Consider a surface reaction that can represent deposition or condensation of gas species on particle C(B):
The rate of this deposition reaction is given in Arrhenius form as
 | (19–77) |
where 
is the symbol for surface reactants and 
is the stoichiometric coefficient for the surface reactants, and
implies product over all surface species.
In principle, the same reaction rate as given by Equation 19–77 , above, can also be calculated from the collision rate between the gas species and the particle. Its contribution to the number density of a class j particle can be obtained from
 | (19–78) |
where 
. The collision frequency between ? and a class j
particle is given by
 | (19–79) |
where 
is the site fraction of surface species 
and 
and 
are, respectively, the collision diameters of gas species
and the class j particle. By assuming that the
particle mass is much greater than that of a gas 
molecule, the reduced mass can be approximated by
 | (19–80) |
where 
is the molar weight of gas species 
.
Hence the collision frequency given by Equation 19–79 becomes
 | (19–81) |
With the collision frequency given above, the contribution of
deposition to the surface-chemistry source term for the
r -th moment takes the form
 | (19–82) |
By assuming 
, the above equation becomes
 | (19–83) |
Equation 19–83 can be rearranged to make a one-to-one mapping between it and the Arrhenius rate expression given by Equation 19–77 can be made. Since the surface site concentration is related to surface site fraction via:
 | (19–84) |
the parameter 
in Equation 19–83
can be rewritten as
 | (19–85) |
in the above equations is the site occupancy of surface species
. The site occupancy of a surface
species is assigned when surface species are declared in the mechanism file. A surface
species by default has a site occupancy of 1. Definition of surface site occupancy is
given in the Chemkin Input Manual
Input
Manual.
By substituting Equation 19–85 into Equation 19–83 and by applying the fact that
 | (19–86) |
the surface source term due to deposition of gas species 
becomes
 | (19–87) |
Hence the Arrhenius rate parameters for the 
deposition reaction can be expressed as
 | (19–88) |
 | (19–89) |
and
 | (19–90) |
It should be noted that Equation 19–88 through Equation 19–90 give a guideline for what the reaction rate parameters should be. The actual rate parameters do not have to be these values and can be any general fit. Particle tracking calculates the rate r is as given by Equation 19–77 using the specified rate parameters and then computes the source terms for moments from the right-most side of Equation 19–87 .
The sectional method can directly use the reaction rate given by equation Equation 19–77 to compute the creation and destruction of particles of a certain size. Thus, when a reaction happens on a particle of size k, the corresponding change in number density is calculated as
In the above equation, A k denotes the surface area of a particle of size k. Note that the reaction creates a particles of size j and therefore
Three things can be noted about the representation of reaction i :
The rate equation applies to particles of "all" sizes.
It involves surface composition of the particle under consideration.
The etching/oxidation reaction may take out more monomers than the particle of given size holds
In Ansys Chemkin these are addressed as follows:
The particles of size k become the representative particles from section k. As in the case of coagulation, the new particle of size j formed due to the growth/etching reaction may not exactly coincide with the representative particle size from any section. The resulting particle is then split such that two properties of the distribution are conserved as indicated by Equation 19–15 . Ansys Chemkin conserves total particle number density and mass.
The surface state of all particles is assumed to be identical. That is, all particles have same surface species coverage. Effectively, Ansys Chemkin considers the rate-of-progress q i to be independent of the particle size.
When the number of monomers in the particle of a given size are smaller than those etched out by a surface reaction, Ansys Chemkin proportionately decreases the number density of that size.