Comparison of Numerical Studies Characterizing Optical Properties of Soot Aggregates for Improved EXSCA Measurements

Abstract

In order to compare EXSCA measurements with light‐scattering calculations, numerical studies characterizing the optical properties of soot aggregates were compared by using different approaches: [1] the Rayleigh‐Debye‐Gans theory for the fractal aggregate model (RDG‐FA), studied by Faeth and Köylü, [2] the rigorous solution model (RS) proposed by Xu, and [3] the discrete dipole approximation model (DDA), developed by Draine and Flatau. The extinction, absorption and scattering cross‐sections, C$\rm{ {_{e}^{a}}}$, C$\rm{ {_{a}^{a}}}$ and C$\rm{ {_{s}^{a}}}$, and matrix scattering coefficients, |S1|2, |S2|2, |S3|2 and |S4|2, were studied, emphasizing the extinction coefficient C$\rm{ {_{c}^{a}}}$ and the scattering coefficient |S1(90°)|2. First, these coefficients for a panel of six aggregates with 64 or 128 primary spheres were compared using the three models. For the absorption and extinction cross‐sections, the results are close and RDG‐FA may be adequate to determine these parameters. For the total scattering cross‐section, the DDA model is close to RS whereas the RDG‐FA model shows limitations with strong relative differences. For the scattering coefficients, we focused on |S1|2 and |S2|2, |S3|2 and |S4|2 being negligible. For the 64‐sphere aggregates, the relative differences between DDA and RDG‐FA are generally great and higher for RDA‐FA than for DDA. These deviations are especially significant for backscattering. If, on the contrary, we focus on |S1(90°)|2, all of the models give a good prediction. To complete this study, computation times for DDA and RS are indicated and cross‐section distributions for a panel of 28 aggregates obtained using RDG‐FA and DDA are presented.

Investigation of Absorption and Scattering Properties of Soot Aggregates of Different Fractal Dimension at 532 nm Using RDG and GMM

“…GMM was developed by Xu (1995Xu ( , 1997 based on the framework of the Mie theory for a single sphere and the addition theorems for spherical vector wave functions. It provides a rigorous and complete solution to nonoverlapping multisphere light scattering problems and can be readily applied to fractal soot aggregates ( Van-Hulle et al 2002;Liu and Snelling 2008). Execution of this numerically exact method requires the positions, diameter, and refractive index of each constituent sphere (primary particle).…”

“…Execution of this numerically exact method requires the positions, diameter, and refractive index of each constituent sphere (primary particle). Although CTM has become the most popular method to study the radiative properties of various scatterers , GMM has also been demonstrated to be a powerful tool to study radiative properties of various particles (Xu 1995(Xu , 1997Van-Hulle et al 2002;Liu and Snelling 2008). In fact, CTM and GMM share a very similar theoretical framework, though differences exist (Xu and Khlebtsov 2003).…”

“…Soot particles resulting from combustion or numerically simulated diffusion limited cluster aggregation (DLCA) exhibit fairly open structure with a fractal dimension in the range of 1.4-1.9 (Brasil et al 2000). To date most studies on the radiative properties of fractal soot particles have focused on the evaluation of the accuracy and the range of the validity of the RDG approximation, (Farias et al 1995;Farias et al 1996;Van Hulle et al 2002;Liu and Snelling 2008). A few studies have investigated the effect of the fractal parameters on the radiative properties of soot particles using more accurate numerical methods than the RDG approximation.…”

Measurement of the Mass Specific Extinction Coefficient of Acetylene, Toluene and Polymethyl Methacrylate Soot Particles in Visible and Near-Infrared Wavelengths

“…The RDG-FA theory has been introduced by Köylü and Faeth [6,13] and its validity has been checked by comparison with more accurate formulations [15,16]. However the main difficulty of the application of the above relations is that the complex refractive index m value of soot particles has to be known.…”

The Influence of Water Coating on the Optical Scattering Properties of Fractal Soot Aggregates

“…Xu (1995Xu ( , 1996Xu ( , 1997 and Xu and Gustafson (2001) continued the development to produce what is known as the GMM method to deal with aggregates of arbitrary size and configuration, formed from monomers that are homogeneous spheres of possibly different radii and compositions. This GMM method was recently used to calculate the singlescattering properties of fractal aggregates by Van-Hulle et al (2002), Liu and Smallwood (2010, 2011), and Li et al (2010. By replacing the Lorenz-Mie theory for homogeneous particles with the core-mantle Mie theory, i.e., providing the amplitude coefficients given by the core-mantle Mie theory, the GMM was extended to compute the scattering properties of the aggregates with coated inhomogeneous monomers (Xu and Khlebtsov 2003).…”