# Mathematical modelling of corrosion measurements

1999

## Degree Name

Doctor of Philosophy

## Department

School of Mathematics and Applied Statistics

## Abstract

The ability to predict the corrosion rate of a metal in a given environment is of great importance to BHP and to the metal industry in general. Because of the electrochemical nature of almost all corrosion reactions, electrochemical methods are commonly used to measure corrosion rates in the laboratory or in the field. The basic approach used in these techniques is to perturb the corrosive system from a known steady state value, and subsequently record its relaxation to a new steady state value. Experimental data are then fitted to a mathematical model in order to calculate the kinetic parameters of the reaction.

Most of the currently used methods for corrosion rate measurements are based on a kinetic equation, which was derived by Wagner and Traud in 1938. One of the most important simplifying assumptions used in the derivation of this equation is that the charge-transfer (or kinetic) processes at the electrode/solution interface rate determining, and thus dominate the rate of reaction. Transport of reactants towards, and products away from the electrode surface is assumed to proceed at a much higher rate compared to the kinetic processes, and thus has a negligible effect on the overall reaction rate. This assumption has been shown to produce significant errors in the calculated corrosion rates for many practical situations, e.g. zinc, zinc coatings and steel in near neutral solutions, where the transport processes proceed at a lower or comparable rate relative to the charge-transfer processes. In these cases, mathematical models based on mixed charge-transfer and mass transport control should be used for corrosion rate measurements, for closer approximation of experimental conditions and greater accuracy of calculation

The central concern of this project is to modify existing and/or find new improved, electrochemical corrosion rate measurement methods, based on mixed transport (diffusion in a finite layer) and charge-transfer control of all reactions, so that corrosion rates can be calculated with more accuracy and efficiency under a greater range of experimental conditions. This is achieved by developing and solving appropriate mathematical models representing different electrochemical techniques, which simultaneously account for kinetic (charge-transfer) and transport processes.

derive a new steady state polarization equation, and show that neglecting the effects of metal-ion build up and diffusion away from the electrode can produce significant errors in the measured corrosion rate. We also present new analytical and approximate solutions to a number of boundary value problems representing transient electrochemical methods. It is shown that compared to the full numerical solutions, the approximate solutions produce very good results, when the applied perturbation is small in magnitude. It is also shown that these can be used for nondestructive corrosion testing, with acceptable levels of accuracy. The existence of these exact and approximate solutions makes possible the calculation of corrosion parameters by merely fitting an elementary class of functions to transient experimental data. This leads to greater accuracy and efficiency compared to currently used steady state methods.

Finally, we develop a numerical scheme for the simulation of electrochemical diffusion-migration transport processes, involving multiple electrochemical reactions and nonlinear boundary conditions. This is in contrast to the currently available algorithms in the literature, which are limited in their application or make restrictive simplifying assumptions. Using this algorithm, we examine the effects of migration on metallic corrosion, and show that this leads to a lower rate of metal dissolution compared to that obtained when diffusion is the sole mechanism for transport.

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Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.