Mouad Daoudi

Philipp Schiffmann

Alessandro Faccinetto

Arnaud Frobert

Pascale Desgroux
email: pascale.desgroux@univ-lille.fr

Comprehensive characterization of particulate matter

Keywords: MiniCAST, aerosol characterization, aggregate morphology, optical extinction, soot volume fraction, catalytic stripper

Introduction

Much of the interest around particulate matter (PM) emission control stems from the adverse effects they can have on human health [START_REF] Bourdrel | Cardiovascular effects of air pollution[END_REF][START_REF] Kopnina | Vehicular air pollution and asthma: Implications for education for health and environmental sustainability[END_REF][START_REF] Ranft | Long-term exposure to traffic-related particulate matter impairs cognitive function in the elderly[END_REF][START_REF] Bernstein | Health effects of air pollution[END_REF][START_REF] Pope | Lung Cancer, Cardiopulmonary Mortality, and Long-term Exposure to Fine Particulate Air Pollution[END_REF], particularly in urban areas [START_REF] Gonzalez | Air quality in Europe -2020 report[END_REF]. This is due to their high specific surface, content of hazardous molecules and micrometric size, hence the use of indicators such as PM 10 and PM 2.5 for air quality monitoring. The presence of PM in ambient air has also important drawbacks on environment and on climate as they are considered to be the second most important emissions after CO 2 (IPCC 2022;[START_REF] Bond | Bounding the role of black carbon in the climate system: A scientific assessment[END_REF][START_REF] Jacobson | Strong radiative heating due to the mixing state of black carbon in atmospheric aerosols[END_REF]). In particular, PM impact the atmosphere radiative exchange in various ways [START_REF] Kärcher | Formation and radiative forcing of contrail cirrus[END_REF][START_REF] Popovicheva | Aircraft-generated soot aerosols: Physicochemical properties and effects of emission into the atmosphere[END_REF][START_REF] Schumann | Formation, properties and climatic effects of contrails[END_REF][START_REF] Seinfeld | Clouds, contrails and climate[END_REF]), hence the need for them to be monitored.

As the world's population grows, and passenger and freight travel expand, the use of petroleum derivatives for internal combustion engines is expected to continue to grow to fulfill the demand for the next 30 years (U.S. Energy Information Administration 2021). This means that the fuel choice is important to lower global pollutant and greenhouse gas emission levels.

For instance, alternative fuels with lower carbon emission potential are extensively researched. This is the case of bio-or e-fuels alone or blended with fossil fuels. Using such fuels can be advantageous since they are compatible with today's engine technologies. On the other hand, the use of new fuels might have an impact on pollutants and PM emissions. The PM generated from the combustion of alternative fuels need to be characterized and closely monitored before these fuels are mass-produced.

To characterize the nature of PM emissions from various combustion sources, laboratory PM sources capable of burning different fuels are needed. Using an engine for such purpose is expensive, complex and does not permit to easily change the emission characteristics. In this regard, diffusion or premixed flames generated in laboratory environment using well documented reference burners such as the McKenna burner [START_REF] Ghazi | Mass, Mobility, Volatility, and Morphology of Soot Particles Generated by a McKenna and Inverted Burner[END_REF]Migliorini et al. 2011;[START_REF] Yon | Examination of wavelength dependent soot optical properties of diesel and diesel/rapeseed methyl ester mixture by extinction spectra analysis and LII measurements[END_REF] or the Santoro burner [START_REF] Kelesidis | Santoro flame: The volume fraction of soot accounting for its morphology & composition[END_REF][START_REF] Santoro | Soot particle formation in laminar diffusion flames[END_REF][START_REF] Santoro | Soot particle measurements in diffusion flames[END_REF]) offer an easier control. These burners were, and continue to be, used to study the soot particles formation process and they can be used for the calibration of measurement systems. However, soot generators are often preferred outside academia since they are much easier to use and operate. In particular, during the last two decades, the so-called miniCAST soot generators (from Jing Ltd., Switzerland) have been widely used to generate soot aggregates [START_REF] Ess | Optical and morphological properties of soot particles generated by the miniCAST 5201 BC generator[END_REF][START_REF] Malmborg | Relating aerosol mass spectra to composition and nanostructure of soot particles[END_REF][START_REF] Marhaba | Aircraft and MiniCAST soot at the nanoscale[END_REF][START_REF] Saffaripour | Raman spectroscopy and TEM characterization of solid particulate matter emitted from soot generators and aircraft turbine engines[END_REF][START_REF] Bescond | Soot optical properties determined by analyzing extinction spectra in the visible near-UV: Toward an optical speciation according to constituents and structure[END_REF][START_REF] Durdina | Response of real-time black carbon mass instruments to mini-CAST soot[END_REF][START_REF] Kim | Assessing Optical Properties and Refractive Index of Combustion Aerosol Particles Through Combined Experimental and Modeling Studies[END_REF][START_REF] Moore | Mapping the Operation of the Miniature Combustion Aerosol Standard (Mini-CAST) Soot Generator[END_REF][START_REF] Mamakos | Characterization of Combustion Aerosol Produced by a Mini-CAST and Treated in a Catalytic Stripper[END_REF][START_REF] Schnaiter | Strong spectral dependence of light absorption by organic carbon particles formed by propane combustion[END_REF] to serve as calibration aerosols, yet they are limited by design to a single gas fuel (i.e., propane).

To burn diesel-like fuels, the more recent diesel miniCAST was developed [START_REF] Mueller | Combustion process apportionment of carbonaceous particulate emission from a diesel fuel burner[END_REF]. A number of other commercial soot generators have been recently under investigation such as the miniature inverted soot generator (from Argonaut Scientific Corp., Canada) [START_REF] Bischof | Characterization of the Miniaturized Inverted Flame Burner as a Combustion Source to Generate a Nanoparticle Calibration Aerosol[END_REF][START_REF] Kazemimanesh | A novel miniature inverted-flame burner for the generation of soot nanoparticles[END_REF][START_REF] Moallemi | Characterization of black carbon particles generated by a propane-fueled miniature inverted soot generator[END_REF]) that allows the use of ethylene, propane, ethane or fuel blends with methane and nitrogen. So far, soot aggregates produced by propane miniCAST have been extensively studied on many aspects [START_REF] Ess | Optical and morphological properties of soot particles generated by the miniCAST 5201 BC generator[END_REF][START_REF] Malmborg | Relating aerosol mass spectra to composition and nanostructure of soot particles[END_REF][START_REF] Marhaba | Aircraft and MiniCAST soot at the nanoscale[END_REF][START_REF] Saffaripour | Raman spectroscopy and TEM characterization of solid particulate matter emitted from soot generators and aircraft turbine engines[END_REF][START_REF] Bescond | Soot optical properties determined by analyzing extinction spectra in the visible near-UV: Toward an optical speciation according to constituents and structure[END_REF][START_REF] Durdina | Response of real-time black carbon mass instruments to mini-CAST soot[END_REF][START_REF] Kim | Assessing Optical Properties and Refractive Index of Combustion Aerosol Particles Through Combined Experimental and Modeling Studies[END_REF][START_REF] Moore | Mapping the Operation of the Miniature Combustion Aerosol Standard (Mini-CAST) Soot Generator[END_REF][START_REF] Mamakos | Characterization of Combustion Aerosol Produced by a Mini-CAST and Treated in a Catalytic Stripper[END_REF][START_REF] Schnaiter | Strong spectral dependence of light absorption by organic carbon particles formed by propane combustion[END_REF] and have shown similar characteristics to soot produced by engines or aircraft [START_REF] Marhaba | Aircraft and MiniCAST soot at the nanoscale[END_REF][START_REF] Moore | Mapping the Operation of the Miniature Combustion Aerosol Standard (Mini-CAST) Soot Generator[END_REF]). However, while the propane miniCAST is able to provide engine-like soot aggregates, it does not meet the need for evaluating PM characteristics when other fuels are used, particularly diesel, kerosene or biofuels. To the best of the authors knowledge, the only available published literature on this diesel miniCAST [START_REF] Mueller | Combustion process apportionment of carbonaceous particulate emission from a diesel fuel burner[END_REF] focused on studying the impact of fuel additives on the chemical composition of soot aggregates. Overall, there seems to be a significant lack of information on soot aggregates generated using liquid fuels.

To determine the physical properties of soot aggregates using a variety of liquid fuels, this article first proposes a protocol to characterize the emissions of a diesel miniCAST, and then applies said protocol to 34 different operating points, therefore setting a reference mapping for liquid-fueled miniCASTs. This characterization involves the measurement of size distributions (using scanning mobility particle sizer), morphology (using electron microscopy), soot volume fraction and optical extinction coefficients. Consequently, a detailed database is provided which can be valuable for future use. Additionally, this article evaluates the impact of the thermal treatment using a catalytic stripper (CS) on PM to understand the impact of oxidizing volatile PM (vPM) on the optical properties of combustion exhaust. Additionally, since emission thresholds set by the current regulations concern only non-volatile PM (nvPM), that can contain organic and inorganic material, the use of the CS on diesel miniCAST exhaust allows using this burner to produce nvPM for calibration purposes. Finally, the soot volume fraction is determined by comparing three procedures based on mobility size distribution accounting for morphological aspects of the soot aggregates, mass concentrations and spectral light extinction taking into account scattering and gas phase absorption.

Experimental setup

A dedicated test bench was built around a liquid-fueled miniCAST fed with diesel B7 as schematized in Figure 1. The chemical composition of liquid diesel B7 is given in Table R.1 (see supplementary information S.1). In this setup, the diesel miniCAST produces an exhaust flow of ~ 30 L/min. This exhaust is sent through a main vein where it is further diluted with air at atmospheric pressure. The following sections describe in more detail the instrumentation used to pretreat, sample and characterize the exhaust.

[Figure 1 near here]

Exhaust from miniCAST burner

Exhaust generation

A miniCAST burner model 5102 D (Jing Ltd., Switzerland) for liquid fuels is used to produce soot aggregates. Figure 2 illustrates the dual burner design where the liquid fuel is preheated by a lower non-sooting C 3 H 8 /air heating flame (1) and burns in a diffusion sooting flame (2) in the upper part of the burner.

[Figure 2 near here] The upper flame is fueled by two coaxially arranged vertical tubes carrying in the center a C 3 H 8 /air mixture and in the peripheral tube the liquid fuel. The lower flame (1) is fueled by a homogeneous mixture of 30 mL/min of C 3 H 8 and 300 mL/min of air and is used for pre-heating the liquid fuel routed through the annular space. The central tube is used to deliver a C 3 H 8 /air mixture (10 mL/min of C 3 H 8 with 20 mL/min of mixing air) to sustain the idle flame on the burner's top, which provides the ignition for the sooting flame supplied with the liquid fuel as shown in Figure 2. Upon each use, a 30 minutes warm-up period during which the burner runs under idle condition is needed to establish a thermal steady state for the system. During this time, the oxidation air flow rate is by default set to 3 L/min to provide enough oxygen for the complete combustion of the heating flame. Once ready, mixing air and oxidation air flow rates can be tuned in the ranges 10-250 mL/min and 1-3 L/min, respectively. By adding the desired liquid fuel flow rate, the idle flame on the top of the burner is replaced by a bright yellow sooting flame (2). To quench residual reactivity and limit particle coagulation, the exhaust is diluted at the tip of the flame using a 7.5 L/min of N 2 . A subsequent dilution with 20 L/min of filtered air further reduces particle coagulation. The factory mass flow controller (e.g., mini-CORI-FLOW) for liquid fuel is limited to 70 µL/min and was found to be a major source of flame instability. To improve test-to-test repeatability, the mass flow controller was replaced with a syringe pump model P-500 (Pharmacia biotech., U.S.A) to deliver precise and constant liquid fuel flow allowing both a wider and stable operating range between 0 and 250 µL/min. In this work, the European standard fuel for light duty vehicles diesel B7 (EN 590 2022) was used over the entire operating range.

Operating points

Overall, 34 operating points (OPs) were investigated (see supplementary information Table S.1.1). Among these OPs, focus was brought on fully characterizing six of them, whose settings are summarized in Table 1. The OPs are chosen to be quasi-evenly spaced within the explored range of stable operating conditions in terms of the flame overall equivalence ratio (ϕ) in 0.103-1.645. ϕ is calculated from the ratio of the experimental (Exp.) and stoichiometric (Stoich.) fuel/air mass flow rate ratios using with being the fuel mass flow rate and the air mass flow rate and by considering as the average chemical formula for diesel B7.

These six OPs (OP2, OP9, OP17, OP27, OP32 and OP34) were fully characterized in terms of particle size distribution, morphology, soot volume fraction and optical extinction coefficients.

Only mobility size distribution and light extinction measurements were performed on the remaining 28 OPs.

[Table 1 near here]

Exhaust aftertreatment

As the exhaust left the burner, ~ 554 L/min of dry filtered air at ambient temperature was added in the first external dilution stage resulting in ~ 19:1 dilution ratio (volumetric). The exhaust was then sampled from the main vein: (1) untreated.

(2) filtered using a microfiber "particle filter" (model DIF.5K, Classic Filters Ltd., U.K), to remove particles and allow to study gas phase independently. (3) treated using a "catalytic stripper" (CS, model CS-015 Catalytic Instruments GmbH., Germany) as shown in Figure 1. The CS, operated at 1.5 L/min nominal flow rate and 350 °C, was used to study the impact of volatile organic compounds (VOCs) on the exhaust properties. Unless mentioned otherwise, the diagnostics described in the following sections are all done on the exhaust sampled at the same dilution ratio (~ 19:1) and have passed through the same sampling lines. If soot aggregates coagulation along the sampling line occurs, this is not a problem as long as all diagnostics are performed at the same location downstream the sampling line (see supplementary information S.1) on the same volume sample.

Diagnostics setup

Size measurement (SMPS):

The mobility-equivalent size distributions of soot aggregates were measured in the range 6-224.7 nm over a scanning period of 120 s of stable soot generation.

This scanning mobility particle sizer (SMPS) combines an electrostatic classifier 3080 (TSI Inc., U.S.A), a L-DMA column 3081 (TSI Inc., U.S.A), along with an X-ray neutralizer 3088 (TSI Inc., U.S.A) and a CPC 3775 (TSI Inc., U.S.A). The sheath flow rate, the inlet flow rate and the impactor nozzle size were set to 15 L/min, 1.5 L/min (10:1 ratio) and 0.071 cm, respectively. For each OP, the size distributions were measured three times in a row, therefore providing statistics on soot aggregates number concentration (PN), mobility-equivalent geometric mean diameter ( , with and the number concentration and mobility diameter of each class of size i, respectively) and geometric standard deviation ( ) provided by the device software (AIM 9.0, TSI Inc., U.S.A). The multiple charging correction integrated in the software was used for all experiments. The losses in the sampling line by diffusion were neglected and the mobility size distributions were visualized in normalized concentration dN/dlog .

Mass measurement:

For PM mass measurement, PM deposit on Pallflex-Emfab borosilicate microfibers filters (Pall Corp., U.S.A) were carried out using an automated antistatic micro tunnel sampler as shown in Figure 1. Before using the filters, they were first heated for 4 hours at 180 °C and left to cool overnight at room temperature in a particle-free environment. The exhaust was then sampled at Q = 1.5 L/min over 10 min. Using an XP6 microbalance (Mettler Toledo Inc., U.S.A) ( 0.4 g repeatability), the weight of the filters was measured prior to sampling and after 4 hours resting period during which they were stored in a particle-free environment at ambient temperature. Soot deposits mass ( ) was then deduced and soot mass concentration calculated, where is the total mass concentration containing both nvPM and (condensable) vPM.

Electron microscopy imaging (TEM):

To acquire more information on the morphology of soot aggregates, electron microscopy images were recorded. For these experiments, a second dilution stage (resulting in ~ 220:1 dilution ratio) located further down the line was deemed necessary to avoid overloading the sampling grids. This second dilution was done using an ejector diluter model DI-1000 (Dekati Ltd., Finland) operated using N 2 as a dilution gas, to sample 1.5 L/min from the exhaust to be compatible with both CS and SMPS nominal flow rates.

Once the exhaust was diluted, soot aggregates were probed downstream the second dilution stage using a mini particle sampler (MPS, Ecomesure, France) as they crossed a perforated 400 mesh Au holey carbon film (Agar Scientific Ltd., U.K) TEM grid located halfway the MPS tube. This sampling was operated at 20 mL/min using a Gilian air sampling pump model GilAir Plus (Sensidyne LP., U.S.A) positioned downstream the MPS tube while varying sampling time between 10 s and 40 s (see supplementary information Table S.3.2).

The loaded TEM grids were then analyzed, within two weeks after their preparation, to acquire scanning transmission electron microscopy (STEM) images on a Nova Nano SEM 450 microscope operated with an acceleration voltage of 30 kV and using STEM II detector with bright field detection under immersion mode and 6 µs scanning time. On average, 20 STEM images, each having a size of 1536 ×1024 pixels, were acquired at fixed magnification (× 60.000), making the optical resolution of ~ 1.4 nm/Pixel. These images were then processed to evaluate soot aggregates morphological key parameters (see supplementary information S.3). For a more detailed characterization, transmission electron microscopy (TEM) images were acquired.

This was done using JEM, models 2100F or F200 (JEOL Ltd., Japan), microscopes operated with an acceleration voltage of either 200 kV or 80 kV, respectively. A lower acceleration voltage was deemed necessary, particularly for fuel-rich OPs, to stabilize the specimen during the image acquisition process.

Light extinction measurement: Optical extinction coefficients were measured inside an optical extinction cell over the 200-1000 nm wavelength range with a 1.5 nm resolution. This was done using a continuous deuterium-halogen light source model DH 2000 (Ocean Optics Inc., U.S.A) that emits in the UV, visible and near-IR range a spectrum on one side of the cell while the transmitted spectrum was analyzed on the opposite end with a Q-mini, model wide UV (Broadcom Inc., U.S.A) spectrometer. The spectrometer has a 20 µm entrance slit, 300 lines/mm transmission grating, 50 mm focal length and uses a 2500-pixel linear CCD sensor. The single pass extinction cell is made of a stainless-steel tube (L = 1 m long, 4 mm inner diameter) and 1.5 L/min of exhaust gases passed through it. Optical connection on both ends were done using a 10 mm focal length collimating lens, model 74-UV (Ocean Optics Inc., U.S.A) and a QP-450-0.25-XSR optical fiber (Ocean Optics Inc., U.S.A). The intensity of transmitted light crossing the exhaust I t ( ) was recorded with 40 ms exposure time and was performed simultaneously to SMPS size distribution measurements. The choice of 40 ms exposure time lays within the linear behavior of the spectrometer. During post-processing, the spectra were averaged over ~ 400 s which is the time needed to acquire 3 consecutive size distribution measurements. A reference baseline was measured on a clean air flow, before and after each recording. The optical extinction coefficients were calculated using Beer-Lambert law [START_REF] Swinehart | The Beer-Lambert Law[END_REF] . Care was taken to avoid lens fouling by cleaning the optical cell upon changing each OP. For both short (< 20 minutes) and long (up to 90 minutes) periods of time, soot PN production was considered to be stable when the standard deviation on the concentration was < 10 % of the measured value (see supplementary information Figure S.1.2).

Results and discussions

The results discussed here focus on the capabilities of the liquid-fueled miniCAST burner supplied with diesel B7 in terms of generating soot aggregates of controlled size distribution, morphology and optical extinction coefficient under various operating conditions (section 3.1).

Then, this study aims to retrieve key parameters that are necessary to evaluate the soot volume fraction used as metric to compare size, mass and optical diagnostics (section 3.2).

Characterization of soot aggregates

Soot aggregates can be described in many ways. Here, it is proposed to describe and compare soot aggregates number concentration, size, morphology and polydispersion for all 34

OPs for untreated exhaust, based on SMPS and TEM analyses and optical properties for OP2, OP9, OP17, OP27, OP32 and OP34. The impact of using the CS is examined on each of those aspects.

Size distributions

Impact of the miniCAST flow rates: Focusing first on untreated exhaust, a parametric study was carried out to evaluate the diesel miniCAST ability of generating soot aggregates with controlled number concentration (PN), mobility-equivalent geometric mean diameter ( ) and geometric standard deviation ( ). To make the comparison of different OPs possible, care was taken to ensure that all measurements could be performed with the same dilution conditions. A compromise had to be found between avoiding the saturation of the SMPS for the rich OPs and being sensitive enough to detect soot light attenuation for the lean OPs. The choice of ~ 19:1 dilution ratio made that compromise possible. As a result, the PN number for some of the richest OPs is slightly above the saturation threshold of the SMPS neutralizer as recommended by TSI (<10 7 cm -3 ). As the impact on the calculation of f v was verified to be limited, this approach was considered acceptable to ensure that all measurements could be performed with the same dilution (see also supplementary information S.1). This study showed Overall, was found to vary between 1.5 and 1.8. This range of variation is similar to what was observed for soot aggregates generated by a propane miniCAST, for which was reported to vary between 1.6 and 1.8 [START_REF] Saffaripour | Raman spectroscopy and TEM characterization of solid particulate matter emitted from soot generators and aircraft turbine engines[END_REF]. All these observations demonstrate the ability of the diesel miniCAST to produce soot aggregates at variable sizes and Using the CS also results in PN losses. In this regard, it is proposed to evaluate the particle penetration measured in this work and compare it with the one accounting for diffusion and thermophoretic losses as proposed by the manufacturer (Catalytic Instruments GmbH & Co.KG 2020) and which are expected to be size dependent. Contrarily to PN losses, the particle penetration refers to the amount of PN able to cross the CS compared to the case where the CS is bypassed. Again, since for each OP the CS was used on the entire aggregates size classes without any prior size selection, the choice was made to consider particle penetration as a function of measured when the CS was bypassed. For the soot aggregates investigated here this particle penetration is found to fluctuate in the range 60-80 % which is in good agreement with the solid particle penetration provided by the manufacturer (Catalytic Instruments GmbH & Co.KG 2020) even though it was obtained for size selected silver spherical particles and was expected to vary in the range 70-74 % for sizes in the range 45-105 nm.

Fit of the size distribution:

To minimize the diffusion losses, the SMPS was operated in high flow mode (1.5 L/min, 1:10 sample: sheath flow ratio, 6-224.7 nm range). As a result, for some OPs the upper tail of the size distributions appears to be truncated as shown in Figure 4.a.

If the soot volume fraction ( ) was evaluated considering solely the measured size distribution, would be underestimated because of the missing large diameter values. To overcome this lack of information, was calculated using the fitting probability density function (PDF)

extrapolated to zero probability at high rather than the measured data. Aerosol size distributions are well described with log-normal PDF (Eq.1).

This observation is merely empirical but has the benefit of describing a size distribution using only three parameters (PN, and ). However, assuming that a size distribution follows a log-normal PDF may yield erroneous values particularly for distribution moments higher than the second order [START_REF] Sorensen | Light Scattering by Fractal Aggregates: A Review[END_REF]) such as which is a 3 rd order moment [START_REF] Greenberg | Soot volume fraction imaging[END_REF]. Figure 5.a shows an example of a log-normal PDF that is not accurate (R² = 0.87, black bold dotted line). In this case, a bi-modal log-normal PDF was found to render a better fit (R² = 0.99, green solid line). On the other hand, Figure 5.b shows an example where a monomodal log-normal PDF function is accurate enough (R² = 0.99, black bold dotted line).

Either way, for all size distributions the PDF (monomodal or bimodal log-normal) that renders the best fit is considered to extrapolate the size distribution tail as illustrated in Figure 5.

[Figure 5 near here] (Eq.1)

Morphology

Impact of the miniCAST flow rates: STEM and TEM images of soot aggregates, shown in Figure 6, were taken for the six investigated OPs (OP2, OP9, OP17, OP27, OP32 and OP34), and reveal morphological changes between fuel-lean and fuel-rich conditions. Although all detected soot particles are fractal-like aggregates, TEM shows that under fuel-lean conditions (OP2, OP9, OP17 and OP27) the primary particles have more clearly perceptible edges than under fuel-rich conditions (OP32 and OP34).

[Figure 6 near here]

The morphology of soot aggregates is usually described using the so-called fractal law linking the number of primary particles per aggregate ( ) to primary particle diameter ( ) and to the particle gyration diameter ( ). The determination of is detailed in supplementary information S.3 (fractal analysis subsection). This power law (Eq.2) introduces a fractal prefactor ( ) and a fractal dimension ( ) (Köylü et al. 1995).

(Eq.2)

The second part of this analysis focuses on the assessment of morphological parameters that was performed a posteriori, by analyzing STEM images. The analysis was performed on isolated aggregates selected on the STEM images. [Table 2 near here]

The results, summarized in Table 2, show that overall increased from 18.0 nm up to 39.2 nm when the burner was switched from fuel-lean to fuel-rich conditions, while was observed to slightly decrease from 1.580 down to 1.394. and showed no obvious trend and were observed to vary in the ranges 1.805-1.941 and 1.960-1.988, respectively. These values are similar to the ones reported for soot aggregates produced by propane miniCAST [START_REF] Bescond | Soot optical properties determined by analyzing extinction spectra in the visible near-UV: Toward an optical speciation according to constituents and structure[END_REF]). These results are in agreement with engine-like aggregate whose mean primary particle diameter and fractal dimension are generally found to vary between 10 nm and 40 nm and between 1.5 and 2.2, respectively [START_REF] Lapuerta | A method to determine the fractal dimension of diesel soot agglomerates[END_REF][START_REF] Lapuerta | Soot reactivity analysis and implications on diesel filter regeneration[END_REF][START_REF] Cadrazco | Chemical and nanostructural characteristics of the particulate matter produced by renewable diesel fuel in an automotive diesel engine[END_REF][START_REF] Soriano | Oxidation reactivity and nanostructural characterization of the soot coming from farnesane -A novel diesel fuel derived from sugar cane[END_REF][START_REF] Ye | Impact of rail pressure and biodiesel fueling on the particulate morphology and soot nanostructures from a common-rail turbocharged direct injection diesel engine[END_REF][START_REF] Agudelo | Impact of crude vegetable oils on the oxidation reactivity and nanostructure of diesel particulate matter[END_REF][START_REF] Li | Evolution of the nanostructure, fractal dimension and size of in-cylinder soot during diesel combustion process[END_REF]. For the sake of simplicity, primary particles are from now on considered monodisperse with a mean primary particle diameter .

Impact of the catalytic stripper:

When the CS was used, and were found similar to those obtained for the untreated aggregates (see Table 2). This suggests that the CS thermal treatment does not have a major impact on monomer size or polydispersion, at least not a clearly visible impact with such diagnostics. On the other hand, it was observed that the primary particles boundaries became more noticeable under CS-treated fuel-rich condition OP34 compared to their respective untreated ones, while remaining fairly similar under OP9 and OP27

(see supplementary information Figure S.3.6). This might suggest that a significant amount of condensed semi-volatile organic compounds might be overlayed all over the aggregate surface and that was partially removed once heated at 350 °C. This is still to be confirmed using adequate tools describing accurately the chemical composition of soot surface.

Optical extinction coefficients

In this section, the optical extinction coefficients ( ) is measured for the miniCAST exhaust under various conditions. Starting with the untreated exhaust, Figure 7.a shows measured over the 200-1000 nm wavelength range for OP2, OP9, OP17, OP27, OP32 and OP34.

Under the fuel-lean conditions OP2 and OP9, exhibits a typical soot response with a maximum between 225 nm and 250 nm [START_REF] Bescond | Soot optical properties determined by analyzing extinction spectra in the visible near-UV: Toward an optical speciation according to constituents and structure[END_REF][START_REF] Schnaiter | UV-VIS-NIR spectral optical properties of soot and soot-containing aerosols[END_REF] followed by a spectral decrease as a function of the wavelength above 400 nm as already seen in numerous studies [START_REF] Bescond | Soot optical properties determined by analyzing extinction spectra in the visible near-UV: Toward an optical speciation according to constituents and structure[END_REF][START_REF] Yon | Examination of wavelength dependent soot optical properties of diesel and diesel/rapeseed methyl ester mixture by extinction spectra analysis and LII measurements[END_REF][START_REF] Tregrossi | Spectral properties of soot in the uvvisible range[END_REF][START_REF] Schnaiter | UV-VIS-NIR spectral optical properties of soot and soot-containing aerosols[END_REF].

Compared to OP2, under OP9 is higher since a higher number of aggregates with larger size are being produced. Looking into OP17 and above, an additional absorption signal with noticeable broad peaks were observed below 400 nm, indicating the presence of other absorbing species, most likely PAHs in the gas phase. This means that is resulting from 2 contributions: soot aggregates extinction ( ), that accounts itself for both soot aggregates absorption ( ) and soot aggregates total scattering ( ) and the sum of all gas species absorption coefficients ( ) (Eq.3).

As detailed further below (Eq.9), is a function of . Therefore, to calculate from extinction measurements, and have to be estimated or removed from (Eq.3).

is quantified by running a second set of measurements with a particle filter interposed between the sampling line and the light extinction cell: once all particles are removed, . Figure 7.b shows that increased with . It also clearly demonstrates that the gas phase absorbs only in the UV and that above 400 nm is solely due to soot aggregates.

Furthermore, once the CS was used, displayed in Figure 7.c shows that the quasi-totality of the produced absorbing gas phase was oxidized bringing the extinction coefficients to the same shape (particularly in the UV) as OP2 or OP9 under untreated conditions.

[Figure 7 near here] (Eq.3)

To identify the contribution of , one needs information on both aggregates size distribution and morphology (see supplementary information S.4). Due to time and resource constraints, morphological parameters were evaluated only for 9 operating conditions that cover the burner's operating range as shown in Table 2. Consequently, for the remaining OPs are interpolated with respect to (see supplementary information Figure S.3.7). For ease of use, interpolation was performed with a second order polynomial function, which seemed to be the best trade-off between lower order fit error and higher order function overfitting. Meanwhile, for the rest of OPs for which and values were not determined, and were fixed at 1.851 and 1.970, respectively. These values correspond to the mean values of the and in Table 2 (all cases combined).

Using this information was obtained. Then was fitted with a power law of the form between 400 nm and 1000 nm, with the Ångström absorption exponent (Ångström 1929). Regardless of the exhaust condition (untreated or CS-treated), the fitting resulted in > 1 as summarized in Table 3. Considering only untreated conditions, was found to vary from 1.32 ± 0.09 (under OP9) up to 2.06 ± 0.12 (under OP32).

[Table 3 near here] Furthermore, was evaluated from the fitting of between 400 nm and 1000 nm of all 34 OPs. Obtained are available in supplementary information Table S.5.1. On average, in this study was observed to increase with from 1.05 (under OP11) to 2.25 (under OP33).

Compared to evaluated for soot aggregates generated by propane miniCAST [START_REF] Ess | Optical and morphological properties of soot particles generated by the miniCAST 5201 BC generator[END_REF][START_REF] Ess | Characterization of a new miniCAST with diffusion flame and premixed flame options: Generation of particles with high EC content in the size range 30 nm to 200 nm[END_REF][START_REF] Lefevre | Spectrally resolved light extinction enhancement of coated soot particles[END_REF][START_REF] Török | Investigation of the absorption Ångström exponent and its relation to physicochemical properties for mini-CAST soot[END_REF][START_REF] Kim | Assessing Optical Properties and Refractive Index of Combustion Aerosol Particles Through Combined Experimental and Modeling Studies[END_REF][START_REF] Schnaiter | Strong spectral dependence of light absorption by organic carbon particles formed by propane combustion[END_REF], much significant increase of with was reported particularly by [START_REF] Kim | Assessing Optical Properties and Refractive Index of Combustion Aerosol Particles Through Combined Experimental and Modeling Studies[END_REF]Ess and[START_REF] Ess | Characterization of a new miniCAST with diffusion flame and premixed flame options: Generation of particles with high EC content in the size range 30 nm to 200 nm[END_REF] with variation between 1.0 and 5.6. This dispersion may be due to differences in experimental conditions under which soot aggregates were obtained as much as it can be explained by how the power law fitting is performed and whether the total scattering has been accounted for. Despite all of that, values obtained in this work are very well embedded in the domain covered by those previously reported in literature. Moreover, for soot aggregates generated by miniCAST using propane in a diffusion type flame Ess and Vasilatou 2019 have reported that increased with the organic content of the aggregates. Similar observations have also been reported by both [START_REF] Schnaiter | Strong spectral dependence of light absorption by organic carbon particles formed by propane combustion[END_REF][START_REF] Lefevre | Spectrally resolved light extinction enhancement of coated soot particles[END_REF]. The point that these studies made is that the more organic compounds the soot aggregates contain, the higher is thus reflecting a sharp decrease in wavelength. In this regard, when the CS was used in the present study, was observed to decrease for both fuel-lean and fuel-rich conditions hence varying between 1.10 and 1.66 (see supplementary information Table S.5.2). These findings suggest that PM obtained under these OPs exhibit different chemical compositions, responsible for such wavelength decrease. Investigating this aspect is beyond the scope of the article, and it will be investigated in a future work.

Comparative methods for the determination of the soot volume fraction

Over the years, many approaches have been reported to evaluate the soot volume fraction ( ). These approaches are based either on a single analyzer or on a combination of different measurement methods and serve to compare different diagnostics and then indirectly to test the different assumptions made in aggregate and optical properties modeling. First, on the base of mobility size measurements, is calculated comparing the spherical particles model with the model accounting for the aggregate's morphology. Then, evaluated from mass concentration measurements and optical extinction coefficients are compared to the fractal aggregate approach using standard literature values for soot bulk density and optical properties.

Aggregate soot volume fraction vs. spherical model

In the most simplified approach, can be evaluated by considering soot particles as agglomerates of polydisperse spheres. In this case, is simply the sum over each class of size i of soot particle volume having a mobility-equivalent diameter and number concentration of particles per unit volume of aerosol (Eq.4), therefore requiring only mobility-equivalent size distributions as provided by the SMPS measurements. This approach, referred to as "spherical approach" (or SMPS), oversimplifies the geometry of soot aggregates and thus is expected to overestimate .

(Eq.4)

The second approach takes into account the fractal-like morphology of soot aggregates. This so-called "fractal-like aggregate approach" (or SMPS + STEM) accounts for morphological aspects by using the soot effective density ( ) which is size-dependent [START_REF] Yon | A simple semi-empirical model for effective density measurements of fractal aggregates[END_REF] and defined as the ratio of an aggregate mass and its volume based on its mobility-equivalent diameter [START_REF] Baron | Nonspherical particle measurements: Shape factors, fractals, and fibers[END_REF]). The aggregate mass may be written as a function of , and soot bulk density ( ), thus one may deduce the ratio (Eq.5) of and which is used to correct the first approach (Eq.4). In this case, soot particles are considered as polydisperse fractal-like aggregates (assuming monodisperse = and spherical primary particles size distribution). So, if an aggregate is a sphere, then = 1 and = .

(Eq.5)

Using the fractal law (Eq.2) describing aggregates morphology, the previous ratio can be then expressed as a function of measured quantities ( , , and ). However, this requires converting the gyration diameter into a mobility-equivalent diameter. A simple conversion law, connecting the gyration diameter ( ) and the electrical mobility diameter ( ), of the form = can be used [START_REF] Rogak | The Mobility and Structure of Aerosol Agglomerates[END_REF]). In fact, the coefficient depends on the flow regime [START_REF] Wang | Diffusive mobility of fractal aggregates over the entire knudsen number range[END_REF], which is characterized by Knudsen number (Kn). In the transient regime (i.e., 0.1 << Kn << 10) which is the case here, was found to fall in the range 1.03-1.35 [START_REF] Kätzel | Dynamic light scattering for the characterization of polydisperse fractal systems: II. Relation between structure and DLS results[END_REF][START_REF] Gwaze | Comparison of three methods of fractal analysis applied to soot aggregates from wood combustion[END_REF][START_REF] Sorensen | Light Scattering by Fractal Aggregates: A Review[END_REF][START_REF] Wang | Diffusive mobility of fractal aggregates over the entire knudsen number range[END_REF][START_REF] Rogak | The Mobility and Structure of Aerosol Agglomerates[END_REF]). Consequently, a conversion ratio of ~ 1.3 is assumed, similarly to [START_REF] Yon | Examination of wavelength dependent soot optical properties of diesel and diesel/rapeseed methyl ester mixture by extinction spectra analysis and LII measurements[END_REF][START_REF] Caumont-Prim | Measurement of aggregates' size distribution by angular light scattering[END_REF]. Combining (Eq.2) and (Eq.4) corrected with the density ratio (Eq.5), can be formulated as in (Eq.6) while considering aggregates with smaller than to be spherical, similarly to the approach proposed by Kelesidis and Pratsinis 2021.

(Eq.6)

Figure 8 compares the calculated using the spherical and the fractal aggregate approaches.

It is found that assuming all particles to be spherical overestimates on average by ~ 70 % the compared to taking the morphology into consideration. This is globally the case for 9 data points (6 OPs of untreated and 3 of CS-treated exhaust) for which all parameters in (Eq.4) and (Eq.6)

were measured except . Adding the rest of the 34 OPs to the analysis (for both untreated and CS-treated exhaust), with assumed particle morphology, seems to corroborate the previous statement. Figure 8 also shows that this overestimation can reach up to a factor of 2.63 if an aggregate gyration and mobility-equivalent diameters were considered equivalent (i.e., = 1.0).

In a recent work, Kelesidis and Pratsinis 2021 showed that derived from mobility data (neglecting aggregates fractal aspect) overestimated up to four times the derived from massmobility measurements and that once the fractal-like morphology was accounted for this deviation decreased down to 6 %. In the light of this, we will consider that calculated considering both mobility and morphological data as the reference .

[Figure 8 near here]

Mass based vs. fractal aggregate volume fraction

Using filter deposition (see supplementary information Figure S.2.2), mass concentrations were measured. Table 3 summarizes the measured particulate mass concentrations ( ) for both untreated and CS-treated exhaust. is obtained from (Eq.7) by assuming :

(Eq.7)

Figure 9 shows for the selected OPs, assuming a value of commonly found in the literature for mature soot = 1800 kg/m 3 [START_REF] Snelling | Determination of the soot absorption function and thermal accommodation coefficient using low-fluence LII in a laminar coflow ethylene diffusion flame[END_REF][START_REF] Choi | Comparisons of the soot volume fraction using gravimetric and light extinction techniques[END_REF]. A roughly linear correlation with is found. On average, using this approach seems to underestimate except for untreated OP34 whose is overestimated.

Modifying the bulk density assumption to = 1296 kg/m 3 yields a slope of 1:1. This parameter tuning is in the range of previously reported values for soot aggregates produced by a propane miniCAST that varied between 1227 kg/m 3 and 1543 kg/m 3 according to [START_REF] Yon | A simple semi-empirical model for effective density measurements of fractal aggregates[END_REF].

[Figure 9 near here]

Volume fraction derived from extinction measurement

Optical extinction coefficients ( ) were measured between 200 nm and 1000 nm. It has been shown in section 3.1.3 that gas phase absorption contribution to is limited to below 400 nm. On the other hand, the average diameter of the primary particles ( ) were found to vary between 18 nm and ~ 39 nm. Considering variation range, it was estimated that the soot total scattering accounts in the worst case for 6% at 700 nm (OP27). Since was determined at 700 nm, the contribution of the scattering was neglected ( ). In this case, could be evaluated using (Eq.9) if the soot absorption function E(m) is known. To a first approximation, a constant E(m, = 700 nm) = 0.35 was used [START_REF] Simonsson | Wavelength dependence of extinction in sooting flat premixed flames in the visible and near-infrared regimes[END_REF].

(Eq.9)

As shown in Figure 10, evaluated for all investigated cases is plotted against . Overall, shows a good agreement with although it underestimated it by ~ 13 %. also agreed with although it overestimated it by ~ 25 % (not shown in the Figure ). The main conclusion of this analysis is that despite the uncertainties inherent to each experimental method, evaluated on the same samples with three methods based on completely different physical phenomena are in reasonable agreement.

Summary and conclusion

The exhaust of the diesel miniCAST was characterized over a wide range of operating conditions covering overall flame equivalence ratios from 0.103 to 1.645 using diesel B7 as fuel.

The generated particulate matter (PM) was analyzed to describe its mobility-equivalent size distribution, morphology, mass concentration and optical extinction coefficient. The impact of adjusting the miniCAST flow rates demonstrated the ability of this burner to produce soot aggregates of variable size distributions and number concentrations offering a panel of choices for the targeted application. The burner was found to generate soot aggregates with geometric mean diameters (mobility diameters) in the range 45-105 nm with a geometric standard deviation in the range 1.5-1.8. Thanks to electron microscopy, key parameters describing the aggregates morphology were evaluated. The mean diameter of primary particles was found to increase from ~ 18 nm in fuel-lean conditions up to ~ 39 nm in fuel-rich conditions. The use of a catalytic stripper (CS) at 350 °C was found to alter soot aggregates size distributions that became more flattened. Soot aggregates PN losses within the CS were also evaluated and were found in good agreement with modeled losses accounting for diffusion and thermophoresis. The CS was not found to significantly alter soot aggregate morphology.

The miniCAST exhaust aerosol consisted not only of a particulate phase but also of a light absorbing gas phase whose contribution was significant to in the UV (< 400 nm) and that increased from fuel-lean to fuel-rich conditions. The Ångström absorption exponent ( ) retrieved from optical absorption coefficients (accounting for total scattering contribution) between 400 nm and 1000 nm was found to increase from 1.05 under fuel-lean conditions up to 2.25 under fuel-rich conditions. Once the exhaust was thermally treated, the contributions to of absorbing species in the gas phase disappeared and the wavelength decrease in the visible and near-IR became less pronounced with varying between 1.11 and 1.66. These observations, supported by TEM imaging suggest that the chemical composition of the exhaust, and most probably its organic content, play a significant role both on the shape and amplitude of .

Finally, a database with the following characteristics: PN, , , , , and was produced for the 34 operating points of the miniCAST including operating points without and with treatment (CS) of the exhaust. This database can be used by future users willing to produce soot aggregates with specific characteristics. In addition, the procedure developed proved to be robust and reproducible and can be extended to new generation liquid fuels to test the influence of their chemical composition on the characteristics of the soot particles.

A second aspect of this work involved the evaluation of three independent measurement methods for determining the volume fraction of soot ( ). These methods were based on the measurement of the aggregate size (combining mobility size distribution and morphology), the deposited mass and the optical extinction measurements. The main conclusions of this study are first that evaluated on the basis of size mobility data alone overestimate by ~ 70 % the one accounting for morphological aspects (fractal aggregate approach), and second that evaluated optically reasonably agreed with both measured adopting the fractal aggregate approach (within 13 %) and evaluated from mass concentration measurements (within 25 %) assuming a soot bulk density of 1800 kg/m 3 . It turns out that the method based on optical extinction at 700 nm is a reliable and robust method. From this perspective and thanks to their simplicity, optical extinction-based sensors are worth exploring. Meanwhile, pressing technical issues of optics fouling and measurement sensitivity also have to be addressed to make this technology compliant with more restrictive tailpipe emission thresholds for modern engines supplied with any future liquid fuel.

Table caption

Table 1. Settings of operating points of the liquid fuel miniCAST burner and resulting flame overall equivalence ratios ( ).

Table 2. Morphological properties of soot aggregates resulting from STEM images analysis. and uncertainties correspond to the 95 % confidence interval of the sigmoid law (Eq.S.3.3) fit.

Table 3. Ångström absorption exponent ( ) evaluated by fitting using a power law of the form between 400 nm and 1000 nm. Uncertainties correspond to day-to-day variations and PM mass concentration ( ) for miniCAST OPs for untreated and CS-treated exhaust. Data not corrected for dilution (~ 19:1). Statistical descriptors of these size distributions are made available in supplementary information Table S.2.1. Table 3. Ångström absorption exponent ( ) evaluated by fitting using a power law of the form between 400 nm and 1000 nm. Uncertainties correspond to day-to-day variations and PM mass concentration ( ) for miniCAST OPs for untreated and CS-treated exhaust.

Figure caption

Data not corrected for dilution (~ 19:1). . Data not corrected for dilution (~ 19:1).

S.1.MiniCAST operating conditions, soot production stability and repeatability

Chemical composition of diesel B7 and some of its properties

Sampling conditions

The miniCAST exhaust was diluted using either one external dilution stage or two external dilutions stages, the use of which may alter soot aggregates size distribution properties through coagulation and agglomeration processes within the sampling line.

Exhaust dilution is mainly performed to lower soot aggregates concentrations, so it does not saturate measuring instruments such as SMPS. stable. To minimize possible variations with time, the choice was made to consider the fuellean condition OP9 as a reference condition to be tested each time the burner was used.

Any significant drift from OP9's triggered a cleaning procedure of the burner. As a result, PN, and varied at worse of 30 % (e.g., OP2), 17 % (e.g., OP2) and 5 % (e.g., OP2), and at best of 4 % (e.g., OP27), 7 % (e.g., OP34) and 0.5 % (e.g., OP34), respectively (see operating points grouped using diesel B7 for both untreated (raw) and CS-treated where P is the number of perimeter pixels and A the total number of pixels considered in each aggregate (Sipkens et al. 2021). Consequently, when the image quality allowed it, care was taken to keep that uncertainty as low as possible. On average, 20 STEM images were processed per configuration. As each image contained more than 5 aggregates, on average more than 150 single aggregate per configuration were successfully retrieved with a satisfying error on aggregate area of at best ~ 7 % and at worse ~ 11 % as summarized in Table 2. In respect to similar studies from literature (Sipkens et al. 2021;[START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF], this was considered to be sufficient enough for a statistically representative result.

Soot aggregates size distributions statistical descriptors

EDM-SBS process

The following processing step consist of applying Euclidian Distance Mapping-Surface

Based Scale (EDM-SBS) method proposed by [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF]. This approach consists of applying series of image transformations, where each single aggregate area (S) is progressively eroded. Consequently, eroded surface areas may be computed as a function of the erosion level (k). The EDM-SBS then consists of studying the dependence of the eroded surface area to erosion magnitude. is then inverted before reapplying the same process (i.e., EDM calculation and thresholding at same 'k' level) once more. As mentioned before, EDM-SBS approach consists of studying the dependence of as a function of the scale 2k+1 [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF]. Knowing that the image resolution is ~ 0.725 pixels/nm, it is then possible to deduce a surface S(D) at each scale diameter (D) using the following conversions:

(Eq.S.3.1)

for each case and the fitting procedure was applied accounting only for data points with > 5. With such log-log representation and can easily be linked to the slope and intercept of the cloud points. Accordingly, Table 2 recapitulates evaluated and values for all studied configurations. 2011. However, looking at OP27's case, these calculations show that indeed for aggregates with higher (~ 35 nm in this case) total scattering cannot necessarily be neglected as it reaches on average ~ 12 % at 400 nm. Therefore, assigning the extinction to be equal to the absorption has to be judged from case-to-case. [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF]. Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot. Aerosol Sci. Technol. 48 (8):831-841.

Impact of the catalytic stripper

Bescond, A., Yon, J., [START_REF] Bescond | Soot optical properties determined by analyzing extinction spectra in the visible near-UV: Toward an optical speciation according to constituents and structure[END_REF]. Soot optical properties determined by analyzing extinction spectra in the

  that, at fixed oxidation air flow rate (2 L/min), soot PN increased from 0decreased from ~ 90 nm down to ~ 55 nm (Figure 3.b) with . For , no obvious trend was observed (Figure 3.c). These observations remained valid regardless of the mixing air flow rate choice, suggesting that the latter has no significant impact over aggregates number concentration, size or polydispersion. In a second parametric study, the mixing air flow rate was kept constant (0.1 L/min) and decreasing the oxidation air flow rate, going from fuel-lean to fuel-rich conditions, made soot PN increase d). Meanwhile, soot aggregates were observed to grow in size from ~ 45 nm up to a maximum of ~ 105 nm around ~ 0.4 before decreasing down to ~ 60 nm for > 1 (Figure 3.e). Using a propane miniCAST, Moore et al. 2014 observed a similar trend, except that the aggregate size reached a maximum under slightly fuel-lean conditions before starting decreasing under fuel-rich conditions, therefore covering the range 10-130 nm in modal diameters. We attribute this difference to the fuel (propane vs. diesel B7) and to the burner's geometry. When decreasing the oxidation air flow rate in the diesel miniCAST, exhibited two distinct behaviors: at a lower liquid fuel flow rate (50 µL/min), decreased rapidly (Figure 3.f) and at a higher liquid fuel flow rate (200 µL/min), remained quasi-constant at ~ 1.7.

  concentrations by controlling only three flow rates (oxidation air, mixing air and liquid fuel flow rates) hence offering the user a panel of choices. Soot production repeatability is discussed in supplementary information S.1 [Figure 3 near here] Impact of the catalytic stripper: Mobility-equivalent size distributions averaged over 3 consecutively measured size distributions representing OP2, OP9, OP17, OP27, OP32 and OP34 are shown in Figure 4.

  Figure 4.b displays their corresponding CS-treated ones. Looking at Figure 4.b, one can observe

  Figure S.3.5).

Figure 1 .

 1 Figure 1. Schematic of the experimental exhaust bench and aerosol characterization setup.

Figure 2 .

 2 Figure 2. Descriptive schematic of the miniCAST burner model 5102 D (Jing Ltd., Switzerland) for liquid fuels. The indicated parameters are used to change soot properties.

Figure 3 .

 3 Figure 3. SMPS measured aggregate number concentration (PN), mobility-equivalent geometric mean diameter ( ) and geometric standard deviation ( ) as function of flame overall equivalence ratio ( ) for 34 OPs for untreated exhaust using diesel B7. OP2, OP9, OP17, OP27, OP32 and OP34 are indicated in colors. (a, b, c) oxidation air = 2 L/min and (d, e, f) mixing air = 0.1 L/min. Uncertainties account for 3 size distributions measured consecutively. Data not corrected for dilution (~ 19:1).

Figure 4 .

 4 Figure 4. Soot aggregates mobility-equivalent size distributions obtained under OP2, OP9, OP17, OP27, OP32 and OP34 for (a) untreated exhaust and (b) CS-treated exhaust using diesel B7. Each size distribution is the average of 3 consecutive size distributions. Data not corrected for dilution (~ 19:1).

Figure 5 .

 5 Figure 5. Fitting measured soot aggregates mobility-equivalent size distributions obtained under (a) OP27 and (b) OP34 for untreated exhaust, with either monomodal or bimodal log-normal PDFs and extrapolating truncated data from 224.7 nm to 400 nm. Data not corrected for dilution (~ 19:1).

Figure 6 .

 6 Figure 6. Scanning transmission electron microscopy (STEM) (left row) and transmission electron microscopy (TEM) (right row) images of representative miniCAST soot aggregates for untreated exhaust obtained under (a) OP2, (b) OP9, (c) OP17, (d) OP27, (e) OP32 and (f) OP34.

Figure 7 .

 7 Figure 7. Optical extinction coefficients ( ) measured under OP2, OP9, OP17, OP27, OP32 and OP34 for (a) untreated (raw) exhaust, (b) filtered exhaust and (c) thermally treated (CS-treated) exhaust.

Figure 8 .

 8 Figure 8. evaluated assuming polydisperse spherical particles vs. calculated assuming polydisperse fractal-like aggregates. Data not corrected for dilution (~ 19:1).

Figure 9 .

 9 Figure 9. evaluated from soot deposits assuming a constant soot bulk density ( = 1800 kg/m 3 ) vs. assuming polydisperse fractal-like aggregates. Data not corrected for dilution (~ 19:1).

Figure 10 .

 10 Figure 10. calculated assuming a constant absorption function (E(m) = 0.35) at 700 nm vs.. Data not corrected for dilution (~ 19:1).

Figure 1 .

 1 Figure 1. Schematic of the experimental exhaust bench and aerosol characterization setup.

Figure 2 .

 2 Figure 2. Descriptive schematic of the miniCAST burner model 5102 D (Jing Ltd., Switzerland) for liquid fuels. The indicated parameters are used to change soot properties.

Figure 3 .

 3 Figure 3. SMPS measured aggregate number concentration (PN), mobility-equivalent geometric mean diameter ( ) and geometric standard deviation ( ) as function of flame overall equivalence ratio ( ) for 34 OPs for untreated exhaust using diesel B7. OP2, OP9, OP17, OP27, OP32 and OP34 are indicated in colors. (a, b, c) oxidation air = 2 L/min and (d, e, f) mixing air = 0.1 L/min. Uncertainties account for 3 size distributions measured consecutively. Data not corrected for dilution (~ 19:1).

Fixed

  Figure 4. Soot aggregates mobility-equivalent size distributions obtained under OP2, OP9, OP17, OP27, OP32 and OP34 for (a) untreated exhaust and (b) CS-treated exhaust using diesel B7. Each size distribution is the average of 3 consecutive size distributions. Data not corrected for dilution (~ 19:1). Statistical descriptors of these size distributions are made available in supplementary information Table S.2.1.

Figure 5 .

 5 Figure 5. Fitting measured soot aggregates mobility-equivalent size distributions obtained under (a) OP27 and (b) OP34 for untreated exhaust, with either monomodal or bimodal lognormal PDFs and extrapolating truncated data from 224.7 nm to 400 nm. Data not corrected for dilution (~ 19:1).

Figure 6 .

 6 Figure 6. Scanning transmission electron microscopy (STEM) (left row) and transmission electron microscopy (TEM) (right row) images of representative miniCAST soot aggregates for untreated exhaust obtained under (a) OP2, (b) OP9, (c) OP17, (d) OP27, (e) OP32 and (f)

Figure 8 .

 8 Figure 8. evaluated assuming polydisperse spherical particles vs. calculated assuming polydisperse fractal-like aggregates. Data not corrected for dilution (~ 19:1).

Figure 9 .

 9 Figure 9. evaluated from soot deposits assuming a constant soot bulk density ( = 1800 kg/m 3 ) vs. assuming polydisperse fractal-like aggregates. Data not corrected for dilution (~ 19:1).

Figure 10 .

 10 Figure 10. calculated assuming a constant absorption function (E(m) = 0.35) at 700 nm vs. . Data not corrected for dilution (~ 19:1).

  Figure S.1.1 describes soot aggregates size distribution parameters (PN, and ) measured by the SMPS for untreated exhaust obtained under OP9 as a function of the global dilution ratio (volumetric). Each sub-figure shows, two data sets. The first data set with global dilution ratios < 30 corresponds to the case where only the first external dilution stage was varied, while the rest of the data points corresponds to the case where both the first and second external dilutions stages were used. It is worth reminding that the second external dilution stage imposes a fixed dilution ratio (~ 11: 1) and that for both data sets variation in the global dilution ratio was obtained by varying the amount of added air using the first external dilution stage.

  Figure S.1.3). Overall, these variations are in line with the propane miniCAST for which PN varied by a factor of 2 over a similar evaluation period (Moore et al. 2014). Indeed, several factors can contribute to such variations, for instance soot accumulation in the sampling lines or valves or clogging issues inside the burner due to its heating system which tends to cause coking on the inside of the burner tube.

Figure S. 1

 1 Figure S.1.3. (a, b, c): SMPS measured aggregates number concentration (PN), mobilityequivalent geometric mean diameter ( ) and geometric standard deviation ( ) as function of flame overall equivalence ratio ( ) for OP2, OP9, OP17, OP27, OP32 and OP34 operating points over time for untreated exhaust using diesel B7. (d, e, f) Their respective deviations to the mean curve accounts for repeatability over 5 months.

Figure S. 2

 2 Figure S.2.2. Soot aggregate samples deposited on borosilicate microfibers filters (Pallflex-Emfab, Pall Corp., U.S.A) generated under OP2, OP9, OP17, OP27, OP32 and OP34

Figure

  Figure S.3.2. Segmentation process showing example of (a) raw STEM image, (b) aggregates contours obtained using SLIDER method (Sipkens and Rogak 2021), (c) the corresponding binary image and (d) isolated aggregates after being inverted. This example corresponds to aggregates obtained under OP9 for untreated exhaust.

  Figure S.3.3 shows a summary of these image transformations applied on the blue aggregate in Figure S.3.2.d.

Figure S. 3

 3 Figure S.3.3. EDM-SBS protocol (Bescond et al. 2014) applied on the blue aggregate of Figure S.3.2. The protocol consists of taking a binary image of an isolated aggregate (a), whose area is , inverting it (b), and getting its corresponding Euclidian distance map (EDM) (c). The process continues through a loop over 'k' gray levels of the EDM image and applying a threshold at level 'k' to get an eroded surface hence image (d), inverting it to get image (e) reapplying an EDM calculation to get image (f) and reapplying a threshold at level 'k' -this is equivalent to a dilatation of the previous eroded surfacehence getting image (g), whose area is . Images (d), (e), (f) and (g) show the example of level k = 10.

Figure

  Figure S.3.6 shows STEM, and TEM images of representative miniCAST soot aggregates for a CS-treated exhaust obtained under OP9, OP27 and OP34. Soot morphological parameters for these conditions were evaluated by analyzing their corresponding STEM images as summarized in Table2.

Figure S. 3

 3 Figure S.3.6. Scanning transmission electron microscopy (STEM) (left row) and transmission electron microscopy (TEM) (right row) images of representative miniCAST soot aggregates for CS-treated exhaust obtained under (a) OP9, (b) OP27 and (c) OP34.

Figure

  Figure S.4.1. Estimated percentages of total scattering in soot extinction coefficients for soot aggregates obtained under OP9 and OP27 (for an untreated exhaust), using RDG-FA

Table 1 .

 1 Settings of operating points of the liquid fuel miniCAST burner and resulting flame overall equivalence ratios ( ).

	Operating point (OP)	Liquid fuel flow rate [µL/min]	Mixing air flow rate [mL/min]	Oxidation air flow rate [L/min]	Internal dilution air flow rate [L/min]	Flame overall equivalence ratio ( ) (diesel B7)
	OP2	50	100	3	20	0.103
	OP9	50	100	2	20	0.291
	OP17	100	10	2	20	0.616
	OP27	250	100	3	20	0.913
	OP32	250	100	2	20	1.457
	OP34	250	10	2	20	1.539

Table 2 .

 2 Morphological properties of soot aggregates resulting from STEM images analysis. and uncertainties correspond to the 95 % confidence interval of the sigmoid law (Eq.S.3.3) fit.

	Operating point (OP)	Condition	Number of analyzed aggregates	Estimated error on area [%] aggregate	[nm]
	OP2	Untreated	139	±10	22.3 ± 0.4 1.518 ± 0.012	1.839	1.967
	OP9	Untreated	198	± 11	18.0 ± 0.4 1.580 ± 0.015	1.805	1.960
	OP17	Untreated	156	± 7	34.4 ± 0.3 1.497 ± 0.007	1.941	1.988
	OP27	Untreated	179	± 8	35.2 ± 0.2 1.431 ± 0.004	1.831	1.966
	OP32	Untreated	138	± 8	34.4 ± 0.4 1.425 ± 0.007	1.862	1.972
	OP34	Untreated	164	± 7	39.2 ± 0.2 1.394 ± 0.003	1.844	1.968
	OP9	CS-treated	141	± 9	19.7 ± 0.3 1.567 ± 0.013	1.849	1.970
	OP27	CS-treated	229	± 8	34.5 ± 0.3 1.377 ± 0.005	1.790	1.957
	OP34	CS-treated	164	± 9	35.2 ± 0.3 1.394 ± 0.005	1.834	1.966

Operating point (OP) Liquid fuel flow rate [µL/min] Mixing air flow rate [mL/min] Oxidation air flow rate [L/min]

  Table.R.1 Chemical composition of liquid diesel B7 and some of its properties.

	OP14	100	150		2		20	0.566
	OP15	100	100		2		20	0.583
	OP16	150	100		3		20	0.548
	OP17	100	10		2		20	0.616
	OP18	200	150		3		20	0.717
	OP19 OP20 OP21 OP22	200 Average chemical Formula 100 Density at T = 15 °C (kg/m 3 ) 200 10 Air-fuel ratio (stoichiometric) 200 100 150 150	3 3 2.8 2	831.5 14.37	20 20 20 20	0.730 0.756 0.789 0.849
	OP23	Centane number 150	100		2	48.2	20	0.874
	OP24	GCxGC-FID analysis of the chemical composition of liquid diesel 200 100 2.6 20	0.859
	OP25	150	10	B7 (wt. %) 2		20	0.923
	OP26	Iso-paraffins 200	100		2.4	27.4	20	0.941
	OP27	Normal-paraffins 250 100		3	7.7	20	0.913
	OP28	Mononaphthenes 200 100		2.2	19.4	20	1.041
	OP29	Di-naphthenes 200	150		2	12.5	20	1.132
	OP30	Di-aromatics 200	100		2	16.4	20	1.165
	OP31	Naphenic-di-aromatics 200 10		2	6.9	20	1.231
	OP32	Monoaromatics 250	100		2	2.7	20	1.457
	OP33	Naphenic-monoaromatics 200 10		1.6	1.5	20	1.645
	OP34	Tri-aromatics 250	10		2	0.3	20	1.539
		Tetra-aromatics				0.1
	9.	Methyl esters				5.1
	Operating points
	8. Table S.1.1. Settings of operating points (OPs) of the liquid fuel miniCAST burner and
	resulting flame overall equivalence ratio ( ). OPs in bold are those for which all diagnostics
	presented in the main text were performed.
						Internal	Flame overall
						dilution air	equivalence
						flow rate	ratio diesel B7
						[L/min]	(
	OP1	16.67	10		2		20	0.103
	OP2	50	100		3		20	0.183
	OP3	50	50		3		20	0.189
	OP4	50	100		2.8		20	0.197
	OP5	50	100		2.6		20	0.215
	OP6	50	100		2.4		20	0.235
	OP7	50	100		2.2		20	0.260
	OP8	50	150		2		20	0.283
	OP9	50	100		2		20	0.291
	OP10	50	10		2		20	0.308
	OP11	50	100		1.8		20	0.331
	OP12	50	10		1.6		20	0.411
	OP13	100	100		3		20	0.365

Table S

 S

	.2.1. Aggregates number concentration (PN), mobility-equivalent geometric mean
	diameter (	) and geometric standard deviation of size distributions displayed in
	Figure 4 for untreated and CS-treated conditions. Uncertainties account for 3 size
	distributions measured consecutively. Data not corrected for dilution (~ 19:1).
	Operating	[# /			[nm]
	point (OP)	Untreated	CS-treated	Untreated	CS-treated	Untreated CS-treated
	OP2	3.9	2.3	60.3 3.6	57.6 1.0	1.746 0.035	1.738 0.034
	OP9	1.1	7.9	79.3 0.2	79.1 0.8	1.612 0.007	1.604 0.007
	OP17	1.3	1.1	96.0 0.6	63.7 0.5	1.632 0.006	1.845 0.007
	OP27	1.9	1.3	92.9	88.3	1.661 0.000	1.708 0.004
	OP32	1.7	1.2	74.2 0.2	62.6 0.9	1.643 0.002	1.877 0.024
	OP34	1.5	1.2	62.3 0.7	54.9 0.3	1.597 0.004	1.797 0.004
	Deposit on filters
	11.

Table S

 S Table S.5.2. Overview of soot aggregates characteristics (PN corrected for dilution, , , , and * ) of soot aggregates generated by a miniCAST burner for CS-treated exhaust using diesel B7. * Evaluated by fitting by a power law ( ) between 400 nm and 1000 nm accounting for total scattering. , values in gray are interpolated according to Figure S.3.7 while is kept constant at 1.851.

	.5.1. Overview of soot aggregates characteristics (PN corrected for dilution, , , and *) of soot aggregates generated by a miniCAST burner for untreated exhaust using diesel B7. *Evaluated by fitting by a power law ( ) between 400 nm and 1000 nm accounting for total scattering. , values in gray are interpolated according to Figure S.3.7 while is kept constant at 1.851. Operating point (OP) PN [#/cm 3 ] [nm] [nm] * OP1 7.1 ± 0.1 × 10 7 87.8 ± 1.0 1.671 ± 0.010 15.5 1.851 1.37 OP2 6.1 ± 0.7 × 10 7 45.0 ± 2.9 1.818 ± 0.013 22.3 ± 0.4 1.839 1.42 ± 0.04 , OP3 1.2 ± 0.0 × 10 8 94.1 ± 0.6 1.597 ± 0.006 18.6 1.851 1.26 OP4 8.1 ± 0.2 × 10 7 49.8 ± 0.5 1.749 ± 0.008 18.9 1.851 -OP5 1.1 ± 0.0 × 10 8 60.5 ± 0.6 1.678 ± 0.012 19.5 1.851 -OP6 1.3 ± 0.0 × 10 8 67.2 ± 1.6 1.631 ± 0.005 20.2 1.851 1.12 OP7 1.4 ± 0.0 × 10 8 72.4 ± 0.2 1.623 ± 0.011 21.1 1.851 1.14 OP8 8.3 ± 0.2 × 10 7 53.4 ± 0.8 1.719 ± 0.011 21.9 1.851 -OP9 1.4 ± 0.0 × 10 8 81.2 ± 1.6 1.590 ± 0.003 18.0 ± 0.4 1.805 1.32 ± 0.09 OP10 1.8 ± 0.1 × 10 8 80.4 ± 1.7 1.784 ± 0.004 22.5 OP11 1.8 ± 0.0 × 10 8 77.8 ± 0.6 1.571 ± 0.006 23.4 OP17 1.9 ± 0.0 × 68.0 ± 1.1 1.849 ± 30.5 1.851 1.44 ± 0.03 1.851 1.05 10 8 95.5 ± 0.8 0.023 29.0 1.851 OP16 2.3 ± 0.1 × 1.627 ± 1.25 1.851 1.52 2.3 ± 0.1 × 1.736 ± 1.77 16. 10 8 0.002 OP12 10 8 67.7 ± 0.2 0.011 25.5 1.851 2.5 ± 0.0 × 1.516 ± 1.21 2.2 ± 0.0 × 1.690 ± 1.18 OP18 10 8 86.2 ± 0.3 0.005 32.5 1.851 OP13 10 8 104.7 ± 0.1 0.000 24.3 1.851 2.7 ± 0.0 × 1.597 ± 1.57 2.3 ± 0.0 × 1.694 ± 1.23 OP19 10 8 87.9 ± 0.4 0.003 32.8 1.851 OP14 10 8 79.3 ± 0.1 0.002 29.7 1.851 2.8 ± 0.0 × 1.616 ± 1.68 2.3 ± 0.0 × 1.759 ± 1.17 OP20 10 8 86.8 ± 0.9 0.010 33.1 1.851 OP15 10 8 83.8 ± 0.5 0.002 30.0 1.851 3.2 ± 0.1 × 1.618 ± 1.51 2.3 ± 0.0 × 1.709 ± 1.22 OP21 10 8 86.3 ± 0.1 0.001 33.7 1.851 OP16 10 8 88.6 ± 4.7 0.026 29.0 1.851 2.7 ± 0.1 × 1.700 ± 1.72 ± 0.20 2.3 ± 0.0 × 1.763 ± 1.66 OP22 10 8 45.9 ± 0.9 0.015 34.7 1.851 OP17 10 8 67.0 ± 2.7 0.015 34.4 ± 0.3 1.941 3.1 ± 0.0 × 1.673 ± 1.45 2.4 ± 0.0 × 1.723 ± 1.51 OP23 10 8 52.2 ± 1.2 0.017 35.0 1.851 OP18 10 8 89.1 ± 0.2 0.001 32.5 1.851 OP19 3.3 ± 0.0 × 10 8 78.8 ± 0.2 1.715 ± 0.002 32.8 1.851 1.56 OP20 3.1 ± 0.0 × 10 8 91.2 ± 0.4 1.708 ± 0.007 33.1 1.851 1.35 OP21 3.4 ± 0.1 × 10 8 85.6 ± 0.3 1.710 ± 0.009 33.7 1.851 1.57 OP22 3.2 ± 0.1 × 10 8 57.5 ± 0.2 1.630 ± 0.014 34.7 1.851 2.19 OP23 3.5 ± 0.0 × 10 8 64.5 ± 0.3 1.590 ± 0.003 35.0 1.851 2.12 OP24 3.3 ± 0.0 × 10 8 81.6 ± 1.3 1.713 ± 0.003 34.7 1.851 1.66 OP25 3.1 ± 0.0 × 10 8 67.4 ± 0.3 1.648 ± 0.008 35.4 1.851 1.70 OP26 3.4 ± 0.0 × 10 8 80.8 ± 0.5 1.709 ± 0.007 35.7 1.851 1.65 OP27 3.7 ± 0.1 × 10 8 70.3 ± 1.8 1.685 ± 0.011 35.2 ± 0.2 1.831 1.68 ± 0.03 OP28 3.3 ± 0.0 × 10 8 75.6 ± 0.0 1.711 ± 0.005 36.6 1.851 1.75 OP29 3.0 ± 0.0 × 10 8 57.7 ± 0.7 1.709 ± 0.020 37.1 OP30 3.4 ± 0.0 × 10 8 60.1 ± 0.4 1.615 ± 0.005 37.2 OP31 3.3 ± 0.0 × 10 8 68.4 ± 0.1 1.630 ± 0.001 37.3 OP32 3.5 ± 0.0 × 10 8 59.7 ± 0.2 1.620 ± 0.006 34.4 ± 0.4 OP33 3.7 ± 0.0 × 10 8 60.9 ± 0.1 1.552 ± 0.003 35.1 OP34 3.4 ± 0.0 × 10 8 69.5 ± 0.2 1.623 ± 0.003 39.2 ± 0.2 10 8 81.8 ± 1.1 0.010 30.0 1.851 OP15 2.1 ± 0.0 × 1.641 ± 1.38 1.844 2.01 ± 0.17 10 8 75.4 ± 1.1 0.004 29.7 1.851 OP14 1.5 ± 0.4 × 1.630 ± 1.24 1.851 2.25 10 8 100.3 ± 0.4 0.003 24.3 1.851 OP13 2.0 ± 0.1 × 1.544 ± 1.22 1.862 2.06 ± 0.12 10 8 61.1 ± 0.7 0.008 25.5 1.851 OP12 1.7 ± 0.0 × 1.784 ± 1.51 1.851 1.83 10 8 80.1 ± 0.9 0.014 23.4 1.851 OP11 1.5 ± 0.0 × 1.563 ± 1.16 1.851 1.99 10 8 82.6 ± 0.1 0.004 22.5 1.851 OP10 1.3 ± 0.0 × 1.821 ± 1.34 1.851 1.94 2.2 ± 0.1 × 1.744 ± 1.22 OP24 10 8 82.4 ± 0.2 0.006 34.7 1.851 Operating point PN [#/cm 3 ] [nm] [nm] * 2.3 ± 0.0 × 1.814 ± 1.45 OP25 10 8 54.1 ± 0.6 0.009 35.4 1.851 (OP) OP1 5.9 ± 0.0 × 10 7 89.3 ± 0.8 1.667 ± 0.014 15.5 1.31 2.2 ± 0.1 × 1.770 ± 1.24 OP26 10 8 77.3 ± 0.2 0.004 35.7 1.851 1.851 OP2 6.1 ± 0.1 × 10 7 49.2 ± 1.0 1.701 ± 0.031 18.4 -2.4 ± 0.0 × 1.718 ± 1.22 ± 0.05 OP27 10 8 87.6 ± 0.5 0.001 34.5 ± 0.3 1.790 1.851 OP3 1.0 ± 0.1 × 10 7 100.9 ± 0.5 1.548 ± 0.007 18.6 1.26 2.1 ± 0.0 × 1.811 ± 1.25 OP28 10 8 68.5 ± 0.0 0.005 36.6 1.851 1.851 OP4 5.9 ± 0.3 × 10 7 53.1 ± 1.2 1.683 ± 0.037 18.9 -2.2 ± 0.0 × 1.863 ± 1.30 OP29 10 8 56.0 ± 0.2 0.007 37.1 1.851 1.851 OP5 6.8 ± 0.2 × 10 7 58.1 ± 0.7 1.666 ± 0.007 19.5 -2.3 ± 0.1 × 1.844 ± 1.28 OP30 10 8 53.9 ± 2.5 0.019 37.2 1.851 1.851 OP6 8.5 ± 0.1 × 10 7 65.2 ± 0.6 1.619 ± 0.006 20.2 1.22 2.4 ± 0.0 × 1.816 ± 1.35 OP31 10 8 57.0 ± 0.9 0.012 37.3 1.851 1.851 OP7 1.0 ± 0.0 × 10 8 72.3 ± 0.5 1.589 ± 0.006 21.1 1.11 2.3 ± 0.0 × 1.869 ± 1.27 ± 0.10 OP32 10 8 52.4 ± 0.1 0.004 36.7 1.851 1.851 OP8 7.1 ± 0.1 × 10 7 55.3 ± 0.7 1.682 ± 0.016 21.9 -2.0 ± 0.0 × 1.796 ± 1.41 OP33 10 8 42.5 ± 0.5 0.003 35.1 1.851 1.851 OP9 1.1 ± 0.0 × 10 8 80.9 ± 0.2 1.596 ± 0.004 19.7 ± 0.3 1.849 1.26 ± 0.15 10 8 55.4 ± 0.4 0.002 35.2 ± 0.3 1.834 OP34 2.4 ± 0.0 × 1.861 ± 1.45 ± 0.21
	67

Acknowledgments

The authors would like to acknowledge Dr. Virgile ROUCHON and Hedwige PONCET help in acquiring electron microscopy images and Jérôme CHEREL for the assistance in building the experimental setup.

Declaration of interest statement

The authors declare no competing interests. OP34.

Supplementary Information:

Comprehensive characterization of particulate matter emission produced by a liquid-fueled miniCAST burner Corresponding author: pascale.desgroux@univ-lille.fr

Mouad

Content

S.1.MiniCAST operating conditions, soot production stability and repeatability

Chemical composition of diesel B7 and some of its properties Operating points Sampling conditions MiniCAST stability over time Soot production repeatability S.2.Size distributions and deposit on filters

Impact of miniCAST flow rates for CS-treated exhaust Soot aggregates size distributions statistical descriptors Deposits on filters S.3.Electron microscopy diagnostic

Sampling conditions STEM images analysis Segmentation process EDM-SBS process Normalized mean EDM-SBS function interpretation Fractal analysis Impact of the catalytic stripper

MiniCAST stability over time

Conducting experiments on a soot containing exhaust requires that properties of soot aggregates size distribution (PN, and ) generated under a given condition remains stable for extended time periods. This is very important if such soot generator must be used as reference for calibrating other instruments. After integrating the soot generator into the experimental setup, improving the control of mass flow controllers and the burner stability, the miniCAST was operated over 6 months for both short (< 20 minutes) and long (up to 90 minutes) periods of time. Soot production stability was monitored using, a Pegasor particle sensor, type M (PPS-M, Pegasor, Oy) (not shown) that was in fact installed after the first external dilution stage and before preparing exhaust for diagnostics as shown previously in Figure 1. Raw exhaust was routed to the PPS-M inlet by means of a wall heater maintained at 180 °C and the sensor body was maintained at 250 °C.

Soot PN was found to be rather stable within 10 % coefficient of variation (i.e., coefficient of

Soot production repeatability

The measurement of soot aggregates PN, and (for OP2, OP9, OP17, OP27, OP32 and OP34) over 5 months testing period showed that soot production remained Uncertainties account for 3 size distributions measured consecutively. Data not corrected for dilution (~ 19:1).

S.2.Size distributions and deposit on filters

Impact of miniCAST flow rates for CS-treated exhaust

S.3.Electron microscopy diagnostic

Sampling conditions

Probing soot aggregates for electron microscopy imaging can be challenging because one must determine optimal sampling conditions to accommodate with soot PN variability.

Conducting these experiments was done using a second dilution stage (see Figure 1) that allowed lowering soot PN therefore avoiding TEM grids overload. To help decide on sampling times, a preliminary investigation was conducted where soot aggregates produced under OP9 and OP27 (since they almost cover the lower and upper bounds of PN variation range) were probed under variable sampling times (10, 30 and 60 seconds) as summarized in Table S.3 although some particles are still observed in few regions of the grid. However, their distribution is absolutely not homogeneous which leads to believe that such contamination is minor. As for optimal sampling times, it seemed that a proper number of aggregate deposits was obtained at 30-seconds and 10-seconds for OP9 and OP27, respectively.

Furthermore, as combustion exhaust are diluted well after being produced in the burner's flame, soot aggregates are considered already mature. Therefore, even though the dilution 52 process might slightly impact aggregate size distribution for some OPs (as seen in section S.1), morphological parameters are assumed to be invariant in respect to the dilution process as suggested by Ouf et al. 2010.

STEM images analysis

Retrieving aggregate morphological parameters ( , and ) from electron microscopy images is a challenging task for many reasons, first of which is the sampling media made of a carbon film that makes it difficult to get aggregates with enough contrast with the background and second, resulting from the sampling protocol itself that uses MPS, where perforated TEM grids are needed, in contrast to thermophoretic sampling that are usually used (Migliorini et al. 2011;[START_REF] Yon | Examination of wavelength dependent soot optical properties of diesel and diesel/rapeseed methyl ester mixture by extinction spectra analysis and LII measurements[END_REF][START_REF] Lee | Design of thermophoretic probe for precise particle sampling[END_REF]Tian et al. 2004) to probe soot aggregates in a flame using filled TEM grids instead. Consequently, this making it even more difficult as the background is not restricted to the carbon film itself but could also be void as shown in Figure S.3.1. The main goal of the following analysis is to retrieve aggregate morphological parameters from STEM microscopy images. This was achieved following four major post processing steps that begins by segmenting raw STEM images into single binary aggregates. To overcome background-related issues, the choice was made to use a semi-automated method (i.e., SLIDER method (Sipkens and Rogak 2021)) allowing the user to intervene, when necessary, to help indicate an aggregate border. Then, a second post processing (i.e., EDM-SBS [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF])) was performed on each single aggregate providing information (i.e., S(D) functions so-called EDM-SBS functions) encompassing scales encountered in each single aggregate. That same information was then interpreted to evaluate soot aggregates the geometric mean diameter of primary particles ( ) and geometric standard deviation ( ) following an approach proposed by [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF]. Finally, a fractal analysis was conducted in order to evaluate both fractal dimension ( ) and fractal prefactor ( ). The following paragraphs will therefore detail each of these steps, explaining the hypotheses that were made and discussing related uncertainties.

Segmentation process

Considering the nature of STEM images acquired in this work, automated segmentation methods proved to be inefficient due to difficulties in distinguishing aggregates from the background. Consequently, segmentation was done using a largely-manual method, wherein the threshold is adjusted with a SLIDER in a Graphical User Interface (GUI) (Sipkens et al. 2021). This method offered the possibility of adjusting a threshold on small regions in each image. The segmentation process is illustrated on an example in Figure The uncertainty of determining an aggregate projected surface was calculated based on the edge pixels (Sipkens et al. 2021). Accordingly, if one considers an average error of 2 pixels on the border, which is equivalent to adding or subtracting twice the perimeter from the overall area, then the percent error in the area would be 1-(Eq.S.3.2)

The EDM-SBS process described before was then applied to the rest of the investigated

Normalized mean EDM-SBS function interpretation

The decay of S(D)/S(0) function, holds information on the different scales encountered in the images and therefore in the aggregates. To extract this information, Bescond et al. 58 2014 proposed many approaches to find an adequate model expressed as a function of and that allow to approximate S(D)/S(0) curves and thus to evaluate these two parameters. The first approach proposed was to consider that the aggregates are made of polydisperse spheres without overlap. This is how equation 4 (in [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF] was proposed. To be more realistic, the authors proposed a second approach to take into account aggregates with complex shapes and overlapping/necking, hence the need to calibrate the S(D)/S(0) function on the basis of controlled soot. To do that, the authors worked first with virtual aggregates in contact point for which S(D)/S(0) functions were obtained. It was then concluded that these curves are superimposed when they are represented as a function of X = (ln(D)-ln( ))/ln( ). This is how the model in equation 5b (in [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF]) was proposed. However, when overlap effects were considered, this last observation was no longer valid, which led the authors to conclude that these curves have to be calibrated on real soot. Therefore, with this third approach, manually determined size distributions were obtained which were used to evaluate two calibration constants at 1.90 ±0.03 and at 0.80 ± 0.03 of a sigmoid law (Eq.S.3.3). The application of the latter approach on miniCAST propane soot allowed its validation against distributions obtained again in a manual way with the method of circles.

(Eq.S.3.3) When this final approach was applied in this work, the fitting of S(D)/S(0), assuming = 1.90 and = 0.80 as proposed by [START_REF] Bescond | Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot[END_REF] resulted in overestimating (by ~ 10 nm) with respect to a obtained manually. Consequently, the calibration constants and were reevaluated considering the case of OP34 for untreated exhaust since it presented the lowest error on aggregate area. For this condition, 506 primary particles were determined manually from STEM images (using Image J software) allowing to build a primary particles size distribution (not shown). As such, and were determined, and then and were reevaluated. This resulted in = 0.6699 ± 0.009 and = 2.1636 ± 0.012. These same calibration constants were then used for the rest of the studied conditions to evaluate and as summarized in Table 2.

Fractal analysis

After determining the diameters of soot primary particles, here it is proposed to evaluate the remaining parameters describing soot aggregates morphology which are the fractal dimension ( ) and the fractal prefactor ( ). To evaluate those two parameters, two laws are used. The first one is the fractal law (Eq.2) expressing the number of primary particles per aggregate ( ) as a function of the aggregate gyration diameter ( ) and the diameter of soot primary particles ( ). In the previous processing step, primary particles were considered polydisperse. For the sake of simplicity, primary particles are from now on considered monodisperse with a mean primary particle diameter .The second law is taken from the previous works of [START_REF] Samson | Structural analysis of soot agglomerates[END_REF]Köylü et al. 1995 who suggested to link to aggregates projected area. As such, (Eq.S.3.4) was proposed where is the prefactor projected area, is the aggregate projected area, is the primary particle projected area and is the projected area exponent.

(Eq.S.3.4)

Following Bescond et al. 2014 approach, using (Eq.S.3.4) by (i) assuming = 1.155 and = 1.095 as suggested by Köylü et al. 1995 and[START_REF] Sorensen | Light Scattering by Fractal Aggregates: A Review[END_REF]Roberts 1997, (ii) computing gyration diameter ( ) using L/ = 1.49 correlation as proposed by Köylü et al. 1995 (L being

S.4.Gas phase and total scattering contribution to extinction

In this work, the optical absorption coefficients of all absorbing molecular species ( ) in the gas phase were measured only for a selection of operating conditions (e.g., untreated exhaust obtained under OP2, OP9, OP17, OP27, OP32 and OP34 shown in Figure 7). Since this gas phase only absorbs UV light (< 400 nm), for all investigated OPs, it is assumed that above 400 nm . Here, it is proposed to use the RDG-FA model [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF] which means that at 400 nm, = 0.14 and 0.27 for OP9 and OP27, respectively. Under such conditions, neglecting total scattering contribution might be judged inconsistent. In their study that concerned soot aggregates generated by a miniCAST burner supplied with propane, F(m) was found to vary, across the operating conditions, between 0.42 and 0.16 for 380 < [nm] < 1000 and with a less noticeable variation when approaching higher wavelengths (i.e., F(m) = 0.23 0.06 at 700 nm). The objective here is not to evaluate the wavelength variations of E(m) and F(m) functions for Interface Sci. 186 (2):447-452.

Tian, K., Liu, F., Thomson, K.A., Snelling, D.R., Smallwood, G.J., and Wang, D. (2004).

Distribution of the number of primary particles of soot aggregates in a nonpremixed


Célestine Angla

Jean-Luc Gennisson

Benoit Larrat

Sylvain Chatillon

Acoustic property homogenization for accurate skull modelling Anglo-French Physical Acoustic

Keywords:

Solution: personalized simulations to optimize and ensure the safety of ultrasound brain therapies.

Problems:

• The skull is a very complex medium.

• The inter/intra skull variability. Without skull With skull CT scan individual n°1 CT scan individual n°2

How to model the skull ?

• The skull geometry can be segmented from CT scans. What about the acoustic properties ?

• Fast simulation tools require homogeneous skull models. How to model the skull as a homogeneous medium ?

Auteur Auteur 5  The acoustic property maps are extracted from the CT scan.

 The property maps are segmented into three homogeneous isotropic layers (cortical bone -trabecular bone -cortical bone).

 Homogenization method to find an homogeneous medium equivalent to the three-layer one.

• The equivalent speed of sound should minimize the time of flight error.

• The equivalent density should minimize the transmission coefficient error.

Method

 The method was developed for flat parallel interfaces.

 It is then tested on various geometries using the Civa Healthcare platform.

State of the art: skull acoustic property modeling and homogeneous models

Homogeneous skull models

 Averaging the acoustic property maps → no impact on the focus shift, but overestimation of the pressure field amplitude (Jones 2015 2 ). This overestimation is due to:

• The underestimation of the impedance difference between water and bone.

• Not taking into account the loss of amplitude inside the skull.

References 1 J.-F. Aubry, M. Tanter, M. Pernot, J.-L. Thomas, and M. Fink, "Experimental demonstration of noninvasive transskull adaptive focusing based on prior computed tomography scans," J. Acoust. Soc. Am., vol. 113, no. 1, pp. 84-93, 2003, doi: 10.1121  Jiang 2020 3

• Use the average properties to compute times of flight.

• Use the maximal properties to compute transmission coefficients.

→ The loss of amplitude inside the skull is not taken into account .

→ Not compatible with all simulation tools.

 At normal incidence, the sound speed giving a time of flight error of 0 is:

𝑐 𝑒𝑞 = 𝑐 𝑐𝑜𝑟𝑡 1 -ℎ 𝑡𝑟𝑎𝑏 + 𝑐 𝑡𝑟𝑎𝑏 ℎ 𝑡𝑟𝑎𝑏 with ℎ 𝑡𝑟𝑎𝑏 = 𝑑 𝑡𝑟𝑎𝑏 𝑑
the proportion of trabecular bone, 𝑐 𝑡𝑟𝑎𝑏 and 𝑐 𝑐𝑜𝑟𝑡 the sound speeds of trabecular and cortical bones.

 At non-normal incidence:

• Error < 5% for angles < 20°.

• Error ≈ 3% for realistic angle distributions on a skull. Comparison of the pressure fields simulated by Civa through a three layer medium (blue), the averaged medium (red) and the equivalent medium (green).

Conclusion

• A new method for skull acoustic property homogenization was developed.

• It has proven to be very efficient on the tested configurations.

Perspectives

• Test the method on many other configurations (generated randomly or by segmenting human skulls) and compute metrics.

• Test the method on experimental results on phantoms.

•

  Local effect (at the ultrasound focal spot) 𝑤𝑎𝑡𝑒𝑟 + 1 -𝜙 𝜌 𝑏𝑜𝑛𝑒 𝑐 = 𝜙𝑐 𝑤𝑎𝑡𝑒𝑟 + 1 -𝜙 𝑐 𝑏𝑜𝑛𝑒 with 𝜙 = 1 -𝐻 1000the porosity and H the voxel intensity.



  Dataset of various three layer medium configurations ( ~45000 ), with different 𝜌 𝑐𝑜𝑟𝑡 , 𝜌 𝑡𝑟𝑎𝑏 , ℎ 𝑡𝑟𝑎𝑏 , 𝜃 𝑖 . → 𝑋  The optimal equivalent density is exhaustively found for each configuration. → 𝑌  A linear regression is performed between X and Y, giving: 𝜌 𝑒𝑞 = 𝛽 0 + 𝛽 1 𝜌 𝑐𝑜𝑟𝑡 + 𝛽 2 𝜌 𝑡𝑟𝑎𝑏 + 𝛽 3 ℎ 𝑡𝑟𝑎𝑏 + 𝛽 4 𝜌 𝑐𝑜𝑟𝑡 (1 -ℎ 𝑡𝑟𝑎𝑏 ) + 𝛽 5 𝜌 𝑡𝑟𝑎𝑏 ℎ 𝑡𝑟𝑎𝑏 Second step: from a three-layer medium to a single-layer one Equivalent density for transmission coefficient error minimization Goal: find 𝜌 𝑒𝑞 minimizing 𝑇 3𝑙𝑎𝑦𝑒𝑟 -𝑇 1𝑙𝑎𝑦𝑒𝑟

  Comparison of the pressure fields simulated by Civa through a three layer medium (blue), the averaged medium (red) and the equivalent medium (green).

		𝑇 3𝑙𝑎𝑦𝑒𝑟	,
	with ൝	𝑇 3𝑙𝑎𝑦𝑒𝑟 = 𝑇 0→𝑐𝑜𝑟𝑡 𝑇 𝑐𝑜𝑟𝑡→𝑡𝑟𝑎𝑏 𝑇 𝑡𝑟𝑎𝑏→𝑐𝑜𝑟𝑡 𝑇 𝑐𝑜𝑟𝑡→0 𝑇 1𝑙𝑎𝑦𝑒𝑟 = 𝑇 0→𝑒𝑞 𝑇 𝑒𝑞→0
		Water Water	𝜌 𝑐𝑜𝑟𝑡 , 𝑐 𝑐𝑜𝑟𝑡 𝜌 𝑡𝑟𝑎𝑏 , 𝑐 𝑡𝑟𝑎𝑏 𝜌 𝑐𝑜𝑟𝑡 , 𝑐 𝑐𝑜𝑟𝑡 𝜌 𝑐𝑜𝑟𝑡 , 𝑐 𝑐𝑜𝑟𝑡 𝜌 𝑡𝑟𝑎𝑏 , 𝑐 𝑡𝑟𝑎𝑏 𝜌 𝑐𝑜𝑟𝑡 , 𝑐 𝑐𝑜𝑟𝑡
		Medium Medium	𝜌 𝑚𝑒𝑎𝑛 , 𝑐 𝑚𝑒𝑎𝑛 𝜌 𝑚𝑒𝑎𝑛 , 𝑐 𝑚𝑒𝑎𝑛
		Water Water	𝜌 𝑒𝑞 , 𝑐 𝑒𝑞 𝜌 𝑒𝑞 , 𝑐 𝑒𝑞

Université Paris-Saclay, CEA, List, F-911120, Palaiseau, France

Université Paris Saclay, CNRS, CEA, DRF/JOLIOT/NEUROSPIN/BAOBAB, Gif-sur-Yvette, France

Université Paris Saclay, CNRS, Inserm, BioMaps, SHFJ,

Pl. du Général Leclerc, 91401 Orsay, France

Commissariat à l'énergie atomique et aux énergies alternatives