Boundary Layer Analysis of Membraneless Electrochemical Cells (original) (raw)

Abstract

A mathematical theory is presented for the charging and discharging behavior of membraneless electrochemical cells that rely on slow diffusion in laminar flow to separate the half reactions. Ion transport is described by the Nernst-Planck equations for a flowing quasi-neutral electrolyte with heterogeneous Butler-Volmer kinetics. Analytical approximations for the current-voltage relation and the concentration and potential profiles are derived by boundary layer analysis (in the relevant limit of large Peclet numbers) and validated against finite-element numerical solutions. Both Poiseuille and plug flows are considered to describe channels of various geometries, with and without porous flow channels. The tradeoff between power density and reactant crossover and utilization is predicted analytically. The theory is applied to the membrane-less Hydrogen Bromine Laminar Flow Battery and found to accurately predict the experimental and simulated current-voltage data for different flow rates and reactant concentrations, during both charging and discharging. This establishes the utility of the theory to understand and optimize the performance of membrane-less electrochemical flow cells, which could also be extended to other fluidic architectures.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (67)

  1. R. Ferrigno, A. D. Stroock, T. D. Clark, M. Mayer, and G. M. Whitesides, J. Am. Chem. Soc., 124, 12930 (2002).
  2. E. R. Choban, L. J. Markoski, A. Wieckowski, and P. J. A. Kenis, J. Power Sources, 128, 54 (2004).
  3. E. Kjeang, R. Michel, D. A. Harrington, N. Djilali, and D. Sinton, J. Am. Chem. Soc., 130, 4000 (2008).
  4. S. A. Mousavi Shaegh, N.-T. Nguyen, and S. H. Chan, Int. J. Hydrogen Energ., 36, 5675 (2011).
  5. E. Kjeang, N. Djilali, and D. Sinton, in Advances in microfluidic fuel cells, p. 99-139, Elsevier (2009).
  6. Tiax, LLC, Cost Analysis of Fuel Cell Systems for Transportation, (2004).
  7. H. Kamath, S. Rajagopalan, and M. Zwillenberg, Vanadium Redox Flow Batteries, Electric Power Research Institute, Palo Alto, CA, (2007).
  8. L. Li, S. Kim, G. Xai, W. Wang, and Z. Yang, Advanced Redox Flow Batteries for Stationary Electrical Energy Storage, U.S. Department of Energy, (2012).
  9. F. R. Brushett et al., J. Am. Chem. Soc., 132, 12185 (2010).
  10. F. R. Brushett, W.-P. Zhou, R. S. Jayashree, and P. J. A. Kenis, J. Electrochem. Soc., 156, B565 (2009).
  11. M. S. Naughton, F. R. Brushett, and P. J. A. Kenis, J. Power Sources, 196, 1762 (2011).
  12. D. A. Finkelstein, J. D. Kirtland, N. D. Mota, A. D. Stroock, and H. D. Abruña, J. Phys. Chem. C, 115, 6073 (2011).
  13. N. Da Mota et al., J. Am. Chem. Soc., 134, 6076 (2012).
  14. E. Kjeang et al., Electrochim. Acta, 52, 4942 (2007).
  15. A. S. Hollinger et al., J. Power Sources, 195, 3523 (2010).
  16. R. S. Jayashree et al., J. Am. Chem. Soc., 127, 16758 (2005).
  17. A. D. Stroock et al., Science, 295, 647 (2002).
  18. P. Tabeling, M. Chabert, A. Dodge, C. Jullien, and F. Okkels, Phil. Trans. R. Soc. Lond. A, 362, 987 (2004).
  19. S. A. Mousavi Shaegh, N.-T. Nguyen, S. H. Chan, and W. Zhou, Int. J. Hydrogen Energ., 37, 3466 (2012).
  20. J. W. Lee, M.-A. Goulet, and E. Kjeang, Lab Chip, 13, 2504 (2013).
  21. A. Bazylak, D. Sinton, and N. Djilali, J. Power Sources, 143, 57 (2005).
  22. R. S. Jayashree et al., J. Power Sources, 195, 3569 (2010).
  23. J. Xuan, M. K. H. Leung, D. Y. C. Leung, M. Ni, and H. Wang, Int. J. Hydrogen Energ., 36, 11075 (2011).
  24. I. B. Sprague, D. Byun, and P. Dutta, Electrochim. Acta, 55, 8579 (2010).
  25. I. B. Sprague and P. Dutta, Electrochim. Acta, 56, 4518 (2011).
  26. V. Edwards and J. Newman, J. Electrochem. Soc., 134, 1181 (1987).
  27. R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis, G. Whitesides, and H. A. Stone, Appl. Phys. Lett., 76, 2376 (2000).
  28. J. Newman and K. E. Thomas-Alyea, Electrochemical Systems, 3rd ed. John Wiley, (2004).
  29. J. Jiménez, J. Fluid Mech., 535, 245 (2005).
  30. A. N. Colli and J. M. Bisang, J. Electrochem. Soc., 160, E5 (2012).
  31. W. A. Braff, M. Z. Bazant, and C. R. Buie, Nat. Commun., 4, 2346 (2013).
  32. W. A. Braff and C. R. Buie, ECS Trans., 33, 179 (2011).
  33. T. S. Zhao, K.-D. Kreuer, and T. V. Nguyen, Advances in Fuel Cells, Elsevier, Ltd, Oxford, UK, (2007).
  34. A. A. Kulikovsky, Analytical Modeling of Fuel Cells, 1st ed. Elsevier, Amsterdam, The Netherlands, (2010).
  35. I. B. Sprague and P. Dutta, SIAM J. Appl. Math., 72, 1149 (2012).
  36. M. Z. Bazant, 10.626 Electrochemical Energy Systems, License: Creative Com- mons BY-NC-SA. Massachusetts Institute of Technology Open Courseware, (2011) http://ocw.mit.edu.
  37. P. M. Biesheuvel, M. van Soestbergen, and M. Z. Bazant, Electrochim. Acta, 54, 4857 (2009).
  38. I. B. Sprague and P. Dutta, Electrochim. Acta, 91, 20 (2013).
  39. P. M. Biesheuvel, A. A. Franco, and M. Z. Bazant, J. Electrochem. Soc., 156, B225 (2009).
  40. M. Eikerling, Y. I. Kharkats, A. A. Kornyshev, and Y. M. Volfkovich, J. Electrochem. Soc., 145, 2684 (1998).
  41. I. V. Zenyuk and S. Litster, J. Phys. Chem. C, 116, 9862 (2012).
  42. P. M. Biesheuvel, Y. Fu, and M. Z. Bazant, Phys. Rev. E, 83, 061507 (2011).
  43. D. R. Lide, Handbook of Chemistry and Physics, CRC Press, (2012).
  44. M. Z. Bazant, Acc. Chem. Res., 46, 1144 (2013).
  45. W. Cooper and R. Parsons, Trans. Faraday Soc., 66, 1698 (1970).
  46. R. F. Probstein, Physicochemical Hydrodynamics, p. 1, Wiley-Interscience, (1989).
  47. R. S. Yeo and D.-T. Chin, J. Electrochem. Soc., 127, 549 (1980).
  48. V. Livshits, A. Ulus, and E. Peled, Electrochem. Commun., 8, 1358 (2006).
  49. T. V. Nguyen and H. Kreutzer, in, vol. 41, p. 3-9, ECS (2012).
  50. K. T. Cho et al., J. Electrochem. Soc., 159, A1806 (2012).
  51. R. W. Ramette and D. A. Palmer, J. Solution Chem., 15, 387 (1986).
  52. P. K. Adanuvor, R. E. White, and S. E. Lorimer, J. Electrochem. Soc., 134, 1450 (1987).
  53. A. J. Bard, R. Parsons, and J. Jordan, Standard Potentials in Aqueous Solution, p. 1, Marcel Dekker, Inc., New York, NY, (1985).
  54. M. Z. Bazant, Proc. Roy. Soc. A, 460, 1433 (2004).
  55. J. Choi, D. Margetis, T. M. Squires, and M. Z. Bazant, J. Fluid Mech., 536, 155 (2005).
  56. L. M. Cummings, Y. E. Hohlov, S. D. Howison, and K. Kornev, J. Fluid Mech., 378, 1 (1999).
  57. M. Z. Bazant, J. Choi, and B. Davidovitch, Phys. Rev. Lett., 91 045503 (2003).
  58. W. M. Deen, in, Oxford University Press (2012).
  59. A. Lévêque, Annales des Mines, 13, 284 (1928).
  60. A. A. Sonin and R. F. Probstein, Desalination, 5, 293 (1968).
  61. D. S. Deng et al., submitted (2013).
  62. M. Chatenet, M. B. Molina-Concha, N. El-Kissi, G. Parrour, and J. P. Diard, Elec- trochim. Acta, 54, 4426 (2009).
  63. M. Duduta et al., Adv. Energy Mater., 1, 511 (2011).
  64. V. E. Brunini, Y.-M. Chiang, and W. C. Carter, Electrochim. Acta, 69, 301 (2012).
  65. V. Presser et al., Adv. Energy Mater., 2, 895 (2012).
  66. S.-I. Jeon et al., Energy Environ. Sci., 6, 1471 (2013).
  67. Z. Nie et al., Lab Chip, 10, 477 (2010).