For a surface reaction to affect the distribution of particle sizes, it must be involved in the production or consumption of the bulk species representing the particle core. A surface reaction can increase the total particle mass if it results in a net gain of the bulk species, and its effect on the particle size distribution function will be to shift the distribution profile to the right (towards the direction of large particle sizes). The surface source terms for the r -th size moment due to the net effect from all surface reactions can be written as

(19–76)

where represents the contribution of the is -th surface reaction to the r -th moment of the particle size distribution. The units of the source term are [cm^-3 -sec^-1 ]. Derivations of surface source term for various types of surface reactions are described in the following sections.