Skip to main content
Log in

Description of the Operation of a Biochemical Reactor by a Diffusion Model

  • Published:
Theoretical Foundations of Chemical Engineering Aims and scope Submit manuscript

Abstract

The operation of an unsteady-state well-stirred flow-through biochemical reactor is studied. Nonlinear boundary-value problems describing the operation of such reactors are considered. Nontrivial solutions under homogeneous boundary conditions are sought. The analysis is based on the equations of the diffusion model. The switch of the operating modes of the reactors in the case of several solutions of the equations of the process is analyzed.

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.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. Gordin, V.A., Differential and Difference Equations: Which Phenomena They Describe and How To Solve Them: A Textbook, Moscow: Izd. Dom Vysshei shkoly ekonomiki, 2016.

  2. Trubetskov, D.I., Introduction to Synergetics: Chaos and Structures, Moscow: Editorial URSS, 2004.

    Google Scholar 

  3. Svirezhev, Yu.M., Nonlinear Waves, Dissipative Structures, and Catastrophes in Ecology, Moscow: Nauka, 1987.

    Google Scholar 

  4. Alekseev, Yu.K. and Sukhorukov, A.P., Introduction to Catastrophe Theory: A Textbook, Moscow: Knizhnyi dom “Librokom”, 2009.

  5. Cole, J.D., Perturbation Methods in Applied Mathematics, Waltham, Mass., USA: Ginn-Blaisdell, 1968.

    Google Scholar 

  6. Nayfeh, A.H., Perturbation Methods, New York: Wiley, 1976.

    Google Scholar 

  7. Arnol’d, V.I., Ordinary Differential Equations, Moscow: Nauka, 1984.

    Google Scholar 

  8. Arnol’d, V.I., Hard and Soft Mathematical Models, Moscow: MTsNMO, 2013.

  9. Moshinskii, A.I., Modeling of Heat- and Mass-Transfer Processes Based on Generalized Diffusion Equations, Moscow: KNORUS, 2019.

    Google Scholar 

  10. Kafarov, V.V., Vinarov, A.Yu., and Gordeev, L.S., Modeling of Biochemical Reactors, Moscow: Lesnaya promyshlennost', 1979.

  11. Moshinskii, A.I., Description of steady-state operation of a biochemical reactor by a diffusion model, Inzh.-Fiz. Zh., 2017, vol. 90, no. 4, p. 814.

    Google Scholar 

  12. Moshinskii, A.I., On the effect of relaxation processes on the stability of steady-state modes of operation of an isothermal flow-through chemical reactor, Inzh.-Fiz. Zh., 1991, vol. 61, no. 1, p. 129.

    CAS  Google Scholar 

  13. Berman, V.S., Kurdyumov, V.N., and Ryazantsev, Yu.S., On the stability of steady-state modes of operation of an isothermal flow-through chemical reactor, Izv. Akad, Nauk SSSR, Ser. Mekh. Zhidk. Gaza, 1985, no. 2, p. 179.

  14. Buchin, V.A. and Larin, O.B., Stabilization of unstable modes of operation of a plug-flow chemical reactor, Dokl. Akad. Nauk SSSR, 1983, vol. 271, no. 6, p. 1440.

    CAS  Google Scholar 

  15. Modern Numerical Methods for Ordinary Differential Equations, Hall, G. and Watt, J.M., Eds., London, UK: Clarendon, 1976.

    Google Scholar 

  16. Aris, R., Elementary Chemical Reactor Analysis, Hoboken, N. J.: Prentice–Hall, 1965.

    Google Scholar 

  17. Polyanin, A.D., Al’vares-Suares, V.A., Dil’man, V.V., and Ryazantsev, Yu.S., Method of asymptotic interpolation of experimental data, Teor. Osn. Khim. Tekhnol., 1986, vol. 20, no. 5, p. 584.

    CAS  Google Scholar 

  18. Dil'man, V.V. and Polyanin, A.D., Methods of Model Equations and Analogy in Chemical Engineering, Moscow: Khimiya, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Yu. Aleksandrova.

Additional information

Translated by V. Glyanchenko

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aleksandrova, L.Y., Moshinskii, A.I. Description of the Operation of a Biochemical Reactor by a Diffusion Model. Theor Found Chem Eng 56, 271–278 (2022). https://doi.org/10.1134/S0040579522030022

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040579522030022

Keywords:

Navigation