  We study a model for corrosion and passivation of a metallic surface after
small damage of its protective layer. The crossover from an initial regime of
slow corrosion rate (pit nucleation) to a regime of rapid corrosion
(propagation of the pit) takes place at the incubation time. The model is
defined in a lattice whose sites represent the possible states of the metal
(bulk, reactive and passive) and the solution (neutral, acidic or basic).
Probabilistic rules describe passivation of the metal surface, dissolution of
the passive layer, which is enhanced in acidic media, and spatially separated
electrochemical reactions, which may create pH inhomogeneities in the solution.
  From a suitable matching of characteristic times of creation and annihilation
of pH inhomogeneities in the solution, a scaling theory gives the average
radius of the dissolved region at the incubation time as a function of the
model parameters. That radius decreases with the rate of spatially separated
reactions and the rate of dissolution in acidic media, and increases with the
diffusion coefficient of H+ and OH- ions in solution. The average incubation
time is written as the sum of a series of characteristic times for the slow
dissolution in neutral media. It linearly increases with the rate of
dissolution in neutral media, under the reasonable assumption that this is the
slowest rate of the process. The results are confirmed by numerical simulation
in two-dimensional lattices, but extension to three dimensions is discussed.
