Numerical Simulation of Soot Aggregates Shapes by Benzene Pyrolysis

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6 Surface growth means the reaction between the nuclei and the growth species. The nuclei grows up to particle by this reaction. The discrete method [13], particles are classified to a certain number of discrete size classes. The changes of the size distributions are calculated by the coagulation rates between the size classes. The surface growth reactions are expressed as follows ; (8) (9) (10) where Py and Px represent the particles which belong to the size class yand x, respectively. Table 2 shows the 10 discrete particle classes based on the work of Jensen [14] which is used in this study. Table 2 Characteristics of discrete particle size classes Class Number of C atoms Particle diameter [nm] Py Py Py 4 nC2H2 4 nC2H3 4 nC4H3 -» -> -> P_, P„ P_. 1 2 3 4 5 6 7 8 9 10 14 50 360 5,080 7.80 x 104 1.44 x 106 1.32 x 107 1.06 x 108 1.47 x 109 2.32 x 10'° 0.64 0.98 1.90 4.60 11.0 30.0 64.0 130.0 300.0 760.0 4. Coagulation Once particles are formed, collisions between two different particles occur and it causes growth in particle size. These coagulation reactions are described as follows ; Py + nPx^Pz, (11) n = (n- - ny)/nx. where Px represents the particle containing x carbon atoms. The equations describing the growth and coagulation symbolized by Eq. (11) is d[Pz]/dt = fxy[Px)[Py\/n. (12) f^ represents the Brownian coagulation rate constant for the particles between the size class A-and y. As shown in Table 2, each of the particles belongs to 10 classes of different