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Incandescence is the emission of electromagnetic radiation (including visible light) from a hot body as a result of its high temperature.[1] The term derives from the Latin verb incandescere, to glow white.[2] A common use of incandescence is the incandescent light bulb, now being phased out.


In practice, virtually all solid or liquid substances start to glow around 798 K (525 C; 977 F), with a mildly dull red color, whether or not a chemical reaction takes place that produces light as a result of an exothermic process. This limit is called the Draper point. The incandescence does not vanish below that temperature, but it is too weak in the visible spectrum to be perceptible.

We have performed a comparison of ten models that predict the temporal behavior of laser-induced incandescence (LII) of soot. In this paper we present a summary of the models and comparisons of calculated temperatures, diameters, signals, and energy-balance terms. The models were run assuming laser heating at 532 nm at fluences of 0.05 and 0.70 J/cm2 with a laser temporal profile provided. Calculations were performed for a single primary particle with a diameter of 30 nm at an ambient temperature of 1800 K and a pressure of 1 bar. Preliminary calculations were performed with a fully constrained model. The comparison of unconstrained models demonstrates a wide spread in calculated LII signals. Many of the differences can be attributed to the values of a few important parameters, such as the refractive-index function E(m) and thermal and mass accommodation coefficients. Constraining these parameters brings most of the models into much better agreement with each other, particularly for the low-fluence case. Agreement among models is not as good for the high-fluence case, even when selected parameters are constrained. The reason for greater variability in model results at high fluence appears to be related to solution approaches to mass and heat loss by sublimation.

Laser-Induced Incandescence is a technique in which a short-duration (nanoseconds) laser pulse heats nano-sized particles to high temperatures and the subsequent incandescence is observed. The incandescence allows the detection of the particles, but comparison of experimental signal and modeled incandescence as a function of time also provides the size distribution of the particles. The modeling of LII signal is performed by a model of heat transfer mechanisms in the arc vicinity, including laser absorption, conduction, sublimation, radiation, thermionic emission and finally the heating by radiation from the plasma. Two variants of LII are used - time-resolved LII (TR-LII) and planar LII (pLII). In pLII, images of the incandescence signal provide spatially resolved detection of the presence of nanoparticles. In TR-LII, modeling of the time evolution of the incandescence signal is used to calculate the size of the particles. The TR-LII detection limit is evaluated particle number density of 108 cm-3.

Soot emissions from flaming combustion are relevant as a significant source of atmospheric pollution and as a source of nanomaterials. Candles are interesting targets for soot characterization studies since they burn complex fuels with a large number of carbon atoms, and yield stable and repeatable flames. We characterized the soot particle size distributions in a candle flame using the planar two-color time-resolved laser induced incandescence (2D-2C TiRe-LII) technique, which has been successfully applied to different combustion applications, but never before on a candle flame. Soot particles are heated with a planar laser sheet to temperatures above the normal flame temperatures. The incandescent soot particles emit thermal radiation, which decays over time when the particles cool down to the flame temperature. By analyzing the temporal decay of the incandescence signal, soot particle size distributions within the flame are obtained. Our results are consistent with previous works, and show that the outer edges of the flame are characterized by larger particles (\(\approx 60\,\hbox nm\)), whereas smaller particles (\(\approx 25\,\hbox nm\)) are found in the central regions. We also show that our effective temperature estimates have a maximum error of 100 K at early times, which decreases as the particles cool.

Previous work has shown the capabilities of laser-based diagnostic techniques to shed new light on the soot production processes within candle flames. Specifically, soot concentrations and temperatures have been measured in candle flames, showing that the wick diameter controls the soot volume fraction6. Although soot morphology from candle flames has been studied using intrusive18,19 and local non-intrusive techniques20, no studies have yet reported field measurements of soot morphology. This paper is thus devoted to the experimental characterization of soot particle diameter and temperature in controlled burning candle flames. The particle diameter measurement is effected by using time-resolved laser induced incandescence (TiRe-LII), which is a well-established and accepted non-intrusive technique available for this purpose21.

Laser induced incandescence (LII) is an in-situ non-intrusive diagnostic which allows studying soot formation22, as well as soot concentration measurements23. In this technique, the incandescence of the soot particles is attained by heating the particles up to \(\approx 4,000\) K with laser irradiation. If the incandescence signal is temporally analyzed, soot particle size distributions can be obtained. This technique, known as Time Resolved LII (TiRe-LII), has been successfully applied in several experimental configurations24,25,26,27. Since different sized particles will have different thermal inertia, the incandescence signal (\(\text S_\text LII\)) from smaller particles decays more rapidly than the signal from larger particles. Particle size distribution is inferred by employing laser fluences that are lower than those used for for applying the classic LII technique, actually decreasing the soot sublimation effects, and allowing an energy balance equation applicable to this problem to be presented and solutions to be obtained iteratively to account for the different particle sizes. In this case, an effective soot particle aggregate temperature is measured using time-resolved two-color optical pyrometry, which is then compared with a numerical LII model to infer a mean soot particle size28,29. Note that the effective temperature represents the instantaneous peak temperature attained by a soot particle ensemble after the laser heating. The effective temperature decays with time after the laser pulse. Typically, TiRe-LII measurements have been carried out with photo-multiplier tubes (PMTs)20,30, which provide good temporal resolution over hundreds of nanoseconds, but limits the analysis to point measurements. To overcome this shortcoming, planar TiRe-LII measurements use intensified cameras (ICCD) to capture the incandescence signals at different delay times after the laser pulse24,31,32,33.

Temporal decay of incandescence signals, measured at 20, 40, 300 and 670 ns after the laser pulse, for the two used detection wavelengths. (a) Fields of \(\text S_\text LII\) (a.u.) at 450 nm and (b) Fields of \(\text S_\text LII\) (a.u.) at 650 nm.

Figure 6 depicts the vertical evolution of a set of properties characterizing the sooting flame. Following the line of maximum soot volume fraction, this figure presents the geometric mean diameter, which exhibits a non monotonic behavior. Soot particles are first detected with \(\text d_\text pg \approx 32\,\hbox nm\), at HAB \(\approx 9\,\hbox mm\), and the diameter is found to increase up to 64 nm at HAB \(\approx 17\,\hbox mm\). A diameter decrease is then observed until HAB \(\approx 35\,\hbox mm\), where the detection limit is again reached. Following previous works6, this figure also shows the radially integrated soot volume fraction evolution with HAB, normalized with respect to the peak value \(\left( \beta = 2\pi \int _0^\infty \text f_\text v\text (r) rdr.\right)\). Note that from the relationship between \(\text f_\text v\) and \(\text S_\text LII\), the normalized \(\beta\) values are related to the incandescence signal, which is taken at the prompt detection time, where the signal reaches its maximum value. For this purpose, either \(\lambda _1\) or \(\lambda _2\) may be used, since \(\text f_\text v\) is a physical property of the flame. The results of the evolution with height of the integrated soot volume fraction are compared in Fig. 6 with previously measured values using Modulated Absorption Emission (MAE) for the same candle flame6. The previous measurements detected soot in significant amounts (\(\beta = 0.3\)) at HAB \(\approx 7\,\hbox mm\), whereas in this work these amounts are observed further downstream (\(\hbox HAB \approx 11\,\hbox mm\)). This discrepancy is related to the different methods used to determine \(\beta\), since in the present work \(\text S_\text LII\) nearly vanishes below \(\hbox HAB \approx 11\,\hbox mm\), whereas the MAE signal is strong in the lower parts of the flame6. The maximum value of \(\beta\) is found to occur nearly at the same position (\(\hbox HAB \approx 20\,\hbox mm\)) for the two measurements, and the progressive integral soot volume fraction decrease rate with HAB is nearly identical. A final characterization of the TiRE-LII application to the studied candle flame is the temperature and diameter error analysis. To that end, Fig. 7 presents both the effective temperature difference (\(\epsilon\)), given by Eq. (14), and the normalized likelihood estimator (\(\chi ^2\)), as defined by Eq. (15). The first figure-of-merit, \(\epsilon\), is examined at two different times, 20 ns and 600 ns in Fig. 7a, b, respectively. These figures show that both the magnitude and the distribution of this error change with time. Indeed, at earlier times the maximum error, which is on the order of 100 K, is found to occur at the innermost parts of the measurement region, whereas at later times the maximum is displaced towards the outer edges of this region. Furthermore, at 600 ns, \(\epsilon\) is smaller than 50 K at the central part of the flame but, at 20 ns it remains larger than 60 K at the upper parts of the flame centerline. These differences between the experimental and theoretical effective temperatures are mainly associated to the \(\text S_\text LII\) measurements. By comparing the signal ratio \(\text S_\text LII,\lambda _1/\text S_\text LII,\lambda _2\), given in Fig. 4a, and \(\epsilon\) at 20 ns (see Fig. 7a), it is possible to verify that the largest temperature difference occurs at the area of the smallest signal ratio value, and vice-versa. This underscores the close relationship that exists between the signals ratio and the effective temperature difference. Furthermore, considering the values of \(\epsilon\) at 600 ns (see Fig. 7b), it can be deduced from Fig. 3a that the \(\text S_\text LII\) ratio decreases with time, so that the difference between the effective temperature is smaller at the selected points. As a consequence, at later times the temperature difference \(\epsilon\) is larger at the outer flame zones, where the temperature decays faster, than at the inner regions. The \(\chi ^2\) likelihood estimator field depicted in Fig. 7c is evaluated at a radial location of 2 mm from the flame axis and a height of 22.5 mm as a function of the diameter distribution parameters, \(\text d_\text pg\) and \(\sigma _\text g\). This position has been chosen because it corresponds to the maximum soot volume fraction region. This figure shows the minimum value of \(\chi ^2\) that characterizes the distribution shown in Fig. 5d. The \(\chi ^2\) determination has been performed for each pair of parameters, for time intervals ranging from 20 ns to 1 \(\upmu\)m. The estimate range for \(\text d_\text pg\) spans from 0 to 50 nm with a 0.05 nm step, and the corresponding one for \(\sigma _\text g\) is from 1 to 2 with a 0.01 step. Figure 7c indicates that a \(\chi ^2\) mathematical minimum exists for the chosen parameter variation of the lognormal distribution. In particular, the region of \(\text d_\text pg\) from 30 to 50 nm and \(\sigma _\text g\) from 1.1 to 1.3 is where an absolute minimum seems to lie, i.e., where the difference between the values of effective temperatures is the smallest. The parameters of the lognormal distribution at this region (seeFig. 5d) are those that minimize the \(\chi ^2\)-value. However, since a minimum value may not be sharply distinguished, the values obtained above (\(\text d_\text pg\) and \(\sigma _\text g\) given in Fig. 5d) are assumed to be representative of those that minimize \(\chi ^2\)-value. 350c69d7ab


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