1 Introduction

In response to environmental and health concerns, regulators are enforcing reduction in particulate matter, a significant air pollutant. Soot is a major component of the particulate matter emitted from hydrocarbon-fueled combustion used for power generation, transportation, and heat. From a different perspective, industrially manufactured soot, i.e., carbon black, is an important product. Improving the knowledge of soot formation is necessary to reduce soot as a pollutant and to create tailored soot particles with specific properties. The formation of soot is a complex process that cannot be fully understood without detailed knowledge of the formation of its precursors, including polycyclic aromatic hydrocarbons (PAHs) [1], tarlike, and non-soot particles and young soot. Mature soot is defined as refractory soot, able to be heated to incandescence temperatures (Fig. 1).

Fig. 1
figure 1

Conceptual representation of the species present in soot-containing flows. Green hexagons: measurement techniques; blue squares: stages of aging soot; orange ellipses: definition of mature soot and precursors discussed in this paper

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The volumetric concentration (i.e., soot volume fraction f V) of soot is often measured by light extinction in the visible spectral range (e.g., [2]). In flames, however, interfering light attenuation can be due to soot precursors. Attributing measured extinctions to soot can therefore lead to an overestimation. On the other hand, laser-induced incandescence (LII) [3] detects only the material that can be heated to incandescence temperatures. Absorption of intense laser light heats the particles to high temperatures well above flame temperature, and only those particles that do not evaporate or decompose contribute to the measured signal.

Measurements of soot precursors help understand the soot formation process but can also cause interference for optical in situ measurements that aim at measuring mature soot. For locating soot precursors, several optical in situ techniques have been used. PAHs have been determined with laser-induced fluorescence (LIF) [4–6] in the UV and visible range. In combination with laser-induced incandescence (LII), two-wavelength excitation has been used to separate PAH-LIF from LII to separate the PAH signal [7]. These techniques measure broadband fluorescence that can describe the presence of PAHs qualitatively but are unable to distinguish them on a molecular basis or to quantify concentration. Some information about the chemical structure of PAH can be gained from a spectral analysis of the PAH fluorescence, where literature agrees that the fluorescence wavelength of PAHs increases with the size of the PAH molecule [8, 9]. Formation of tarlike and non-soot particles up to young soot was studied in detail by [10] and described in a review paper [11]. More detailed information of the PAH contents in rich and sooting flames was gained from sampling techniques with jet-cooled LIF [12] and photoionization mass spectrometry [13].

In this work, we combine LII and extinction measurements to simultaneously measure mature soot and qualitatively assess the contribution of “non-mature” soot. In a first step, an experiment for the application of time-resolved LII (TiRe-LII) [14–16] in non-premixed flames was implemented. The spatial resolution was increased to resolve the steep spatial gradients of the soot volume fraction (f V). This approach is required to obtain an independent measurement technique for comparison of the results with those of extinction techniques that are often used for measuring soot concentration in non-premixed flames. Extinction in the visible is not caused by mature soot only, but also by soot precursors. While LII measures the mature soot only, a comparison of extinction and LII will theoretically provide a (qualitative) indicator for the concentration of mature soot relative to soot precursors (called here the soot maturity). Another definition of soot maturity [17] is related to the proportion of hydrocarbon components in the soot. For this definition, the maturity is one when the H/C ratio is zero (no hydrogen in the particle). As mature soot may contain some trace amounts of hydrogen, this definition of soot maturity is not fully consistent with our definition, although both are very similar in approach.

The size of the probe volume for LII measurements is defined by the intersection of the laser spatial profile and the field-of-view of the detection optics and, in general, is in the range of 1 mm3 [3]—though some work has aimed at minimizing the spatial resolution of LII point measurements [18]. Alternatively, light sheets in combination with cameras have been used for mapping the spatial distribution of the soot volume fraction [16, 19]. This work aims at maximizing spatial resolution to provide detailed measurements in systems with steep gradients in soot concentration. In laminar non-premixed flames, the change in radial soot concentration can exceed 5 ppm/mm. With conventional TiRe-LII resolution, the steep gradients will not be resolved and information is lost. This work intends to improve the radial resolution by one order of magnitude and the volumetric resolution by two orders of magnitude.

In parallel, spatially resolved extinction measurements were performed. While extinction along the line of sight occurs due to both, mature soot and soot precursors, the combination with LII allows separating both contributions. While prior work has targeted PAHs, this work also includes the effect of larger soot precursors, such as clusters of PAH, which had condensed but do not yet have the properties of mature (refractory) soot.

Extinction is a well-established soot diagnostic method for detecting soot volume fraction [2]. Two-dimensional extinction measurements were first applied by Greenberg and Ku [20] and later improved by Snelling et al. [21] by using an arc lamp instead of a laser to improve the measurement resolution. Arana et al. [22] further investigated the use of a laser in performing extinction measurements. While results from extinction measurements are often reported as a soot concentration, in reality the extinction is due to absorption and scattering from both soot and its precursors. Studies on the wavelength dependence of extinction signals [18, 23–25] were performed to investigate variations in the absorption and scattering. To improve the sensitivity of two-dimensional extinction measurements, Thomson et al. [2] implemented diffuse two-dimensional extinction which reduces beam steering effects. A common implementation of two-dimensional extinction is to pass a collimated light beam whose cross-sectional area is large enough to cover the complete source region to be measured. The signal from the attenuated beam is then recorded on a camera where each pixel represents a specific cross-sectional area of the light beam. By correcting this signal for inhomogeneities in the light beam and for flame radiation, spatially resolved extinction can be determined over the full two-dimensional area of the region to be measured. Line-of-sight measurements are only suitable for the investigation of flames that are homogeneous in the direction of the light beam or that are radially symmetric. For the latter, inversion [26] is needed to convert the line-of-sight data to radially resolved information.

For calculating the soot volume fraction from the LII signal, Melton [27] described a linear relationship between soot volume fraction (f V) and the LII signal intensity. The quantitative interpretation of measured signal intensities requires the correlation of the LII signal and a reference measurement of the soot concentration for at least one measurement point. Various deficiencies of this approach have been identified (e.g., [28]). To avoid calibration measurements, Snelling et al. [29] developed an auto-compensating LII method (AC-LII), which uses a conversion function for the LII detection system, found by absolutely calibrating light intensities and detector sensitivities with a light source that is well characterized in terms of its spectral radiance. In AC-LII, the time-resolved absolute intensity of the incandescence is detected at two wavelengths, and two-color pyrometry is employed to determine the particle temperature.

After correction for elastic scattering, the two-dimensional extinction technique provides an apparent absorption coefficient which is due to the combined effect of mature soot and its precursors. A value for the optical absorption function E(m) obtained from mature soot was used. The combination of both methods allows derivation of the contribution of soot precursors from their difference in volume fraction. This difference provides quantitative information about the light absorption attributed to the soot precursors, and the ratio of LII to absorption provides an indicator of the fraction of absorption caused by mature soot. Previously, an approach comparing dimensionless extinction coefficients of flame soot measurements and sampled soot from the same flame was applied by Vander Wal and Jensen [30]. However, during this sampling process, PAHs and tarlike components were also collected. As a result, the comparison with direct flame soot extinction only offered a separation of extractable particulate matter and non-extractable PAHs. In contrast to that, this work presents a clearer separation between mature soot and its precursors by performing LII instead of sampling in addition to the extinction measurements.

Various comparisons of extinction and LII soot volume fraction have been performed [31–33], and for many cases, extinction was used to calibrate the concentration of soot measured with LII [3]. The novelty of this work is in using the combination of both techniques to get additional information, combined with highly spatially resolved TiRe-LII measurements. This combination does deliver not only the f V of mature soot and the contribution of soot precursors to the locally measured extinction, but also particle size information, although the latter is beyond the scope of this paper.

2 Theory

2.1 Extinction

The measured variable in extinction is the transmittance along the linear path through the aerosol sample. The transmittance τ at the wavelength λ is defined as the ratio of the incident intensity I λ,0 and the transmitted intensity I λ. The transmittance τ is an exponential function of the line integral of the extinction coefficients \(K_{{{\text{e}},\lambda }}^{ + }\) along the path s through the medium:

$$\tau_{\lambda } = \frac{{I_{\lambda } }}{{I_{\lambda ,0} }} = \exp \left( { - \int\limits_{0}^{L} {K_{{{\text{e}},\lambda }}^{ + } {\text{d}}s} } \right)$$
(1)

where the extinction coefficient \(K_{{{\text{e}},\lambda }}^{ + }\) in the context of this paper includes both the effect of soot and soot precursors. In case of radial symmetry, an inversion algorithm [26, 34] can be used to determine local extinction \(K_{{{\text{e}},\lambda }}^{ + }\) from the path-averaged attenuation data. The local apparent absorption \(K_{{{\text{a}},\lambda }}^{ + }\) of soot and soot precursors was calculated from the extinction-derived local extinction \(K_{{{\text{e}},\lambda }}^{ + }\) after a scattering correction:

$$K_{{{\text{a}},\lambda }}^{ + } = \frac{{K_{{{\text{e}},\lambda }} }}{{1 + \rho_{{{\text{sa}},\lambda }} }} + K_{{{\text{a}},\lambda }}^{\text{pre}}$$
(2)

K e,λ is the local extinction due to mature soot, \(K_{{{\text{a}},\lambda }}^{\text{pre}}\) is the local absorption due to soot precursors, and the term ρ sa,λ describes the ratio of the absorption and scattering extinction coefficients of soot. In previous work, the contribution of scattering from non-soot components was usually assumed to be negligible (cf, e.g., [35]). The scattering coefficient can be estimated from the Rayleigh–Debye–Gans polydisperse-fractal aggregate (RDG-PFA) theory as described in detail by Sorensen [36] and Coderre et al. [37]. This approach requires detailed knowledge of the soot morphology (i.e., the primary particle size, number of particles per aggregate), e.g., from transmission electron microscopy (TEM) of soot samples. This approach assumes that scattering is from mature soot only, not from any of its precursors (due to their small size). To determine K e,λ and a precursor component \(K_{{{\text{e}},\lambda }}^{\text{pre}}\), Eq. 2 needs to be solved iteratively.

  • 1st step

    $$\begin{aligned} K_{{{\text{a}},\lambda }}^{ + } \left( 1 \right) & = \frac{{K_{{{\text{e}},\lambda }}^{ + } }}{{1 + \rho_{{{\text{sa}},\lambda }} }} \\ K_{{{\text{a}},\lambda }}^{\text{pre}} \left( 1 \right) & = K_{{{\text{a}},\lambda }}^{ + } \left( 1 \right) - K_{{{\text{a}}\left( {\text{LII}} \right)}} \\ K_{{{\text{e}},\lambda }} \left( 1 \right) & = K_{{{\text{e}},\lambda }}^{ + } - K_{{{\text{e}},\lambda }}^{\text{pre}} \left( 1 \right) = K_{{{\text{e}},\lambda }}^{ + } - K_{{{\text{a}},\lambda }}^{\text{pre}} \left( 1 \right) \\ \end{aligned}$$
    (3)

  • 2nd step and further

    $$\begin{aligned} K_{{{\text{a}},\lambda }}^{ + } \left( i \right) & = \frac{{K_{{{\text{e}},\lambda }} \left( {i - 1} \right)}}{{1 + \rho_{{{\text{sa}},\lambda }} }} + K_{{{\text{a}},\lambda }}^{\text{pre}} \left( {i - 1} \right) \\ K_{{{\text{a}},\lambda }}^{\text{pre}} \left( i \right) & = K_{{{\text{a}},\lambda }}^{ + } \left( i \right) - K_{{{\text{a}}\left( {\text{LII}} \right)}} \\ K_{{{\text{e}},\lambda }} \left( i \right) & = K_{{{\text{e}},\lambda }}^{ + } - K_{{{\text{a}},\lambda }}^{\text{pre}} \left( i \right) \\ \end{aligned}$$
    (4)

This iterative procedure is performed until convergence of \(K_{{{\text{e}},\lambda }}^{\text{pre}}\) is achieved. K a(LII) is the local absorption due to mature soot, calculated from LII data. The convergence criterion is

$$\frac{{\left| {K_{{{\text{a}},\lambda }}^{\text{pre}} \left( i \right) - K_{{{\text{a}},\lambda }}^{\text{pre}} \left( {i - 1} \right)} \right|}}{{K_{{{\text{a}},\lambda }}^{\text{pre}} \left( {i - 1} \right)}} < 1\;\%$$
(5)

The RDG-PFA theory [36, 38–40] provides an effective description of the relationship between absorption and scattering for fractal aggregates, such as soot particles. To meet the requirements of the RDG-PFA theory, the particles must be in the Rayleigh regime; i.e., they must be smaller than the wavelength of light. The effective particle concentration can then be calculated from the apparent absorption coefficient according to

$$f_{\text{V}}^{ + } = \frac{{K_{{{\text{a}},\lambda }}^{ + } \lambda }}{{6\pi \;E\left( {m_{\lambda } } \right)^{ + } }}$$
(6)

As both soot and non-soot (precursor) components affect the extinction measurements, the resulting volume fraction f +V is called an apparent particle volume fraction. There may be a continuous transition in E(m λ) from precursors to mature soot, but for the purposes of this study, it was assumed to be constant. For the scattering correction via ρ sa,λ , we apply results from Migliorini et al. [41] for the three detection wavelengths (465, 577, and 825 nm) and four measurement positions in the flame. These results were obtained at the centerline for height-above-burner (HAB) positions of 42 and 50 mm, and at the radial position of 3.5 mm, the peak soot concentration location for HAB 10 mm [41]. Without a priori information on the morphology of the soot particles at all locations in the flame, assumptions had to be made about the variation of ρ sa,λ with location. A cubic fit to the data was used for the HAB positions between 10 and 50 mm (in steps of 5 mm), as shown in Fig. 2, assuming that the change in ρ sa,λ with HAB was monotonic. As there is no information available on the radial variation in ρ sa,λ at each height, it was assumed that ρ sa,λ is uniform for all radial positions at each height. While these may be broad assumptions, the resulting error is limited [37]. The maximum scattering occurs for the largest aggregates, which are present in the regions of maximum soot concentration. As the data presented in Fig. 2 is from these regions, the ρ sa,λ values are the maximum values that would be found in this flame. Therefore, the bias is in one direction only, such that the local value of ρ sa,λ may be less than the uniform value applied for that height. A 20 % uncertainty in ρ sa,λ , covering morphology effects including aggregate size distribution, fractal dimension, and primary particle diameter, has been assumed in the literature [41] and has been applied in this work. No additional studies about the influence of particle size and aggregate morphology to the scattering were performed.

Fig. 2
figure 2

Ratio ρ sa,λ of absorption and scattering coefficient over HAB position for the three detection wavelengths from [41]. Dashed lines show a cubic fit for 10–50 mm HAB

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2.2 LII

Laser-induced incandescence (LII) has been widely applied for in situ diagnostics of soot particulate matter to measure the soot volume fraction (f V) and the primary particle size [3]. For point measurements, the time history of the signal is commonly recorded and the primary particle size can be deduced from fitting the temporal temperature decay curve [3, 42, 43].

Although time-resolved LII data contain information about both particle size and soot volume fraction, this work focuses on f V for determining the absorption coefficient of the soot particles. An advanced approach was found in the auto-compensating LII method [29] for which an absolute intensity calibration of the LII system is required. With this calibration, quantitative soot concentration can be directly determined as:

$$f_{\text{V}} = \frac{{V_{\text{EXP}} \, \lambda^{6} \left( {\exp \left[ {\frac{hc}{{k\;\lambda \;T_{\text{pe}} }}} \right] - 1} \right)}}{{\eta G_{\text{EXP}} \, 12\pi \;c^{2} h\;E\left( {m_{\lambda } } \right) \, w_{\text{e}} }}$$
(7)

V EXP and G EXP are voltage and gain of the detector, while η is the calibration constant of the LII system. λ is the center wavelength of the detection filter, w e is the equivalent laser sheet thickness, and T pe is the effective temperature of the soot particles. The soot absorption function at the detection wavelength is represented by E(m λ ), while h is the Planck constant, k is the Boltzmann constant, and c is the speed of light.

With the RDG-PFA theory, the soot absorption K a,λ is related to the volumetric soot concentration (f V) as:

$$K_{{{\text{a}},\lambda }} = f_{\text{V}} \frac{{6\pi \, E\left( {m_{\lambda } } \right)}}{\lambda }$$
(8)

The soot absorption K a,λ can be determined at the same wavelengths as the extinction wavelengths λ (465, 577, and 825 nm), while E(m λ) describes the soot absorption function at these wavelengths.

2.3 Determination of the soot maturity by combining LII and extinction data

The difference between the light absorption determined from the extinction measurement and the one reconstructed from the LII measurement will produce the absorption due to the soot precursors \(K_{{{\text{a}},\lambda }}^{\text{pre}}\) at each of the three wavelengths of 465, 577, and 825 nm:

$$K_{{{\text{a}},\lambda }}^{\text{pre}} = K_{{{\text{a}},\lambda }}^{ + } - K_{{{\text{a}},\lambda }}$$
(9)

The ratio of the LII- to extinction-derived absorption will then provide an indicator of the fraction of absorption that is due to mature soot. This is represented by the maturity ratio, R m,λ , of the obtained material:

$$R_{{{\text{m}},\lambda }} = \frac{{K_{{{\text{a}},\lambda }} }}{{K_{{{\text{a}},\lambda }}^{ + } }}$$
(10)

For consistency between two-dimensional extinction and LII measurements, E(m λ ) is assumed to be wavelength independent with a value of 0.4 in all the measurements [44]. E(m λ ) is also assumed to be temperature independent. PAH absorption [45] and fluorescence spectra are known to red-shift with increasing molecule size [8, 9, 46]. By determining the maturity ratio at three different wavelengths, it may thus be possible to infer a general trend in the relative size of the precursor molecules—comparable to the soot-precursor absorption coefficients.

3 Experimental

A co-annular burner was used to produce a non-premixed laminar ethylene/air flame at the standard Gülder conditions [21]. Fuel flows through a mild steel central pipe (d i = 10.9 mm, d out = 12.7 mm), and air flows through a co-annular tube (d i = 88.4 mm). The air flow was homogenized by glass beads and a sintered metal plate. The flow rate was 194 sccm for the ethylene and 284 slm (cm3/min and l/min, respectively, reference point for both 21 °C and 1.013 bar). Measurements were performed two-dimensionally for extinction and evaluated as radial scans at several HAB positions. LII measurements were performed as radial scans of 60 point measurements at 10 HABs.

The extinction measurements have previously been described in detail [21], and results from applying extinction to a non-premixed laminar flame can be found in [41]. Briefly, a mercury arc lamp was used as a light source, and the transmission through the flame was analyzed at 465, 577, and 825 nm. The transmitted light was detected with a CCD camera with an estimated spatial resolution of 34 μm, about 1.5× the camera pixel dimensions, based on the full-angle divergence of the effective light source [21].

For the quantification of the transmittance τ of the attenuating medium, the intensities I λ,0 and I λ cannot be measured directly [2]. Instead, a set of four signals needs to be acquired: (1) the lamp signal (no flame), (2) the dark signal (no lamp, no flame), (3) the emission (no lamp), and (4) the transmission itself. Then, the transmittance can be calculated via

$$\tau_{\lambda } = \frac{\text{transmission{-}emission}}{\text{lamp{-}dark}}$$
(11)

For the LII measurements, the apparatus is shown in Fig. 3. A frequency-doubled Nd:YAG laser (Big Sky Ultra CFR) with an energy of 30 mJ per pulse (top-hat profile) and a pulse width of 7 ns FWHM was used as light source. A variable attenuator consisting of two half-wave plates and a polarizing beam splitter was used to adjust the laser fluence to 70 mJ cm−2. With excitation at 532 nm, delayed detection (~40 ns) is performed to avoid possible interference from short-lived fluorescence.

Fig. 3
figure 3

Schematics of the LII diagnostics for the non-premixed laminar ethylene/air flame

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An approximately 8:1 relay imaging of an aperture (vertical slit) was used to demagnify the laser beam while providing a uniform energy distribution across the laser beam profile at the probe volume focal plane. The aperture is located 1128 mm before a cylindrical lens (f = 150 mm) which reduces the beam width from 0.78 mm to 0.10 mm the probe volume. The height of the beam is limited by two stainless steel razor edges that are located directly behind the aperture. The cylindrical lens is positioned 165 mm from the probe volume to generate the desired magnification. For monitoring the stability of the laser pulse energy, a quartz plate positioned between the aperture and the lens of the relay imaging system sends a fraction of the beam (4 %) to a volume-absorbing disk calorimeter head (Scientech model 380201).

The incandescence signal was collected perpendicular to the laser sheet by two uncoated achromats (Ross Optical, f = 150 mm). An aperture (d = 40 mm) was mounted between these two lenses to limit the depth of focus. With a magnification of 1:1, the incandescence signal is imaged onto a 200-µm-core-diameter fiber (Thorlabs) and transferred to the LII detection system where the LII signal is spectrally separated onto three fast photomultipliers (PMT 1–3) that record signals with center wavelengths of 445, 558, and 750 nm via a combination of two dichroic mirrors and band-pass filters. The first mirror (488-nm low-pass filter, Semrock, LP02-488RS-25) is mounted at an incident angle of 15° and reflects the ~445 nm radiation through a 532-nm notch filter (Semrock, NF01-532U-25) and a band-pass filter (445 ± 30 nm, Semrock, FF409-EM02-25) onto PMT 3 (Hamamatsu, H5783), focused by a AR-coated lens (f = 50 mm). The second mirror (633-nm low-pass filter, Semrock, LP02-633RS-25) is mounted at an incident angle of 15° and reflects the ~558 nm radiation through an identical 532-nm notch filter and a band-pass filter (559 ± 20 nm, Semrock, FF01-559/34-25) onto PMT 2 (Hamamatsu, H5783-01), also focused by a AR-coated lens (f = 50 mm). The radiation that is transmitted through the 633-nm low-pass filter strikes a neutral density (ND3) filter and passes then through a custom band-pass filter (Semrock, FF01-750-50-25.4) onto PMT 1 (Hamamatsu, H5783-20), focused by a AR-coated lens (f = 50 mm).

For TiRe-LII, only two wavelength ranges need to be detected. The highest and lowest wavelengths (445 and 750 nm) were used, as recommended in [47]. With this optical setup, the detected probe volume had a diameter of 200 µm and a width of 100 µm. The temperature T pe of the soot, needed to determine f V via AC-LII, is measured via two-color pyrometry at the same two wavelengths.

4 Results and discussion

As the flame is radially symmetric, data are presented for one half of the flame only. To precisely determine the center position of the flame, measurements with reduced resolution were performed for the other half (not presented). The data were analyzed as radial scans from center to the edge of flame for extinction and LII at height-above-burner (HAB) positions of 10, 15, 20, 25 (set 1) and 30, 35, 40, 42 mm (set 2). The HAB of 42 mm also represents a common measurement position for many soot diagnostics applied to the Gülder flame [10]. While this flame reaches a height of ~67 mm, at heights of 50 mm and above minor flame flicker created fluctuations in the extinction data and reduced the effective spatial resolution of the LII data, preventing comparison of data from the two techniques.

The f +V results determined from the extinction data were scaled to be equal to the soot volume fraction derived from the LII data on the centerline at a HAB of 42 mm, as a method of calibrating the extinction data, with the assumption that there is a negligible soot-precursor concentration at this position. This is reasonable because the maximum soot concentration at this height is on the centerline, and it does not increase at greater heights in the flame. This indicates that the soot formation is complete, and hence, no soot precursors are present. The scaling factors determined for each wavelength at this position were applied for the evaluation of the f +V throughout the flame.

As a reminder, further assumptions that may affect the uncertainty were (1) to neglect scattering from soot precursors, (2) use of a uniform scattering/absorption ratio for the mature soot in the radial direction and its monotonic change with HAB, and (3) assuming wavelength independence of E(m) for both extinction and LII. The consistency of the reported data supports the validity of these assumptions.

4.1 Advantages of LII with high spatial resolution over conventional LII point measurements

LII allows measuring soot volume fraction (and particle sizes) with high spatial resolution and thus with high fidelity, even in cases with steep gradients in f v, such as in the annular regions of non-premixed laminar flames. With a probe volume of 200 µm in diameter (i.e., tangentially to the gradients) and 100 µm in width (i.e., in radial direction), a spatial resolution of 100 µm (scanning steps) in the direction of the gradient can be realized. In comparison with that, the commercial Artium LII 200 instrument has a laser beam cross section of 2.8 × 2.8 mm2 and a diameter of the detected area of a few millimeters, depending upon the selected receiver lens.

Both systems were applied to perform f V measurements on identical non-premixed laminar flames in Ottawa, Canada (high spatial resolution LII) and Duisburg, Germany (Artium LII 200). The results are shown in Fig. 4, where the stark contrast in spatial resolution is clearly illustrated. The limited spatial resolution of conventional LII systems, of the order of 1–2 mm, blurs the sharp features of the annular region of the non-premixed laminar flame at a height of 10 mm and blurs the sharp transition through the flame front at HAB = 42 mm. As a result, the radial positions of the regions of maximum soot concentration obtained with the two methods are not identical. This is due to the integration not only in the radial direction but also in the height (HAB). The application of LII with high spatial resolution allows one to elucidate minute details regarding the structure of the non-premixed laminar flame and clearly identify the regions containing soot.

Fig. 4
figure 4

Comparison of the high spatial resolution LII (red dots with short-dashed lines) and the commercial LII system (black squares with short-dashed lines) for HAB of 10 and 42 mm

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4.2 Comparison of extinction and LII particle volume fractions

The f +V value determined from extinction measurements is composed of the soot volume fraction (f V) and an “apparent” non-soot volume fraction. In contrast, LII measures the soot volume fraction (f V) only. The comparison of f +V to f V indicates the presence of soot precursors which can be attributed to regions where soot formation takes place.

As described in chapter 2.1, due to the radial symmetry of the flame, an inversion algorithm [26, 34] was used to determine local extinction \(K_{{{\text{e}},\lambda }}^{ + }\) from the path-averaged attenuation data. With scattering correction, a radially resolved dataset of absorption coefficients \(K_{{{\text{a}},\lambda }}^{ + }\) was determined for the summation of soot and non-soot absorbance, and with Eq. (6), the apparent particle volume fraction f +V was calculated. Radial profiles of f +V (extinction, for three wavelengths) and f V (LII) are compared for HAB = 10–42 mm (Fig. 5). For LII, the signal traces from 400 laser pulses were averaged for each measurement location. The measurements were repeated three times to derive an average and to determine the reproducibility. The results for both f +V and f V indicate the annular nature expected for this flame, with relatively good agreement with the radial position of the signal maximum at each HAB. For regions on the fuel side of the peak (closer to the burner axis), the f +V is moderately to significantly larger than the f V for all HAB. This effect is due to the summation of soot and precursor contributions in f +V . Note that the extinction data are corrected for scattering, with the caveat that the scattering correction is based on assumptions (cf Sect. 4) that introduce some uncertainty.

Fig. 5
figure 5

Comparison of volume fractions from extinction [41] (soot and precursors) and LII (soot) data for HAB = 10–42 mm. Left axis represents the apparent volume fraction (f +V ; solid lines) from extinction; the right axis stands for the soot volume fraction (f V; black squares with short-dashed lines) from LII

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The contribution from precursors is not only due to large PAH hydrocarbon molecules, but also due to other non-soot condensed nanoparticles. Species in this intermediate state between the molecular PAH species and the final soot primary particles also contribute to the total absorption determined by extinction. This technique cannot distinguish on a molecular basis between the non-soot absorbing components. However, qualitative differences can be observed by analyzing the absorption at the three extinction wavelengths, 465, 577, and 825 nm. Figure 5 shows that the absorption at 825 nm is the weakest for all HAB positions. At 465 and 577 nm, the relative strength of the absorption is changing as a function of both the HAB and radial position. This indicates a possible variation in the composition of the soot precursors as a function of spatial location in the flame. The difference between f +V and f V disappears on the outer edges of the flame as would be expected. These regions are outside of the maximum temperature region, where no precursors are anticipated to be present, soot has formed already, and oxidation may start.

4.3 Separation of soot-precursor absorbance

With Eq. (9), the non-soot (precursor) absorption coefficient \(K_{{{\text{a}},\lambda }}^{\text{pre}}\) can be calculated for the three wavelengths 465, 577, and 825 nm, as the difference of \(K_{{{\text{a}},\lambda }}^{ + }\) (absorption coefficient for the summation of soot and non-soot absorbance) and K a,λ (soot absorption coefficient). The comparison of the non-soot absorption at the three wavelengths provides qualitative information about the relative contributions from different precursors. A comparison with the signal due to soot indicates the relative spatial distributions of the precursors and soot in the diffusion flame.

In Fig. 6, the non-soot absorption coefficient \(K_{{{\text{a}},\lambda }}^{\text{pre}}\) of the extinction data is compared at the three wavelengths. The f V derived from LII is shown to illustrate the location of the soot for HAB = 10–42 mm. The precursor absorption peaks are shifted toward the flame centerline relative to the soot, indicating the soot precursors are located on the fuel side of the flame front, with the highest levels close to the flame front. This shift is approximately 0.2 mm, becoming smaller with increasing height above 30 mm HAB. At the outer edge of the flame, \(K_{{{\text{a}},\lambda }}^{\text{pre}}\) occasionally becomes slightly negative. This is caused by minor imperfections in matching the radially resolved datasets from extinction and LII. These uncertainties are most apparent in the regions of steep gradients in concentration at the outer edge of the flame, which accentuates the effect of slightly different spatial resolution for the two experimental techniques.

Fig. 6
figure 6

Radial position of soot precursors and soot for HAB = 10–42 mm: On the left y axis, precursors are indicated in terms of their absorption coefficients (\(K_{{{\text{a}},\lambda }}^{\text{pre}}\)), while the volume fraction of soot (f V) is shown on the right y axis

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4.4 Wavelength-normalized absorption of soot and its precursors

Normalized absorption coefficients can be used to compare the precursor absorbance at the three wavelengths and also in relationship to the normalized soot absorption coefficient. The normalization was done by multiplying the precursor absorption coefficients by their corresponding wavelengths (cf, Eq. 9). For the soot absorbance, Eq. (8) shows that the normalized absorption coefficients for soot (λ K a,λ ) do not directly depend on the wavelength. E(m λ ) was found to be independent of λ over the wavelength ranges of interest to this work, in a detailed study by Yon et al. [48].

In Fig. 7, the normalized absorption coefficients (λ K a,λ ) are shown for the precursors and soot for HAB positions of 10–42 mm. It can be seen that the normalized absorption of the precursors at the three different wavelengths is varying with height. For HAB = 10–25 mm, the absorption at 465 nm is greater than that at 577 nm, while the 825 nm absorption is weakest at all HAB between 10 and 25 mm. With increasing height, the difference in the absorption at the three wavelengths is reduced, until all three become nearly equal at all radial positions at heights above 30 mm. These effects indicate possible differences in the precursor mixture composition. Even though this technique is not able to distinguish individual precursor species, it does indicate possible information about the relative concentration of different precursor species as a function of height and radial position.

Fig. 7
figure 7

Normalized absorption coefficients of soot precursors and soot for HAB = 10–42 mm

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4.5 Maturity of soot

While LII measures the mature soot only and the absorption represents a combined value of mature soot and its precursors, the ratio of LII to absorption will provide an indicator of the fraction of absorption that is due to mature soot. This is represented by the maturity ratio, R m,λ , of the obtained material, with a value of 1 indicating that only mature soot is present. PAH absorption [45] and fluorescence spectra red-shift with increasing molecule size [8, 9, 46]. By determining the maturity ratio at three different wavelengths, it may thus be possible to infer a general trend in the relative size of the precursor molecules (Fig. 8).

Fig. 8
figure 8

Maturity ratio R m,λ of detected absorbing matter for HAB = 10–42 mm

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At HAB below 40 mm, the maturity ratio of the 825 nm absorption wavelength is consistently greater than that at the other wavelengths, 577 and 465 nm. This is an indication that the precursor material absorption at 825 nm is much less than for 577 and 465 nm. As the soot increases in maturity, the maturity ratio at all three wavelengths converges. The region where the (mature) soot is present can be identified, moving from the outer edge of the flame at lower HAB to a nearly homogeneous distribution profile at HAB 30. Above HAB 30, all radial locations indicate relatively mature soot, with the most mature soot present toward the center of the flame.

4.6 Relative absorption coefficients as an indicator of wavelength dependence of E(m λ )

The optical properties of soot and precursors can be also studied with the extinction method by comparing the ratio of normalized absorption coefficients as they are equal to the ratio of the soot absorption function E(m λ ), both at two different wavelengths [41]. This was demonstrated by Migliorini et al. [41] with a spectrally resolved extinction method in the same non-premixed laminar flame as studied in this work. Therefore, the relative normalized absorption coefficients obtained here were compared to prior data [41] at the three wavelengths used in this work.

In Fig. 9, the normalized absorption coefficients (λ \(K_{{{\text{a}},\lambda }}^{ + }\)) of the extinction data are shown as ratios of the normalized absorption coefficients at the three wavelengths relative to 577 nm. For this data, the f +V data were not scaled to be equal to the f V data on the centerline at a HAB of 42 mm, as was done for the data presented in Figs. 5, 6, 7, and 8. The data are shown for three HAB positions (10, 42, and 50 mm). The prior data are plotted as dashed lines, while the results of this work are given as symbols. The comparison shows reasonable agreement between the current work and the prior results, obtained with a different method. The current work enhances the interpretation of these results with the knowledge that it is the combined impact of soot and precursors that is affecting the optical properties, not soot alone. As mature soot properties are not changing with wavelength [48], the changes observed here are attributed to precursors of mature soot.

Fig. 9
figure 9

Relative absorption coefficients [41], normalized with their respective absorption wavelengths

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5 Conclusions

Laser-induced incandescence (LII) measurements with high spatial resolution are used to investigate regions with steep gradients in soot concentration in a co-annular laminar ethylene/air non-premixed laminar flame at the standard Gülder conditions. LII was combined with extinction measurements to investigate the region of soot-precursor formation in this non-premixed flame. With the comparison of particle volume fraction from both methods, the zones of soot and soot-precursor formation, growth, and consumption were spatially distinguished. This was achieved by comparing the absorption from the extinction technique, which is due to both soot and soot precursors (such as gas-phase PAHs and condensed PAH), to the absorption of soot only as determined via LII.

It was demonstrated that:

  1. (1)

    LII with high spatial resolution is necessary to adequately resolve the steep gradients in soot concentration in the non-premixed flame studied here.

  2. (2)

    The f +V determined from extinction is greater than or equal to the f V determined from LII.

  3. (3)

    The absorbance due to soot precursors can be separated from the absorbance due to soot with the combined LII and extinction technique.

  4. (4)

    The variation in the precursor absorption at the different wavelengths can be interpreted to suggest differences in the precursor composition at various spatial locations.

The comparison showed that the apparent particle volume fractions (f +V ) determined from extinction were greater and shifted toward the centerline with regard to the soot volume fractions (f V) obtained by the LII measurements. By calculating absolute absorption coefficients for the data of extinction and LII, the absorption due to precursors was determined from the difference between extinction and LII-derived absorption values. The results provide relative information about the spatially resolved precursor absorbance in the flame. Attenuation measurements with extinction were performed at three wavelengths 465, 577, and 825 nm to investigate the wavelength-dependent absorption of the precursors. The wavelength-resolved precursor absorbance provides the possibility of detecting variation in the composition of the soot precursors as a function of height-above-burner (HAB) and the radial position in the flame. This was also supported by a comparison of wavelength-normalized absorption coefficients of precursors. Ratios of these wavelength-normalized absorption coefficients were compared to the literature and showed good agreement.

The technique of soot-precursor diagnostics, presented in this work, is novel in that soot precursors are interpreted by their absorption, not fluorescence. This approach, combining LII and two-dimensional extinction, should provide valuable in understanding the formation, growth, and consumption processes of soot precursors and soot.