Gas phase production of particles in reactive turbulent flows

Aerosol dynamics modeling of silicon nanoparticle formation during silane pyrolysis: a comparison of three solution methods

“…4b where both nucleation and coagulation modes exist. The approximation to the size distribution by the MOM tends to reduce the maximum in the polydispersity caused by the bimodal distribution, as was also observed by Xiong and Pratsinis (1991). One interesting feature in this ÿgure is that the standard deviation in the SM does not reach the value for self-preserving size distribution in either the free molecular or continuum regime and shows a dip towards the end.…”

“…Thus, there is some degree of overlap present between nucleation and coagulation that gives rise to this bimodal peak. Bimodal distributions at short times have also been observed in other systems (Park et al, 1999;Xiong & Pratsinis, 1991). At longer residence time, the SM agrees with the MOM and looks almost lognormal due to the attainment of the self-preserving size distribution, which predicts at that su ciently long times, coagulating particles reach a distribution which is independent of the initial conditions reaching the same value irrespective of the speciÿc system considered (Friedlander, 2000).…”

“…mean average of the continuum and free-molecular regime as employed by Pratsinis (1988) and Xiong and Pratsinis (1991), shown in more detail in Appendix A. The spacing factor (f s ) is deÿned as the ratio of the width of bin i + 1 to the width of bin i.…”

“…However, conventional moment methods have the disadvantage that the shape of the particle size distribution must be speciÿed in advance to obtain closure of the equations (Pratsinis & Kim, 1989). This could be a limitation if size distributions at early stages of particle formation are to be studied, where bimodal distributions are often observed (Landgrebe & Pratsinis, 1990;Park, Lee, & Choi, 1999;Xiong & Pratsinis, 1991). To avoid specifying the shape of the distribution a priori, the quadrature method of moments (QMOM) developed by McGraw (1997) approximates the integral moments of the size distribution by an n-point Gaussian quadrature (Gordon, 1968;Hulburt & Katz, 1964).…”

“…Sectional methods (SM), based on dividing the continuous particle size distribution into discrete sections and dealing with one integral property at a time have been extensively used for more than 20 years Hounslow, Ryall, & Marshall, 1988;Kumar & Ramkrishna, 1996a;Landgrebe & Pratsinis, 1990;Xiong & Pratsinis, 1991). Coagulation is generally the most computationally expensive part of aerosol dynamics calculations using SM, due to the presence of complex kernels and the fact that it involves double summations over the particle size bins to account for coagulation of each size with all other sizes.…”