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Generalization of the bimodal impact wave model to shock compression of gas mixtures

https://doi.org/10.18384/2949-5067-2026-1-38-45

Abstract

Aim: to modify the well-known analytical bimodal model of the Tamm – Mott-Smith shock wave for the case of shock compression of a binary gas mixture.

Methods. Asymptotic and approximation methods of mathematical physics were used.

Results. An analytical nonlinear single-parameter model has been developed for the structure of a shock-compressed binary gas mixture, where, in particular, the classical Tamm-Mott-Smith distribution parameter is used as a parameter.

Research implications: The proposed generalization of the classical bimodal shock wave model to the case of a binary gas mixture retains its simplicity and convenience for use in solving theoretical problems and in gas-dynamic experiments.

About the Authors

M. M. Kuznetsov
Federal State University of Education
Russian Federation

Mihail M. Kuznetsov  – Dr. Sci. (Phys.-Math.), Prof., Department of Fundamental Physics and Nanotechnology

Moscow



D. G. Satyukov
Federal State University of Education
Russian Federation

Dmitry G. Satyukov – Postgraduate student, Department of Fundamental Physics and Nanotechnology

Moscow



Yu. D. Kuleshova
Federal State University of Education
Russian Federation

Juliya D. Kuleshova – Cand. Sci. (Phys.-Math.), Assoc. Prof., Department of Higher Algebra, Mathematical Analysis and Geometry

Moscow



E. Ya. Vladimirova
Federal State University of Education
Russian Federation

Elena Ya. Vladimirova – Postgraduate student, Department of Fundamental Physics and Nanotechnology

Moscow



G. V. Kuznetsov
Federal State University of Education
Russian Federation

Gleb V. Kuznetsov – Postgraduate student, Department of Fundamental Physics and Nanotechnology

Moscow



R. F. Khalikov
Federal State University of Education
Russian Federation

Ruslan F. Halikov – Postgraduate student, Department of Fundamental Physics and Nanotechnology

Moscow



References

1. Tanenbaum, B. S. & MacDonald, R. S. (1966). Comments on “Kinetic-theory approach to the problem of shock-wave strukture in a binary mixture”. In: The Physics of Fluids, 9 (5), 1048–1049. DOI: 10.1063/1.1761772/.

2. Fujimoto, T. (1965). Shock-Wave Structure in Binary Gas Mixtures with No Chemical Reaction. In: Rarefied Gas Dynamics. Vol. 1: Proceedings of the Fourth International Symposium held at the Institute for Aerospace Studies (Toronto, 1964). New York: Academic Press, pp. 223–239.

3. Bratos, M. & Herczynski, R. (1983). Shock waves in noble gases and their mixtures. In: Archives of Mechanics (Archiwum Mechaniki Stosowanej), 35 (2), 215–239.

4. Kuznetsov, M. M., Kuznetsov, G. V., Parenkina, V. I., Satyukov, D. G. & Khalikov, R. F. (2023). Analytical models of translationally nonequilibrium dynamics of shockcompressed binary gas mixtures. In: Bulletin of the Federal State University of Education. Series: Physics and Mathematics, 4, 34–48. DOI: 10.18384/2949-5067-2023-4-34-48 (in Russ.).

5. Kuznetsov, M. M., Kuleshova, Yu. D. & Satyukov, D. G. (2024). Analytical models of translationally nonequilibrium dynamics of shock-compressed binary gas mixtures. In: Bulletin of the Federal State University of Education. Series: Physics and Mathematics, 3, 50–57. DOI: 10.18384/2949-5067-2024-3-50-57 (in Russ.).

6. Kuznetsov, M. M., Satyukov, D. G., Kuleshova, Yu. D., Vladimirova, E. Ya., Kuznetsov, G. V. & Khalikov, R. F. (2025). Analytical properties of distribution functions for relative velocities of molecules in a shock-compressed binary mixture of gases. In: Bulletin of the Federal State University of Education. Series: Physics and Mathematics, 1, 52–65. DOI: 10.18384/2949-5067- 2025-1-52-65.

7. Kogan, M. N. (1967). Dynamics of a rare gas (Kinetic Theory). Moscow: Nauka publ. (in Russ.).

8. Cherchignani, K. (1978). Theory and applications of the Boltzmann equation. Moscow: Mir publ. (in Russ.).


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ISSN 2949-5083 (Print)
ISSN 2949-5067 (Online)