# Soot aggregate sizing in an extended premixed flame by high-resolution two-dimensional multi-angle light scattering (2D-MALS)

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## Abstract

The spatial distribution of soot aggregate size and morphology within a premixed flat flame (McKenna-type burner and ethyne–air mixture at an equivalence ratio of *Φ* = 2.7) is characterized by two-dimensional multi-angle light scattering (2D-MALS). A profound investigation of such an extended, radially symmetrical sooting flame with 2D-MALS requires a sophisticated camera calibration to correct for non-linear image scaling and a careful evaluation of the scattering data. Sharp scattering images were acquired in the angular range from 20° to 155° using a rotatable camera system and an automated Scheimpflug adapter. To correct for non-linear variations in horizontal and vertical image magnification occurring at scattering angles differing from perpendicular view, a polynomial-based image transformation algorithm was developed to convert all scattering images into a common coordinate system. Effective radii of gyration and fractal dimensions of soot aggregates were then derived from scattering data by two different approaches. Due to limited amount of angular positions, the classical method based on Guinier and power law analysis shows limitations, as it yields discontinuous results, predominantly in axial direction of the burner. Bayesian analysis was then used for a data fit of the complete structure factor conducting a least square minimization leading to more consistent results. The use of prior knowledge in the Bayesian evaluation allows for improved data fitting and reduced uncertainties in radius of gyration and fractal dimension even for small aggregate sizes.

## Notes

### Acknowledgements

The authors gratefully acknowledge funding by the German Research Foundation (DFG) under Grant no. WI 1602/6-1. We thank Rolf Eigenheer and Charlie Gfeller of GFAE GmbH Switzerland for their operating assistance and hardware improvements of the CAPcam Scheimpflug adapter. We are grateful to Julia Kufner, Robert Müller, Andreas Knerr, and Nicolas Fechter for their help concerning the ELS measurements and evaluation strategies.

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