Mathematical description and analysis of the corrosion of metals under lacquer coatings in seawater

Abstract

We propose a mathematical model for the analytic investigation of the processes of corrosion fracture of metals under lacquer coatings in seawater on the basis of an experimentally established dependence of the corrosion rate of a metal without coatings on the concentration of a passivator. It is shown that, for the examined type of coatings, the corrosion rate first linearly increases with time but then, on attainment of a certain level, its subsequent increase is substantially decelerated. If the corrosion rate of the uncoated metal is higher than 0.05 mm/yr, then the rate of corrosion under coatings is lower by at least an order of magnitude.Some model representations of the mechanism of aging and fracture of lacquer coatings in seawater, the corresponding boundary-value problems formulated on the basis of the relevant mathematical model, and analytic-numerical methods for their solution can be found in [1,2]. These results were obtained for small deflections (blisters) of a lacquer film over the corrosion center and an almost linear law of increase in the corrosion rate to a certain fixed value.In these works, we refined the boundary-value problem proposed for the description of the osmotic growth of corrosion centers in the stage of corrosion fracture of a metal under the coating. On the basis of the solution of this problem obtained in terms of the empirical dependence of the rate of corrosion on the uncoated metal surface vs. the concentration of a passivator in seawater, we gave quantitative estimates for the growth rate of the radius of the corrosion center and the rate of fracture processes in the metal under the coating.Seawater contains both sodium and chlorine ions and oxygen. It saturates the coating and penetrates into the uncoated microareas of the metal, which later turn into corrosion centers. In [1], it was discovered that the times for which they are filled with different components of seawater are practically equal and much shorter than the service life of the coating. This is why, in what follows, we can speak about the diffusion of seawater. Water washes out passivating and some other components from the coating and, as a result, they appear in the cavities. The presence of sufficiently large amounts of passivating components in the cavity under the coating protects the metal against corrosion. As soon as these admixtures are dissolved, the molar concentration of pure water in the corrosion center becomes lower than its concentration in seawater (the same is true for its chemical potential). Therefore, even if the cavities are completely filled with water, it penetrates into the centers to equalize the indicated molar concentrations.In course of time, osmosis promotes blistering of the coating film over the corrosion center. As a result, the volume of the center increases. The results of theoretical analysis performed in [1] (and corroborated by the experimental data) show that, for some values of strength and thickness of the film, concentration of the passivator, and linear adhesion on th...

A mathematical model for lifetime prediction of lacquer‐paint coatings in sea water

“…At stage 1 the process of diffusive filling of the volume of the coating and empty cavities under it with sea water is described by the diffusion equations of water, oxygen, chlorine and sodium ions in a coating film with appropriate initial and boundary conditions [1,3]. The time moment τ 1 of the diffusive filling of the cavities under the coating with sea water is determined according to the prescribed degree of fullness of the cavities with sea water.…”

“…In addition to the equations of the previous stage, the mathematical model of the 5th stage includes the following equations: the equation of the osmotic transportation of water through a coating film, but with account for the sources of absorption of water according to the chemical reaction in the site [3]; equation, which connects the change in time of mass of corrosion products with corrosion rate. These equations together with appropriate initial conditions for passivator concentration, rust mass and radius of the corrosion site and the experimentally determined dependence of corrosion rate on passivator concentration constitute the complete system of the equations of the model for calculation of osmotic and corrosion processes at this stage.…”

“…In contrast to previous stages, when it was possible to obtain analytical solution, at this stage we can get a solution only by the numerical method [2,3].…”