Skip to main content
SpringerLink
Log in

An arbitrary Lagrangian–Eulerian model for studying the influences of corrosion product deposition on bimetallic corrosion

  • Original Paper
  • Published:
Journal of Solid State Electrochemistry Aims and scope Submit manuscript

Abstract

In this paper, a model is established to simulate the time-dependent deposition of corrosion product on the metal surface by considering mass transfer, electrochemical reactions and precipitation reaction. The model is also capable of tacking the movement of metal corrosion interface and the growing interface of the corrosion product deposits via arbitrary Lagrangian–Eulerian finite element method. The current model not only can be used to predict the time-dependent metal corrosion but also for investigating the influences of the deposits’ nature on metal corrosion. The numerical results of current density and corrosion rate are in good agreement with experiments. The presented model predicts that an exponential relationship exists between the maximum corrosion depth and the porosity of corrosion product deposits, and it is also predicted that the growth of the corrosion product layer is linear relative with the root of time, which is consistent with the existing theories.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

a:

Anode

c:

Cathode

c i :

Concentration of species i, mol/m3

c i,bluk :

Concentration of species i in bulk solution, mol/m3

D i :

Diffusion coefficient of species i, m2/s

D ie :

Effective diffusion coefficient of species i, m2/s

F :

Faraday’s constant, C/mol

f(ϕ):

Piecewise linear interpolation of polarization data

J C :

Current density of deposits model, A/m2

J N :

Current density of non-deposit model, A/m2

k :

Reaction rate constant for the precipitation reaction of Mg(OH)2, m6/(mol2 s)

k sp :

Apparent solution product constant of Mg(OH)2, mol3/m9

L c :

The length of cathode, m

m :

Cementation exponent

M i :

Molecular weight of species i, kg/mol

n :

Saturation coefficient

n :

Normal vector

n i :

Electrons number of species i

N i :

Molar flux of species i, mol/(m2 s)

N i,e :

Effective molar flux of species i, mol/(m2 s)

N M,PE :

MacMullin number

R :

Universal gas constant, J/(K mol)

R i :

Reaction rate of species i, mol/(m3 s)

s L :

Fluid saturation

t :

Time, s

T :

Temperature, K

u mi :

Mobility of species i, mol m2/(J s)

u mi,e :

Effective mobility of species i, mol m2/(J s)

v :

Velocity vector, m/s

\( \overline{x} \) :

Distance along the metal surface, m

x :

x co-ordinate in spatial frame, m

y :

y co-ordinate in spatial frame, m

X :

X co-ordinate in reference frame, m

Y :

Y co-ordinate in reference frame, m

z i :

Charge of species i

ϕ :

Potential, V vs SCE

σ :

Conductivity of the electrolyte, S/m

σ e :

Effective conductivity of the deposits, S/m

Γ:

Boundary

ε :

Porosity of the deposits

τ :

Tortuosity of the deposits

v i :

Stoichiometric coefficient for species i

υ :

Relative permittivity

ρ i :

Density of species i, kg/m3

ζ :

The dependent variable in step function H

ξ :

Factor in step function H

References

  1. Revie RW, Uhlig HH (2008) Metallic coatings, in corrosion and corrosion control: An introduction to corrosion science and engineering, 4th edn, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi:10.1002/9780470277270.ch1

  2. Wang L, Liu G, Xue D (2010) Electrochim Acta 55:6796–6801

    Article  CAS  Google Scholar 

  3. Wang L, Liu G, Xue D (2011) Electrochim Acta 56:6277–6283

    Article  CAS  Google Scholar 

  4. Wang L, Liu G, Zou L, Xue D (2011) Appl Surf Sci 257:5519–5523

    Article  CAS  Google Scholar 

  5. Wang L, Liu G, Xue D (2010) Mater Lett 64:2475–2478

    Article  Google Scholar 

  6. Gojkovic SL, Zecevic SK, Drazic DM (1994) Electrochim Acta 39:975–982

    Article  CAS  Google Scholar 

  7. Volovitch P, Allely C, Ogle K (2009) Corros Sci 51:1251–1262

    Article  CAS  Google Scholar 

  8. Sancy M, Gourbeyre Y, Sutter EMM, Tribollet B (2010) Corros Sci 52:1222–1227

    Article  CAS  Google Scholar 

  9. Liu W, Cao F, Jia B, Zheng L, Zhang J, Cao C, Li X (2010) Corros Sci 52:639–650

    Article  Google Scholar 

  10. Shinozaki J, Muto I, Ogawa H, Hara N (2009) J Jpn Inst Met 73:533–541

    Article  CAS  Google Scholar 

  11. Yuan Y, Ji Y, Jiang J (2009) Mater Struct 42:1443–1450

    Article  CAS  Google Scholar 

  12. Yuan Y, Ji Y (2010) Int J Struct Eng 1:199–206

    Article  Google Scholar 

  13. North RF, Pryor MJ (1970) Corros Sci 10:297–311

    Article  CAS  Google Scholar 

  14. Yamashita M, Shimizu T, Konishi H, Mizuki J, Uchida H (2003) Corros Sci 45:381–394

    Article  Google Scholar 

  15. Jönsson M, Persson D, Thierry D (2007) Corros Sci 49:1540–1558

    Article  Google Scholar 

  16. Chang J, Guo X, Fu P, Peng L, Ding W (2007) Electrochim Acta 52:3160–3167

    Article  CAS  Google Scholar 

  17. García KE, Morales AL, Barrero CA, Greneche JM (2006) Corros Sci 48:2813–2830

    Article  Google Scholar 

  18. Zhang GA, Cheng YF (2011) Electrochim Acta 56:1676–1685

    Article  CAS  Google Scholar 

  19. Jeannin M, Calonnec D, Sabot R, Refait P (2011) Electrochim Acta 56:1466–1475

    Article  CAS  Google Scholar 

  20. Hamdy AS, Sa’eh AG, Shoeib MA, Barakat Y (2007) Electrochim Acta 52:7068–7074

    Article  CAS  Google Scholar 

  21. Keresztes Z, Felhősi I, Kálmán E (2001) Electrochim Acta 46:3841–3849

    Article  CAS  Google Scholar 

  22. Witte F, Fischer J, Nellesen J, Crostack H, Kaese V, Pisch A, Beckmann F, Windhagen H (2006) Biomaterials 27:1013–1018

    Article  CAS  Google Scholar 

  23. Chen J, Wang J, Han E, Dong J, Ke W (2007) Electrochim Acta 52:3299–3309

    Article  CAS  Google Scholar 

  24. Li Y, Zhang T, Wang F (2006) Electrochim Acta 51:2845–2850

    Article  CAS  Google Scholar 

  25. Gong Y, Cao J, Meng XH, Yang ZG (2009) Mater Corros 60:899–908

    Article  CAS  Google Scholar 

  26. Yang W, Ni R, Hua H (1984) Corros Sci 24:691–707

    Article  CAS  Google Scholar 

  27. Sharland SM (1987) Corros Sci 27:289–323

    Article  CAS  Google Scholar 

  28. Lin B, Hu R, Ye C, Li Y, Lin C (2010) Electrochim Acta 55:6542–6545

    Article  CAS  Google Scholar 

  29. Lv G, Xu C, Lv Y, Cheng H, He Z (2008) Chin J Chem Eng 16:646–649

    Article  Google Scholar 

  30. Perrin M, Gailleta L, Tessiera C, Idrissib H (2010) Corros Sci 52:1915–1926

    Article  CAS  Google Scholar 

  31. Lia L, Lia X, Donga C, Huang Y (2009) Electrochim Acta 54:6389–6395

    Article  Google Scholar 

  32. Królikowski A, Kuziak J (2011) Electrochim Acta 56:7845–7853

    Article  Google Scholar 

  33. van Hunnik EWJ, Pots BFM, Hendriksen ELJA (1996) The formation of protective FeCO3 corrosion product layers in CO2 corrosion. CORROSION/96, paper no. 6. NACE International, Houston

    Google Scholar 

  34. Melchers RE (2003) Corros Sci 45:923–940

    Article  CAS  Google Scholar 

  35. Melchers RE, Jeffrey R (2005) Corros Sci 47:1678–1693

    Article  CAS  Google Scholar 

  36. Melchers RE, Chernov BB (2010) Corros Sci 52:449–454

    Article  CAS  Google Scholar 

  37. Melchers RE (2006) Corros Eng Sci Technol 41:38–44

    Article  CAS  Google Scholar 

  38. Melchers RE, Jeffrey R (2008) Electrochim Acta 54:80–85

    Article  CAS  Google Scholar 

  39. Melchers RE (2006) Corros Sci 48:4174–4201

    Article  CAS  Google Scholar 

  40. di Caprioa D, Stafiej J (2011) Electrochim Acta 56:3963–3968

    Article  Google Scholar 

  41. Aarão Reis FDA, Stafiej J (2007) Crossover of interface growth dynamics during corrosion and passivation. J Phys Condens Matter. doi:10.1088/0953-8984/19/6/065125

  42. Saunier J, Dymitrowska M, Chaussé A, Stafiej J, Badiali JP (2005) J Electroanal Chem 582:267–273

    Article  CAS  Google Scholar 

  43. di Caprioa D, Stafiej J (2010) Electrochim Acta 55:3884–3890

    Article  Google Scholar 

  44. Taleb A, Chaussé A, Dymitrowska M, Stafiej J, Badiali JP (2004) J Phys Chem B 108:952–958

    Article  CAS  Google Scholar 

  45. Aarão Reis FDA, Stafiej J (2007) Scaling behavior in corrosion and growth of a passive film. Phys Rev E. doi:10.1103/PhysRevE.76.011512

  46. Deshpande KB (2010) Corros Sci 52:3514–3522

    Article  CAS  Google Scholar 

  47. Deshpande KB (2010) Corros Sci 52:2819–2826

    Article  CAS  Google Scholar 

  48. Archie GE (1942) Trans Am Inst Min Metall Pet Eng 146:54–62

    Google Scholar 

  49. Yan JF, Nguyen TV, White RE, Griffin RB (1993) J Electrochem Soc 140:733–742

    Article  CAS  Google Scholar 

  50. MacMullin RB, Muccini GA (1956) AIChE J 2:393–403

    Article  CAS  Google Scholar 

  51. Deslouis C, Festy D, Gil O, Maillot V, Touzain S, Tribollet B (2000) Electrochim Acta 45:1837–1845

    Article  CAS  Google Scholar 

  52. Sun W, Liu G, Wang L, Li Y (2012) Electrochim Acta 78:597–608

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Materials Science and Chemical Engineering, School of Chemical Engineering, Dalian University of Technology, 2 Linggong Road, Dalian, 116024, China

    Wen Sun, Guichang Liu, Lida Wang, Tingting Wu & Yang Liu

Authors
  1. Wen Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guichang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lida Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tingting Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guichang Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, W., Liu, G., Wang, L. et al. An arbitrary Lagrangian–Eulerian model for studying the influences of corrosion product deposition on bimetallic corrosion. J Solid State Electrochem 17, 829–840 (2013). https://doi.org/10.1007/s10008-012-1935-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10008-012-1935-9

Keywords

Search

Navigation