Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Scale-up of bipolar electrode stack dimensionless numbers for current bypass estimation

  • 128 Accesses

  • 20 Citations


New electrochemical reactors with high specific electrode surface area and low investment and operation cost are needed for the industrial application of electrochemistry. Due to its high productivity and low cost, the bipolar electrochemical reactor is a very promising candidate for industrial application. The main disadvantage of the bipolar electrochemical reactor is the presence of parasitic electrical currents, or current bypass at the lower and upper parts of the electrode stack. For the scale-up, a relation between the current bypass (Ψ) and two dimensionless numbers (Gb and Bn) has been derived.

$$\Psi = Gb(Bn + 1)$$

The bipolar number Bn depends on the electrochemical system used and on the process parameters (σ, i 0) in contrast to the geometric number Gb, which depends only on the geometry of the bipolar reactor. Measured current bypass in a bipolar electrode stack demonstrates the validity of the scale-up relation for Ψ ⩽ 0.68.

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


A :

electrode area (m2)

e :

interelectrode gap (m)

F :

Faraday constant (C mol−1)

Gb :

dimensionless number given by Equation 7

H :

electrode length (m)

I 0 :

feeding current (A)

i 0 :

feeding current density (A m−2)

L :

length of the electrolyte manifold insulating channel (m)

L e :

unitary equivalent length (m)

l :

electrode width (m)

n :

number of elements

P :

pressure (Pa)

R :

ohmic resistance in electrolyte feeder/ collector channel (Ω)


gas constant (J mo1−1 K−1)

R i :

ohmic resistance in electrolyte feeder channel (Ω)

R 0 :

ohmic resistance in electrolyte collector channel (Ω)

T :

temperature (K)

V c :

constant potential in the n elements (V)

Vd :

decomposition voltage (V)

Bn :

dimensionless bipolar number

\(\dot V_{\exp } \) :

experimental gas flow rate (m3 s−1)

\(\dot V_0 \) :

theoretical gas flow rate (equation 21) (m3 s−1)

εP :

electrolyte porosity due to a packing in the manifold channels (−)


current bypass (portion of lost current) (−)


electrolyte conductivity (Ω−1 m−1)

σp :

apparent electrolyte conductivity with a packing in the manifold channels (Ω−1 m−1)


  1. [1]

    J. D. Genders and D. Pletcher, in ‘Electrosynthesis from Laboratory to Pilot, to Production”, (edited by J. D. Genders and D. Pletcher), New York (1990).

  2. [2]

    J. C. Burnett and D. E. Danly, AICHE Symp. 75 (8), (1979) 185.

  3. [3]

    E. A. Kaminski and R. F. Savinell, J. Electrochem. Soc. 130 (1983) 1103.

  4. [4]

    M. Z. Yang, H. Wu and J. R. Selman, J. Appl. Electrochem. 19 (1989) 247.

  5. [5]

    M. Zahn, et al., US Patent 4 197 169 (1980).

  6. [6]

    S. Szpak, C. Gabriel and J. J. Smith, J. Electrochem. Soc., 137 (1990) 850.

  7. [7]

    J. A. Holmes and R. E. White, in Electrochemical Cell Design (edited by R. White), Plenum Press, New York (1984) p. 311.

  8. [8]

    P. Bolomey, Swiss Federal Institute of Technology, Lausanne, thesis 753 (1988).

  9. [9]

    J. Divisek, K. Jung and D. Britz, J. Appl. Electrochem. 20 (1990) 186.

  10. [10]

    E. C. Dimpault-Darcy and R. E. White, J. Electrochem. Soc. 135 (1988) 656.

  11. [11]

    C. Comninellis, E. Plattner and P. Bolomey, J. Appl. Eleetrochem. 21 (1991) 415.

  12. [12]

    D. S. Miller, ‘Internal Flow: a Guide to Losses in Pipe and Duct Systems’, BHRA, England, (1991) p. 23.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bonvin, G., Comninellis, C. Scale-up of bipolar electrode stack dimensionless numbers for current bypass estimation. J Appl Electrochem 24, 469–474 (1994). https://doi.org/10.1007/BF00249844

Download citation


  • Electrode Surface
  • Industrial Application
  • Electrical Current
  • Promising Candidate
  • Electrochemical Reactor