Mathematical Models and Computer Simulations

, Volume 5, Issue 5, pp 429–438 | Cite as

Processes in the porous electrode: Case of distributed flow-through electrolyte velocity

  • A. N. Koshev
  • V. K. Varentsov
  • I. F. Sukhov
  • I. G. Gvozdeva


This article reports the development of a mathematical model of the electrochemical process in the flow-through three-dimensional electrode that takes into account changes in the electrolyte flow velocity in the local volume of the electrode that are influenced by the velocity of the process characteristics. Electrolyte flow rate, porosity, and the specific reaction surface of the electrode are regarded as functions of time and of the electrode coordinate. A set of algorithms and programs for model implementation has been developed. The processes of electrodeposition of copper on the cathodes of carbon graphite fiber materials with low and high conductivity, as well as with different initial electrolyte flow velocities have been calculated. The results of the calculations and of experimental studies were compared and have shown satisfactory agreement, which points to the workability of the model.


mathematical model three-dimensional flow electrode flow velocity of the electrolyte electrodeposition of metals 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. S. Daniel-Bek, “On polarization of porous electrodes,” Zh. Fiz. Khim. 22, 697 (1948).Google Scholar
  2. 2.
    B. S. Daniel-Bek, “On polarization of porous electrodes,” Elektrokhimiya. 2, 672 (1966).Google Scholar
  3. 3.
    A. N. Frumkin, “On the distribution of the corrosion process along the tube,” Zh. Fiz. Khim. 23, 1477–1482 (1949).Google Scholar
  4. 4.
    Ya. B. Zel’dovich, “The theory of reaction on porous and powdery material,” Zh. Fiz. Khim. 13, 163 (1939).Google Scholar
  5. 5.
    O. S. Ksenzhek and V. V. Stender, “Current distribution in the porous electrode,” Dokl. Akad. Nauk SSSR 107, 280–283 (1956).Google Scholar
  6. 6.
    N. G. Gurevich and V. S. Bagotskii, “Work of liquid porous electrodes under the forced feeding of reagents,” Fuel Elements (Moscow, 1964), 93–107 [in Russian].Google Scholar
  7. 7.
    Yu. A. Chizmadzhiyev, V. S. Markin, M. R. Tarasevich, and Yu. G. Chirkov, Microkinetics Processes in Porous Media (Nauka, Moscow, 1971).Google Scholar
  8. 8.
    R. E. Sioda, “Current-potential dependence in the porous electrode under conditions of flow electrolysis,” Electrochim. Acta 16, 1569–1576 (1971).CrossRefGoogle Scholar
  9. 9.
    R. E. Sioda, “Flow through electrodes composed of parallel screens,” Electrochem. Acta, 22(4) 439–443 (1977).CrossRefGoogle Scholar
  10. 10.
    R. E. Sioda, “Mass transfer problem in electrolysis with flowing solution on single and straced screens,” J. Electroanal. Chem. 70(1) 49–54 (1976).CrossRefGoogle Scholar
  11. 11.
    R. Alkire and B. Grason, “Flow-through porous electrodes,” J. Electrochem. Sos. 122(12) 1594–1601 (1975).CrossRefGoogle Scholar
  12. 12.
    N. Olive and G. Lacoste, “Application of volumetric electrodes to the recuperation of metal in industrial effluents,” Electrochem. Acta 24(10) 1109–1114 (1979).CrossRefGoogle Scholar
  13. 13.
    O. Schmal, J. Ercel, and P. Van Puin, “Mass transfer at carbon fibre electrodes,” J. Appl. Electrochem. 16, 422–430 (1986).CrossRefGoogle Scholar
  14. 14.
    E. O. Vilar and F. Ceuret, “Mass transfer to flow-through thin porous electrodes under laminar flow,” Electrochemica acta 40(5) 585–590 (1995).CrossRefGoogle Scholar
  15. 15.
    J. Kryasa, S. A. Maixner, R. Mraz, and I. Rouzar, “Effect of coating thickness on the properties of IrO2±Ta2O5 anodes,” Electrochemica acta, No. 8, 369–372 (1998).Google Scholar
  16. 16.
    M. Saleh Mahmoud, “Mathematical modeling of gas evolving flow-through porous electrodes,” Electrochemica acta, No. 45, 959–967 (1999).Google Scholar
  17. 17.
    J. S. Newman and C. W. Tobias, “Theoretical analysis of current distribution in porous electrodes,” / J. Electrochim Soc. 109, 1183–1191 (1962).CrossRefGoogle Scholar
  18. 18.
    O. Schmal, J. Ercel, and P. Van Puin, “Mass transfer at carbon fibre electrodes,” J. Appl. Electrochem. 16, 422–430 (1986).CrossRefGoogle Scholar
  19. 19.
    R. Yu. Bek, A. P. Zamyatin, A. N. Koshev, and N. P. Poddubnyi, “Mathematical modeling of electrolytic separation process in the pores of the metal flow volume-porous electrode,” Izv. Sib. Akad. Nauk, Ser. Chem., No. 2 (Suppl. 1), 110 (1980).Google Scholar
  20. 20.
    T. Doherty, J. G. Sunderland, P. L. Roberts, and D. J. Pickett, “An improved model of potential and current distribution within a flow-trough porous electrode,” Electrochem. Acta 41(4) 519–526 (1996).CrossRefGoogle Scholar
  21. 21.
    A. N Koshev, V. K. Varentsov, M. A. Chirkina, and V. G. Kamburg, “Mathematical modeling and theory of polarization distribution in electrochemical reactors with flow volume-porous cathodes,” Mat. Model. 23(8) 110–126 (2011).MATHGoogle Scholar
  22. 22.
    A. N. Koshev, V. K. Varentsov, and M. A. Chirkina, “Analysis of mathematical models and the theory of polarization distribution of volume-flow porous electrodes,” Fiz. Khim. Pov. Zashch. Mat. 45(4) 441–448 (2009).Google Scholar
  23. 23.
    A. N. Koshev, M. A. Chirkina, and V. K. Varentsov, “Time-dependent mathematical models of electrochemical processes in reactors with flow-through volume-porous electrodes,” Electrochim. 43(11) 1372–1378 (2007).Google Scholar
  24. 24.
    V. K. Varentsov and A. N. Koshev, “Mathematical modeling of electrochemical processes in the flow-through three-dimensional electrodes,” Izv. Sib. Akad. Nauk, Ser. Khim., No. 17, 117–125 (1988).Google Scholar
  25. 25.
    A. I. Masliy, N. P. Poddubnyi, and A. Zh. Medvedev, “Dynamics of metal depositing on a porous electrode with a low initial permeability at straight-flow mode of electrode operation and a high flow rate of the solution,” Electrochim. 42(10) 1237–1244 (2006).Google Scholar
  26. 26.
    A. N. Koshev, G. N. Gleizer, and V. K. Varentsov, “The effect of gas formation in the pores of the flow-through porous volume cathode on the electrical conductivity of the electrolyte,” Electrochim. 28(8) 1160–1170 (1992).Google Scholar
  27. 27.
    A. N. Koshev, G. N. Gleizer, and V. K. Varentsov, “The effect of filling the flow-through porous cathode by the deposited metal on the electrical conductivity of the solid phase of the electrode-electrolyte system,” Electrochim. 28(8) 1170–1176 (1992).Google Scholar
  28. 28.
    A. N. Koshev, G. N. Gleizer, and V. K. Varentsov, “Mathematical model of the electrolysis process on the flowthrough volume-porous electrode at alternating electroconductivity of the system,” Elektrokhim. 28(8) 1270–1274 (1992).Google Scholar
  29. 29.
    A. N. Koshev, A. A. Davidenko, and V. K. Varentsov, “Theoretical basis of the calculation of flow-through volume-porous carbon and graphite cathodes of fibrous materials,” Electrochim. 33(1) 20–25 (1997).Google Scholar
  30. 30.
    A. I. Masliy, N. P. Poddubnyi, and A. Zh. Medvedev, “Dynamics of infilling the porous cathode with deposited metal,” Electrochim. 41(3) 333–342 (2005).Google Scholar
  31. 31.
    S. K. Godunov and V. S. Ryaben’kii, Difference Schemes (Introduction to Theory) (Nauka, Moscow, 1977) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • A. N. Koshev
    • 1
  • V. K. Varentsov
    • 2
    • 3
  • I. F. Sukhov
    • 1
  • I. G. Gvozdeva
    • 1
  1. 1.Penza State University of Architecture and BuildingPenzaRussia
  2. 2.Institute of Solids and Mechanochemistry, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  3. 3.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations