While the implementation of particle etching/oxidation is relatively straightforward for the sectional method as described in Implementation for Sectional Method , it needs somewhat special treatment for the method of moments. The particle depletion model included with Particle Tracking is a phenomenological one that mimics the decrease in particle number density and in particle size during reduction (for example, during soot-particle oxidation). When a particle population undergoes oxidation or gasification, the particles start shrinking in size and the particle population loses mass. Because the particle population covers a wide size range, two different outcomes can be expected for the particles, depending on their sizes. If the particle is large enough, it will primarily decrease in size during the reduction. On the other hand, the smallest particles will disintegrate into gas species as they cannot shrink any further. Of course, in reality, some large-size particles can break down into smaller particles. However, this particle breakdown process is too complicated for our purposes, because it depends on factors related to the structure of the particle and the fluid dynamic forces.

The particle depletion model instead aims to capture the essence of the particle reduction process to the extent possible, given the statistical nature of the problem. The basic concept of the depletion model is that, when the average particle class is above a critical value, the number density of the population remains the same and the particles only undergo size/class reduction. Once the average particle class reaches a minimum value, the smallest particles stop shrinking and begin to disintegrate into gaseous species, that is, the number density of the particle population decreases.