A numerical aerosol model Fractal Aggregate Moment Model (FAMM) to simulate simultaneous nucleation, coagulation, surface growth, and sintering of fractal aggregates

Figures & data

Table 1. Definition of variables.

$N_1$	Particle number concentration of Mode 1 (nuclei mode)
$M_0$ (=$N_2$)	Particle number concentration of Mode 2 (accumulation mode)
$M_1$	Particle volume concentration of Mode 2
$M_2$	Particle volume-squared concentration of Mode 2
$N_p$	Primary particle number concentration of Mode 2
$N_{\mathrm{vap}}$	Number concentration of precursor vapor molecules
$d_1$ and ${\nu }_1$	Particle diameter and volume of Mode 1
$d_g$ and ${\nu }_g$	Volume-equivalent geometric mean particle diameter and volume of Mode 2
${\nu }_2$ ($=M_1/M_0$)	Average particle volume of Mode 2
$\sigma$	Geometric standard deviation of volume-equivalent particle diameter of Mode 2
$Z$	$\mathrm{Exp}\left(9{\ln }^2\sigma \right)$
$d_p$ and ${\nu }_p$	Average-mass primary particle diameter and volume of Mode 2
$d_{\mathit{gt}}$	Volume-equivalent geometric mean particle diameter of the whole particle size distribution (Modes 1 and 2)
${\sigma }_t$	Geometric standard deviation of volume-equivalent particle diameter of the whole particle size distribution
$d_{\mathit{pt}}$	Average-mass primary particle diameter of the whole particle size distribution

Figure 1. Comparison of the predictions of SAM and FAMM for the aggregate coagulation: (a) number concentration decay; (b) particle size distribution change.

Figure 2. Comparison of the predictions of SAM and FAMM for the surface growth of aggregate particles with $m=1:$ (a) mass concentration; (b) $\sigma ;$ (c) $v_g;$ (d) particle size distribution.

Figure 3. Comparison of the predictions of SAM and FAMM for the surface growth of aggregate particles with $m=2/3:$ (a) mass concentration; (b) $\sigma ;$ (c) $v_g;$ (d) particle size distribution.

Figure 4. Comparison of the predictions of SAM and FAMM for the simultaneous nucleation and coagulation: (a) number concentration; (b) mass concentration; (c) $\sigma ;$ (d) particle size distribution.

Figure 5. Comparison of the predictions of SAM and FAMM for the simultaneous nucleation and surface growth: (a) number concentration; (b) mass concentration; (c) particle size distribution.

Figure 6. Comparison of the predictions of SAM and FAMM for the flame synthesis of titania nanoparticles undergoing simultaneous nucleation, coagulation and surface growth (Tsantilis, Kammler, and Pratsinis 2002, 2139–2156): (a) number concentration; (b) mass concentration; (c) $\sigma ;$ (d) $v_g;$ (e) particle size distribution.

Figure 7. Primary particle diameter of average mass predicted by FAMM compared with measured data and the SAM prediction.

Tsantilis, S., H. K. Kammler, and S. E. Pratsinis. 2002. Population balance modeling of flame synthesis of titania nanoparticles. Chem. Eng. Sci. 57 (12):2139–2156. doi: 10.1016/S0009-2509(02)00107-0.

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