1 Introduction

Emission of soot particles is an environmental issue as well as a health hazard [1–4]. As an example of the former, soot particles are deposited on the polar ice caps, thereby increasing the melting rate due to increased absorption of electromagnetic radiation. Additionally, they act as cloud formation nuclei and as carriers of species such as condensed hydrocarbons as coatings on the surface. Due to the small size range of soot particles, they can also deposit in the respiratory system of humans and animals, acting as carriers of toxic substances. Additionally, the coating alters the optical properties of soot, effectively increasing the absorption and scattering cross sections [4]. Since soot particles are emitted from various combustion processes, for example, truck engines, ship engines, furnaces and forest fires, they are globally spread and present in our everyday life. Regardless, if it is fossil fuel, biofuel or biomass, there may be soot emissions related to the efficiency of the combustion process. Hence, even though we are striving for a reduction in the consumption of fossil fuels, soot emissions will persist also with the use of biofuels. However, since soot particles only have a lifetime of a few days to weeks in the atmosphere [4], a decrease in soot emissions would have a direct impact on the environment as opposed to a decrease in, e.g., CO2 with lifetime of decades. Yet there is a lack of knowledge regarding soot characteristics and impact, knowledge that is needed to reduce soot emissions and improve climate models.

With various soot sources burning different fuels, there is also an inherent disparity between the properties of soot, both physical and optical, originating from these sources. Soot characteristics that are dissimilar depending on source, fuel and aging of the soot are, for example, soot primary particle size, aggregate size/morphology, complex refractive index, density, and potentially coating [5–8]. It is essential to acquire knowledge about these properties to adequately model soot formation, growth and aging, and to predict climate and health effects. However, characterizing soot is a challenging task, and there is a great variety of measurement techniques for this purpose. While there are advanced probing techniques for characterization of soot, they are often of limited use for in situ studies of combustion processes. For this purpose, optical diagnostic techniques are better suited, since the measurements can then be accomplished with only minor or no perturbation of the combustion process.

A commonly used laser diagnostic technique for soot characterization is laser-induced incandescence (LII). LII can be considered as a relatively mature diagnostic technique in many aspects, and it was first introduced already in the 1970s by Weeks and Duley [9] and Eckbreth [10]. The first work thoroughly describing LII and its potential for soot particle characterization was published by Melton in 1984 [11], where he suggested how soot volume fractions and particle sizes could be evaluated from soot incandescence. Since then, tremendous work has been done on developing physical models for the LII process [12] as well as on experimental development and application to laboratory flames and practical devices [13]. When applying LII for characterization of practical combustion systems, it is usually done in an imaging arrangement for 2D visualization of soot which by proper calibration can be interpreted as soot volume fractions, see [13] and references therein. Additionally, LII can also be utilized for more advanced soot characterization e.g., to evaluate particle sizes and some optical properties, but this typically requires more sophisticated procedures with LII model comparisons [14–16] and/or combination with other diagnostic techniques [17–20]. However, quantitative interpretation of LII signals utilizing modeling of the LII process is limited by the uncertainty of the input parameters in the data evaluation, e.g., the debated values of the accommodation coefficient and the absorption function (including the complex refractive index) and how they vary with soot maturity [5, 21–26].

Previous studies have revealed large difference between the properties of nascent and mature soot [6, 27–29]. Indications of nascent soot exhibiting a liquid-like structure have been found in some studies [6, 30, 31], while mature soot shows a more graphitized surface structure [32–34]. In this paper, we will use the term nascent for the small soot particles we probe at the lowest flame heights during the soot growth process and mature for the particles we probe at higher flame heights where aggregated particles are found [15]. The graphitization of the mature particles can be related to a decrease in the H/C ratio when the soot evolves from nascent to mature, effectively increasing the number of sp 2-bonded carbon atoms, leading to a graphitic carbon structure [5]. During the last years, there has been an increased interest within the LII research field about nascent soot particles and their characteristics. Much attention has been put into studying the differences between nascent and mature soot and how these differences affect the LII signal response, and how well the existing LII models predict this response. In a recent study in diffusion flames, some variation of optical properties related to maturity of soot particles has been observed [23]. Several similar studies have been conducted in premixed flames [7, 20, 21, 35], where the soot formation can be followed with height above burner (HAB). From these studies of soot maturity, it is clear that the degree of maturity has a strong impact on the LII signal response, mainly through an increase in the absorption efficiency with increasing soot maturity. It can be concluded that knowledge is lacking with regard to inherent soot particle properties, with a major knowledge gap for nascent soot, resulting in high uncertainty for LII modeling and measurements. Hence, deepened knowledge about soot properties is highly desired within the LII research field.

Within the LII community, there are three target flames intended to be used for LII and soot studies [13, 36]. Two are co-flow ethylene diffusion flames, one produced by a Gülder burner [37] and the other by a Santoro burner [38], and one is a flat premixed ethylene/air flame burning at an equivalence ratio, Φ, of 2.1 on a McKenna burner [39]. All three have been subject to numerous soot studies, and results show clear differences between the soot formed in the diffusion flames and the premixed flame, regarding both physical and optical properties. Unsurprisingly, the largest differences are found between nascent and mature soot particles, radially in the diffusion flames and along the centerline axis in the premixed flame. Generally, the soot found in diffusion flames has a more mature character, i.e., lower H/C ratio, more graphitic structure and higher absorption efficiency than the soot in premixed flames [40]. In the premixed flame, the soot formation evolves with HAB, with nascent soot low in the flame and more mature soot at higher HAB. These are called one-dimensional flames, since the combustion chemistry and soot formation (apart from flame edge effects) should vary only in the dimension along the centerline axis [6, 20, 21, 41, 42]. Due to the one-dimensional character, the premixed flame is appropriate for studies of nascent soot and the further growth process.

In the present work, a study of the soot growth regions of premixed ethylene/air flames at Φ = 2.1 and Φ = 2.3 was made. Since the Φ = 2.1 flame is a standard flame within the LII community, it has been the focus of many studies. Particle sizing using LII and TEM (transmission electron microscopy), soot volume fractions using LII, and CARS temperature profiles have been presented by our group [15, 20, 43], and other research groups have also given significant contributions to data for this specific flame [35, 41, 44, 45]. The slightly richer Φ = 2.3 flame has not been as extensively studied. We have therefore initiated some work also on this target flame lately. The work includes a study carried out in parallel to the study described in this paper where the same flames were characterized using a diode-laser-based extinction setup [46]. From extinction, the Φ = 2.3 flame was found to produce around a factor of four higher soot volume fractions than the Φ = 2.1 flame [46]. In addition, a recent unpublished CARS study in this flame has shown that the axial temperature profile is close to the one from the Φ = 2.1 flame, with values just a few tens of K lower. There are also other studies in flames very similar to the Φ = 2.3 flame used in this work; see, for example, [21, 41, 42, 47, 48].

The aim of the present study is to follow how characteristic properties change from nascent particles low in the flames to mature particles at increasing heights above the burner in the two selected flames, and the work follows naturally from two previous studies by our group. Firstly, in the work by Bladh et al. [15], two-color LII and TEM measurements were made at various heights in the Φ = 2.1 flame, and a strong increase in the extracted absorption function, E(m), was observed. Secondly, we made a combined LII and elastic light scattering (ELS) experiment [20], where ELS was used to probe changes in the soot optical properties as function of laser fluence of the 1064 nm heating laser pulse used for LII. It was clearly observed that sublimation occurred at much higher fluence at lower flame heights, i.e., nascent soot particles at lower heights appeared more transparent than the more mature soot particles at higher heights. In the present study, we continue the work from these previous studies [15, 20] by using two-color LII as well as combining LII with ELS in a more extensive study including two flames, Φ = 2.1 and Φ = 2.1. Absorption properties of the soot are studied as a function of height (and thereby soot maturity) and soot peak temperatures are measured using two-color pyrometry and evaluated using two different methods, using either a constant or a wavelength-dependent E(m). By using the combined two-color LII and ELS technique, the sublimation temperature of nascent as well as mature soot could be estimated. The experimental results are also compared to model predictions obtained using the Lund LII model.

2 Theory

2.1 Laser-induced incandescence (LII)

The LII process involves rapid heating of soot particles up to temperatures of ~4000 K, at which the soot particles are sublimed, by means of nanosecond laser pulses. The increased thermal radiation from the particles is detected and can be interpreted in terms of soot volume fraction and primary particle size. In this work, the LII technique is applied for point measurements using two-color laser-induced incandescence (2C-LII), a time-resolved detection scheme. By utilizing detection at two separate wavelengths, it is possible to infer the temperature of the heated soot by pyrometry. The principle is based on the fact that the spectral characteristics of the blackbody function provide unique solutions for a pair of input values on the signal level at two wavelengths. Utilizing the Wien approximation for the blackbody radiation function, the temperature can be given in closed form as

$$T = {{\frac{hc}{{k_{\text{B}} }}\left( {\frac{1}{{\lambda_{2} }} - \frac{1}{{\lambda_{1} }}} \right)} \mathord{\left/ {\vphantom {{\frac{hc}{{k_{\text{B}} }}\left( {\frac{1}{{\lambda_{2} }} - \frac{1}{{\lambda_{1} }}} \right)} {{ \ln }\left( {\frac{{I_{1} }}{{I_{2} }}\frac{{E(m(\lambda_{2} ))}}{{E(m(\lambda_{1} ))}}\left( {\frac{{\lambda_{1} }}{{\lambda_{2} }}} \right)^{6} } \right)}}} \right. \kern-0pt} {{ \ln }\left( {\frac{{I_{1} }}{{I_{2} }}\frac{{E(m(\lambda_{2} ))}}{{E(m(\lambda_{1} ))}}\left( {\frac{{\lambda_{1} }}{{\lambda_{2} }}} \right)^{6} } \right)}},$$
(1)

where h is the Planck constant, c the speed of light, k B the Boltzmann constant, λ 1 and λ 2 the two detection wavelengths, and I 1 and I 2 the emitted intensity at the two detection wavelengths. E(m(λ 1)) and E(m(λ 2)) denote the values of the soot absorption function at the two wavelengths, the soot absorption function being defined as

$$E(m) = - {\text{Im}}\left( {\frac{{m^{2} - 1}}{{m^{2} + 2}}} \right),$$
(2)

where m = n − ik is the complex refractive index of soot [5].

The heating and cooling of the soot particles during the LII process are modeled using heat and mass balance equations for the energy deposited into the soot particles by light absorption and the subsequent loss of energy, and for high laser fluences also mass, during and after the end of the laser pulse. The two time-dependent coupled differential equations are solved iteratively for the particle temperature, T(t), and diameter, D(t). These functions are then used to calculate the predicted LII signal response by means of the Planck radiation law adjusted for soot emissivity. The model has been described in detail elsewhere, and the reader is referred to [49] for the details.

2.2 Elastic light scattering (ELS) by soot particles

Elastic light scattering has been used in numerous soot studies for characterization of the soot particle size and morphology, both in combination with other techniques and on its own; see, for example, [18, 19, 42, 50, 51]. The theory presented here for elastic light scattering is a short version of what is more thoroughly described in [52, 53].

The scattering from a spherical soot particle of radius a, within the Rayleigh regime \(a \ll \lambda\) (λ is the wavelength of the scattered light) is proportional to the differential scattering cross section of that particle,

$$\frac{{{\text{d}}\sigma }}{{{\text{d}}\varOmega }}_{p} = k^{4} a^{6} F(m),$$
(3)

where \(k = \frac{2\pi }{\lambda }\) and \(F(m) = \left| {(m^{ 2} - 1)/(m^{ 2} + 2)} \right|^{ 2}\). For an aggregated soot particle, assuming that it is built up of spherical primary particles in point contact and that Rayleigh-Debye-Gans theory holds [53, 54], the differential scattering cross section can be expressed as

$$\frac{{{\text{d}}\sigma }}{{{\text{d}}\varOmega }}_{\text{agg}} = N_{p}^{2} \frac{{{\text{d}}\sigma }}{{{\text{d}}\varOmega }}_{p} S(q),$$
(4)

where N p is the number of primary particles per aggregate, and S(q) is the structure factor with q denoting the scattering wave vector i.e., \(q = 2k { \sin }\left( \theta \right)\), θ being the scattering angle. The structure factor contains information about the morphology of the aggregated particles, which experimentally translates to describing the scattered intensity as function of scattering angle. Depending on the magnitude of qR g, with R g denoting the radius of gyration of the aggregate, i.e., a measure of the total aggregate radius, the structure factor can be described by the following expressions for the Rayleigh regime, Guinier regime and the power-law regime, respectively,

$$\begin{array}{*{20}c} {S(q) = 1} &\quad {qR_{g} \ll 1} \\ \end{array} ,$$
(5a)
$$\begin{array}{*{20}c} {S(q) = 1 - q^{2} R_{\text{g}}^{2} /3} &\quad {qR_{\text{g}} { \lesssim }1} \\ \end{array} ,$$
(5b)
$$\begin{array}{*{20}c} {S(q) = C\left( {qR_{\text{g}} } \right)^{{ - D_{\text{f}} }} } &\quad {qR_{\text{g}} > 1} \\ \end{array} ,$$
(5c)

where C is a coefficient for the cutoff level between the Guinier and power-law regimes, and D f is the fractal dimension of the soot aggregate. Using (3)–(5), the intensity of the scattered light from an aggregate, which is proportional to the differential scattering cross section, can be expressed as

$$I_{s} \propto \frac{{{\text{d}}\sigma }}{{{\text{d}}\varOmega }}_{\text{agg}} = N_{p}^{2} \frac{{{\text{d}}\sigma }}{{{\text{d}}\varOmega }}_{p} S(q) = N_{p}^{2} k^{4} a^{6} F(m)S(q).$$
(6)

Thus, a change of scattering signal can be used to estimate size changes of soot particles or aggregates, providing that the complex refractive index is unchanged or that a change of m is known.

3 Experiment

Sooting flat premixed ethylene/air flames burning on a bronze plug McKenna burner [39] were used as measurement targets in this work. Flames with two different equivalence ratios, Φ, were used, Φ = 2.1 and Φ = 2.3. The total gas flow of the ethylene/air mixture was 10 l/min (at 273 K and 1 atm), shielded by a co-flow of air with a flow speed matched to the cold flow speed of the ethylene/air mixture. A stainless steel flame stabilizer (60 mm diameter) was placed at 21 mm height above the burner surface for stabilization of the flame. Five different heights above the burner were used as target heights for the measurements: 8, 9, 10, 12 and 14 mm.

A sketch of the experimental setup can be seen in Fig. 1. The setup closely resembles the one in [20], with some minor changes and adjustments to improve the signals and laser top-hat spatial profile. Two pulsed Nd:YAG lasers were used in the experiment, one operating at the fundamental wavelength of 1064 nm for heating the soot particles and the other, frequency doubled to 532 nm, for probing the laser heated soot particles by elastic light scattering. From here on, they are referenced to as the heating laser and the scattering laser, respectively. Both lasers produced beams with near-Gaussian intensity profiles. A digital delay/pulse generator was used to trigger and synchronize the lasers in time, making it possible to adjust the time position of the laser pulses. The 1064 nm laser light first passed an attenuator consisting of two thin-film polarizers (polarization ratio 1:200) and a half-wave plate, making it possible to adjust the pulse energy. Following the attenuator was a diaphragm, cutting out a central 4 mm in diameter part of the 9 mm in diameter laser beam. By relay imaging of the transmitted laser light into the center of the flame, a 2.7 mm in diameter top-hat intensity profile was obtained at the flame center. For the ELS measurements, the 532 nm laser light was compressed by a 1000 mm focal length lens, placed at a position from the flame so that the laser beam diameter at the flame center was 1 mm (1/e 2) and centered inside the 1064 nm laser beam also passing the center of the flame. For monitoring of the laser light, a beam profiler CCD camera was utilized to measure the spatial intensity profile and a pyroelectric laser power meter was used to measure the pulse energy.

Fig. 1
figure 1

A sketch of the utilized experimental setup displaying the optical parts of the combined LII and ELS experiment

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Detection of LII and ELS was made at a 90° angle to the 532 nm laser beam path, and the detection wavelength bands for LII were centered around 575 nm (bandwidth 25 nm) and 684 nm (bandwidth 24 nm). Two wavelengths for the LII detection made it possible to evaluate soot particle temperatures by two-color pyrometry, using the same procedure as in our previous work [20]. Two achromatic doublets were used to image the center of the flame where the laser beams crossed onto a 1 × 8 mm (height × width) aperture after which the light was collimated by another achromatic doublet and then detected at the three wavelengths (532, 575 and 684 nm) by three photomultiplier tubes (PMT, Hamamatsu H6780). The PMTs were connected to a digital oscilloscope to display and store the signals. A calibration lamp (Labsphere IES 1000) with a known emission spectrum was used for calibration of the two-color pyrometry technique. For more details about the setup and experimental procedure, readers are referred to [20].

The investigated flame heights and equivalence ratios were chosen to achieve measurement locations with a clear variation of soot maturity. The lowest height, 8 mm HAB, was selected due to weak and noisy signals below this position for the Φ = 2.1 flame, resulting in too low measurement precision. The height 14 mm was chosen as the highest measurement location since the influence of the flame stabilizer on flow field and flame temperature is still limited at this height. The measurement resolution in the vertical direction was kept at 1 mm. This was deemed as a properly chosen resolution, as a trade-off between achieving adequate signal-to-noise ratio at the lower flame heights, while still obtaining high enough spatial resolution to be able to follow spatial variations as a function of HAB.

For the measured LII signal peak value, the resulting standard deviation was ~5 %, leading to a ~5 % standard deviation of the evaluated single-shot peak temperatures as well. Tests were made to evaluate single-shot two-color LII temperatures, and in regions with strong LII signals, the average temperature of the evaluated single-shot data agreed well with the temperature from averaged signals of 350 single shots. In order to obtain high-quality data also in spatial regions with low signal levels, all LII data presented in this study are based on signal averaging over 350 shots. ELS was measured over 400 single shots and each shot was compensated for pulse-to-pulse energy fluctuations before signal averaging was done. The resulting standard deviation for the ELS signal was ~10 % after compensation for laser pulse energy fluctuations.

By using the same procedure as in [20] for two-color pyrometry, the evaluated soot temperature does not require a quantitative value of the complex refractive index of the soot. Instead, it depends on the ratio of the values of E(m) at the two detection wavelengths as can be seen in Eq. (1). Thus, the large uncertainty associated with the absolute value of E(m) [5, 55, 56] could be avoided in the temperature evaluation. Instead, the main sources of error were the wavelength dependence of E(m) (discussed later) and the calibration procedure. The temperature uncertainty invoked by the calibration procedure was estimated to be lower than ~125 K.

4 Results and discussion

In this chapter, all experimental results are presented at first in Sect. 4.1, Figs. 2, 3, 4, 5, 6, 7, 8 and 9. These results are then compared with LII modeling results in Sect. 4.2, Figs. 10, 11 and 12.

Fig. 2
figure 2

Normalized time-resolved LII signals detected at 684 nm from the Φ = 2.1 flame (top plate). The bottom plate shows the decay time (1/e) for both flames. The presented data have been derived from measurements using a laser fluence of 0.14 J/cm2

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Fig. 3
figure 3

Peak LII signal detected at 684 nm as function of laser fluence for the five studied HABs in the two flames. The peak signal is evaluated using a 0.8-ns integration interval centered around the peak of the LII signals. All curves are normalized at the measurement point corresponding to the highest laser fluence

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Fig. 4
figure 4

Soot particle peak temperatures as function of laser fluence for the five studied HABs in the two flames. The temperatures have been evaluated using a 0.8-ns integration interval centered around the peak of the LII signals at 575 and 684 nm, assuming a wavelength-independent soot absorption function E(m)

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Fig. 5
figure 5

Soot particle peak temperatures as function of laser fluence for the five studied HABs in the two flames. The temperatures have been evaluated using a 0.8-ns integration interval centered around the peak of the LII signals at 575 and 684 nm, assuming a spectral function of the soot emissivity inferred from extinction measurements [46]

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Fig. 6
figure 6

ELS signal ratio B/A (defined in text) plotted as function of laser fluence of the heating 1064 nm laser for the five studied HABs in the two flames. The top plot represents the Φ = 2.1 flame, and the bottom one represents the Φ = 2.3 flame

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Fig. 7
figure 7

Relative primary particle radius after laser heating estimated from ELS measurements plotted as function of laser fluence of the heating 1064 nm laser for the five studied HABs in the two flames. The top plot represents the Φ = 2.1 flame, and the bottom one represents the Φ = 2.3 flame

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Fig. 8
figure 8

Sublimation threshold fluences, evaluated from combined LII/ELS measurements, plotted for each of the five HABs in the two studied flames

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Fig. 9
figure 9

Evaluated sublimation threshold temperatures plotted for each of the five HABs in the two studied flames. The black symbols represent temperatures evaluated without compensation for a wavelength dependence of E(m), while the red symbols represent the temperatures after compensation for wavelength dependence of E(m) from [46]

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Fig. 10
figure 10

LII fluence curves as predicted by the LII model with input parameters corresponding to the conditions at the measurement points in the two studied flames

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Fig. 11
figure 11

Soot temperatures as function of laser fluence, modeled with input parameters corresponding to the conditions at the measurement points in the two studied flames

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Fig. 12
figure 12

Change of primary particle radii due to sublimation, estimated by our numerical LII model as a function of irradiating laser fluence for both of the investigated flames

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4.1 Experimental results

The normalized time-resolved LII signals at 684 nm (induced by a laser fluence of 0.14 J/cm2) from the Φ = 2.1 flame are displayed in Fig. 2, together with the inferred decay times at each height in both flames, i.e., the time it takes for the signal to decay from peak to 1/e. The LII signal decay time is related to the soot particle size and level of aggregation, where the larger and more aggregated particles give rise to longer LII signals [16, 57, 58]. Larger primary particle size means a lower surface-to-volume ratio, thus less effective heat loss by conduction, and in addition, aggregation reduces this ratio even further by shielding parts of the particles [16, 59]. When comparing the signal decays from the two flames at corresponding heights, it is evident that the Φ = 2.3 flame gives rise to longer signals, indicating larger soot particles and also a faster soot formation process. Another factor influencing the time decays is the flame temperature. According to previous work, e.g., [20], the flame temperature decreases by ~140 K from the height 8–14 mm in these flames, which also influences the observed time decays making them slightly shorter because of more effective cooling at the lower flame temperature [60].

In Fig. 3, the peak LII signal as function of heating laser fluence, i.e., LII fluence curve, is plotted for detection at 684 nm. In this work, we define the peak LII signal as the time-integrated value of the time-resolved LII signal when applying an integration window of 800 ps width, centered on the time position of maximum signal. All the presented curves follow the conventional shape of an LII fluence curve, where the signal increases rapidly with fluence in the region below ~0.4 J/cm2. At higher fluences, where major sublimation is present, the signal increase ceases and a plateau is reached. The two presented plots show the same trends, with the fluence curves at lower heights requiring higher laser fluences to undergo the rapid signal increase and reach a maximum signal, a behavior previously seen in similar premixed flames, see, for example, [7, 20, 21]. This behavior can be interpreted as the nascent particles at the lower flame heights being more transparent than the more mature soot higher up in the flame. The fluence curves for the Φ = 2.1 flame presented in Fig. 3 show a relatively large change from 8 to 10 mm HAB and approach a more similar shape from 10 mm HAB toward higher heights. This is likely due to the particle properties rapidly changing below 10 mm HAB as the soot undergoes large structural changes. This observation is in agreement with analysis of TEM data of soot sampled in the same flame where smaller isolated particles dominated below 10 mm and primary particles with relatively constant size and increased aggregation were observed above 10 mm [15]. Both the physical and optical properties of these nascent soot particles low in the flame seem to differ much from those of the more mature soot found at higher HAB [6, 15, 35]. Previous studies in flat premixed flames indicate that nascent soot particles have a liquid-like shell, enclosing a more solid core [6, 42, 61], and also seem to be less effective absorbers than the more mature soot particles [7, 15, 20, 21]. A closer study of the curves in Fig. 3, reveals that the signal increase and maximum signal actually are attained at somewhat lower laser fluences at corresponding HAB in the Φ = 2.3 flame, as would be expected, considering the faster soot growth process toward mature soot with higher absorption efficiency.

From the LII signals detected at 575 and 684 nm, the soot temperature after laser heating was evaluated through two-color pyrometry, assuming the E(m)-ratio for the two detection wavelength bands equal to unity in Eq. (1). The resulting temperature plots are displayed in Fig. 4 where the soot particle peak temperature is plotted as function of laser fluence. The temperatures can be seen to increase rapidly with laser fluence up to about 0.3–0.4 J/cm2 where a temperature plateau is reached for the soot. Hence, although sublimation increases drastically for increasing fluences above ~0.15–0.25 J/cm2 for the various flame positions (as discussed later), the particle temperature will attain a nearly constant value. As can be seen in Fig. 4, the results from the two flames display the same trends. If acknowledging the absorption of laser light to be more effective for the mature soot particles at higher heights, it means that the mature soot does not require as high laser fluence as nascent soot to get heated. This is indeed shown by the temperature curves in Fig. 4 where the plateau temperature is reached at lower laser fluence for the higher HAB, i.e., more mature soot. This can also be seen by studying the data corresponding to the same fluences below ~0.25 J/cm2, where sublimation is still minor. For the Φ = 2.1 flame, we observe much lower temperatures at lower flame heights (8 and 9 mm) than at 10–14 mm, where the temperature is higher and approximately the same at the three heights. Hence, for a given fluence below ~0.25 J/cm2, the soot absorption is stronger at higher heights, giving rise to higher particle temperatures.

When comparing the evaluated plateau temperatures in Fig. 4, which are in the region 4200–4600 K, to those found in other studies, good agreement is found, see, for example, [21, 60, 62–64], where the reported temperatures range from 4100 to 4600 K. An interesting observation when inspecting the results is that nascent soot at lower heights in the flame appears to reach higher temperatures than more mature soot at higher HAB. This trend has been verified by several measurement series and can also be seen in [21]. These results may be unforeseen, since graphite is known to have a very high sublimation temperature in comparison with most other substances, and the soot becomes more graphitic as it matures. A question that arises is whether there may be other explanations for this trend, and a potential reason may be a change in the optical properties of soot during the formation process. A possible source of uncertainty that could give rise to the observed difference in evaluated temperature between different HAB is a varying E(m) ratio between the two detection wavelength bands with HAB, i.e., a wavelength dependence of E(m(λ)) varying with HAB. There are studies that indeed suggest such an effect for nascent soot particles [7, 35]. It is possible to derive a wavelength dependence for E(m(λ)) from the results of a recent study by our group in the same flames as those studied here, where extinction measurements were conducted in the wavelength range 405–1064 nm [46]. The wavelength dependence was extracted from the region 685–1064 nm to minimize interference from absorption by polyaromatic hydrocarbons [65, 66]. The methodology was as follows. In [46], a deviation was observed from the inverse relationship with λ of the extinction coefficient predicted by Rayleigh theory. This deviation was accounted for by introducing a dispersion coefficient α and expresses the extinction coefficient as \(K_{\text{ext}} \propto 1/\lambda^{\alpha }\), with the wavelength dependence contained in the dispersion coefficient. At high HAB, α was found to be close to one, meaning that the extinction coefficient in this wavelength range could be modeled using Rayleigh theory with inverse wavelength dependence. For a HAB of 5 mm, α was estimated to be in the range 4–5 for the studied flames (Φ = 2.1 and Φ = 2.3), and for increasing height, this value decreased until an α-value close to one was approached [46]. As the extinction coefficient is directly proportional to the absorption function, the observed deviation from a 1/λ dependence of K ext can likely be explained by a wavelength dependence of the absorption function. By interpreting the deviation from unity of the dispersion coefficient, estimated for the two flames in [46], as a wavelength dependence of the absorption function, E(m(λ)) ∝ λ 1−α, and applying this for the detection wavelengths of 575 and 684 nm in the evaluation of the peak temperatures (Eq. 1), new peak temperatures were evaluated. These are shown as function of laser fluence in Fig. 5. Compared to the appearance of the peak temperatures shown in Fig. 4, a substantial difference is noted. All peak temperatures in Fig. 5 are lower than those in Fig. 4. For mature soot at high HAB, the difference is typically ~100 K, but the difference is higher for lower HAB, and for nascent soot at 8 mm HAB, we get a discrepancy of more than 1000 K for the Φ = 2.1 flame. The reason for the larger difference for nascent soot is that the deviation from the inverse relationship with λ is predicted to increase [46]. Interestingly, the inclusion of a wavelength dependence in the E(m) results in a trend change for the plateau temperatures in the sublimation regime and the highest plateau temperature is now reached at the highest HAB, at around 4100 K (Fig. 5), instead of at the lowest HAB which was inferred when assuming the E(m) ratio being unity (Fig. 4). We note that this trend complies better with what is expected from a physical point of view considering the gradual graphitization process during soot aging.

So far the presented results have been interpreted from the 2C-LII measurements. In the following discussion, we will present results from the combined LII and ELS measurements. This technique was introduced by Yoder et al. [67] and was further developed by our group by the use of the 2C-LII for simultaneous temperature measurements. The procedure follows that described in [20]. The ELS pulse was moved in time from before to several hundred nanoseconds after the LII pulse, and it was shown that the ELS signal, after the LII pulse had ended, stayed constant during several hundred nanoseconds [20]. For the analysis in the present paper, the elastic light scattering was measured at two time positions, one position (A) before the heating laser pulse and one position (B) 200 ns after the heating pulse. The relative ELS signal decrease as a result of the heating 1064 nm laser was evaluated as the ELS signal ratio B/A and is plotted in Fig. 6 as function of the heating laser fluence for the studied flames and heights. In the following discussion, it is assumed that the ELS signal decrease originates solely from sublimation of the soot due to the heating laser pulse although there might be other effects also adding to the change of the ELS signal. Examples of such effects are potential swelling of particles with temperature and changes of the complex refractive index as a result of change in composition/structure through thermal annealing, affecting the scattering through F(m) as seen in Eq. (4). Due to lack of knowledge on the variation of F(m) as a result of thermal annealing, it is however not possible to predict the influence on the scattering signal. The measurement series for the Φ = 2.1 flame were repeated from [20] showing agreement within experimental uncertainties, and in addition, the results from the measurement series at Φ = 2.3 are shown, see Fig. 6. Both flame series show the same general trends, and three main observations can be established: (1) The threshold at which the ELS signal drops is higher at lower flame heights, indicating a higher transparency of the particles at these heights, (2) the decrease in ELS signal is clearly smaller in the sublimation region at lower flame height, and comparison of the B/A signal ratio, for example, at a fluence of 0.63 J/cm2 in the Φ = 2.1 flame shows a drastic drop from 0.73 at 8 mm height to 0.07 at 14 mm height, and (3) in both flames, the normalized B/A ratio changes clearly from 8 to 12 mm height, while the data at 12 and 14 mm are nearly identical, indicating that the soot has reached some maturity with minor structural changes as function of height in the flame.

The data in Fig. 6 are unprocessed experimental data and hence cannot be used directly as validation data for our LII model. In order to do such a comparison (see Fig. 12 in the model predictions section), a size reduction in the soot particles was estimated from the presented B/A signal ratio by using Eq. (6) and the initial primary particle sizes and aggregate morphologies [15, 35, 42] (It should be noted that we evaluate the data under the assumption of a size reduction; however, we do not state that this is an adequate description of the sublimation process. Moreover, the influence of processes such as thermal annealing is uncertain). For these flames and HAB, where the soot aggregates are small with an average number of particles per aggregate less than 10 [35, 42], the scattering signal scales very close to d 6 p . Even at the highest HAB in the Φ = 2.3 flame, the estimated deviation from a d 6 p dependence of the signal is less than 1 % when using the soot particle parameters found in [15, 35, 42] together with the theory presented in Sect. 2.2. The largest uncertainty in the size reduction estimation can be related to the interpretation of the sublimation process as a pure size reduction without accounting for e.g., thermal annealing effects. In Fig. 7, the relative size, derived from the data in Fig. 6, has been plotted as function of laser fluence of the heating laser. The soot particle size is unchanged at low laser fluence and starts to decrease when the heating laser fluence is high enough for sublimation to occur. The laser fluence at which the decrease starts is defined as the sublimation threshold fluence (STF) and can be estimated following the same procedure as in [20]. The STF is found by fitting two straight lines to the scattering data, i.e., B/A ratio in Fig. 6, and finding their crossing point. The first line is an almost horizontal line through the data points below sublimation, and the second line is fitted to the nearly linear region of the curves from above sublimation until ~0.35 J/cm2. Using this evaluation procedure which does not rely on the absolute value of the ratio B/A (i.e., no threshold value of B/A is used for determining the STF), a potential effect of thermal annealing on the scattering should have a negligible influence on the evaluated STF. From Figs. 6 and 7, it becomes clear that the STF is higher for the lower flame heights and that the soot particle size reduction is more pronounced the higher in the flames the measurements are done. This, together with the other presented results, implies that there indeed is a difference in absorptive properties between the soot at different heights and that nascent soot is not as effective absorber as the more mature soot higher in the flame. When comparing the results of the two flames, it becomes clear that the size of the soot produced by the Φ = 2.3 flame is significantly more reduced by the heating laser. The largest difference is seen at 8 mm HAB where the radius decreases about 5 % in the Φ = 2.1 flame at a laser fluence of 0.63 J/cm2 while it decreases about 21 % in the Φ = 2.3 flame. Comparing the curves of the flames directly to each other, the best match is found between HAB 10 mm at Φ = 2.3 and HAB 12 mm at Φ = 2.1, indicating that the soot at these heights have very similar absorptive properties.

Based on the data presented in Fig. 6, the STF was estimated using the previously outlined approach, and the results are plotted in Fig. 8. As already discussed in connection with Figs. 6 and 7, there is an apparent decrease in the STF with increasing flame height. Since higher STF means that more energy is needed for the particles to reach sublimation temperatures, it is a strong indication that the nascent soot particles low in the flame are more transparent at 1064 nm. Furthermore, the threshold fluences are slightly lower in the Φ = 2.3 flame as could be expected due to more mature soot and thus more effective absorption at corresponding heights for the two flames. From Fig. 8, it can also be seen that the evaluated STFs for the two flames seem to converge toward a horizontal asymptote around 0.14 J/cm2 at the higher heights. It should be noted that this value is strongly connected to the flame temperature as well as the sublimation temperature. We have measured the flame temperatures in both flames using rotational CARS, and the data for the Φ = 2.1 flame are presented in [20] with temperatures around 1760 K at 8 mm and falling to ~1620 K at 14 mm, while the temperatures for the Φ = 2.3 flame are generally lower by a few tens of K in the probed region (unpublished results). If assuming the soot optical properties to be the same at 8 and 14 mm height, a temperature drop of ~140 K means that the STF would be ~0.01 higher at 14 mm compared to 8 mm. This may be part of the explanation to the slightly higher STF at 14 mm in comparison with 12 mm for the Φ = 2.3 flame.

The combined ELS and LII technique was well suited to identify the STF presented in Fig. 8, and from the data in Figs. 4 and 5, the corresponding sublimation threshold temperatures (STT), i.e., soot peak temperature corresponding to the sublimation threshold, have been derived. These data are plotted in Fig. 9 for each of the five heights in the two investigated flames, both with and without compensation for the wavelength-dependent E(m(λ)) derived at each observed flame height. For the uncompensated STT, a slightly decreasing trend can be seen for increasing HAB, especially for the Φ = 2.1 flame. However, after compensation, the trend is the opposite, with the nascent soot having a lower STT slightly above 3000 K. For increasing heights, the STT seems to converge toward a temperature of around 3400 K for both flames (and both evaluation strategies). It can be noted that this value is in good agreement with predictions by our current model, predicting an STT around 3300–3400 K, as was also found in the study by Liu et al. [68].

In addition to the presented data, the values of the absorption function at 1064 nm at the measurement points in the two flames were evaluated following the same methodology as described in [15, 26] by utilizing the LII measurement data from this work at a laser fluence of 0.14 J/cm2 together with our numerical model for LII.

Table 1 displays the resulting E(m) values, and as expected from the results in this work, the evaluation for the Φ = 2.1 flame results in lower values of E(m). It can be noted that the value at 12 mm HAB for Φ = 2.1 is very close to the evaluated E(m) at 10 mm HAB for Φ = 2.3, further strengthening the implication of similar absorptive properties seen in Fig. 7 at these two heights in the flames. Another observation is that E(m) seems to converge toward a value of ~0.35 for both flames, suggesting that the soot found at the highest heights in these flames is similar when it comes to optical properties and “degree of maturity,” assuming that E(m) can be used as an indicator of soot maturity. This value of the absorption function matches well with previously reported values, see, for example, [55] and references therein. It should be noted that the variation of E(m) with HAB at 1064 nm is more pronounced in a previous study by our own group, where E(m) was evaluated to 0.42 at 14 mm [15]. The reason for this difference is not obvious but can be a result from differences in the experimental setup and methodology. Noteworthy is that the detection wavelengths as well as the laser pulse energy are somewhat different in the two experiments.

Table 1 Absorption function, E(m), evaluated for the two flames using our LII model with α T  = 0.48
Full size table

4.2 Model predictions

Our numerical model for LII [49] has been utilized to make model predictions corresponding to the experimental results presented in this study to gain insight into the processes influencing the behavior of the signal and to investigate how the model behaves in the various fluence regimes.

Modeled LII fluence curves corresponding to the ones presented in Fig. 3 are displayed in Fig. 10. Two parameters are varied as function of HAB to simulate the transition from nascent to mature soot. The first parameter is the absorption function, which is assigned the values derived from the experiments and previously shown in Table 1. Secondly, the primary particle diameter is varied. The thermal accommodation coefficient was kept constant at a value of 0.48 [15] while previously measured gas temperatures were utilized [15, 69]. When comparing the experimental results to the model results, it is clear that the model reproduces the same trend as seen in Fig. 3, where the rapid signal increase is shifted toward lower laser fluence for the higher HAB. The most influential parameter in this context is the absorption function E(m), which scales the strength of the absorption rate in the model, hence essentially compressing the curve along the fluence axis with increasing soot maturity. The particle size, on the other hand, has marginal influence on the fluence curves. As the results are compared to the experimentally obtained fluence curves shown in Fig. 3, the largest difference seen between model and measurements is the behavior at high laser fluence. While the experimental signal levels off and even decreases somewhat at high laser fluence, the model predicts an ever increasing signal with laser fluence. This behavior has been discussed previously [63] and occurs for all models using the thermal sublimation model that can be traced back to Melton [11] and Eckbreth [10]. The particles are allowed to be superheated in the model, thus reaching predicted temperatures substantially higher than the sublimation temperature of the material for high laser fluences, a behavior not seen experimentally.

The effect of superheating is clearly seen in the modeled soot temperatures, which are shown in Fig. 11 as function of laser fluence for both flames. The dependence of the particle temperature on soot maturity is also evident, as the mature soot reaches higher temperatures than the nascent soot in the low-fluence regime. The predicted particle temperature in the high-fluence regime is also dependent on soot maturity, which is found to increase with height in the flame, see Fig. 5. The model results can be explained as follows. First of all, as soot maturity is here only simulated by varying the absorption function and the particle diameter, these are the only parameters that may introduce differences as function of height. The absorption function has large influence on the results in the low-fluence regime but less so for high fluence at which the signal will be much less dependent on the absorption rate and instead increasingly dependent on the sublimation rate. The particle size will, however, have an influence on the maximum signal as the sublimation rate is essentially proportional to the surface area, whereas the absorption and internal energy rates are volume dependent. Thus, smaller particles are predicted to reach lower maximum temperatures.

The modeled peak temperature may be compared to its experimentally obtained counterpart (Figs. 4, 5). Here, it must be stressed that the model predictions have been obtained using the assumption that the E(m) ratio between the detection wavelengths is unity. Thus, comparison should focus on the results in Fig. 4. In the low-fluence regime, the temperatures agree very well. This is, however, a result from the methodology used: As the E(m) values input to the model are inferred using the data in Fig. 4, the model predictions will essentially be normalized to the point at the laser energy 0.14 J/cm2 where the evaluation of E(m) was performed. The high-fluence behavior will, however, be unaffected by E(m), and here we see a generally good agreement in absolute temperature, but a disagreement in trend with HAB. Comparison may also be made to the two-color pyrometry temperatures in Fig. 5 derived with the wavelength-dependent E(m) ratio, but should focus on the high-fluence regime where the data are essentially independent of the methodology used to infer the E(m) values at 1064 nm (Table 1). The pyrometry temperatures derived with the wavelength-dependent E(m) ratio (Fig. 5) are substantially lower than those derived using a unity ratio (Fig. 4), and hence the absolute temperatures show a worse agreement between model and experiment. The trend of an increasing peak temperature with HAB is, however, in agreement.

In order to compare the elastic light scattering results in Fig. 7 with model predictions, the relative primary particle size change inferred by the model after the end of the sublimation process has been plotted as function of height and laser fluence in Fig. 12. For the low-fluence regime, we see a small increase in the particle size which is a result from using a temperature-dependent soot density in the model which thus simulates particle swelling. At a specific threshold laser fluence, unique for each HAB, we see a decrease in the predicted size with fluence which is a result from mass loss due to sublimation. The model results agree qualitatively with the experimental measurements (Fig. 7). Looking at the onset of sublimation, i.e., where the particle size starts to decrease, the model predictions agree quite well with the experimental results. This is expected as it results from using values of E(m) inferred from the experiments by the use of the model. Agreement between model and experimental results gets worse for increasing laser fluence, the dominant discrepancy being the inability of the model to predict the large variation as function of HAB seen experimentally. It can be noted that for the Φ = 2.3 case, the profile corresponding to 12 mm HAB indicates a slightly more pronounced decrease in the particles size than for 14 mm HAB. This can be explained by the higher evaluated E(m) value at 12 mm HAB, presented in Table 1, which was used in the simulation. For the other discrepancies seen between model and experiments in the high-fluence region, there are several potential reasons. The experimental results are derived from scattering data using RDG theory and may be biased at high HAB where aggregation is more influential, thus potentially exaggerating the real effect of laser sublimation on the size. However, as previously mentioned, the aggregate sizes typically found in these flames are expected to have negligible influence on the results. Furthermore, a monodisperse size distribution is assumed for the primary particles in the simple evaluation in conjunction with Fig. 7, whereas in reality, the size distribution is polydisperse. The results presented in Fig. 7 are thus heavily biased toward the larger particles in the distribution due to the a 6 dependence of scattering seen in Eq. (6). In addition, we do not have knowledge of the variation of F(m) with soot maturity. However, most likely, the main part of the explanation lies within the model, as it is well known that the mechanisms involved during laser heating at high fluences are uncertain in the present models [12]. Additionally, soot parameters used in the sublimation mechanisms may in turn be dependent on soot maturity.

Comparison of experimental and model results shows that while the signals in the low-fluence regime are quite well predicted, there remain large uncertainties that need to be addressed. It is hard to predict the behavior of the signal when going from nascent to mature soot due to the intrinsic differences. In this work, the soot maturity was modeled using variation only of the E(m) and the primary particle size. This is obviously a simplification of the processes involved during the graphitization of nascent soot. Previous experimental investigations with TEM [40, 70] show large changes of soot structural properties when subject to high laser fluences, and it is also known that the H/C ratio decreases significantly during the aging process [5, 71, 72]. During such material transformation, it is thus highly likely that many optical and physical properties undergo significant changes. Thus, for LII modeling, a more rigorous approach would require implementing variations also in other parameters such as the soot density, the specific heat and the thermal accommodation coefficient. However, there is currently a crucial lack of knowledge on these parameters as function of soot maturity, even if such work has been intensified [23]. Furthermore, it is evident that the sublimation process and its effect in the high-fluence regime need much more development. In its current state, the model clearly fails to predict the high-fluence regime and mass loss rate of the soot. The processes are likely much more complex than the currently incorporated sublimation process in our model.

5 Conclusions

A combined ELS and two-color LII setup was used for an experimental study of soot during its formation process in flat premixed ethylene/air flames (at Φ = 2.1 and Φ = 2.3) to elucidate changes in soot properties in the transition from nascent to more mature soot particles. By utilizing ELS to probe the soot particles heated by an LII laser pulse at different laser fluences, sublimation threshold fluences for the various flame heights were estimated. The evaluated threshold fluence was used to determine sublimation threshold temperatures from the two-color LII data. These thresholds are important indicators of the transition from the low-fluence to high-fluence regime in LII measurements. The results show decreasing sublimation threshold fluences with increasing HAB, a result which may be explained by the more effective light absorption by mature soot. Sublimation threshold fluences were found to approach a value of ~0.14 J/cm2 (at 1064 nm) for soot at higher heights in both flames, suggesting only marginal variation of soot properties in this spatial region. These sublimation fluences correspond to a sublimation threshold temperature of ~3400 K, evaluated by 2C-LII.

The decrease in the ELS signal in the LII high-fluence regime was found to be strongly dependent on the maturity of the soot. At a fluence of 0.63 J/cm2, less than 10 % of the ELS signal remained for the mature soot at higher heights in both flames, whereas 73 % of the ELS signal remained at the lowest studied flame height in the Φ = 2.1 flame.

Soot peak temperatures evaluated by two-color pyrometry using an assumption of a wavelength-independent absorption function, E(m), resulted in temperatures decreasing with increasing soot maturity, i.e., the nascent soot particles were predicted to reach higher temperatures than the more graphitized mature soot. If instead employing a wavelength-dependent absorption function, E(m(λ)) derived from a recent study on extinction in the same flames [46], the trend of the evaluated maximum temperatures was the opposite with highest temperatures for the mature soot. The difference in evaluated peak temperature was found to be as high as 1000 K for nascent soot, suggesting that inclusion of a wavelength dependence in E(m) is crucial for accurate measurements using optical techniques on nascent soot.

Results for the two investigated flames showed essentially the same trends in the evolution of soot optical properties with height reaching nearly similar and constant values at the higher flame heights, indicating that both flames produce soot with similar mature properties. The main differences between the flames are a higher soot volume fraction by a factor of ~4 in the Φ = 2.3 flame [46] in addition to a significantly faster soot growth process.

Comparison between experimental data and the Lund LII model shows generally good agreement in the low-fluence regime and more significant deviations at higher laser fluences. It is clear that a more refined treatment is required in the high-fluence regime, e.g., by incorporating more advanced sublimation models and additional physical processes not yet implemented.