Skip to main content
Log in

Reaction Rates in a Deformable Solid in Terms of the Thermodynamics of Irreversible Processes

  • Published:
Russian Physics Journal Aims and scope

Based on the thermodynamics of irreversible processes, the relationship between the reaction rate in a deformable solid and the stresses is demonstrated without introducing any additional hypotheses. Well known procedures of accounting for the dependence of the reaction rate on the structure are described. A possible generalization of the classical models by extending the thermodynamics is presented. An example of a transition from the continuum modeling to a two-level modeling is given, which makes it possible to establish a relationship between the parameters affecting the reaction rate at different scale levels. A similar approach can be applied to any scalar process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Th. De Donder and P. Van Rysselberghe, Thermodynamic Theory of Affinity. A Book of Principles, Stanford University Press, Stanford (1936).

    Google Scholar 

  2. Miloslav Pekâ, Z. Naturforsch. A, 64, 289 (2009).

    Article  Google Scholar 

  3. Miloslav Pekâ, Helvetica Chimica Acta, 90, 1897 (2007).

    Article  Google Scholar 

  4. Juan Qui´lez, Science & Education, 18, 1203 (2009).

  5. Masahiro Nabeshima, J. Nucl. Sci. Technol., 31, No. 4, 1084 (1994).

    Article  Google Scholar 

  6. Kaspar Loeffel and Lallit Anand, Int. J. Plasticity, 27, 1409 (2011).

    Article  Google Scholar 

  7. Gaёlle Rambert, Jean-Claude Grandidier, and Elias C.Aifantis, Eur. J. Mech. A/Solid, 26, 68 (2007).

    Article  ADS  Google Scholar 

  8. A. B. Freidin, Mech. Solids, 50, No. 3, 260 (2015).

    Article  ADS  Google Scholar 

  9. J. Fort, J. Casas-Va´zquez, V. Méndez, J. Phys. Chem. B, 103, No. 5, 860 (1999).

  10. S. I. Serdyukov, Entropy, 20, Paper 802 (2018).

  11. A. N. Gorban, E. M. Mirkes, and G. S. Yablonsky, Physica A, 392, 1318 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  12. E. Veveakis, S. Alevizos, and I. Vardoulakis, J. Mech. Phys. Solids, 58, 1175 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  13. S. K. Godunov, Elements of Continuum Mechanics [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  14. I. Prigogine and R. Defay, Chemical Thermodynamics, Longmans, Green (1954).

    Google Scholar 

  15. A. G. Knyazeva, J. Appl. Mech. Tech. Physics, 40, No. 6, 1088 (1999).

    Article  ADS  Google Scholar 

  16. I. Diarmati, Nonequilibrium Dynamics. Field Theory and Variational Principles [in Russian], Moscow, Mir (1974).

  17. K. P. Gurov, Phenomenological Thermodynamics of Irreversible Processes [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  18. B. Delmon, Kinetics of Heterogenous Reactions [in Russian], Moscow, Mir (1972).

    Google Scholar 

  19. Yu. D. Tretyakov, Solid-Phase Reactions [in Russian], Khimiya, Moscow (1978).

    Google Scholar 

  20. A. P. Aldushin, A. G. Merzhanov, and B. I. Khaikin, Dokl. Akad. Nauk USSR, 204, No. 5, 1139 (1972).

    Google Scholar 

  21. A. P. Aldushin, T. M. Martemianova, A. G. Merzhanov, et al., Combustion, Explosion and Shock Waves, 8, No. 2, 159 (1972).

    Google Scholar 

  22. A. G. Knyazeva and O. N. Kryukova, Appl. Solid State Chem., No. 3, 32 (2019).

    Google Scholar 

  23. M. F. Horstemeyer and D. J. Bammann, Int. J. Plasticity, 26, 1310 (2010).

    Article  Google Scholar 

  24. G. A. Maugin and W. Muschik, J. Non-Equilib. Thermodyn., 19, No. 3, 217 (1994).

    Google Scholar 

  25. G. A. Maugin and W. Muschik, J. Non-Equilib. Thermodyn., 19, No. 3, 250 (1994).

    Google Scholar 

  26. C. Papenfuss and W. Muschik, Entropy, 20, No. 1, Paper 81 (2018).

  27. P. Van, A. Berezovski, and J. Engelbrecht, J. Non-Equilib. Thermodyn, 33, No. 3, 235 (2008).

  28. J. Engelbrecht and A. Berezovski, J. Mech. Mater. Struct., 7, No. 10, 983 (2012).

    Article  Google Scholar 

  29. Yu. V. Solovieva, L. A. Valuyskaya, Ya. D. Lipatnikova, and V. A. Starenchenko, Russ. Phys. J., 62, No. 12 2240 (2020).

  30. A. G. Knyazeva, Chemistry for Sustainable Development, 10, No. 1–2, 57 (2002).

    Google Scholar 

  31. A. G. Knyazeva, J. Non-Equilib. Thermodyn., 45, No. 4, 401 (2020).

    Google Scholar 

  32. A. G. Knyazeva, Vestnik PermGTU. Mekhanika, No. 4, 88 (2011).

    Google Scholar 

  33. E. A. Dyukarev and A. G. Knyazeva, Combustion, Explosion and Shock Waves 34, No. 5, 556 (1998).

  34. P. V. Trusov, A. I. Shveikin, E. S. Nechaeva, and P. S. Volegov, Phys. Mesomech., 15, Iss. 3–4, 155 (2012).

  35. P. V. Trusov and N. S. Kondratyev, Phys. Mesomech., 22, No. 3, 230 (2019).

    Article  Google Scholar 

  36. O. B. Kovalev and V. A. Neronov, Combustion, Explosion and Shock Waves, 40, No. 2, 172 (2004).

  37. E. A. Nekrasov, Yu. M. Maksimov, and A. P. Aldushin, Combustion, Explosion and Shock Waves, 16, No. 3, 342 (1980).

  38. Florence Baras and Dilip Kondepudi, J. Phys. Chem. B, 111, 6457 (2007).

    Article  Google Scholar 

  39. A. Maslov, O. Kryukova, and N. Bukrin, AIP Conf. Proc., 2051, 020188 (2018).

    Google Scholar 

  40. Roy A. B. Engelen, Marc G. D. Geers, and Frank P. T. Baaijens, Int. J. Plasticity, 19, 403 (2003). and

  41. Nikolaos Aravas and Ioanna Papadioti, J. Mech. Phys. Solids, 146, 104190 (2021).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Knyazeva.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 111–116, October, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Knyazeva, A.G. Reaction Rates in a Deformable Solid in Terms of the Thermodynamics of Irreversible Processes. Russ Phys J 64, 1907–1914 (2022). https://doi.org/10.1007/s11182-022-02540-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-022-02540-5

Keywords

Navigation