During the particle formation phase, surface reactions only affect the size distribution of the particles but not the total number of the particles. However, during the reduction phase, the particle number density has to be decreased when the smallest possible particles (size class = ) are gasified. The particle-depletion model assumes that the particle-reduction process consists of two distinct steps. When the average particle size is large enough, the size-reduction process will reduce the mean particle diameter first without affecting the particle number density. Once the mean particle class reaches a critical value (size class = ), reduction of the total particle number will occur when the smallest particles start disintegrating into gaseous products. Three important model parameters are required in this depletion model: minimum particle class, critical particle class to activate the sink term for the zero-th size moment, that is, the number density, and the functional form of the sink term. The minimum particle class is assumed to be equal to the smallest inception class of the particle, that is,

(19–95)

The smallest particles are assumed to begin to disappear when the mean particle size drops below a pre-determined critical size class, . By default, the critical size class is computed by

(19–96)

This parameter can also be specified on the input panel for the Dispersed Material options of the reactor model in the Ansys Chemkin Interface. The sink term for the zero-th size moment will be activated when the condition

(19–97)

is satisfied. The functional expression of the sink term, S₀, can be easily obtained when the average size class is equal to the minimum size class

(19–98)

If the average size class is between and , a transition function is needed to describe how S 0, increases from 0 to . For simplicity, a sine function is implemented

(19–99)

Other functional forms such as linear and exponential are also possible candidates for the transition function in the particle depletion model. An appropriate functional form can be derived from measurements of particle number density profiles in the particle reduction region.