Consider a surface reaction in which all reactants are surface species, such as:
This surface reaction will affect the particle size distribution because it increases the particle class, that is, the number of bulk molecules, by
[cm-2 -sec-1
],
where 
is the production rate of bulk species due to the is
-th surface reaction. Also, 
is the rate of progress of the surface reaction in
[mole/cm2 -sec] and is evaluated by Ansys Chemkin from the Arrhenius
coefficients given in the reaction data, that is,
 | (19–91) |
where 
is the symbol for surface species participating in the surface
reaction.
 | (19–92) |
in which 
and 
and 
are the surface area for particle class i and
j, respectively. Accordingly, the change in the
r -th size moment due to this surface reaction is found to
be
 | (19–93) |
By assuming 
, the above equation becomes
 | (19–94) |
Note that the surface source term for the r -th moment is proportional to the total particle surface area.
The sectional method can directly use the rate expressions for each particle size. Thus, the treatment is identical to that in section Implementation for Sectional Method .