Phase-field modeling for pH-dependent general and pitting corrosion of iron

Abstract

This study proposes a new phase-field (PF) model to simulate the pH-dependent corrosion of iron. The model is formulated based on Bockris’s iron dissolution mechanism to describe the pH dependence of the corrosion rate. We also propose a simulation methodology to incorporate the thermodynamic database of the electrolyte solutions into the PF model. We show the applications of the proposed PF model for simulating two corrosion problems: general corrosion and pitting corrosion in pure iron immersed in an acid solution. The simulation results of general corrosion demonstrate that the incorporation of the anodic and cathodic current densities calculated by a Corrosion Analyzer software allows the PF model to simulate the migration of the corroded iron surface, the variation of ion concentrations in the electrolyte, and the electrostatic potential at various pH levels and temperatures. The simulation of the pitting corrosion indicates that the proposed PF model successfully captures the anisotropic propagation of a pit that is affected by the local pH of the electrolyte solution and the aggregation of Cl− ions in the pit.

Computational modeling of pitting corrosion

“…This type of nonlocal model leads to a diffuse layer at the pit boundary which happens to match well the experimentally observed microstructure in several alloys (Li et al, 2016(Li et al, , 2018Badwe et al, 2018;Vallabhaneni et al, 2018;Yavas et al, 2018). PF models of pitting corrosion (Mai et al, 2016;Ansari et al, 2018;Chadwick et al, 2018;Mai and Soghrati, 2018;Nguyen et al, 2018;Tsuyuki et al, 2018) also use a diffuse region instead of a mathematically sharp transition between the electrolyte and the metal, and the governing equations in this case consist of two coupled PDEs in which the "thickness" of the diffuse layer introduces a length scale in the model. All these models are discussed in detail below.…”

“…For models that include the electromigration term, an additional equation is required in order to find the electric potential ϕ. Commonly used for this purpose is the Poisson-type equation for ϕ (Sharland et al, 1989;Tsuyuki et al, 2018), which, in the case of negligible charge density compared with electric permittivity of the electrolyte, reduces to the electro-neutrality equation (Sharland et al, 1989;Xiao and Chaudhuri, 2011):…”

“…In this equation, δ δϕ ℱ is the variational differentiation of the energy functional with respect to the PF variable, and L is a scalar coefficient. In PF models, the free energy functional ℱ(ϕ, C) can be selected in different forms according to the physical assumptions of the corrosion problem (Mai et al, 2016;Chadwick et al, 2018;Nguyen et al, 2018;Tsuyuki et al, 2018). In Eq.…”

Modeling the effect of insoluble corrosion products on pitting corrosion kinetics of metals

“…More recently, Mai and Soghrati 21 and Chadwick et al 22 proposed a similar PF models showing good agreement with experimental findings and have the ability to simulate complex microstructures. Tsuyuki et al 23 proposed a PF model that incorporates the pH effect on corrosion rate by considering pH-dependent interface mobility, where pH is approximated for each case by Corrosion Analyzer software. Their model qualitatively describes the overall phenomenon quite well but lacks any validation with experimental results, as identified by the authors.…”

Comparison Study of Produced Water Treatment Using Electrocoagulation and Adsorption

“…The experimental results of this work show that the iron electrode corroded inside the electrolyte solution after 3 min due to the local dissolution of the iron and the spreading of pits within the electrode surface resulting in the deterioration of the iron electrode ( Figure 2). According to (Tsuyuk et al, 2018) [28], the dissolution of iron during pitting corrosion is localized to the surface of the electrode where the passive protective film is destroyed. Also, according to (Wellner et al, 2018) [29] the pH solution inside the pit decreases due to generation of H + ion in the pit.…”