Dynamic scaling of pit-size distribution in corrosion patterns

A growth model is presented to simulate the corrosion pattern in pitting corrosion in three dimensions. The pitting corrosion is controlled by diffusion of anions toward the metal surface. The computer simulation is performed to study the scaling structure of pit-size distribution in the corrosion pattern. It is shown that a transition occurs in the overall corrosion pattern from disconnected pits to a percolating structure at the percolation threshold. Below the percolation threshold, it is found that the pit-size distribution ${\mathit{n}}_{\mathit{s}}$(t) obeys the dynamic scaling ${\mathit{n}}_{\mathit{s}}$(t)≊${\mathit{t}}^{\mathrm{-}\mathit{w}}$${\mathit{s}}^{\mathrm{-}\mathrm{\tau }}$f(s/${\mathit{t}}^{\mathit{z}}$) (τ=0.93±0.03, z=1.43±0.02, and w=0.66±0.02), where the cutoff function f(x) is a constant for x≪1.