J. Mater. Sci. Technol. ›› 2021, Vol. 62: 254-267.DOI: 10.1016/j.jmst.2020.04.061
• Invited Review • Previous Articles
Bangalore Gangadharacharya Koushika,*(
), Nils Van den Steena, Mesfin Haile Mammea,b, Yves Van Ingelgema, Herman Terryna,*()
Received:2020-02-21
Revised:2020-04-18
Accepted:2020-04-30
Published:2021-01-30
Online:2021-02-01
Contact:
Bangalore Gangadharacharya Koushik,Herman Terryn
About author:herman.terryn@vub.be (H. Terryn).Bangalore Gangadharacharya Koushik, Nils Van den Steen, Mesfin Haile Mamme, Yves Van Ingelgem, Herman Terryn. Review on modelling of corrosion under droplet electrolyte for predicting atmospheric corrosion rate[J]. J. Mater. Sci. Technol., 2021, 62: 254-267.
Fig. 1. Classifications of various modelling and simulation methods for droplet corrosion along with their formation and evolution.
Fig. 2. Schematic of corrosion of metal (iron) under droplet electrolyte cross section.
Fig. 3. Droplet volume as a function of evaporation time. Inset: Cross-section of 1. hemispherical, 2. flattened hemispheric cap and 3. planar cylindrical droplet geometries [17].
Fig. 4. (a) Anode-to-cathode resistance, (b) anode-to-cathode iR voltage drop and (c) total limiting oxygen reduction current as a function of evaporation time (increasing concentration of electrolyte), (d) anode-to-cathode iR voltage drop as a function of droplet height (assuming constant concentration) [17].
Fig. 5. The schematic diagram of the geometry of TPB zone. (a) A vertical electrode under partial immersion in electrolyte and (b) an electrolyte droplet attached on a planar electrode surface [49].
Fig. 6. Comparison between simulation result and experimental data simulation for the model validation [49].
| No. | Approach | Key considerations | Key outcome | Shortcomings |
|---|---|---|---|---|
| 1 | Analytical by Lyon et al. [ | (1) Evaporating droplet. (2) Wetting and drying effects. (3) Different droplet geometries. (4) Oxygen diffusion by Fick’s law. (5) Electrolyte conductivity by Debey-Huckel-Onsager equation. | Evaporative condition: | (1) Gives a qualitative trend but not quantitative understanding. (2) The initial droplet radius is always 1?mm. (3) Arbitrary quantity of ionic species. (4) Fixed ratio of cathode to anode area. |
| (1) For hemispherical droplet: anode-to-cathode resistance did not limit the corrosion rate. (2) For planar droplet: corrosion rate was subjective to resistive control. | ||||
| Non-evaporative condition: | ||||
| Corrosion rate was under resistive control for all geometries. | ||||
| 2 | Analytical by Jiang et al. [ | (1) Droplet divided into bulk and three phase boundary (TPB) zones. (2) Droplet contact angle (<90 deg.) (3) Droplet distribution (liquid dispersion). (4) Relationship between liquid dispersion and TPB length. (5) Relationship between cathodic current density and TPB length. | (1) The effect of TPB characteristic length (‘g’) on cathodic process was depended only on the electrochemical process, independent of material properties. (2) Calculated cathodic limiting current density linearly increases with increasing’ g’. (3) Increase in liquid dispersion on the metal surface leads to increase in total cathodic limiting current. | (1) Limited to a contact angle between zero and ninety degrees. (2) Assumes equal drop-size distribution to account for liquid dispersion during atmospheric corrosion. (3) Static droplet. |
Table 1 Comparison of key differences between analytical modelling approaches of corrosion under droplet electrolyte.
| No. | Approach | Key considerations | Key outcome | Shortcomings |
|---|---|---|---|---|
| 1 | Analytical by Lyon et al. [ | (1) Evaporating droplet. (2) Wetting and drying effects. (3) Different droplet geometries. (4) Oxygen diffusion by Fick’s law. (5) Electrolyte conductivity by Debey-Huckel-Onsager equation. | Evaporative condition: | (1) Gives a qualitative trend but not quantitative understanding. (2) The initial droplet radius is always 1?mm. (3) Arbitrary quantity of ionic species. (4) Fixed ratio of cathode to anode area. |
| (1) For hemispherical droplet: anode-to-cathode resistance did not limit the corrosion rate. (2) For planar droplet: corrosion rate was subjective to resistive control. | ||||
| Non-evaporative condition: | ||||
| Corrosion rate was under resistive control for all geometries. | ||||
| 2 | Analytical by Jiang et al. [ | (1) Droplet divided into bulk and three phase boundary (TPB) zones. (2) Droplet contact angle (<90 deg.) (3) Droplet distribution (liquid dispersion). (4) Relationship between liquid dispersion and TPB length. (5) Relationship between cathodic current density and TPB length. | (1) The effect of TPB characteristic length (‘g’) on cathodic process was depended only on the electrochemical process, independent of material properties. (2) Calculated cathodic limiting current density linearly increases with increasing’ g’. (3) Increase in liquid dispersion on the metal surface leads to increase in total cathodic limiting current. | (1) Limited to a contact angle between zero and ninety degrees. (2) Assumes equal drop-size distribution to account for liquid dispersion during atmospheric corrosion. (3) Static droplet. |
Fig. 7. Radial distribution of total density at the electrode surface with time as parameter [86,158].
Fig. 8. Oxygen concentration in the droplet as a function of kR/D, where ‘k’ is the cathodic reaction rate constant, ‘R’ is the radius of the droplet, and ‘D’ is the diffusion coefficient of dissolved oxygen [50].
| No. | Approach | Key considerations | Key outcome | Shortcomings |
|---|---|---|---|---|
| 1 | Numerical simulation by Venkatraman et al. [ | (1) Three-dimensional transient finite element model. (2) Droplet on bare zinc surface in the absence of oxide layer. (3) Spatio-temporal variation of ionic species concentration. (4) Early stage of corrosion: no formation of precipitates. | (1) Concentration profile of zinc ions and plot of current density vectors. (2) Concentration of the zinc ions was high near the metal surface, with an accumulation towards the cathodic region. | (1) Does not consider heterogeneous or homogeneous chemical reactions in the droplet. (2) Static droplet. (3) Anode-cathode separation was not described. |
| 2 | Numerical simulation by Chang et al. [ | (1) Two-dimensional transient finite element model of droplet on iron. (2) Contribution of migration; primary precipitates; local electroneutrality and homogeneous reaction. (3) Anodic and cathodic regions were not assumed prior. (4) Active-passive transition due to corrosion precipitates. (5) Simulated both at corrosion and at an applied potential. (6) Extended to simulate corrosion in the presence of CO2 instead of O2. | (1) Galvanic effects due to precipitates. (2) Alkaline cathodic region at the periphery and slightly acidic at the center. (3) Active-passive transition of anode due to of Fe(OH)3 precipitates, with active cathodic region. (4) With dissolved CO2 found that the species FeCO3 accumulated in the anodic reaction | (1) Static droplet. (2) Needs extension to include parameters like surface wettability and spatio-temporal variation of involved ionic species with 3D model. |
| 3 | Combination of empirical and numerical simulation by Cole et al. [ | (1) Multiscale model w.r.t. production, transport, and deposition of aerosols. (2) Dynamic droplet. (3) Spatio-temporal variations of involved ionic species. (4) Porous oxide layer. | (1) Oxygen concentration in the droplet as a function of droplet radius, cathodic reaction rate constant, diffusion of O2. (2) Porous oxide promotes sufficient alkalinity at the oxide-metal interface, promoting the formation of a compact oxide layer. | (1) Empirical models describing transport of aerosols doesn’t give a general understanding. (2) Droplet model needs extension to include surface energy and evolution of anode-cathode separation. (3) The porous oxide model needs extension to account for oxide layer evolution due to corrosion precipitates and pH variations within the droplet. |
Table 2 Comparison of key differences between numerical modelling approaches of corrosion under droplet electrolyte.
| No. | Approach | Key considerations | Key outcome | Shortcomings |
|---|---|---|---|---|
| 1 | Numerical simulation by Venkatraman et al. [ | (1) Three-dimensional transient finite element model. (2) Droplet on bare zinc surface in the absence of oxide layer. (3) Spatio-temporal variation of ionic species concentration. (4) Early stage of corrosion: no formation of precipitates. | (1) Concentration profile of zinc ions and plot of current density vectors. (2) Concentration of the zinc ions was high near the metal surface, with an accumulation towards the cathodic region. | (1) Does not consider heterogeneous or homogeneous chemical reactions in the droplet. (2) Static droplet. (3) Anode-cathode separation was not described. |
| 2 | Numerical simulation by Chang et al. [ | (1) Two-dimensional transient finite element model of droplet on iron. (2) Contribution of migration; primary precipitates; local electroneutrality and homogeneous reaction. (3) Anodic and cathodic regions were not assumed prior. (4) Active-passive transition due to corrosion precipitates. (5) Simulated both at corrosion and at an applied potential. (6) Extended to simulate corrosion in the presence of CO2 instead of O2. | (1) Galvanic effects due to precipitates. (2) Alkaline cathodic region at the periphery and slightly acidic at the center. (3) Active-passive transition of anode due to of Fe(OH)3 precipitates, with active cathodic region. (4) With dissolved CO2 found that the species FeCO3 accumulated in the anodic reaction | (1) Static droplet. (2) Needs extension to include parameters like surface wettability and spatio-temporal variation of involved ionic species with 3D model. |
| 3 | Combination of empirical and numerical simulation by Cole et al. [ | (1) Multiscale model w.r.t. production, transport, and deposition of aerosols. (2) Dynamic droplet. (3) Spatio-temporal variations of involved ionic species. (4) Porous oxide layer. | (1) Oxygen concentration in the droplet as a function of droplet radius, cathodic reaction rate constant, diffusion of O2. (2) Porous oxide promotes sufficient alkalinity at the oxide-metal interface, promoting the formation of a compact oxide layer. | (1) Empirical models describing transport of aerosols doesn’t give a general understanding. (2) Droplet model needs extension to include surface energy and evolution of anode-cathode separation. (3) The porous oxide model needs extension to account for oxide layer evolution due to corrosion precipitates and pH variations within the droplet. |
Fig. 9. Schematic of distribution of cluster on substrate [98].
| No. | Approach | Features |
|---|---|---|
| 1 | Atomistic approach | Accounts for: |
| Adsorption of monomers. | ||
| Surface diffusion of monomers. | ||
| Agglomeration | ||
| Cluster formation | ||
| Droplet nucleation. | ||
| Mostly uses: | ||
| Random distribution functions to describe the nucleation sites. | ||
| Monte-Carlo or molecular dynamics simulations. | ||
| 2 | Continuum approach | Accounts for: |
| Instantaneous nucleation of droplets. | ||
| Growth of droplets further in macroscopic scale. | ||
| Mostly uses: | ||
| Randomly distributed nucleation sites. | ||
| Heat and mass transfer formulations. | ||
| 3 | Coupled approach | Combination of atomistic and continuum approaches. |
Table 3 Comparison of key differences between modelling approaches of formation and evolution of droplet.
| No. | Approach | Features |
|---|---|---|
| 1 | Atomistic approach | Accounts for: |
| Adsorption of monomers. | ||
| Surface diffusion of monomers. | ||
| Agglomeration | ||
| Cluster formation | ||
| Droplet nucleation. | ||
| Mostly uses: | ||
| Random distribution functions to describe the nucleation sites. | ||
| Monte-Carlo or molecular dynamics simulations. | ||
| 2 | Continuum approach | Accounts for: |
| Instantaneous nucleation of droplets. | ||
| Growth of droplets further in macroscopic scale. | ||
| Mostly uses: | ||
| Randomly distributed nucleation sites. | ||
| Heat and mass transfer formulations. | ||
| 3 | Coupled approach | Combination of atomistic and continuum approaches. |
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