Improved sizing of soot primary particles using mass-mobility measurements

ABSTRACT

The properties and impacts of aggregated aerosol particles (i.e., soot, metal oxide fumes) depend on their morphology, as characterized by fractal dimension, prefactor, and primary particle diameter. The morphology may be measured directly by time-consuming ex situ microscopy or rapid but indirect in situ methods. Previously, it was found that particle mass and mobility measurements could be used for the estimation of the primary particle diameter of zirconia aggregates, using plausible assumptions related to the fractal structure (specifically, prefactor and exponent ). Since the formation and growth of zirconia aggregates are different from carbon soot, here we compare primary particle diameters measured directly from transmission electron microscopy analysis of soot particles with the diameters estimated from mass–mobility measurements. Performing extensive measurements on soot emissions from two reciprocating engines over a range of operating conditions, we found that there are no universal values of and that can be used for all conditions. However, new optimized values of and are estimated here for soot particles. The variation of the primary particle diameter with particle size is also taken into consideration and is shown to be essential to obtain physically realistic results. Using optimized values of and , the average primary particle sizing error is reduced for all soot types. This suggests that with some calibration, in situ sizing of the primary particle diameter, using mass and mobility measurements, can provide useful accuracy.

Copyright © 2016 American Association for Aerosol Research

EDITOR:

• Matti Maricq

Introduction

Soot particles are typically aggregated structures composed of primary particles, and have negative impacts on human health (Maynard and Kuempel 2005; Franchini and Mannucci 2012) and environment (Jacobson 2010). Soot properties depend nonlinearly on the primary particle diameter, : for example, soot mass and surface area (important parameter in toxicity studies) are proportional to and , whereas scattering and absorption (Sorensen 2001) are proportional to and , respectively. It is difficult to measure directly using any single aerosol instrument.

Transmission Electron Microscopy (TEM) is an ex situ method for direct characterization of soot morphology (Medalia and Heckman 1969; Samson et al. 1987; Brasil et al. 1999; Gaddam and Vander Wal 2013; Kholghy et al. 2013; Dastanpour and Rogak 2014; Johnson et al. 2015; Thajudeen et al. 2015). Statistically reliable primary particle sizes can only be acquired by time-consuming analysis of a great number of TEM images.

In an another approach, Eggersdorfer et al. (2012a,b) proposed an indirect method for the measurement of the primary particle diameter using particle mobility, particle mass and two constants, projected area exponent and prefactor , estimated from either numerical simulations (Medalia 1967; Meakin et al. 1989; Pierce et al. 2006; Al Zaitone et al. 2009; Eggersdorfer et al. 2012a) or experiments (Megaridis and Dobbins 1990; Köylü and Faeth 1992; Köylü et al. 1995). Average primary particle diameters of flame-made zirconia particles estimated by this model have been shown to be in good agreement with those obtained from standard TEM analysis. However, the model was validated for aggregates with quite uniform primary particle sizes. Additionally, the model was developed for cluster–cluster aggregates formed by coagulation and is also shown to work for sintered structures. However, carbon soot does not sinter; and mainly grows by cluster–cluster collisions and surface growth. The validity of this method is investigated here for soot particles emitted from two reciprocating engines. Here, it is shown that using previously published values of and (Eggersdorfer et al. 2012a,b), soot primary particle diameters estimated from mass and mobility measurements are inconsistent with those obtained directly from the analysis of TEM images.

In most engineered combustion systems, soot particles are typically formed in turbulent conditions with large variation in local stoichiometry (Mühlbauer et al. 2013) and time spent in conditions affecting soot formation, growth, and oxidation (Park and Rogak 2003; Park et al. 2005). Dastanpour and Rogak (2014) have recently shown that the average diameter of the primary particles changes with the aggregate size in many combustion sources. They have also shown that the primary particles are more uniform in individual aggregates compared to ensembles of aggregates. These findings are consistent with the aggregates being formed in relatively homogenous microscopic regions; after formation and growth, aggregates formed in different regions, with different residence time and/or formation and growth patterns, are mixed. Although this explanation is plausible (indeed, there is no doubt that there are substantial spatial variations in soot formation conditions in combustion devices) (Mühlbauer et al. 2013), it is exceedingly difficult to model the impact of these variations on soot structure. In fact, quantitative predictions of soot mass and mean particle size remain very challenging (Boiarciuc, Foucher, and Mounaïm-Rousselle 2006).

Considering this size variation, it is shown in the online supplementary information (SI) of this article that using the model constants and prefactor determined by Eggersdorfer et al. (2012a) results in inaccurate estimation of the primary particle size for carbon soot. Here, it is shown for the first time that their power-law correlation is also true for clusters grown by surface growth (instead of sintering) if correct values of parameters and are used. These parameters are determined for a broad range of experimental conditions of two reciprocating engines. Although values of and are found to be sensitive to the operating conditions, soot primary particle diameter can still be estimated with reasonable accuracy by mass–mobility measurements using new constant values for and .

Experimental

Two types of reciprocating engines were considered for this study. The first was a high pressure direct injection (HPDI) natural gas compression-ignition engine operating with Westport Innovations HPDI natural gas combustion system. Natural gas ignition is provided by a diesel pilot. The engine was operated on a single cylinder at seven different operating conditions according to the European Stationary Cycle (ESC-13; EU Directive 1999/96/EC). Most test points were operated at 15% exhaust gas recirculation (EGR) while the lower-load test points were operated at 20% EGR. The engine was run at 25%, 37%, 50%, and 75% of maximum load at an engine speed of 1500 RPM (denoted as B25, B37, B50, and B75, respectively). The highest load (B75) test point was run at 0%, 20%, and 25% exhaust gas recirculation. The HPDI engine was also run at 63% maximum load and a lower speed of 1200 RPM at 0% EGR (denoted as A63). At this operating condition, the majority (˜80%) of the natural gas was injected into the combustion chamber during the intake stroke, allowing the bulk of the gas to premix before ignition. The second engine used Gasoline Direct Injection (GDI) and was operated at simulated highway cruise condition (2600 RPM and 58 N.m of torque), and a higher speed and lower torque setting (3000 RPM and 38 N.m), denoted by Highway and Speed thereafter, respectively. The GDI engine was fueled by mixtures of gasoline and 0% (E0), 10% (E10), and 30% (E30) ethanol by volume.

All measurements were carried out downstream of a thermodenuder operating at approximately 200°C (Patychuk 2013). For HPDI tests, higher TD temperatures were also tested and no significant change was observed in particle number and size distributions. Although this is not a precise way to determine the mass of organics on the soot, but a change in the size distribution (Graves et al. 2015) will be observed for semi-volatile mass fractions of 10% or more. Even if 10% of the particle mass was composed of volatile material, primary particle diameter would have approximately decreased by only 5% under the vacuum condition of the TEM (considering densities of the particle core and coating to be 1800 and 1200 , respectively).

A TSI 379020A two-stage rotary disk diluter was also used upstream of the TD in GDI campaign (Dastanpour and Rogak 2014). The first and second stages of the diluter were heated to 80°C and 300°C, respectively. The thermodenuder and heated dilution removed volatile components from the particulate sample, and what remained were non-volatile particles, predominantly composed of elemental carbon. More information on the effects of denuding and heated dilution on particle volatility is presented in the SI (Section S1).

Soot samples were collected on TEM grids using a thermophoretic precipitator and images were produced by a Hitachi H7600 transmission electron microscope operating at 80 kV under high-resolution mode. Soot particles were size classified using a TSI differential mobility analyser (Model 3081) and their masses were measured by a cambustion centrifugal particle mass analyser (CPMA) (Olfert and Collings 2005).

Details of the experimental methods are further described in Dastanpour and Rogak (2014) and Graves et al. (2015).

Theory

As discussed by Eggersdorfer et al. (2012a), the average projected area () of fractal-like aggregates can be related to the number of their constituent primary particles by the following power-law (Medalia 1967) correlation:[1] where is the projected area of a primary particle with surface area mean (Sauter) diameter of , and and are the prefactor and projected area exponent that depend on aggregate morphology and collision type. For aggregates of monodisperse point-touching primary particles, and are the actual number and diameter of the monomers in the cluster, respectively. However, real soot aggregates are composed of polydisperse primary particles and are partially coalesced. Surface-area equivalent diameter () and number () of the primary particles in polydisperse aggregates are defined as following (Kruis et al. 1993):[2] [3] where and are volume and surface area of the aggregate, respectively, and and are usually extracted from fitting Equation (1) to the results obtained from numerical simulations (Medalia 1967; Meakin et al. 1989; Köylü et al. 1995; Pierce et al. 2006; Al Zaitone et al. 2009; Eggersdorfer et al. 2012b) or experimental measurements (Köylü and Faeth 1992; Köylü et al. 1995). Values reported in literature for and are in the range of 1.0–1.18 and 1.07–1.15, respectively (summary of the reported values is reported in Table 1). These values were obtained for cases where average is statistically independent of the aggregate size.

Table 1. and values reported in literature.

Eggersdorfer et al. (2012a): agglomerates	1.08 ± 0.002	1.11 ± 0.015
Eggersdorfer et al. (2012a): aggregates	1.07 ± 0.03	1.0 ± 0.04
Pierce et al. (2006)	1.07	—
Al Zaitone et al. (2009)	1.08	1.07
Medalia (1967)	1.15	—
Köylü et al. (1995): numerical simulation	1.10	1.16
Köylü et al. (1995): TEM micrographs	1.09 ± 0.02	1.15 ± 0.18
Köylü and Faeth (1992)	1.08	—

^a Confidence interval.

^b Agglomerates sintered by viscous flow and grain boundary diffusion simulations.

^c Estimated by the authors from the correlation reported in the article.

^d Estimated by the authors from the correlation .

The number of the primary particles in individual aggregates can also be correlated to the mass of the aggregate, m, by,[4] where , and is the material density. Different values in the range of 1770–2100 kg/m³ are reported for soot density (Dobbins at al. 1994; Park et al. 2004a, 2004b); here = 1800 kg/m³ is used.

The mobility diameter () of aggregates in the free molecular (Meakin et al. 1989) and transition (Rogak et al. 1993) regimes is approximately equal to the projected area equivalent diameter () of the aggregates () (Eggersdorfer et al. 2012a). Park et al. (2004a,b) showed that this approximation is accurate for diesel aggregates of up to nm. Considering this approximation, and by combining Equations (1) and (2), can be written in terms of and (Eggersdorfer et al. 2012a):[5]

Substituting Equation (4) into Equation (1) and taking the natural logarithm, Equation (6) can be derived. This equation can be used for the estimation of and from combined mass, mobility, and electron microscopy measurements.[6]

As shown by Dastanpour and Rogak (2014), primary particle diameter scales with aggregate size in many soot sources, including those considered here. Based on examination of individual aggregates, there is substantial variation about the mean trend, so it is difficult to determine an exact functional relation between the primary particle and aggregate diameters. A power-law relation similar to Equation (7) is consistent with the measurements (see Figures S2 and S3 and Tables S1 and S2 in the online SI), and is mathematically convenient.[7]

Sauter diameters of the primary particles estimated by power-law correlations are used for mass and mobility diameter normalizations in Equation (6).

Results and discussion

Model accuracy using D_α =1.07 and k_a = 1.0

Sample TEM images produced in this study are shown in Figure 1. Particles were stable under the electron beam for all cases considered here. Images shown here are samples of the images taken for each operating condition and their characteristic dimensions do not necessarily represent the averaged parameters obtained from the analysis of tens to hundreds of images produced for each test point.

Figure 1. Sample TEM images taken from different operating conditions of HPDI and GDI engines. Images are selected randomly. Illustrated images have the same magnification. Scale bar is 100 nm.

Average Sauter diameters of the primary particles were estimated at different mass–mobility test points using the prefactor and projected area exponent parameters obtained by Eggersdorfer et al. (2012b) ( and ) and Equation (5). These diameters are compared with those directly obtained from the analysis of the TEM images as shown in Figures S2 and S3 in the online SI. On average, primary particle diameters determined by this algorithm were 41% and 21% different from those obtained from the analysis of TEM images produced for HPDI and GDI engines, respectively. TEM analysis provides scattered and discrete information on the primary particle and aggregate sizes. Consequently, TEM-based Sauter diameters of the primary particles corresponding to each mobility diameter, , were estimated using Equation (7) fitted to TEM results obtained at different operating conditions. Details of this procedure and values obtained for and are discussed in online SI (Section S2).

As shown in Figures S2 and S3, although this model predicts an increase in primary particle size with aggregate size, qualitatively consistent with TEM measurements (Dastanpour and Rogak 2014), it does not estimate primary particle size accurately, especially for large aggregates.

Estimation of D_α and k_a for soot particles using experimental measurements and optimization

The accuracy of primary particle size measurement from mass–mobility measurements is sensitive to model parameters and . Here, two approaches are used for the calculation of these parameters at different operating conditions of the engines considered in this study.

First, TEM-determined Sauter diameters of the primary particles were estimated for all mass–mobility measurement test points with the application of Equation (7) on TEM image processing data. Optimum values of and (referred to as and thereafter) were calculated using regression to minimize the difference between TEM-determined and the results of Equation (5). Using this method, the average primary particle sizing error was reduced to approximately 11% and 5% for HPDI and GDI soot samples, respectively. These primary particle sizing errors are the minimums that could be achieved from mass–mobility measurements; these include measurement uncertainties of instruments, TEM image processing uncertainties, and regression accuracy.

Second, mass–mobility data (obtained from CPMA and differential mobility analyser measurements) and TEM-obtained (and ) were used in Equation (6); and model parameters and were determined at each operating condition using regression.

Model constants derived from both approaches are reported in Table 2; prefactor and projected area exponent change considerably (up to 22% for and 82% for ) from one test point to another. Additionally, means of these parameters are different for the combustion sources considered here. Consequently, accurate estimation of the primary particle diameter requires this model to be calibrated for each operating condition or at least soot source. Furthermore, both approaches used for the estimation of and (“optimized” and “measured”) from combined mass–mobility and TEM measurements result in approximately similar parameter values.

Table 2. Prefactor and projected area exponent measured with different methods.

Engine	Mode
HPDI	B25	1.01	1.18	1.40	1.40
	B37	1.13	1.15	1.20	1.28
	B50	1.13	1.14	1.13	1.10
	B75 20% EGR	1.08	1.13	0.83	0.84
	B75 0% EGR	1.20	1.21	0.79	0.81
	A63 80% Premixed	1.10	1.14	1.19	1.12
	B75 25% EGR	1.05	1.16	1.40	1.20
GDI	E0-Highway	1.21	1.21	0.72	0.71
	E0-Speed	1.23	1.23	0.77	0.74
	E10-Highway	1.19	1.17	0.84	0.86
	E10-Speed	1.10	1.11	1.17	1.15
	E30-Highway	1.20	1.19	0.82	0.84
	E30-Speed	1.19	1.20	0.80	0.77

* Detailed description of the test points and their naming are described in the experimental section.

** and values are calculated with ±0.005 uncertainty.

It should be mentioned that the variation of the primary particle diameter with the mobility diameter of the aggregate has to be considered when Equation (6) is used. Assuming average to be constant and independent of the mobility diameter (set to the arithmetic mean TEM-based Sauter primary particle diameter), normalized particle mass () can be measured from Equation (6) using and parameters suggested by Eggersdorfer et al. (2012a,b). As shown in Figure 2, negative values are measured for logarithms of normalized mass and mobility diameters for many test points in this case. This means that the aggregates had mass and/or mobility diameters smaller than a single primary particle, which is physically impossible. The assumption of a constant average for the whole size distribution of the aggregates is erroneous for systems having a considerable variation in average primary particle diameter with aggregate size.

Figure 2. Logarithmic plot of normalized aggregate mass in relation to the normalized mobility-equivalent diameter when average is assumed to be constant and independent of the aggregate size. Left panel: HPDI engine. Right panel: GDI engine.

Considering correlation between primary particle and aggregate sizes as described by Equation (7) and discussed in Section S2 of the online SI, was measured for each mobility diameter. Results obtained for the normalized mass and mobility of soot aggregates with this adjustment are shown in Figure 3. As illustrated, logarithms of normalized mass and mobility diameter are no longer negative for most points (except for two which could be ascribed by the measurement uncertainties).

Figure 3. Logarithmic plot of normalized aggregate mass in relation to the normalized mobility-equivalent diameter when average is correlated to the aggregate size. Left panel: HPDI engine. Right panel: GDI engine.

Modified model parameters

Average () and () measured for the HPDI engine were used for the calculation of the primary particle sizes in both engines. Using and instead of and (Eggersdorfer et al. 2012b), the average error in the estimation of the primary particle size was reduced from 41% and 21% to 19% and 12% for different operating conditions of HPDI and GDI engines, respectively. The accuracy of the model using these “modified parameters” is compared to cases where optimized parameters (minimum error) and parameters governed by Eggersdorfer et al. (2012b) were used; results are reported for individual operating conditions in Figure 4.

Figure 4. Average Δd_va measured for different sets of and at multiple operating conditions. Eggersdorfer et al. (2012b) model uses = 1.0 and = 1.07; and parameters are determined for each operating condition separately. Modified model uses = 1.13 and = 1.1.

Primary particle diameter estimated from Equation (3) (for the original and modified values of and ) for a particular mobility diameter is plotted against the TEM-obtained diameter, , for the same particle projected area equivalent diameter (i.e., assuming ) in Figure 5. is measured from the application of Equation (6), where and are determined from regressions to the whole TEM analysis data (described in the online SI, Section S3). As shown, using newly proposed values of and , the difference between estimated Sauter diameters and those obtained from TEM analysis, especially at large mobility diameters, was reduced at all operating conditions of both soot sources. At each operating condition, primary particle size has a considerable wide size distribution that is associated with variations in the aggregate size. Note that in all cases, the original parameters ( and ) resulted in the primary particle diameter increasing faster with than indicated by TEM. As shown in this Figure 5, for some operating conditions such as B75 20% EGR, and B75 0% EGR, neither the old nor the new models agree well with TEM measurements. After re-examining these measurements, it appears that they are similar to other points except for especially low values of —that is, primary particle diameter has a weak correlation with aggregate size. However, a clear trend was not observed between the accuracy of the model and .

Figure 5. Sauter primary particle diameter measured from Equation (5) using parameters suggested by Eggersdorfer et al. (2012b) and those obtained in this study versus TEM data for both HPDI and GDI engines.

Conclusions

Models developed for in situ estimation of Sauter diameters of the primary particles with mass–mobility measurements were compared with TEM measurements. We have found that good agreement between TEM and in situ estimations can be obtained using model parameters that depend on source and operating conditions. Variation of the primary particle diameter with aggregate size is also taken into account in the estimation of the new model parameters. Consideration of this size correlation is essential in order to obtain physically realistic mass and mobility. We have also found that for nearly all cases, agreement can be improved with the application of new, constant values for the model parameters and , but it remains to be seen whether these values will work for a broad range of soot sources.

Acknowledgments

The authors would like to thank James Wallace, Phillip Mireault, and Manuel Ramos (University of Toronto), and Bronson Patychuk (Westport Innovations, Inc.) for their contributions to the sampling campaigns for GDI and HPDI engines, respectively.