Rudyak
Novosibirsk State University of Architecture and Civil Engineering; Siberian Federal University
Email: valery.rudyak@mail.ru
Novosibirsk, Russia; Novosibirsk, Russia
References
- Loitsyanskii L.G. Mechanics of liquids and gases. Oxford–N.-Y.: Pergamon Press, 1966. 804 p. https://doi.org/10.1016/C2013-0-05328-5
- Loitsyansky L.G., Lurie A.I. Course of theoretical mechanics. V. 2. Dynamics. Moscow: Nauka, 1984. 604 p. (In Russian).
- Batchelor G.K. An introduction to fluid dynamics. Cambridge: University Press, 2012. 615 p. https://doi.org/10.1017/CBO9780511800955
- Landau L.D., Lifshits E.M. Fluid mechanics. Elsiver, 2013. 558 p. https://doi.org/10.1016/C2013-0-03799-1
- Sedov L.I. A course in continuum mechanics. Wolters-Noordhoff, 1971. 305 p. https://lib.ugent.be/catalog/rug01:002004556
- De Groot S., Mazur P. Nonequilibrium thermodynamics. Courier Corporation, 2013. 528 p.
- Arnold V.I. Mathematical methods of classical mechanics. Springer-Verlag New York Inc., 1989. 511 p. https://doi.org/10.1007/978-1-4757-2063-1
- Rudyak V.Ya. Statistical aerohydromechanics of homogeneous and heterogeneous media. Vol. 1. Kinetic theory. Novosibirsk: NSUACE, 2004. 320 p. (In Russian)
- Buckingham E., Clavier P., Rein R. et al. Intermolecular interactions: from diatomics to biopolymers. New York: Pullman Wiley-Interscience, 1978. 447 p.
- Sinai Ya.G. Dynamical systems. Collection of papers. Singapore: World Scientific, 1991. 673 p.
- Zaslavskiy G.M. Stochasticity of dynamical system. Moscow: Science Press, 1984. 271 p.
- Lichtenberg A., Lieberman M. Regular and stochastic dynamics. New York: Springer, 2010. 692 p.
- Zubarev D. Nonequilibrium statistical thermodynamics. New York: Consultants Bureau, 1974. 489 p.
- Zubarev D., Morozov V., Repke G. Statistical mechanics of nonequilibrium processes. V. 1. Wiley, 1996. 375 p.
- Klimontovich Yu.L. Statistical theory of open systems // Fundamental Theories of Physics, 1994, vol. 67. https://doi.org/10.1007/978-94-011-0175-2
- Kadomtsev B.B. Dynamics and information. Moscow: Physics-Uspekhi, 1999. 397 p. (In Russian).
- Chapman S. Cowling T.G. The Mathematical theory of non-uniform gases. Cambridge: University Press. 1990. 423 p.
- Burnett D. The distribution of molecular velocities in a slightly non-uniform gas // Proc. London Math. Soc. 1935, vol. 30, no. 6, pp. 385–430.
- Allen M.P., Tildesley D.J. Computer simulation of liquids. Oxford: University Press, 2017. 640 p.
- Chandler D. Introduction to modern statistical mechanics. Oxford: University Press, 1987. 286 p.
- Rudyak V. Ya. Statistical aerohydromechanics of homogeneous and heterogeneous media. Vol. 2, Hydromechanics. Novosibirsk: NSUACE, 2005. 468 p.
- Kubo R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems // J. Phys. Soc. Japan, 1957, vol. 12, no. 6, pp. 570–584. https://doi.org/10.1143/JPSJ.12.570
- Kubo R., Yokota M., Nakajima S. Statistical-mechanical theory of irreversible processes. II. Reaction on thermal disturbances // J. Phys. Soc. Japan, 1957, vol. 12, no. 11, pp. 1203–1226. https://doi.org/10.1143/JPSJ.12.1203
- Green H.S. Theories of transport in fluids // J. Math. Phys., 1961, vol. 2, no. 2, pp. 344–348. https://doi.org/10.1063/1.1703720
- Lebowitz J.L. Hamiltonian flows and rigorous results in non-equilibrium statistical mechanics // Statistical mechanics, new concepts, new problems, new applications. Proc. of I.U.P.A.P. Conf. on Statistical Mech. Chicago: University Press, 1971, pp. 41–66.
- Résibois P., De Leener M. Classical kinetic theory of fluids. N.Y., London: Wiley-Interscience, 1977. 412 p.
- Ernst M.H. Formal theory of transport coefficients to general order in the density // Physica, 1966, vol. 32, no. 2, pp. 209–243. https://doi.org/10.1016/0031-8914(66)90055-3
- 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 Math. Phys., 1970, vol. 5, pp. 1029–1037.
- Thompson A.P., Aktulga H.M., Berger R. et al. LAMMPS — A flexible simulation tool for particle-based materials modelling at the atomic, meso, and continuum scales // Comp. Phys. Comm., 2022, vol. 271, pp. 108171. https://doi.org/10.1016/j.cpc.2021.108171
- Lide D.R. (ed.) Handbook of chemistry and physics. CRC, 2010. 2760 p.
- Bird R.B., Armstrong R.C., Hassager O. Dynamics of polymeric liquids. V.1. Fluid mechanics. New York: Wiley, 1987. 649 p.
- Tanner R.I., Walters K. Rheology: an historical perspective. Amsterdam: Elsevier, 1998. 255 p.
- Chhabra R.P., Richardson J.F. Non-Newtonian flow and applied rheology. Oxford: Butterworth-Heinemann, 2008. 536 p. https://doi.org/10.1016/B978-0-7506-8532-0.X0001-7
- Mewis J., Wagner N.J. Colloidal suspension rheology. Cambridge: University Press, 2011. 393 p. https://doi.org/10.1017/CBO9780511977978
- Maxwell J.C. A treatise on electricity and magnetism. Oxford: Clarendon Press, 1881. 528 p. https://doi.org/treatiseonelectr01maxwrich
- Einstein A. Eine neue Bestimmung der Moleküldimensionen // Ann. Phys., 1906, vol. 324, pp. 289–306. https://doi.org/10.1002/andp.19063240204
- Minakov A.V., Rudyak V.Yа., Pryazhnikov M.I. Rheological behavior of water and ethylene glycol based nanofluids with oxide nanoparticles// Colloids& Surfaces A: Physicochem.&Engin. Aspects, 2018, vol. 554, pp. 279–285. https://doi.org/10.1016/j.colsurfa.2018.06.051
- Rudyak V.Ya. Thermophysical characteristics of nanofluids and transport process mechanisms // J. Nanofluids, 2019, vol. 8, pp. 1–16. https://doi.org/10.1166/jon.2019.1561
- Rudyak V., Minakov A., Pryazhnikov M. Preparation, characterization, and viscosity studding the single-walled carbon nanotube nanofluid // J. Molecular Liquids, 2021, vol. 329, pp. 115517. https://doi.org/10.1016/j.molliq.2021.115517
- Rudyak V.Ya., Dashapilov G.R., Minakov A.V. et al. Comparative characteristics of viscosity and rheology of nanofluids with multi-walled and single-walled carbon nanotubes // Diamond Related Mat., 2023, vol. 132, pp. 109616. https://doi.org/10.1016/j.diamond.2022.109616
- Rudyak V.Ya., Minakov A.V., Pryazhnikov M.I. Rheology and thermal conductivity of nanofluids with carbon nanotubes // Adv. Material Sci Research, 2022, vol. 66, pp. 1–92.
- Rudyak V.Ya., Krasnolutsky S.L. Diffusion of nanoparticles in a rarefied gas // Tech. Phys., 2002, vol. 47, pp. 807–813.
- Rudyak V.Ya., Krasnolutskii S.L., Ivanov D.A. The interaction potential of nanoparticles // Doklady Physics, 2012, vol. 57, pp. 33–35.
- Stuart S.J., Tutein A.B., Harrison J.A. A reactive potential for hydrocarbons with intermolecular interactions // J. Chem. Phys., 2000, vol. 112, no. 14, pp. 6472–6486. https://doi.org/10.1063/1.481208
- Batchelor G.K. The effect of Brownian motion on the bulk stress in a suspension of spherical particles // J. Fluid Mech., 1977, vol. 83, no.01, pp. 97–117. https://doi.org/10.1017/S0022112077001062
- Minakov A.V., Rudyak V.Ya., Pryazhnikov M.I. Systematic experimental study of the viscosity of nanofluids // Heat Transfer Eng., 2020, vol. 42, no. 10, pp. 1–17. https://doi.org/10.1080/01457632.2020.1766250
- Montroll E.V. On the statistical mechanics of transfer processes // Thermodynamics of irreversible processes. M.: IL, 1962. pp. 233–283.
- Lattinger J.M. Theory of thermal transport coefficients // Phys. Rev. A., 1964, vol. 135, no. 6, pp. 1505–1514.
- Rudyak V.Y., Belkin A.A., Ivanov D.A., et al. The simulation of transport processes using the method of molecular dynamics. Self-diffusion coefficient // High Temp., 2008, vol. 46, pp. 30–39.
- Rudyak V. Diffusion of nanoparticles in gases and liquids // Handbook of Nanoparticles, 2016, pp. 1–21. https://doi.org/10.1007/978-3-319-13188-7_54-1
- Belkin A., Rudyak V., Krasnolutskii S. Molecular dynamics simulation of carbon nanotubes diffusion in water // Mol. Simulation, 2022,vol. 48, no. 9, pp. 752–759. https://doi.org/10.1080/08927022.2022.2053119
- Ikeshoji T., Hafskjold B. Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface // Mol. Phys., 1994, vol. 81, no. 2, pp. 51–261. https://doi.org/10.1080/00268979400100171
- Evans D.J., Morris G.P. Statistical mechanics of nonequilibrium liquids. Canberra: Australian National University, 2007. 296 p. https://doi.org/10.1016/C2013-0-10633-2
- Muller-Plathe F., A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity // J. Chem. Phys., 1997, vol. 106, no. 14, pp. 6082–6085. https://doi.org/10.1063/1.473271
- Jabbari F., Rajabpour A., Saedodin S. Thermal conductivity and viscosity of nanofluids: A review of recent molecular dynamics studies // Chem. Eng. Sci., 2017, vol. 174, pp. 67–81. https://doi.org/10.1016/j.ces.2017.08.034
- Rudyak V.Yа., Pryazhnikov M.I., Minakov A.V. et al. Comparison of thermal conductivity of nanofluids with single-walled and multi-walled carbon nanotubes // Diamond Related Mat., 2023, vol. 139, pp. 110376.
Supplementary files




