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A computationally fast method to determine values and their uncertainty for particulate system volume median diameter, volume fraction, and size distribution width is presented. These properties cannot be obtained for submicrometer particulate by diffraction-based methods. The technique relies on a least-mean-squares method applied over a prespecified size range and distribution width. Prespecifying the range significantly reduces the number of calculations required to determine the particulate parameters from experimental data, allowing the practical evaluation of large data sets. The solution method that was developed has significant advantages over ratio-style calculations that are more commonly performed, the primary of which is a simple method to determine errors in the measurement parameters. We evaluated the predicted performance for a specific experimental system for various levels of noise, with monodisperse and log-normal distributions, by analyzing synthetic data with the algorithm. Results were a quantitative statement of system accuracy. In addition, synthetic log-normal data evaluated with monodisperse models revealed significant and systematic errors in the predicted volume median diameter. These errors indicate that, in general, systems with a significant size distribution width must be analyzed with a model that includes this size distribution. Finally, calibrated polystyrene spheres were measured with an experimental system that used four simultaneous scattering measurements, and all diameters were within the reported uncertainty.

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Flow field non-uniformity effects on the sizing results from inversion of multi-angle elastic light scattering signals were investigated and found to be significant for measurement systems where the scale of the flow field variation and the scattering probe volume were similar. Particulate flow fields, such as those produced by multi-element diffusion burners used in flame synthesis processes, generally form two-dimensional patterns perpendicular to the axis of the carrier flow. Expansion of the spatial particle number density field in terms of the double Fourier series is used to derive relationships that quantitatively estimate the accuracy of measurement results. In this paper, we present the Fourier analysis used to quantify effects of probe volume size and alignment. Special attention is given to measurements of low spatial resolution, i.e. measurements that provide information on the global (cross-sectional) average particle size distribution. After brief discussions on the general requirements for the diagnostics layout (probe volume size) and incorporation of the systematic errors in signal inversion for global average measurements, the analysis for a typical flow field produced by a Hencken burner is presented. The results of this analysis indicate that the dimensions of the probe volume have to be about three times larger than the characteristic length of the particle field in order to avoid excessively large uncertainties in measurement results.