Formation and arrangement of pits by a corrosive gas

When corroding or otherwise aggressive particles are incident on a surface, pits can form. For example, under certain circumstances rock surfaces that are exposed to salts can form regular tessellating patterns of pits known as “tafoni.” We introduce a simple lattice model in which a gas of corrosive particles, described by a discrete, biased diffusion equation, drifts onto a surface. Each gas particle has a fixed probability of being absorbed and causing damage at each contact. The surface is represented by a lattice of strength numbers which reduce after each absorbtion event, with sites being removed when their strength becomes negative. Regular formations of pits arise spontaneously, with each pit having a characteristic trapezoidal geometry determined by the particle bias, absorbtion probability, and surface strength. The formation of this geometry may be understood in terms of a first order partial differential equation and is a consequence of particle concentration gradients which arise in the pits. By viewing pits as particle funnels, we are able to relate the gradient of pit walls to absorbtion probability and particle bias.