Numerical investigation of the effect of signal trapping on soot measurements using LII in laminar coflow diffusion flames

Laser-induced incandescence has been rapidly developed into a powerful diagnostic technique for measurements of soot in many applications. The incandescence intensity generated by laser-heated soot particles at the measurement location suffers the signal trapping effect caused by absorption and scattering by soot particles present between the measurement location and the detector. The signal trapping effect was numerically investigated in soot measurements using both a 2D LII setup and the corresponding point LII setup at detection wavelengths of 400 and 780 nm in a laminar coflow ethylene/air flame. The radiative properties of aggregated soot particles were calculated using the Rayleigh–Debye–Gans polydisperse fractal aggregate theory. The radiative transfer equation in emitting, absorbing, and scattering media was solved using the discrete-ordinates method. The radiation intensity along an arbitrary direction was obtained using the infinitely small weight technique. The contribution of scattering to signal trapping was found to be negligible in atmospheric laminar diffusion flames. When uncorrected LII intensities are used to determine soot particle temperature and the soot volume fraction, the errors are smaller in 2D LII setup where soot particles are excited by a laser sheet. The simple Beer–Lambert exponential attenuation relationship holds in LII applications to axisymmetric flames as long as the effective extinction coefficient is adequately defined.     

Relationship between soot volume fraction and LII signal in AC-LII: effect of primary soot particle diameter polydispersity

Theoretical analysis and numerical calculations were conducted to investigate the relationship between soot volume fraction and laser-induced incandescence (LII) signal within the context of the auto-compensating LII technique. The emphasis of this study lies in the effect of primary soot particle diameter polydispersity. The LII model was solved for a wide range of primary soot particle diameters from 2 to 80 nm. For a log-normally distributed soot particle ensemble encountered in a typical laminar diffusion flame at atmospheric pressure, the LII signals at 400 and 780 nm were calculated. To quantify the effects of sublimation and differential conduction cooling on the determined soot volume fraction in auto-compensating LII, two new quantities were introduced and demonstrated to be useful in LII study: an emission intensity distribution function and a scaled soot volume fraction. When the laser fluence is sufficiently low to avoid soot mass loss due to sublimation, accurate soot volume fraction can be obtained as long as the LII signals are detected within the first 200 ns after the onset of the laser pulse. When the laser fluence is in the high fluence regime to induce significant sublimation, however, the LII signals should be detected as early as possible even before the laser pulse reaches its peak when the laser fluence is sufficiently high. The analysis method is shown to be useful to provide guidance for soot volume fraction measurements using the auto-compensating LII technique.     

Laser induced incandescence measurements of soot volume fraction and effective particle size in a laminar co-annular non-premixed methane/air flame at pressures between 0.5–4.0 MPa

An auto-compensating laser-induced incandescence (AC-LII) technique was applied for the first time to measure soot volume fraction (SVF) and effective primary particle diameter (dp_eff) in a high pressure methane/air non-premixed flame. The measured dp_eff profiles had annular structures and radial symmetry, and the particle size increased with increasing pressure. LII-determined SVFs were lower than those measured by a line of sight attenuation (LOSA) technique. The LOSA measured soot volume fractions were corrected for light scattering using the Rayleigh–Debye–Gans polydisperse fractal aggregate (RDG-PFA) theory, the dp_eff data, and assumptions regarding the soot aggregate size distribution. The correction dramatically improved agreement between data obtained using these two measurement techniques. Qualitatively, soot volume distributions obtained using LII had more annular shapes than those obtained using LOSA. Nonetheless, it has been demonstrated that the AC-LII technique is very well suited for application in media where attenuation of the excitation laser pulse energy can exceed 45%. This paper also underlines the importance of correcting LOSA SVF measurements for light scattering in high pressure flames. PACS 07-60.-j; 47.70.Pq; 65.80.+n; 78.67.-n     

The interpretation of the LII signal in optically dense combusting sprays

A numerical investigation was made of the generation and behaviour of the LII signal in optically dense combusting sprays at conditions similar to those in the combustion chamber of compression ignition engines and gas turbines. The influence of particle size, particle morphology and size distribution on the behaviour of the LII signal, and the scattering and absorption of light, and the consequences that different calibration procedures have on the accuracy of the results were studied. Results show that, as the particle size or aggregation increases, light extinction is not caused only by absorption but also by scattering, which contributes more than 10% to the total extinction of light. Particle shape effects are important, irrespective of particle size. The form, soot concentration gradients and optical thickness of the flame cause an uneven laser fluence across the measuring volume that affects the generation of the LII signal. In addition, the quotient between the transmitted and incoming laser pulses across the flame borders can be as small as a percentage of unity. The interpretation of the induced signal is further challenged by the loss of signal between the measuring volume and the detection arrangement, thus causing the detection of spectrally distorted and weaker signals with an erroneous profile of the local amount of carbonaceous particles. An appropriate calibration procedure must be followed to obtain results that are quantitatively representative. External calibration was found to be inappropriate for these systems since it can lead one to underestimate the local volume fraction for almost two orders of magnitude. Implementing an in situ calibration along a line can lead to underestimate or overestimate the local mean volume fraction by a factor of two. However, the use of an in situ calibration procedure using a laser sheet that propagates through the complete measuring volume can reduce the error in estimating the mean soot volume fraction to a 30%. The latter was found to be the most adequate among the studied calibration routines.     

Laser-induced incandescence for soot-particle sizing at elevated pressure

This paper describes the applicability of laser-induced incandescence (LII) as a measurement technique for primary soot particle sizes at elevated pressure. A high-pressure burner was constructed that provides stable, laminar, sooting, premixed ethylene/air flames at 1–10 bar. An LII model was set up that includes different heat-conduction sub-models and used an accommodation coefficient of 0.25 for all pressures studied. Based on this model experimental time-resolved LII signals recorded at different positions in the flame were evaluated with respect to the mean particle diameter of a log-normal particle-size distribution. The resulting primary particle sizes were compared to results from TEM images of soot samples that were collected thermophoretically from the high-pressure flame. The LII results are in good agreement with the mean primary particle sizes of a log-normal particle-size distribution obtained from the TEM-data for all pressures, if the LII signals are evaluated with the heat-conduction model of Fuchs combined with an aggregate sub-model that describes the reduced heat conduction of aggregated primary soot particles. The model, called LIISim, is available online via a web interface. PACS 65.80.+n; 78.20.Nv; 42.62.-b; 47.70.Pq     

Modeling of time-resolved laser-induced incandescence transients for particle sizing in high-pressure spray combustion environments: a comparative study

In this study experimental single-pulse, time-resolved laser-induced incandescence (TIRE-LII) signal intensity profiles acquired during transient Diesel combustion events at high pressure were processed. Experiments were performed between 0.6 and 7 MPa using a high-temperature high-pressure constant volume cell and a heavy-duty Diesel engine, respectively. Three currently available LII sub-model functions were investigated in their performance for extracting ensemble mean soot particle diameters using a least-squares fitting routine, and a “quick-fit” interpolation approach, respectively. In the calculations a particle size distribution as well as the temporal and spatial intensity profile of the heating laser was taken into account. For the poorly characterized sample environments of this work, some deficiencies in these state-of-the-art data evaluation procedures were revealed. Depending on the implemented model function, significant differences in the extracted particle size parameters are apparent. We also observe that the obtained “best-fit” size parameters in the fitting procedure are biased by the choice of their respective “first-guess” initial values. This behavior may be caused by the smooth temporal profile of the LII cooling curve, giving rise to shallow local minima on the multi-parameter least squares residuals, surface sampled during the regression analysis procedure. Knowledge of the gas phase temperature of the probed medium is considered important for obtaining unbiased size parameter information from TIRE-LII measurements. PACS 42.62.-b; 51.30.+i; 82.20.Wt     

High-vacuum time-resolved laser-induced incandescence of flame-generated soot

We have measured time-resolved laser-induced incandescence of flame-generated soot under high-vacuum conditions (4.1×10⁻⁶ mbar) at an excitation wavelength of 532 nm with laser fluences spanning 0.06–0.5 J/cm². We generated soot in an ethylene/air diffusion flame, introduced it into the vacuum system with an aerodynamic lens, heated it using a pulsed laser with a spatially homogeneous and temporally smooth laser profile, and recorded LII temporal profiles at 685 nm. At low laser fluences LII signal decay rates are slow, and LII signals persist beyond the residence time of the soot particles in the detection region. At these fluences, the temporal maximum of the LII signal increases nearly linearly with increasing laser fluence until reaching a plateau at ∼0.18 J/cm². At higher fluences, the LII signal maximum is independent of laser fluence within experimental uncertainty. At these fluences, the LII signal decays rapidly during the laser pulse. The fluence dependence of the vacuum LII signal is qualitatively similar to that observed under similar laser conditions in an atmospheric flame but requires higher fluences (by ∼0.03 J/cm²) for initiation. These data demonstrate the feasibility of recording vacuum LII temporal profiles of flame-generated soot under well-characterized conditions for model validation.     

LII–lidar: range-resolved backward picosecond laser-induced incandescence

A novel concept for remote in situ detection of soot emissions by a combination of laser-induced incandescence (LII) and light detection and ranging (lidar) is presented. A lidar setup based on a picosecond Nd:YAG laser and time-resolved signal detection in the backward direction was used for LII measurements in sooty premixed ethylene–air flames. Measurements of LII–lidar signal versus laser fluence and flame equivalence ratio showed good qualitative agreement with data reported in literature. The LII–lidar signal showed a decay consisting of two components, with lifetimes of typically 20 and 70 ns, attributed to soot sublimation and conductive cooling, respectively. Theoretical considerations and analysis of the LII–lidar signal showed that the derivative was proportional to the maximum value, which is an established measure of soot volume fraction. Utilizing this, differentiation of LII–lidar data gave profiles representing soot volume fraction with a range resolution of ~16 cm along the laser beam propagation axis. The accuracy of the evaluated LII-profiles was confirmed by comparison with LII-data measured simultaneously employing conventional right-angle detection. Thus, LII–lidar provides range-resolved single-ended detection, resourceful when optical access is restricted, extending the LII technique and opening up new possibilities for laser-based diagnostics of soot and other carbonaceous particles.     

Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames

Absorption and scattering of laser-induced incandescence (LII) intensities by soot particles present between the measurement volume and the detector were numerically investigated at detection wavelengths of 400 and 780 nm in a laminar coflow ethylene/air flame. The radiative properties of aggregated soot particles were calculated using the Rayleigh-Debye-Gans polydisperse fractal aggregate theory. The radiative transfer equation in emitting, absorbing, and scattering media was solved using the discrete-ordinates method. The radiation intensity along an arbitrary direction was obtained using the infinitely small weight technique. The effects of absorption and scattering on LII intensities are found to be significant under the conditions of this study, especially at the shorter detection wavelength and when the soot volume fraction is higher. Such a wavelength-dependent signal-trapping effect leads to a lower soot particle temperature estimated from the ratio of uncorrected LII intensities at the two detection wavelengths. The corresponding soot volume fraction derived from the absolute LII intensity technique is overestimated. The Beer-Lambert relationship can be used to describe radiation attenuation in absorbing and scattering media with good accuracy provided the effective extinction coefficient is adequately.     

Experimental and theoretical comparison of spatially resolved laser-induced incandescence (LII) signals of soot in backward and right-angle configuration

In-situ measurements of soot volume fraction in the exhausts of jet engines can be carried out using the laser-induced incandescence (LII) technique in backward configuration, in which the signal is detected in the opposite direction of the laser beam propagation. In order to improve backward LII for quantitative measurements, we have in this work made a detailed experimental and theoretical investigation in which backward LII has been compared with the more commonly used right-angle LII technique. Both configurations were used in simultaneous visualization experiments at various pulse energies and gate timings in a stabilized methane diffusion flame. The spatial near-Gaussian laser energy distribution was monitored on-line as well as the time-resolved LII signal. A heat and mass transfer model for soot particles exposed to laser radiation was used to theoretically predict both the temporal and spatial LII signals. Comparison between experimental and theoretical LII signals indicates similar general behaviour, for example the broadening of the spatial LII distribution and the hole-burning effect at centre of the beam due to sublimation for increasing laser pulse energies. However, our comparison also indicates that the current heat and mass transfer model overpredicts signal intensities at higher fluence, and possible reasons for this behaviour are discussed. PACS 42.62.Fi; 44.40.+a     

Laser-induced incandescence for soot particle size and volume fraction measurements using on-line extinction calibration

A novel technique for two-dimensional measurements of soot volume fraction and particle size has been developed. It is based on a combined measurement of extinction and laser-induced incandescence using Nd:YAG laser wavelengths of 532 nm and 1064 nm. A low-energy laser pulse at 532 nm was used for extinction measurements and was followed by a more intense pulse at 1064 nm, delayed by 15 ns, for LII measurements. The 532-nm beam was split into a signal beam passing the flame and a reference beam, both of which were directed to a dye cell. The resulting fluorescence signals, from which the extinction was deduced, together with the LII signal, were registered on a single CCD detector. Thus the two-dimensional LII image could be converted to a soot volume fraction map through a calibration procedure during the same laser shot. The soot particle sizes were evaluated from the ratio of the temporal LII signals at two gate time positions. The uncertainty in the particle sizing arose mainly from the low signal for small particles at long gate times and the uncertainty in the flame temperature. The technique was applied to a well-characterized premixed flat flame, the soot properties of which had been previously thoroughly investigated. Received: 21 June 2000 / Revised version: 11 September 2000 / Published online: 7 February 2001     

Determining aerosol particle size distributions using time-resolved laser-induced incandescence

The particle size distribution within an aerosol containing refractory nanoparticles can be inferred using time-resolved laser-induced incandescence (TR-LII). In this procedure, a small volume of aerosol is heated to incandescent temperatures by a short laser pulse, and the incandescence of the aerosol particles is then measured as they return to the ambient gas temperature by conduction heat transfer. Although the cooling rate of an individual particle depends on its volume-to-area ratio, recovering the particle size distribution from the observed temporal decay of the LII signal is complicated by the fact that the LII signal is due to the incandescence of all particle size classes within the sample volume, and because of this, the particle size distribution is related to the time-resolved LII signal through a mathematically ill-posed equation. This paper reviews techniques proposed in the literature for recovering particle size distributions from TR-LII data. The characteristics of this problem are then discussed in detail, with a focus on the effect of ill-posedness on the stability and uniqueness of the recovered particle size distributions. Finally, the performance of each method is evaluated and compared based on the results of a perturbation analysis. PACS  44.05.+e; 47.70.Pq; 78.70.-g; 65.80.+n; 78.20.Ci     

Characterization of Nano‐Particles Using Laser‐Induced Incandescence

Laser‐induced incandescence (LII) is introduced as a valuable tool for the characterization of nanoparticles. This optical measurement technique is based on the heating of the particles by a short laser pulse and the subsequent detection of the thermal radiation. It has been applied successfully for the investigation of soot in different fields of application, which is described here in the form of an overview with a focus on work done at the LTT‐Erlangen during the last 10 years. In laboratory flames the soot primary particle size, volume concentration, and relative aggregate size have been determined in combination with the number density of primary particles. Furthermore, the primary particle sizes of carbon blacks have been measured in situ and online under laboratory conditions and also in production reactors. Measurements with different types of commercially available carbon black powders, which were dispersed in a measurement chamber yielded a good correlation between LII results and the specified product properties. Particle diameters determined by LII in a furnace black reactor correlate very well with the CTAB‐absorption number, which is a measure for the specific surface area. It turned out that the LII method is not affected by variations of the aggregate structure of the investigated carbon blacks. The LII signal also contains information on the primary particle size distribution, which can be reconstructed by the evaluation of the signal decay time at, at least, two different time intervals. Additionally, soot mass concentrations have been determined inside diesel engines and online measurements were performed in the exhaust gas of such engines for various engine conditions simultaneously providing information about primary particle size, soot volume, and number concentration. The LII results exhibit good correlation with traditional measurement techniques, e.g., filter smoke number measurements. In addition to the soot measurements, primarily tests with other nanoparticles like TiO₂ or metal particles are encouraging regarding the applicability of the technique for the characterization of such different types of nanoparticles.     

Investigation on the influence of soot size on prompt LII signals in flames

Theoretical papers predict that prompt LII signals are weakly dependent on the soot size due to the fact that larger particles reach higher temperatures during the heating process by nanosecond laser pulses. This question is of crucial importance for establishing LII as a practical technique for soot volume fraction measurements. In this work two-color prompt LII measurements have been performed in several locations of diffusion and rich premixed ethylene-air flames. The experimental apparatus was carefully designed with a probe volume of uniform light distribution and sharp edges, a 4 ns integration time around the signal pulse peak and narrow spectral bandwidth. Measurements did not confirm the theoretical predictions concerning an increase of temperature for larger particles. On the contrary, larger particles in richer premixed flames exhibit a lower 400/700 signal ratio. This can probably be attributed to small differences in the refractive index of soot.     

Laser-induced incandescence of flame-generated soot on a picosecond time scale

This paper presents measurements of time-resolved laser-induced incandescence (LII) from soot recorded on a picosecond time scale. The 532-nm output from a picosecond Nd:YAG laser was used to heat the soot, and a streak camera was used to record the LII signal. The results are compared with data collected on a nanosecond time scale and with a time-dependent model that solves the energy- and mass-balance rate equations. Relative to the laser timing, the picosecond and nanosecond results are very similar. Signals increase during the laser pulse as soot temperatures increase and decrease after the laser pulse. The signal decay rates increase significantly with increasing laser fluence. The LII model gives good agreement with the nanosecond data at fluences ≤0.2 J/cm² and underpredicts the signal decay rates at higher fluences. The picosecond temporal profiles increase significantly faster and earlier in the laser pulse than predicted by the model. This disagreement between the model and picosecond LII data may be attributable to perturbations to the signal by laser-induced fluorescence from polycyclic aromatic hydrocarbons or other large organic species. The excited state or states responsible for this fluorescence appear to be accessed via a two-photon transition and have an effective lifetime of 55 ps. PACS 44.40.+a; 78.67.Bf; 78.47.+p     

Influence of soot particle aggregation on time-resolved laser-induced incandescence signals

Laser-induced incandescence (LII) is a versatile technique for quantitative soot measurements in flames and exhausts. When used for particle sizing, the time-resolved signals are analysed as these will show a decay rate dependent on the soot particle size. Such an analysis has traditionally been based on the assumption of isolated primary particles. However, soot particles in flames and exhausts are usually aggregated, which implies loss of surface area, less heat conduction and hence errors in estimated particle sizes. In this work we present an experimental investigation aiming to quantify this effect. A soot generator, based on a propane diffusion flame, was used to produce a stable soot stream and the soot was characterised by transmission electron microscopy (TEM), a scanning mobility particle sizer (SMPS) and an aerosol particle mass analyzer coupled in series after a differential mobility analyzer (DMA-APM). Despite nearly identical primary particle size distributions for three selected operating conditions, LII measurements resulted in signal decays with significant differences in decay rate. However, the three cases were found to have quite different levels of aggregation as shown both in TEM images and mobility size distributions, and the results agree qualitatively with the expected effect of diminished heat conduction from aggregated particles resulting in longer LII signal decays. In an attempt to explain the differences quantitatively, the LII signal dependence on aggregation was modelled using a heat and mass transfer model for LII given the primary particle and aggregate size distribution data as input. Quantitative agreement was not reached and reasons for this discrepancy are discussed.     

Soot formation characteristics in a lab-scale turbulent pulverized coal flame with simultaneous planar measurements of laser induced incandescence of soot and Mie scattering of pulverized coal

Soot formation characteristics of a lab-scale pulverized coal flame were investigated by performing carefully controlled laser diagnostics. The spatial distributions of soot volume fraction and the pulverized coal particles were measured simultaneously by laser induced incandescence (LII) and Mie scattering imaging, respectively. In addition, the radial distributions of the soot volume fraction were compared with the OH radical fluorescence, gas temperature and oxygen concentration obtained in our previous studies [1], [2]. The results indicated that the laser pulse fluence used for LII measurement should be carefully controlled to measure the soot volume fraction in pulverized coal flames. To precisely measure the soot volume fraction in pulverized coal flames using LII, it is necessary to adjust the laser pulse fluence so that it is sufficiently high to heat up all the soot particles to the sublimation temperature but also sufficiently low to avoid including a too large of a change in the morphology of the soot particles and the superposition of the LII signal from the pulverized coal particles on that from the soot particles. It was also found that the radial position of the peak LII signal intensity was located between the positions of the peak Mie scattering signal intensity and peak OH radical signal intensity. The region, in which LII signal, OH radical fluorescence and Mie scattering coexisted, expanded with increasing height above the burner port. It was also found that the soot formation in pulverized coal flames was enhanced at locations where the conditions of high temperature, low oxygen concentration and the existence of pulverized coal particles were satisfied simultaneously.     

Influence of polydisperse distributions of both primary particle and aggregate size on soot temperature in low-fluence LII

An improved aggregate-based low-fluence laser-induced incandescence (LII) model has been developed. The shielding effect in heat conduction between aggregated soot particles and the surrounding gas was modeled using the concept of the equivalent heat transfer sphere. The diameter of such an equivalent sphere was determined from direct simulation Monte Carlo calculations in the free molecular regime as functions of the aggregate size and the thermal accommodation coefficient of soot. Both the primary soot particle diameter and the aggregate size distributions are assumed to be lognormal. The effective temperature of a soot particle ensemble containing different primary particle diameters and aggregate sizes in the laser probe volume was calculated based on the ratio of the total thermal radiation intensities of soot particles at 400 and 780 nm to simulate the experimentally measured soot particle temperature using two-color optical pyrometry. The effect of primary particle diameter polydispersity is in general important and should be considered. The effect of aggregate size polydispersity is relatively unimportant when the heat conduction between the primary particles and the surrounding gas takes place in the free-molecular regime; however, it starts to become important when the heat conduction process occurs in the near transition regime. The model developed in this study was also applied to the re-determination of the thermal accommodation coefficient of soot in an atmospheric pressure laminar ethylene diffusion flame. PACS 44.05.+e; 61.46.Df; 65.80.+n     

Comparison of LII derived soot temperature measurements with LII model predictions for soot in a laminar diffusion flame

Laser-induced incandescence (LII) was used to derive temperatures of pulsed laser heated soot particles from their thermal emission intensities detected at two wavelengths in a laminar ethylene/air co-annular diffusion flame. The results are compared to those of a numerical nanoscale heat and mass transfer model. Both aggregate and primary particle soot size distributions were measured using transmission electron microscopy (TEM). The model predictions were numerically averaged over these experimentally derived size distributions. The excitation laser wavelength was 532 nm, and the LII signal was detected at 445 nm and 780 nm. A wide range of laser fluence from very low to moderate (0.13 to 1.56 mJ/mm²) was used in the experiments. A large part of the temporal decay curve, beginning 12–15 nsec after the peak of the laser excitation pulse, is successfully described by the model, resulting in the determination of accommodation coefficients, which varies somewhat with soot temperature and is in the range of 0.36 to 0.46. However, in the soot evaporative regime, the model greatly overpredicts the cooling rate shortly after the laser pulse. At lower fluences, where evaporation is negligible, the initial experimental cooling rates, immediately following the laser pulse, are anomalously high. Potential physical processes that could account for these effects are discussed. From the present data the soot absorption function, E(m), of 0.4 at 532 nm is obtained. A procedure for correcting the measured signals for the flame radiation is presented. It is further shown that accounting for the local gas temperature increase due to heat transfer from soot particles to the gas significantly improves the agreement in the temperature dependence of soot cooling rates between model and experiments over a large range of laser fluences.     

Laser-induced incandescence technique to identify soot nucleation and very small particles in low-pressure methane flames

This paper presents the study we carried out on the formation of soot particles in low-pressure premixed CH₄/O₂/N₂ flames by using Laser-Induced Incandescence (LII). Flames were stabilised at 26.6 kPa (200 torr). Four different equivalence ratios were tested (Φ = 1.95, 205, 2.15 and 2.32), Φ = 1.95 corresponding to the equivalence ratio for which LII signals begin to be measurable along the flame. The evolution of the LII signals with laser fluence (fluence curve), time (temporal decay) and emission wavelength is reported at different heights above the burner. We specifically took advantage of the low-pressure conditions to probe with a good spatial resolution the soot inception zone of the flames. Significant different behaviours of the fluence curves are observed according to the probed region of the flames and Φ. In addition, while the surface growth process is accompanied by an increase in the LII decay-times (indicator of the primary particle diameter) at higher Φ, decay-times become increasingly short at lower Φ reaching a constant value along the flame at Φ = 1.95. These behaviours are consistent with the detection of the smallest incandescent particles in the investigated flames, these particles having experienced very weak surface growth. Flame modelling including soot formation has been implemented in flames Φ = 2.05 and 2.32. Experimental quantitative soot volume fraction profiles were satisfactorily reproduced by adjusting the fraction of reactive soot surface available for reactions. The qualitative variation of the computed soot particle diameter and the relative weight of surface growth versus nucleation were consistent with the experimental observations.