The study of evaporation and condensation should include consideration of heat and mass transfer processes inside the liquid, in the inter-phase transition domain, in the Knudsen layer, and in the outer area. Possible way to realize it is to use the conjugate approach, in which the description of these regions is carried out employing a single computational method. This method allows us to consider the condensed phase and gas as a single system and use the solution of kinetic equations throughout the region. Currently, processes in the gas phase have been studied quite well. The greatest obstacle to the use of kinetic equations in the condensed phase is the description of collisions involving multiple particles at the same time. In this paper a procedure is proposed to take the multi-particulate interactions within the condensed phase into account. Such approach is applied to the test study of the thermal conductivity problem for argon, neon, xenon, and krypton. Values of thermal conductivity coefficients for different quantities of interacting particles have been obtained. The comparison with corresponding experimental data is presented. Thus, the integral of paired collisions in the Boltzmann kinetic equation can be replaced by the proposed computational procedure. This approach provides a description of both liquid and gas at the level of the distribution function and ensures that the conditions at the interface are set correctly.
| Published in | American Journal of Physics and Applications (Volume 9, Issue 5) |
| DOI | 10.11648/j.ajpa.20210905.13 |
| Page(s) | 116-120 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
Boltzmann Equation, Interface Phenomena, Joint Solution
| [1] | A. Frezzotti and P. Barbante. Simulation of shock induced vapor condensation flows in the Lennard-Jones fluid by microscopic and continuum models. Phys. Fluids 32, 2020, 122106. |
| [2] | P. Barbante and A. Frezzotti. A comparison of models for the evaporation of the Lennard-Jones fluid. Eur. J. Mech.: B/Fluids 64, 2017, pp. 69–80. |
| [3] | M. Kon, K. Kobayashi, and M. Watanabe. Method of determining kinetic boundary conditions in net evaporation/condensation. Phys. Fluids 26, 2014, 072003. |
| [4] | M. Kon, K. Kobayashi, M. Watanabe, Liquid temperature dependence of kinetic boundary condition at vapor-liquid interface. Int. J. Heat Mass Transfer 99, 2016, pp. 317–326. |
| [5] | S. Busuioc, L. Gibelli, D. A. Lockerby, and J. E. Sprittles. Velocity distribution function on spontaneously evaporating atoms. Phys. Rev. Fluids 5, 2020, 103401. |
| [6] | Shishkova I. N., Kryukov A. P., Levashov V. Yu. Study of evaporation–condensation problems: from liquid through interface surface to vapor. International Journal of Heat and Mass Transfer. V. 112, 2017, pp. 926-932. |
| [7] | V. Ya. Rudyak. Statistical theory of dissipative processes in gases and liquids. Novosibirsk. 1987 (in Russian). |
| [8] | A. A. Tsykalo, M. M. Kontsov. Study of the effect of three-particle non-additive interactions on the thermodynamic properties of dense gases and liquids. Journal of Technical Physics. T. 47, No. 12, 1977, pp. 2601-2607 (in Russian). |
| [9] | Shishkova I. N., Kryukov A. P., Levashov V. Y. Vapour–liquid jointed solution for the evaporation–condensation problem. International Journal of Heat and Mass Transfer. Vol. 141, 2019, pp. 9–19. |
| [10] | I. N. Shishkova, A. P. Kryukov and V. Yu. Levashov. Joint liquid-vapor approach development at solution of different heat and mass transfer problems. Journal of Physics: Conference Series. ICFEPT 2019, 2019, 1370: 012019. doi: 10.1088/1742-6596/1370/1/012019 |
| [11] | F. G. Tcheremissine, Discrete approximation and examples of solutions of the Boltzmann equation, in: Computational Dynamics of Rarefied Gas, Computer Center of the Russian Academy of Sciences, 2000, pp. 37–74. |
| [12] | I. N. Shishkova, S. S. Sazhin, J. -F. Xie. A solution of the Boltzmann equation in the presence of inelastic collisions. J. Computational Physics. V. 232, 2013, pp. 87-99. |
| [13] | V. V. Zhakhovsky, A. P. Kryukov, V. Yu. Levashov, I. N. Shishkova, S. I. Anisimov Mass and heat transfer between evaporation and condensation surfaces: Atomic simulation and solution of Boltzmann kinetic equation. Proceedings of the National Academy of Sciences, PNAS April 16, 2018. 201714503; published ahead of print April 16. https://doi.org/10.1073/pnas. 1714503115 or Proc. Nat. Acad. Sci. 116 18209, 2019. |
| [14] | M. N. Kogan, Rarefied Gas Dynamics, Plenum, New York, 1969. |
| [15] | NIST-JANAF Thermochemical Tables. https://janaf.nist.gov/. |
APA Style
Irina Shishkova, Alexei Kryukov. (2021). Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems. American Journal of Physics and Applications, 9(5), 116-120. https://doi.org/10.11648/j.ajpa.20210905.13
ACS Style
Irina Shishkova; Alexei Kryukov. Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems. Am. J. Phys. Appl. 2021, 9(5), 116-120. doi: 10.11648/j.ajpa.20210905.13
AMA Style
Irina Shishkova, Alexei Kryukov. Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems. Am J Phys Appl. 2021;9(5):116-120. doi: 10.11648/j.ajpa.20210905.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajpa.20210905.13,
author = {Irina Shishkova and Alexei Kryukov},
title = {Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems},
journal = {American Journal of Physics and Applications},
volume = {9},
number = {5},
pages = {116-120},
doi = {10.11648/j.ajpa.20210905.13},
url = {https://doi.org/10.11648/j.ajpa.20210905.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20210905.13},
abstract = {The study of evaporation and condensation should include consideration of heat and mass transfer processes inside the liquid, in the inter-phase transition domain, in the Knudsen layer, and in the outer area. Possible way to realize it is to use the conjugate approach, in which the description of these regions is carried out employing a single computational method. This method allows us to consider the condensed phase and gas as a single system and use the solution of kinetic equations throughout the region. Currently, processes in the gas phase have been studied quite well. The greatest obstacle to the use of kinetic equations in the condensed phase is the description of collisions involving multiple particles at the same time. In this paper a procedure is proposed to take the multi-particulate interactions within the condensed phase into account. Such approach is applied to the test study of the thermal conductivity problem for argon, neon, xenon, and krypton. Values of thermal conductivity coefficients for different quantities of interacting particles have been obtained. The comparison with corresponding experimental data is presented. Thus, the integral of paired collisions in the Boltzmann kinetic equation can be replaced by the proposed computational procedure. This approach provides a description of both liquid and gas at the level of the distribution function and ensures that the conditions at the interface are set correctly.},
year = {2021}
}
TY - JOUR T1 - Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems AU - Irina Shishkova AU - Alexei Kryukov Y1 - 2021/09/30 PY - 2021 N1 - https://doi.org/10.11648/j.ajpa.20210905.13 DO - 10.11648/j.ajpa.20210905.13 T2 - American Journal of Physics and Applications JF - American Journal of Physics and Applications JO - American Journal of Physics and Applications SP - 116 EP - 120 PB - Science Publishing Group SN - 2330-4308 UR - https://doi.org/10.11648/j.ajpa.20210905.13 AB - The study of evaporation and condensation should include consideration of heat and mass transfer processes inside the liquid, in the inter-phase transition domain, in the Knudsen layer, and in the outer area. Possible way to realize it is to use the conjugate approach, in which the description of these regions is carried out employing a single computational method. This method allows us to consider the condensed phase and gas as a single system and use the solution of kinetic equations throughout the region. Currently, processes in the gas phase have been studied quite well. The greatest obstacle to the use of kinetic equations in the condensed phase is the description of collisions involving multiple particles at the same time. In this paper a procedure is proposed to take the multi-particulate interactions within the condensed phase into account. Such approach is applied to the test study of the thermal conductivity problem for argon, neon, xenon, and krypton. Values of thermal conductivity coefficients for different quantities of interacting particles have been obtained. The comparison with corresponding experimental data is presented. Thus, the integral of paired collisions in the Boltzmann kinetic equation can be replaced by the proposed computational procedure. This approach provides a description of both liquid and gas at the level of the distribution function and ensures that the conditions at the interface are set correctly. VL - 9 IS - 5 ER -
Email: