Surface Growth
A large number of soot nuclei are generated during soot inception stage. The soot nuclei grow in size as the gaseous products of fuel molecule fragmentation deposit on the surface of nuclei. The typical fuel has atomic H/C ≥ 2 while soot has H/C in the range 0.1 to 0.2. Soot growth is caused more likely by the condensation of species with right H/C ratio on the nuclei surface with subsequent dehydrogenation. Gas-phase deposition of acetylene proposed in the HACA reactions is one of the mechanisms of surface growth. Here, in the Reactions 1 to 3 as above, the aromatic radical (AR*) is substituted by a carbon atom (Cs) on the edge of the soot surface and the process repeats itself. Deposition of radicals of PAHs and small aliphatic hydrocarbons, which are present in high concentrations in sooting flames, may also result in surface growth of the soot particles.
Coagulation and Agglomeration
Collision of two spherical soot particles may form a larger spherical particle. This process occurs in the beginning when the particles are still small (<10nm) and are formed of a tarry liquid produced from pyrolysis of hydrocarbons. Once the particles have become larger and solidified, the particles resulting from collision resemble a cluster, like a bunch of grapes. Once the surface growth ceases, particles coalesce in the shape of chainlike structure and this process is termed as aggregation.
The rate of decrease of particle number density, N during coagulation is given by
k is a rate constant that depends on pressure, temperature, gas density, particle size etc.
On integration the Eq. 2.43 yields,
where N0 is the initial number of particles. N/ N0 is inversely proportional to time and the initial number of particles. Thus, the soot coagulation as a result of particle collision decreases as the number of particles reduces due to coagulation and agglomeration.
The number of soot particles due to coagulation and agglomeration decrease rapidly during early part of expansion process and agglomeration is almost complete at the end of expansion stroke in the engine.
The soot concentration is expressed by a term soot volume fraction, Fv. The soot volume fraction in units of soot volume per unit volume of gas, is given by
where d is diameter of the spherical soot particles or diameter of a sphere of volume equivalent to an aggregated particle and N is the number of particles in unit volume. Due to agglomeration, number of soot particles decrease but the Fv. remains unchanged. It changes with surface growth or soot oxidation.
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