When a given aggregate is not completely coalesced to a sphere, the apparent collision diameter of the aggregate is different from that of the sphere of the same mass. Consequently, modifications to the collision frequency formulation are required to account for the difference in collision diameter. In general, all aggregates of the same mass (or volume) do not necessarily have the same number of primary particles. Not only can the primary particles that make up an aggregate have different diameters, they can also have different shapes as well. In addition, a given aggregate can have differing apparent collision diameters that depend on the direction vector along which the aggregate collides. (For example, consider the case of an aggregate consisting of a straight chain of primary particles.)

From a modeling perspective, accounting for such effects would require resolution in another coordinate dimension. The computational cost of such resolution would be prohibitive. It is also quite likely that the physical insight obtained would not be of high fidelity to justify the added expense, due to the uncertainties and further assumptions/sub-models that would be required to capture these effects.

Two simplifying assumptions are therefore made in the aggregation model implemented in the Ansys Chemkin Particle Tracking feature as a result of the above considerations. These are:

For correctly capturing first-order particle aggregate properties (that is, aggregate area and volume or equivalently number density of primary particles and number density of aggregates), these two simplifying assumptions are appropriate.

With these assumptions, the following quantities can be defined:

(19–132)

(19–133)

(19–134)

(19–135)

In Equation 19–132 through Equation 19–135 , subscript p and j indicate primary particle and the class (that is, the number of atoms of the bulk material) of the aggregate, respectively, while N is the number density and V denotes the volume. The number of primary particles in the aggregate changes as the aggregate coalesces. The collision diameter of the aggregate depends on the primary particle size and the mass fractal dimension, D _f.

The collision diameter of the aggregates influences the frequency of collision and thus evolution of the particle system. The collision diameter of an aggregate is larger than the corresponding (volume-equivalent) sphere. Thus, there is a more pronounced scavenging effect, that is, the larger aggregate "consumes" a smaller one, when larger particles are aggregates rather than completely coalesced spheres.

The fractal dimension can be considered as a measure of how densely packed the primary particles are in an aggregate. Its value varies from 3 for completely fused spheres to about 1.7 for cluster-cluster aggregation [148] in Brownian collisions. In principle, the evolution of the fractal dimension may also be modeled as a function of physical processes, such as particle collision frequency and fusion time. However, little fundamental work has been done in this area. Therefore, at present, the Particle Tracking feature assumes that the fractal dimension is fixed and specified by the user.