Diffusion-limited corrosion rate

Chapters 1 to 3 describe the theory of corrosion engineering and offer analyzed case studies and solved problems in the thermodynamics of corrosion processes, the relevance of electrochemical kinetics to corrosion, low field approximation theory, concentration polarization, the effects of polarization behavior on corrosion rate, the effect of mass transfer on electrode kinetics, and diffusion-limited corrosion rates. 

The sloth characteristic liquid diffusion means that diffusion often limits the overall rate of processes occurring in liquids. In chemistry, diffusion limits the rate of acid-base reactions in physiology, diffusion limits the rate of digestion in metallurgy, diffusion can control the rate of surface corrosion in the chemical industry, diffusion is responsible for the rates of liquid-liquid extractions. Diffusion in liquids is important because it is slow. 

In Section 1.4 see Fig. 1.31h) it has been shown that when a corrosion reaction is controlled by the rate of oxygen diffusion, both the rate of corrosion and the corrosion potential increase with / l. the limiting current density, i.e. 

For many cooling waters, including seawater and also drinking water, where corrosion rates are 70 to 100% of the limiting diffusion current, the use of dimensionless group analysis can then be applied. 

By substituting the appropriate values for viscosity and diffusion at various temperatures, they found that corrosion rates could be calculated which were confirmed by experiment. The corrosion rates represent maxima, and in real systems, corrosion products, scale and fouling would reduce these values often by 50%. The equation was useful in predicting the worst effects of changing the flow and temperature. The method assumes that the corrosion rate is the same as the limiting diffusion of oxygen at least initially this seems correct. 

Film-free conditions It has been observed for many metals that the magnitude of / i, (see Section 1.4) increases with temperature and that the activation energy for dissolution is low, suggestive of a diffusion-limited anode process when the migration of corrosion products away from the surface is rate controlling. Some examples of the value of the activation energy for this process are given in Table 2.4. 

Mechanistically, in approximately neutral solutions, solid state diffusion is dominant. At higher or lower pH values, iron becomes increasingly soluble and the corrosion rate increases with the kinetics approaching linearity, ultimately being limited by the rate of diffusion of iron species through the pores in the oxide layer. In more concentrated solutions, e.g. pH values of less than 3 or greater than 12 (relative to 25°C) the oxide becomes detached from the metal and therefore unprotective . It may be noted that similar Arrhenius factors have been found at 75 C to those given by extrapolation of Potter and Mann s data from 300°C. 

Chemical/Physical. Matheson and Tratnyek (1994) studied the reaction of fine-grained iron metal in an anaerobic aqueous solution (15 °C) containing chloroform (107 pM). Initially, chloroform underwent rapid dehydrochlorination forming methylene chloride and chloride ions. As the concentration of methylene chloride increased, the rate of reaction appeared to decrease. After 140 h, no additional products were identified. The authors reported that reductive dehalogenation of chloroform and other chlorinated hydrocarbons used in this study appears to take place in conjunction with the oxidative dissolution or corrosion of the iron metal through a diffusion-limited surface reaction. 

At 60 minutes only, dc potentiodynamic curves were determined from which the corrosion current was obtained by extrapolation of the anodic Tafel slope to the corrosion potential. The anodic Tafel slope b was generally between 70 to 80 mV whereas the cathodic curve continuously increased to a limiting diffusion current. The curves supported impedance data in indicating the presence of charge transfer and mass transfer control processes. The measurements at 60 minutes indicated a linear relationship between and 0 of slope 21mV. This confirmed that charge transfer impedance could be used to provide a measure of the corrosion rate at intermediate exposure times and these values are summarised in Table 1. 

In SNF corrosion tests, there has been a tendency to use the release of more soluble species Tc, Cs, and Mo as markers for fuel corrosion (Finn et al. 2002). As none of these elements are present in the U02 matrix, this approach may not reveal the actual fuel matrix corrosion rate. Furthermore, short-term leaching tests may not expose possible diffusion-limited (tl/2) release of gap and grain boundary species and assume excessive rates of reaction based on initial fast release rates. The microstructure, radiation field, and composition will change over time, so that tests carried out on fuel today may not be relevant to fuel behaviour 300 to 1000 years from now, once the high p-,y-field has decayed. 

There are several factors that can lead to non-Tafel behavior. Diffusion limitations on a reaction have already been introduced and can be seen in the cathodic portion of Fig. 27. Ohmic losses in solution can lead to a curvature of the Tafel region, leading to erroneously high estimations of corrosion rate if not compensated for properly. The effects of the presence of a buffer in solution can also lead to odd-looking polarization behavior that does not lend itself to direct Tafel extrapolation. 

For the case where diffusion of the corrosive ions is the rate controlling reaction, it has been found that P = po (1 + Ac/Aa) where p is the penetration that is proportional to the corrosion rate and p0 is the corrosion rate of the less noble uncoupled metal Ac and Aa are the areas of the more noble and active metal respectively (Uhlig and Revie, pp. 101-103).7 If a galvanic cell is not avoidable, a large anode and a limited size of cathode are recommended. Stagnant conditions and weak electrolytes may lead to pitting in spite of the large area of the exposed active metal. 

The sequence of reactions involved in the overall reduction of nitric acid is complex, but direct measurements confirm that the acid has a high oxidation/reduction potential, -940 mV (SHE), a high exchange current density, and a high limiting diffusion current density (Ref 38). The cathodic polarization curves for dilute and concentrated nitric acid in Fig. 5.42 show these thermodynamic and kinetic properties. Their position relative to the anodic curves indicate that all four metals should be passivated by concentrated nitric acid, and this is observed. In fact, iron appears almost inert in concentrated nitric acid with a corrosion rate of about 25 pm/year (1 mpy) (Ref 8). Slight dilution causes a violent iron reaction with corrosion rates >25 x 1()6 pm/year (106 mpy). Nickel also corrodes rapidly in the dilute acid. In contrast, both chromium and titanium are easily passivated in dilute nitric acid and corrode with low corrosion rates. 

The effect of fluid velocity on the corrosion of several commercial materials in seawater is shown in Fig. 7.31 (Ref 51). Three generalized types of materials are indicated by the corrosion behavior. The copper-base alloys, cast iron, and carbon steels tend to progressively increase in corrosion rate with increasing velocity. This is consistent with the schematic representation shown in Fig. 4.10, where the limiting current density for diffusion control of the cathodic reaction increases with... 

In addition the actual corrosion rate may be limited by the availability (diffusion to the surface) of the reactants, even though the raised temperature could increase the rate of reaction... 

The foregoing survey was focused on situations where bnlk diffusion processes were rate determining. Such systems are amenable to analysis using an electrochemical approach. Other factors such as transport down pores or cracks, volatilization or melting of the oxide scale may occur and require different analyses but diffusion controlled processes may be mathematically modeled and correlated with the defect chemistry of the corrosion product. These limiting cases provide a guide to understanding the more complex phenomena frequently encountered. 

A most surprising behavior was found when the polarization current of a corroding specimen was observed as a function of flow rate. Fig.20 shows the results which were obtained. Anodic and cathodic polarization currents in milliamps at potentials of 50 millivolts from the corrosion potential are plotted against flow rate. In several runs reproducible behavior was observed. The cathodic current varies with flow rate to the th power, while the anodic current varies with flow rate to the th power. This relationship holds true over more than one decade of flow rates. It is very difficult to explain such results in terms of conventional mass transfer limitations. It is well known that the diffusion limited current varies approximately proportionally to the flow rate in the turbulent region and with the square root of flow rate in the laminar region. If on the other hand the polarization current was transport limited across the corrosion... 

The corrosion rate cannot exceed the diffusion-limited cathodic current. This fact can be used for an estimation of the probable maximum value of the corrosion rate. 

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