Effective Density Characterization of Soot Agglomerates from Various Sources and Comparison to Aggregation Theory

Figures & data

Figure 1 FIG. 1 Schematic illustration of the experimental setup.

Table 1 TABLE 1 Summary of experiments

Source	Types	Conditions	Notation
Diesel exhaust	Heavy-duty engine	Idling	Heavy-duty idling
		Urban transient cycle	Heavy-duty transient
	Light-duty vehicle	Idling	Light-duty idling
Flame soot (propane)	Flame soot generator	Low air-to-fuel ratio	Flame soot 100
	(diffusion type)	High air-to-fuel ratio	Flame soot 50
Candle soot	Tapered candle	Sooting burn	Candle

Figure 2 FIG. 2 The effect of considering doubly charged particles in the DMA-APM data analysis compared to not doing so. Each point corresponds to the average correction at each size selected per soot type.

Figure 3 FIG. 3 (a) APM peak voltages at the settings tested, illustrating the effect of increasing mass of the selected particles with increasing alignment in the DMA. (b) The APM raw spectra for 350 nm particles selected using two different sheath flows.

Table 2 TABLE 2 Summary of measured quantities of the soot particles

	Number distr.		Mass distr.	Density		Mass-mobility relation		TEM image analysis
								dpp ±1 SD
	GMDsoot			ρeff				by number
	(σg)		GMDsoot	(100/300 nm)	PM1, ρapp		Kforced	(by mass)	SAsp	Dgraph ±1 SD
Source	[nm]	NFsoot	[nm]	[g/cm^3]	[g/cm^3]	ϵm (K)	ϵm fixed to 2.31	[nm]	[m^2/g]	[Å]
Heavy-duty transient	90 (1.9)	1	194	0.61/0.30	0.34	2.37 (1.32 × 10^−2)	4.80 × 10^−3	24 ± 7 (31)	115	3.67 ± 0.18
Heavy-duty idling	95 (1.9)	1	272	0.82/0.51	0.53	2.56 (3.34 × 10^−1)	7.57 × 10^−3	27* ± 11 (43)	–	3.66 ± 0.18
Light-duty idling	108 (1.9)	0.50	225	0.68/0.31	0.35	2.28 (3.43 × 10^−3)	5.01 × 10^−3	28 ± 8 (35)	100	3.69 ± 0.15
Candle	282 (2.1)	0.20	870	0.62/0.26	0.15	2.23 (1.25 × 10^−3)	4.41 × 10^−3	28 ± 6 (33)	107	3.78 ± 0.24
Flame soot 50	53 (1.4)	1	70	0.39/0.20	0.46	2.41 (1.46 × 10^−2)	3.04 × 10^−3	11 ± 3 (14)	262	3.68 ± 0.21
Flame soot 100	97 (1.5)	1	143	0.41/0.18	0.29	2.28 (1.83 × 10^−3)	3.10 × 10^−3	13 ± 3 (16)	228	3.68 ± 0.19

Effective densities are from parameterizations of mass mobility relations, and mass apparent density estimated for PM₁ from measured distributions and effective densities. ϵ_m and K (given in parenthesis) are the results from fitting the parameters describing the mass-mobility relations for the soot dominated exhaust types according to m_agg = K·d_m^ϵm, where units are in [m] and [kg]. K_forced is from a fit of the mass-mobility relation where ϵ_m is kept fix at 2.31 (ϵ_m average). d_pp is estimated two ways, either from the d_pp number distributions of or from mass weighted d_pp distributions, given in parenthesis (CMD). SA_sp is the specific SA and D_graph the distance between the graphene layers in the graphite segments, ±1 SD. *Not fully reliable due to high content organic coating not captured by the TEM.

Figure 4 FIG. 4 Cumulative distributions of the primary particle diameter determined from TEM image analysis. Lines correspond to normal distributions fitted to the data. (Color figure available online.)

Figure 5 FIG. 5 HR-TEM images of soot particles generated by (a) light-duty idling, (b) heavy-duty idling, (c) heavy-duty transient, (d) flame soot 50, (e) flame soot 100, and (f) candle. The scale bar is 10 nm. The insert in (a) shows a typical agglomerate where the scale bar corresponds to 50 nm.

Figure 6 FIG. 6 The measured effective densities for (a) diesel exhausts of different types and (b) flame soot and candle smoke. For guidance two identical power functions are shown in both graphs: solid (black) line (fit to heavy duty transient), and dashed (red) line (fit to flame soot 100). The grey line corresponds in (a) to the power law function fitted to heavy duty idling (blue) and in (b) to candle smoke (green). (Color figure available online.)

Figure 7 FIG. 7 Particle mass as a function of mobility diameter.

Figure 8 FIG. 8 Aggregate mobility diameter normalized by the CMD of the primary particle size (number weighted), versus number of monomers in the aggregate, N_pp. The DMA-APM dataset is divided into two groups of d_pp with particles sizes 11–13 (Group 1) and 24–28 nm (Group 2).