The constant interaction among particles in an aerosol system can affect the particle distribution. Agglomeration is the process in which particles collide with one another and adhere to form larger particles. As mentioned in Creation/Selection of Sections , we use the term aggregation when two particles collide and stick to each other and the term coagulation when, after forming an aggregate, the particles fuse completely to form a spherical particle. This is described in more detail in Particle Aggregation Model . In the current discussion, the term coagulation is used as a generic term in the sense of agglomeration.

The Particle Tracking feature considers only the thermal coagulation of the particles or coagulation due to Brownian motion. Since coagulation simply re-distributes the particle size population, it does not affect the total particle mass of the aerosol system.

Ansys Chemkin uses the frequency or kernel of collision (beta) based on the Knudsen number (Kn) regime of particles, which is defined as Knj = 2λ/Dj where λ is the mean free path of the surrounding gas and D _j is the diameter of the particle. Chemkin offers three choices to the user: free-molecular (Knj >> 1), continuum (Knj << 1), and transition (Knj˜1). The first two have relatively simple expressions and are written as

(19–50)

(19–51)

An interpolating polynomial that is supposed to be valid in the entire Knudsen number regime, ranging from continuum to free molecular, can be used for the transition regime. It is written as

(19–52)

Various terms appearing in the above equations are given below:

(19–53)

In the equations Equation 19–50 through Equation 19–53 , K _B is the Boltzmann constant, D is particle (collision) diameter, V is particle volume, ρP is particle material’s bulk density, and N av the Avogadro’s number along with T, η, ρ, indicating temperature, viscosity, density, and molecular mass of the surrounding gas, respectively. C _j is the mean speed, δ_j is the diffusivity, F is the slip correction factor, α_j is the Knudsen number, and λ is the mean free path of the surrounding gas.

It can be seen that although equation Equation 19–52 is most general, it is also complicated and hence computationally expensive. Moreover, its form is too involved for effective use with the method of moments. Therefore, for the method of moments Ansys Chemkin uses the harmonic mean of the two limiting values and employs equation Equation 19–52 for the sectional method. For typical systems modeled using Chemkin, the particles for which the collision kernel in the free-molecular regime is applicable are less than 200 nm in sphere-equivalent diameter.