Universal relations between soot effective density and primary particle size for common combustion sources

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Figure 1. Typical transmission electron microscopy (TEM) image of soot from a large laboratory scale turbulent, nonpremixed flame.

Figure 2. Schematic of the “external mixing hypothesis”: different flame zones would produce aggregates (green, blue, red, black) with primary particle size d _p independent of area-equivalent diameter d _a (upper right hypothetical graph). Effective density plotted in lower right panel.

Figure 3. Compilation of effective density measurements.

Figure 4. Sample of TEM measurements from a buoyant, turbulent non-premixed flame.

Table 1. Summary of fit parameters for studies including both effective density and TEM measurements.

Source type	From effective density				From TEM
	D m	ρ 100 (kg/m^3)	D TEM	d va,100 (nm)	D TEM	d p,100 (nm)
Flare (Kazemimanesh et al. 2019)	2.56	502	0.45	17.4	0.50	17.1
Inverted Burner
N2 diluted (Dastanpour et al. 2017)	2.51	528	0.39	18.5	0.38	17.8
High EC (Dastanpour et al. 2017)	2.46	647	0.33	23.9	0.34	17.7
EQR 0.57 (Ghazi et al. 2013)	2.29	461	0.11	15.7	0.33	14.5
HPDI Compression Ignition Engine
B75 20% EGR (Graves et al. 2015)	2.35	543	0.19	19.2	0.13	27.1
B75 0% EGR (Graves et al. 2015)	2.50	557	0.38	19.8	0.13	21.9
B50 20% EGR (Graves et al. 2015)	2.43	543	0.29	19.2	0.20	17.2
B37 20% EGR (Graves et al. 2015)	2.59	643	0.49	23.7	0.39	18.4
B25 20% EGR (Graves et al. 2015)	2.62	694	0.53	26.1	0.45	25.7
Average GDI (Dastanpour et al. 2016)	2.53	508	0.41	17.7	0.26	19.0
Aircraft Engine (Johnson et al. 2015)	2.78	590	0.73	21.3	0.39	30.2
Average	2.51	565	0.39	20.2	0.32	20.6

Kazemimanesh, M. , R. Dastanpour , A. Baldelli , A. Moallemi , K. A. Thomson , M. A. Jefferson , M. R. Johnson , S. N. Rogak , and J. S. Olfert . 2019. Size, effective density, morphology, and nano-structure of soot particles generated from buoyant turbulent diffusion flames. J. Aerosol Sci . 132:22–31. doi:10.1016/j.jaerosci.2019.03.005.

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