the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Nov 2025
Analysing the light-to-heat conversion of Black Carbon agglomerates to interpret results from different light absorption instruments
Abstract. Black Carbon (BC) is an important pollutant due to its climatic and health effects. Most BC detection devices rely on light absorption but measured BC concentrations may vary due to different light settings. Here, we propose a theoretical model that can be used to interpret and correct the signal of optoacoustic devices. It is based on Laser Induced Incandescence (LII) theory, but advancing the description of light absorption and heat conduction by agglomerate particles. It is validated with existing experimental literature data and with new optoacoustic measurements. The model predicts that high fractal dimensions are associated with weaker signal and that the volume to surface ratio can be used as a signal reduction predictor. Then, we introduce a dimensionless metric which very well corelates with the measured signal from BC particles. The new metric can be used to harmonize measurements from different devices and also extract particle morphological information from optoacoustic signals.
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Status: open (until 11 Jan 2026)
- RC1: 'Comment on egusphere-2025-4498', Anonymous Referee #1, 06 Jan 2026 reply
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- 1
This manuscript pulls from the laser-induced incandescence (LII) literature and expands its application to optical-acoustic phenomena, with a specific focus on the effect of agglomeration and characteristics cooling times. It is proposed that such a model may be useful in accounting or correcting for particle composition and morphology. The manuscript does not adequately reference the existing LII literature on the topic, which must be improved (both in the introduction and but also in terms of recurring references to the literature throughout the text). However, the application of a simple version of existing LII models to optical-acoustic measurements remains interesting. The manuscript is reasonably well-written overall.
Thus, while the manuscript requires some reframing and improvements in references to the existing literature and could benefit from further model validation (comparison of temporal signals), the manuscript could be a good addition to the literature and should be considered for publication following several changes.
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(1) The review of the LII modeling literature is seemingly random. Given the perceived focus on models in the literature, a key omission was the review and comparison of LII models by Michelsen et al. in 2007. This would cover many of the earlier models, while covering some missed by the authors. There are also key manuscripts that discuss conduction that are likely relevant, including a key manuscript by Filippov et al. (2000) and several other manuscripts by Liu et al. and Daun (2010). Some of these manuscript also mention the effect of shielding, which results in an uneven distribution of temperature in the aggregate. This reviewer would encourage the authors to re-review the corresponding literature. Liu et al. (Appl. Phys. B, 2006b) is mentioned later but seems like an omission in the literature review earlier in the manuscript. Given these omissions, the choice to cite a manuscript for 3D LII that is marginally relevant is poor, even if such a study is interesting and robust.
Michelsen, H.A., Liu, F., Kock, B.F., Bladh, H., Boïarciuc, A., Charwath, M., Dreier, T., Hadef, R., Hofmann, M., Reimann, J. and Will, S., 2007. Modeling laser-induced incandescence of soot: a summary and comparison of LII models. Applied physics B, 87(3), pp.503-521.
Filippov, A.V., Zurita, M. and Rosner, D.E., 2000. Fractal-like aggregates: relation between morphology and physical properties. Journal of colloid and interface science, 229(1), pp.261-273.
Liu, F., Smallwood, G.J. and Snelling, D.R., 2005. Effects of primary particle diameter and aggregate size distribution on the temperature of soot particles heated by pulsed lasers. Journal of Quantitative Spectroscopy and Radiative Transfer, 93(1-3), pp.301-312.
Liu, F., Yang, M., Hill, F.A., Snelling, D.R. and Smallwood, G.J., 2006a. Influence of polydisperse distributions of both primary particle and aggregate size on soot temperature in low-fluence LII. Applied Physics B, 83(3), pp.383-395.
Liu, F., Daun, K.J., Snelling, D.R. and Smallwood, G.J., 2006b. Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence. Applied physics B, 83(3), pp.355-382.
Liu, F. and Smallwood, G., 2008. Study of heat conduction between fractal aggregates and the surrounding gas in the transition regime using the DSMC method. In 40th Thermophysics Conference (p. 3917).
Daun, K.J., 2010. Effect of selective accommodation on soot aggregate shielding in time-resolved laser-induced incandescence experiments.
(2) The authors should consider rewriting the model description. The reliance on Hadef et al. as a starting point both seems both arbitrary and inefficient. The model resembles others in the LII literature in key ways (e.g., Liu et al., 2006), with the two key terms (conduction and absorption) not resembling that in Hadef et al. It would seem that the better way to introduce the model is to state how all of the terms are being treated explicitly before stating that remaining terms are treated the same as or have the same parameters as Hadef et al. The authors should consider the broader set of models presented in Michelsen et al. (2005, 2015) and newer models when presenting their own model.
(3) Why do the authors place so much emphasis on the agglomeration for conduction but still apply Mie theory for modeling the absorption? Why is Mie theory applied to the individual monomers and then RDG-FA applied to the agglomerates? In regards to the validity of RDG-FA, consider citing work by Sorensen, Liu, Yon, and co-workers (see below), who provide overviews of the approximate validity of RDG-FA as well as when errors can be incurred. Of particular note, Liu et al. (2010) looks at the effect of inaccuracies in RDG-FA on LII temperature decays, with some interplay with conduction.
Liu, F. and Smallwood, G.J., 2010. Effect of aggregation on the absorption cross-section of fractal soot aggregates and its impact on LII modelling. Journal of Quantitative Spectroscopy and Radiative Transfer, 111(2), pp.302-308.
Yon, J., Liu, F., Bescond, A., Caumont-Prim, C., Rozé, C., Ouf, F.X. and Coppalle, A., 2014. Effects of multiple scattering on radiative properties of soot fractal aggregates. Journal of Quantitative Spectroscopy and Radiative Transfer, 133, pp.374-381.
Sorensen, C.M., Yon, J., Liu, F., Maughan, J., Heinson, W.R. and Berg, M.J., 2018. Light scattering and absorption by fractal aggregates including soot. Journal of Quantitative Spectroscopy and Radiative Transfer, 217, pp.459-473.
(4) “The diameter of gyration is a proxy of the wetted surface of the particle, which is relevant for heat conduction.” – Minor point, but can the authors provide a citation supporting this statement.
(5) “The thermal relaxation time of a spherical particle can be calculated on the basis of Eq. (1) as shown in Starke et al. (2003).” – Better references for this may be the original papers by Eckbreth and Melton.
Eckbreth, A.C., 1977. Effects of laser‐modulated particulate incandescence on Raman scattering diagnostics. Journal of Applied Physics, 48(11), pp.4473-4479.
Melton, L.A., 1984. Soot diagnostics based on laser heating. Applied optics, 23(13), pp.2201-2208.
(6) Sec. 2.4. This kind of observation has been observed previously, relating the cooling time to the Sauter mean diameter of the particles (Liu et al., 2005, 2006). This was also stated in the review by Schulz et al. (2006). This has been affirmed in later literature when examining uncertainties from experimental data (Daun et al., 2007; Sipkens et al., 2014). It is thus unsurprising and not particularly novel that the data collapsed when a Sauter mean diameter (or surface-to-volume ratio) is considered, though the extension to optical-acoustic measurements is notable. The authors should acknowledge the corresponding literature. Polydispersity also disrupts this trend, causing some scatter that the authors should acknowledge and was observed in the above studies.
Liu, F., Snelling, D.R. and Smallwood, G.J., 2005, January. Numerical study of temperature and incandescence intensity of nanosecond pulsed-laser heated soot particles at high pressures. In ASME International Mechanical Engineering Congress and Exposition (Vol. 42215, pp. 355-364).
Schulz, C., Kock, B.F., Hofmann, M., Michelsen, H., Will, S., Bougie, B., Suntz, R. and Smallwood, G., 2006. Laser-induced incandescence: recent trends and current questions. Applied Physics B, 83(3), pp.333-354.
Daun, K.J., Stagg, B.J., Liu, F., Smallwood, G.J. and Snelling, D.R., 2007. Determining aerosol particle size distributions using time-resolved laser-induced incandescence. Applied Physics B, 87(2), pp.363-372.
Sipkens, T.A., Mansmann, R., Daun, K.J., Petermann, N., Titantah, J.T., Karttunen, M., Wiggers, H., Dreier, T. and Schulz, C., 2014. In situ nanoparticle size measurements of gas-borne silicon nanoparticles by time-resolved laser-induced incandescence. Applied Physics B, 116(3), pp.623-636.
(7) As a supplement to Table 1, it may be worth having a table stating what properties are used in the model (e.g., thermal accommodation coefficient, density, specific heat, etc.). This will make clear which parameters were used in the model and how they compare to others in the literature.
(8) Instead of Table 1, the authors should also consider adding temperature-time decays to show how the models compare. The authors could also add the diameter and heat transfer modes, in separate panels, if they wanted.
(9) Could the authors show sample temporal signals in general, with both the experimental and simulated results. For example, show experimental data alongside the heat conduction profile results from Fig. 3. How well do these signals match? This would be a far better test of the model and may show some of the reason for remaining discrepancies in Fig.4, which is currently unexplored.
(10) Why did the authors choose to normalize by a 20 nm spherical particle in Sec. 3.3 (e.g., it is far enough into the free molecular conduction and Rayleigh absorption regimes). What if the authors chose a smaller size to ensure these two conditions are satisfied?
(11) Could the authors clarify (i.e., remind the reader) how the fractal dimension is implemented into the simulations? To which fractal dimension are the authors referring?
(12) The signal decrease observed in Fig. 6 assumes a constant morphology, which will undoubtedly change between BC and ash. Further, similar trends may result in some of these features being correlated and thus difficult to distinguish from another. The authors should, at a minimum, note this caveat and weaken the statement.
It is noted that the authors add a caveat to the effect of the above statement in a later section, but the current phrasing and flow could be improved. Do all of these trends need to be shown when they are mathematically equivalent? Could the authors instead spend the time showing that they are mathematically equivalent (i.e., the chosen dimensionless time yields a compact equation that applies universally).
(13) Could the authors propose a different quantity than “TOA”, given the common use of the acronym in reference to thermal optical analysis in overlapping literature. Also consider using the symbol tau for a dimensionless time decay.
(14) The paper could benefit from a practical implementation dimensionless quantity calculated for some of the proposed particle classes, to show how they might differ or be used to correct measurements.
(15) A key limitation of the current paper is that the applied model is rather simplistic, despite trying to capture the complex effect of fractal morphology. For example, the authors do not consider polydispersity, which disrupts the simple collapse of the data that the authors observed. This may lead to overly optimistic results, which cannot be easily validated against experiments (which would require precise control of the fractal dimension for particles of the same size). The paper is then too confident in the correction that can be applied. The manuscript remains useful, as the brief comparison to experimental data shows, but the conclusions from the simulations must be made less confident. Appropriate caveats need to be added that this is a rather simple treatment (which is both an advantage and a limitation).
(16) “… optoacoustic (OA) and optothermal (OT) ones and Laser Induced Incandescence (LII) …” Like the other techniques, “laser-induced incandescence” does not need to be capitalized.