Journal of Applied Electrochemistry

, Volume 48, Issue 6, pp 725–737 | Cite as

Effect of the design parameters on mass transfer and energy consumption inside a lithium electrolysis cell

  • Elaheh Oliaii
  • Martin Désilets
  • Gaétan Lantagne
Research Article


A 2D axisymmetric electrochemical model of a lithium experimental cell is solved using a finite element method. The model is considering the coupled effect of momentum, electric, kinetic and mass transfer phenomena. The dense diaphragm used in the setup, which is not hydraulically permeable, separates the cell into two regions: 1 (a) turbulent region, between the anode and the diaphragm, and 2 (a) laminar region between the diaphragm and the cathode. The k-epsilon model is used to solve the turbulent flow resulting from bubbles generation at the anode. A two-phase flow model is also developed to simulate the volume fractions of bubbles and electrolyte in the cell. The non-uniform bubbles distribution over the anode surface, derived from the non-uniform current distribution, has been added to the two-phase model. The effects of the diaphragm length, position and porosity on the electric and two-phase flow fields are simulated. In fact, the diaphragm position and length both influence the current distribution at the surface of electrodes and the velocity distribution in the cell, all of which influence ohmic and kinetic overpotentials. The results show that up to 40% of energy can be saved when running the lithium electrolysis cell with a shorter porous diaphragm located as far as possible from the anode. The maximum current density, found at the bottom corner of anode, is higher when the diaphragm is longer and when it is closer to the anode.

Graphical Abstract


Lithium electrochemical cell Mass transfer Turbulent two-phase flow Finite element model 

List of symbols


Area (m2)


Drag coefficient


Concentration (mol m−3)


Effective diffusion coefficient (m2 s−1)


Bubble diameter (m)


Faraday’s constant (A s mol−1)


Volume force (kg m s−2)


Drag force (kg m s−2)


Gravity acceleration constant (m s−2)


Local current density (A m−2)


Exchange current density (A m−2)


Turbulent kinetic energy (m2 s−2)


Length (m)


Molecular weight (kg mol−1)


Ions flux (mol m−2 s−1)


Normal vector


Pressure (kg m−1 s−2)


Gas constant (J K−1 mol−1)


Reynolds number


Temperature (K)


Stress tensor (kg m−1 s−2)


Time (s)


Velocity magnitude (m s−1)


Mobility (m2 s−1 V−1)


Bubbles terminal velocity (m s−1)


Velocity vector (m s−1)


Mole fraction


Charge number

Greek letters


Transfer coefficient


Electrolyte conductivity (S m−1)


Rate of dissipation of kinetic energy (m2 s−3)




Activation overpotential (V)


Viscosity (kg m−1 s−1)


Density (kg m−3)




Volume fraction

\({\emptyset _{\text{g}}}\)

Bubble coverage

Subscripts and superscripts




Continuous phase


Disperse phase




Species i








Resistive layer





The authors wish to thank Dr. Kamyab Amouzegar for his useful suggestions. We also appreciate Hydro-Québec for their financial support, for providing us with the experimental results and giving us the opportunity to publish this work. The authors are also grateful to the Natural Sciences and Engineering Council of Canada (NSERC) for its financial support.


  1. 1.
    James CD (1924) Electrolytic process and cell. US Patent 1,501,756Google Scholar
  2. 2.
    Muller J, Bauer R, Sermond B, Dolling E (1988) Process and apparatus for producing high-purity lithium metal by fused-salt electrolysis. US Patent 4,740,279Google Scholar
  3. 3.
    Verdier JM, Jacubert S, Grosbois J, Dumousseau JY (1986) Continuous electrolysis of lithium chloride into lithium metal. US Patent 4,617,098Google Scholar
  4. 4.
    Nakamura E, Takata H, Yokoyama Y, Miyamoto H (2010) Process for producing metallic lithium. US Patent 20,100,051,470Google Scholar
  5. 5.
    Le Roux E, Nataf P, Jacubert S (1988) Continuous production of lithium metal by electrolysis of lithium chloride. US Patent 4,724,055Google Scholar
  6. 6.
    Bergmann OR, Blank HM, Diemer RB et al (2000) Modified electrolyte and diaphragm for fused salt electrolysis. US Patent 6,063,247Google Scholar
  7. 7.
    Blank HM, Bergmann OR, Simmons WJ (1999) Fused chloride salt electrolysis cell. US Patent 5,904,821Google Scholar
  8. 8.
    Li D, Chattopadhyay K, Gao L, Davis B, Schwarze R, Asad A, Kratzsch C (2017) Mathematical modeling of molten salt electrolytic cells for sodium and lithium production. Applications of process engineering principles in materials processing, energy and environmental technologies. Springer, New York, pp 129–138CrossRefGoogle Scholar
  9. 9.
    Oliaii E, Désilets M, Lantagne G (2017) Numerical analysis of the effect of structural and operational parameters on electric and concentration fields of a lithium electrolysis cell. J Appl Electrochem 47(6):711–726CrossRefGoogle Scholar
  10. 10.
    Amouzegar K, Harrison S (1996) Electrolytic production of lithium metal. Report, HydroQuebec, ShawiniganGoogle Scholar
  11. 11.
    Thonstad J, Fellner P, Haarberg GM, Híves J, Kvande H, Sterten A (2001) Aluminium electrolysis: fundamentals of the Hall-Héroult process. Aluminium-Verlag, DusseldorfGoogle Scholar
  12. 12.
    Vogt H, Balzer RJ (2005) The bubble coverage of gas-evolving electrodes in stagnant electrolytes. Electrochim Acta 50(3):2073–2079CrossRefGoogle Scholar
  13. 13.
    Vogt H (2011) On the gas-evolution efficiency of electrodes. II: Numerical analysis. Electrochim Acta 56:2404–2410CrossRefGoogle Scholar
  14. 14.
    Liu C-L, Sun Z, Lu G-M, Song X-F, Yu J-G (2015) Experimental and numerical investigation of two-phase flow patterns in magnesium electrolysis cell with non-uniform current density distribution. Can J Chem Eng 93(3):565–579CrossRefGoogle Scholar
  15. 15.
    Aldas K, Pehlivanoglu N, Mat MD (2008) Numerical and experimental investigation of two-phase flow in an electrochemical cell. Int J Hydrog Energy 33(14):3668–3675CrossRefGoogle Scholar
  16. 16.
    Taylor R, Krishna R (1993) Multicomponent mass transfer. vol 2., Wiley, New York, p 243Google Scholar
  17. 17.
    Nelissen G, Van Den Bossche B, Deconinck J, Van Theemsche A, Dan C (2003) Laminar and turbulent mass transfer simulations in a parallel plate reactor. J Appl Electrochem 33(10):863–873CrossRefGoogle Scholar
  18. 18.
    Calmet I, Magnaudet J (1997) Large-eddy simulation of high-schmidt number mass transfer in a turbulent channel flow. Phys Fluids 9(2):438–455CrossRefGoogle Scholar
  19. 19.
    Lyons SL, Hanratty TJ, McLaughlin JB (1991) Large-scale computer simulation of fully developed turbulent channel flow with heat transfer. Int J Numer Methods Fluids 13(8):999–1028CrossRefGoogle Scholar
  20. 20.
    Tjaden B, Cooper SJ, Brett DJ, Kramer D, Shearing PR (2016) On the origin and application of the Bruggeman correlation for analysing transport phenomena in electrochemical systems. Curr Opin Chem Eng 12:44–51CrossRefGoogle Scholar
  21. 21.
    Chung DW, Ebner M, Ely DR, Wood V, García RE (2013) Validity of the Bruggeman relation for porous electrodes. Model Simul Mater Sci Eng 21(7):74009CrossRefGoogle Scholar
  22. 22.
    Ebner M, Wood V (2015) Tool for tortuosity estimation in lithium ion battery porous electrodes. J Electrochem Soc 162(2):A3064–A3070CrossRefGoogle Scholar
  23. 23.
    Díaz ME, Iranzo A, Cuadra D, Barbero R, Montes FJ, Galán MA (2008) Numerical simulation of the gas-liquid flow in a laboratory scale bubble column. Influence of bubble size distribution and non-drag forces. Chem Eng J 139(2):363–379CrossRefGoogle Scholar
  24. 24.
    Alexiadis A, Dudukovic M, Ramachandran P, Cornell A, Wanngård J, Bokkers A (2011) On the electrode boundary conditions in the simulation of two phase flow in electrochemical cells. Int J Hydrogen Energy 36:8557–8559CrossRefGoogle Scholar
  25. 25.
    Oldham K, Myland J, Bond A (2011) Electrochemical science and technology: fundamentals and applications. Wiley, New YorkCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemical and Biotechnological EngineeringUniversité de SherbrookeSherbrookeCanada
  2. 2.IREQ (Hydro-Québec’s Research Institute)VarennesCanada

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