Topics in the Mathematical Modeling of Localized Corrosion

  • Kurt R. Hebert
  • Bernard Tribollet
Part of the Modern Aspects of Electrochemistry book series (MAOE, volume 44)


Localized corrosion describes dissolution processes concentrated at specific areas on the surfaces of metals. In some types of localized corrosion, enhanced dissolution rates arise from partial or complete destruction of the protection normally afforded by the passive oxide film covering the metal surface. Oxide breakdown can be due to mechanical rupture (stress corrosion cracking), the chemical action of aggressive anions such as chloride (pitting corrosion), the impaction of solid particles on the surface (erosion corrosion), or the concentration of corrosion products within small solution-filled gaps (crevice corrosion). Other localized corrosion processes are initiated at metal compositional inhomogeneities such as grain boundaries in alloys (intergranular corrosion), or interfaces between dissimilar metals (galvanic corrosion). The economic impact of all forms of localized corrosion is severe. For example, pitting and stress corrosion cracking together account for about one fourth of equipment failures in the chemical process industries.

Metal dissolution rates during localized corrosion are high enough so that large concentration or potential gradients are typically found near the dissolving metal surface. Characterization of these gradients is a necessary precursor for understanding the mechanisms controlling the corrosion rate. Thus, experimental research on localized corrosion has always been closely coupled to quantitative analysis of mass transport processes by mathematical modeling. In this chapter, three examples are presented which illustrate the range of models applied to localized corrosion processes, reflecting the particular interests of the authors. Section II, written by Hebert, is a review of recent work on the modeling of pitting corrosion. The remainder of the chapter communicates results of recent work by Tribollet on galvanic corrosion (Sect. III) and on the simulation of the impedance in crevice-type geometries.


Crevice Corrosion Electrolyte Film Diffusion Impedance Transmission Line Model Repassivation Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J.A. Collins and M.L. Monack, Mater. Prot. Perform. 12 (1973) 11.Google Scholar
  2. 2.
    G. Engelhardt and D.D. Macdonald, Corrosion 54 (1998) 469.CrossRefGoogle Scholar
  3. 3.
    G. Engelhardt and D.D. Macdonald, Corros. Sci. 46 (2004) 2755.CrossRefGoogle Scholar
  4. 4.
    D.D. Macdonald, C. Liu, M. Urquidi-Macdonald, G.H. Stickford, B. Hindin, A.K. Agrawal and K. Krist, Corrosion 50 (1994) 761.CrossRefGoogle Scholar
  5. 5.
    A. Turnbull, L.N. McCartney and S. Zhou, Corros. Sci. 48 (2006) 2084.CrossRefGoogle Scholar
  6. 6.
    A. Anderko, N. Sridhar and D.S. Dunn, Corros. Sci. 46 (2004) 1583.CrossRefGoogle Scholar
  7. 7.
    D.S. Dunn, G.A. Cragnolino and N. Sridhar, Corrosion 56 (2000) 90.CrossRefGoogle Scholar
  8. 8.
    N. Sridhar and G.A. Cragnolino, Corrosion 49 (1993) 885.CrossRefGoogle Scholar
  9. 9.
    T.T. Lunt, J.R. Scully, V. Brusamarello, A.S. Mikhailov and J.L. Hudson, J. Electrochem. Soc. 149 (2002) B163.CrossRefGoogle Scholar
  10. 10.
    C. Punckt, M. Bolscher, H.H. Rotermund, A.S. Mikhailov, L. Organ, N. Budiansky, J.R. Scully and J.L. Hudson, Science 305 (2004) 1133.CrossRefGoogle Scholar
  11. 11.
    J. Newman and K.E. Thomas-Alyea, Electrochemical Systems, Third ed., Wiley, Hoboken, NJ, 2004.Google Scholar
  12. 12.
    S.M. Sharland, Corros. Sci. 27 (1987) 289.CrossRefGoogle Scholar
  13. 13.
    A. Turnbull, Br. Corros. J. 28 (1993) 297.Google Scholar
  14. 14.
    S.M. Sharland, C.P. Jackson and A.J. Diver, Corros. Sci. 29 (1989) 1149.CrossRefGoogle Scholar
  15. 15.
    S.M. Sharland and P.W. Tasker, Corros. Sci. 28 (1988) 603.CrossRefGoogle Scholar
  16. 16.
    A. Turnbull and M.K. Gardner, Corros. Sci. 22 (1982) 661.CrossRefGoogle Scholar
  17. 17.
    J.N. Harb and R.C. Alkire, J. Electrochem. Soc. 138 (1991) 3568.CrossRefGoogle Scholar
  18. 18.
    J.N. Harb and R.C. Alkire, Corros. Sci. 29 (1989) 31.CrossRefGoogle Scholar
  19. 19.
    M.L. Kronenberg, J.C. Banter, E. Yeager and F. Hovorka, J. Electrochem. Soc. 110 (1963) 1007.CrossRefGoogle Scholar
  20. 20.
    J.N. Harb and R.C. Alkire, J. Electrochem. Soc. 138 (1991) 2594.CrossRefGoogle Scholar
  21. 21.
    M.W. Verbrugge, D.R. Baker and J. Newman, J. Electrochem. Soc. 140 (1993) 2530.CrossRefGoogle Scholar
  22. 22.
    G. Engelhardt and H.H. Strehblow, Corros. Sci. 36 (1994) 1711.CrossRefGoogle Scholar
  23. 23.
    H.K. Kuiken, J.J. Kelly and P.H.L. Notten, J. Electrochem. Soc. 133 (1986) 1217.CrossRefGoogle Scholar
  24. 24.
    G. Engelhardt, M. Urquidi-Macdonald and D.D. Macdonald, Corros. Sci. 39 (1997) 419.CrossRefGoogle Scholar
  25. 25.
    G. Engelhardt and D.D. Macdonald, Corros. Sci. 46 (2004) 1159.CrossRefGoogle Scholar
  26. 26.
    M. Verhoff and R. Alkire, J. Electrochem. Soc. 147 (2000) 1349.CrossRefGoogle Scholar
  27. 27.
    M. Verhoff and R. Alkire, J. Electrochem. Soc. 147 (2000) 1359.CrossRefGoogle Scholar
  28. 28.
    E.G. Webb and R.C. Alkire, J. Electrochem. Soc. 149 (2002) B286.CrossRefGoogle Scholar
  29. 29.
    M. Kamrunnahar, R.D. Braatz and R.C. Alkire, J. Electrochem. Soc. 151 (2004) B90.CrossRefGoogle Scholar
  30. 30.
    J.R. Gray, C. Homescu, L.R. Petzold and R.C. Alkire, J. Electrochem. Soc. 152 (2005) B277.CrossRefGoogle Scholar
  31. 31.
    N.J. Laycock and S.P. White, J. Electrochem. Soc. 148 (2001) B264.CrossRefGoogle Scholar
  32. 32.
    N.J. Laycock, S.P. White, J.S. Noh, P.T. Wilson and R.C. Newman, J. Electrochem. Soc. 145 (1998) 1101.CrossRefGoogle Scholar
  33. 33.
    T. Hakkarainen, Mater. Sci. Forum 8 (1986) 81.CrossRefGoogle Scholar
  34. 34.
    G.T. Gaudet, W.T. Mo, T.A. Hatton, J.W. Tester, J. Tilly, H.S. Isaacs and R.C. Newman, AlChE J. 32 (1986) 949.CrossRefGoogle Scholar
  35. 35.
    T. Hakkarainen, in: A. Turnbull (Ed.), Corrosion Chemistry within Pits, Crevices and Cracks, Her Majesty’s Stationery Office, London, 1987, p. 17.Google Scholar
  36. 36.
    P.C. Pistorius and G.T. Burstein, Philos. Trans. R. Soc. Lond., Ser. A 341 (1992) 531.Google Scholar
  37. 37.
    U. Steinsmo and H.S. Isaacs, J. Electrochem. Soc. 140 (1993) 643.CrossRefGoogle Scholar
  38. 38.
    R.S. Alwitt, H. Uchi, T.R. Beck and R.C. Alkire, J. Electrochem. Soc. 131 (1984) 13.CrossRefGoogle Scholar
  39. 39.
    D. Goad, J. Electrochem. Soc. 144 (1997) 1965.CrossRefGoogle Scholar
  40. 40.
    K.R. Hebert, J. Electrochem. Soc. 148 (2001) B236.CrossRefGoogle Scholar
  41. 41.
    Y.S. Tak and K.R. Hebert, J. Electrochem. Soc. 141 (1994) 1453.CrossRefGoogle Scholar
  42. 42.
    Y.S. Tak, E.R. Henderson and K.R. Hebert, J. Electrochem. Soc. 141 (1994) 1446.CrossRefGoogle Scholar
  43. 43.
    N. Sinha and K.R. Hebert, J. Electrochem. Soc. 147 (2000) 4111.CrossRefGoogle Scholar
  44. 44.
    Y. Tak, N. Sinha and K.R. Hebert, J. Electrochem. Soc. 147 (2000) 4103.CrossRefGoogle Scholar
  45. 45.
    K. Hebert and R. Alkire, J. Electrochem. Soc. 135 (1988) 2146.CrossRefGoogle Scholar
  46. 46.
    Y. Zhou and K.R. Hebert, J. Electrochem. Soc. 145 (1998) 3100.CrossRefGoogle Scholar
  47. 47.
    J.R. Galvele, J. Electrochem. Soc. 123 (1976) 464.CrossRefGoogle Scholar
  48. 48.
    K. Hebert and R. Alkire, J. Electrochem. Soc. 135 (1988) 2447.CrossRefGoogle Scholar
  49. 49.
    J.O.M. Bockris and A.K.N. Reddy, Modern Electrochemistry, Plenum, New York, 1977.Google Scholar
  50. 50.
    K.R. Hebert, Proc. – Electrochem. Soc. 99–14 (1999) 54.Google Scholar
  51. 51.
    R.A. Robinson and R.H. Stokes, Electrolyte Solutions; The Measurement and Interpretation of Conductance, Chemical Potential, and Diffusion in Solutions of Simple Electrolytes, 2nd ed., Butterworths, London, 1959.Google Scholar
  52. 52.
    R.H. Perry and C.H. Chilton (Eds.), Perry’s Chemical Engineers’ Handbook, 5th ed., McGraw-Hill, New York, 1973.Google Scholar
  53. 53.
    J. Newman, J. Electrochem. Soc. 113 (1966) 1235.CrossRefGoogle Scholar
  54. 54.
    J. Newman, J. Electrochem. Soc. 113 (1966) 501.CrossRefGoogle Scholar
  55. 55.
    J.B. Jorcin, C. Blanc, N. Pebere, B. Tribollet and V. Vivier, J. Electrochem. Soc. 155 (2008) C46.CrossRefGoogle Scholar
  56. 56.
    N. Dimitrov, J.A. Mann and K. Sieradzki, J. Electrochem. Soc. 146 (1999) 98.CrossRefGoogle Scholar
  57. 57.
    M.B. Vukmirovic, N. Dimitrov and K. Sieradzki, J. Electrochem. Soc. 149 (2002) B428.CrossRefGoogle Scholar
  58. 58.
    C.R. Christensen and F.C. Anson, Anal. Chem. 35 (1963) 205.CrossRefGoogle Scholar
  59. 59.
    A.T. Hubbard and F.C. Anson, Anal. Chem. 36 (1964) 723.CrossRefGoogle Scholar
  60. 60.
    A.T. Hubbard and F.C. Anson, Anal. Chem. 38 (1966) 58.CrossRefGoogle Scholar
  61. 61.
    A.T. Hubbard and F.C. Anson, in: A.J. Bard (Ed.), Electroanalytical Chemistry, Marcel Dekker, New York, 1970, pp. 129.Google Scholar
  62. 62.
    C. Fiaud, M. Keddam, A. Kadri and H. Takenouti, Electrochim. Acta 32 (1987) 445.CrossRefGoogle Scholar
  63. 63.
    E. Remita, E. Sutter, B. Tribollet, F. Ropital, X. Longaygue, C. Taravel-Condat and N. Desamais, Electrochim. Acta 52 (2007) 7715.CrossRefGoogle Scholar
  64. 64.
    K. Micka, K. Kratochvilova and J. Klima, Electrochim. Acta 42 (1997) 1005.CrossRefGoogle Scholar
  65. 65.
    T. Jacobsen and K. West, Electrochim. Acta 40 (1995) 255.CrossRefGoogle Scholar
  66. 66.
    R. de Levie, in: P. Delahay (Ed.), Advances in Electrochemistry and Electrochemical Engineering, New York, Interscience, 1967, pp. 329.Google Scholar
  67. 67.
    C. Gabrielli, M. Keddam, N. Portail, P. Rousseau, H. Takenouti and V. Vivier, J. Phys. Chem. B 110 (2006) 20478.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Kurt R. Hebert
    • 1
  • Bernard Tribollet
    • 2
  1. 1.Department of Chemical and Biological EngineeringIowa State UniversityAmesUSA
  2. 2.Laboratoire Interfaces et Systèmes Electrochimiques, UPR 15 du CNRSUniversité Pierre et Marie CurieParis Cedex 05France

Personalised recommendations