Further Modeling of Chloride Concentration and Temperature Effects on 1D Pit Growth

Abstract

The product of diffusion coefficient and saturation concentration of metal ions (D M+ · C tot ) is associated with steady state dissolution of metal in corrosion pits. In our previous paper, D M+ · C tot was modeled for one dimensional (1D) pit dissolution of super 13Cr stainless steel (S13Cr) by taking into account the common ion effect, as well as viscosity and temperature influences. However, the modeled values were only half of the experimentally-measured D M+ · C tot , implying that D M+ and/or C tot were underestimated. To improve the modeling of D M+ · C tot , the effects of complexation and electromigration were additionally considered, which led to the definition of effective diffusion coefficient (D eff ) applicable for the diffusion of metal ionic species under the combined effect of viscosity, temperature and electric field inside a growing 1D pit. The newly modeled D eff · C tot values were very close to the experimental values, validating the modeling approach described in this paper. Dissolution of metal under steady state diffusion can be described by the modified Fick's first law, which relates the limiting current density (i lim ) with the product of diffusion coefficient (D M+ ) and concentration difference ( C M+ ) of the metal ion through the diffusion length (L):where F is the Faraday constant, and n is the charge of the metal ion.For the dissolution of metal in a one dimensional (1D) pit electrode, the concentration of metal ion outside of the pit is commonly assumed to be zero, 1-8 so that C M+ is simply the concentration of metal ion at the pit bottom (C M+ ). It is also usually supposed that L is equal to the pit depth (δ), 9-12 although the diffusion of metal ions may extend out of pit, forming additional layer of hemispherical diffusion and causing L to be longer than δ.11 The effect of this additional diffusion layer on i lim was found to diminish if δ of 1D pit with 1 mm diameter was greater than 0.4 mm (aspect ratio of pit depth/mouth: 0.4) for SS 304 11 and super martensitic stainless steel. 10 More recent study on 1D pit growth of SS 316L, however, has suggested that the length of additional diffusion layer (L') is approximately 40% of pit diameter, and δ should be much larger than L' to apply the L ≈ δ condition for the calculation of i lim . 13In a previous paper, the authors suggested that i lim in 1D pit electrode of super 13Cr stainless steel (S13Cr) can be related to the sum of D M+ · C M+ from each metal component, if the transport of all metal ions is under diffusion control.14 In this case, i lim can be expressed as:Here each C M+ is replaced by the concentration of metal ions at the pit bottom (C Fe2+/pb , C Cr3+/pb and C Ni2+/pb ). The content of Mo in S13Cr is small (2 wt% or 1.16 at%), so it was omitted for the calculation of i lim . For Eq. 2, three conditions were postulated: 1) The diffusion coefficients of all metal ions are the same (, 2) Fe 2+ is the major dissolved species, and the precipitating metal salt at the pit bottom is considered to be FeCl 2 at which ...

Numerical Investigation of Critical Electrochemical Factors for Localized Corrosion using a Multi-species Reactive Transport Model

“…Because of the common ion effect, the solubility of the metal cation decreases significantly with an increase in chloride concentration. This inverse relationship between the saturation concentration of metal cation and the bulk concentration of sodium chloride has also been noted by several experimental [8] and numerical studies [39,43]. In Figure 5(b), we show the dependence of pH at the pit base on the temperature and bulk concentrations.…”

“…The metal chloride solution near the corroding surface will reach saturation when a high enough electrical potential is applied. As demonstrated by Jun et al [43], the effect of electrolyte viscosity on mass transport in such a concentrated electrolyte cannot be ignored. The effect of viscosity η and temperature T on the diffusion coefficient can be described using the Stokes-Einstein equation…”

“…However, the main drawback of the 1-D diffusion model is that it ignores the effect of electromigration and viscosity on species transport. Therefore, Jun et al further extended their model to calculate the flux inside the pit by incorporating the effect of electro-migration and viscosity into the species diffusion coefficient based on the Stokes-Einstein equation [43]. But this improvement is based only on parametric calibration which does not fundamentally correct the governing physics of species mass transport, and thus may not be applicable when focusing on the species concentration and the electrical potential instead of solely the flux.…”

The Critical Pitting Chloride Concentration of Various Stainless Steels Measured by an Electrochemical Method

“…Nishimoto et al 35 have also reported a sharp decrease of pH and increase of [C1 − ] resulted from the generation of micro-pits inside the crevice. Jun, Frankel and Sridhar 36,37 studied the diffusioncontrolled pit growth of Super 13Cr stainless steel and modeled the diffusion coefficient and the saturation concentration of metal ions for one-dimensional pit dissolution. They reported that the pit growth was more stable in bulk solutions with higher NaCl concentration and explained how the bulk NaCl concentration can affect the diffusion coefficients of metal ions and FeCl 2 precipitation in a growing pit.…”

On the Critical Factors for Estimating the Pit Stability Product under a Salt Film

“…Jun et al, and Srinivasan et al have demonstrated the importance of solution viscosity on diffusivity, indicating that the diffusion coefficient would decrease with an increase in pit depth 8,19,31. Thus, it was necessary to consider a variable diffusion coefficient due to the concentration gradient inside the pit.…”