Study of the wavelength dependence of the absorption function of diesel soot by LII modeling integrating the effect of multiple scattering within aggregates

Abstract This work represents a first attempt at proposing a refined LII model suitable for simulating signals collected with excitation wavelengths (EWs) of 266, 355, 532 and 1064 nm. In this context, we implemented a comprehensive version of laser-irradiated soot heat and mass balance equations integrating terms representing the saturation of linear, single- and multi-photon absorption processes, cooling by sublimation, conduction, radiation and thermionic emission, as well as mechanisms depicting soot oxidation and annealing, non-thermal photodesorption of carbon clusters and corrective factors accounting for the shielding effect and multiple scattering (MS) within aggregates. This simulation tool was fully parameterized, by coupling design of experiments with a genetic algorithm-based solver, against data collected at different heights above the burner (HAB) in a diesel spray flame. This allowed to assess values of different model parameters involved in absorption and sublimation terms, which, to date, have never been reported in LII modeling studies for UV EWs (e.g., multi-photon absorption cross sections for C 2 photodesorption and saturation coefficients for linear- and multi-photon absorption). The simulation work proposed herein then enabled to infer information regarding the evolution of the absorption function of soot ( $$E\left(m,\lambda \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>λ</mml:mi> </mml:mfenced> </mml:mrow> </mml:math> ). $$E\left(m,266\right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>266</mml:mn> </mml:mfenced> </mml:mrow> </mml:math> , $$E(m,355)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>355</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$E(m,532)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>532</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> ranging from 0.25 to 0.51, 0.20 to 0.38 and 0.18 to 0.30, respectively, were notably estimated as a function of the HAB. Alternatively, values ranging from 0.31 to 0.53, 0.26 to 0.44 and 0.22 to 0.38 were assessed while neglecting the effect of MS and provided constant $$E(m,266)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>266</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> / $$E(m,1064)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1064</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , $$E(m,355)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>355</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> / $$E(m,1064)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1064</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$E(m,532)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>532</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> / $$E(m,1064)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1064</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> ratios of 1.4, 1.2 and 1.0, regardless of the HAB. In addition, the obtained results showed that the wavelength dependence of the soot absorption function was quite negligible for EWs higher than 532 nm, irrespective of whether the effect of MS was considered or neglected. On the other hand, aggregate properties were proven to substantially influence the $$E(m,\lambda )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> / $$E(m,1064)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1064</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> ratios for decreasing $$\lambda$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> and increasing HAB, thus illustrating the significant effect of aggregation on the optical properties of soot. Finally, the results issued from the different analyses we conducted on the diesel flame investigated in this paper led to the conclusion that values of $$E\left(m,\lambda \right),$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>λ</mml:mi> </mml:mfenced> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> falling within the 0.38 ± 0.15 and 0.29 ± 0.11 range at 266 and 355 nm, versus 0.25 ± 0.09 at 532 and 1064 nm could be considered as suitable for simulating LII signals of progressively aging aggregated particles.

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