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The 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 convection 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. The model generates regular formations of pits, 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. By viewing pits as particle funnels, we are able to relate the gradient of pit walls to absorbtion probability and particle bias.