A method to determine the fractal dimension of diesel soot agglomerates

Soot agglomerates emitted by diesel engines are composed of primary particle forming irregular clusters. Such irregularity can be quantified by the fractal dimension, whose determination depends on certain parameters not unanimously established, such as the prefactor of the power law relationship. Mean values of the fractal dimension of large collections of agglomerates are usually determined in literature by least-square regression fittings to the power law relationship. In this paper, an iterative method to determine the fractal dimension of individual agglomerates is proposed instead, thus making possible a better discrimination of effects. Functions depending on the fractal dimension and the number of primary particles are proposed for the prefactor and for the overlapping parameter (a measure of the overlap that the primary particles provoke among themselves when projected). Therefore, extreme cases (agglomerates forming a compact sphere and an aligned chain of primary particles) were taken as boundary conditions, for which a geometrical analysis has been performed. The method has been adjusted by comparison with cluster–cluster aggregation models taken from literature, and has proved to have good sensitivity and low loss of information. Some examples are shown from transmission electron microscopy (TEM) images of agglomerates obtained with thermophoretic sampling from the exhaust gas of a diesel engine under different operating conditions.

Graphical abstractAn iterative method to determine the fractal dimension of every single agglomerate is proposed, thus making possible a better discrimination of effects. Functions depending on the fractal dimension and the number of primary particles are proposed for the prefactor and for the overlapping parameter. Extreme cases (agglomerates forming a sphere and an aligned chain) were taken as boundary conditions, for which a geometrical analysis has been performed. An abacus for the direct determination of the fractal dimension and apparent density from the image analysis is also presented.Figure optionsDownload full-size imageDownload high-quality image (85 K)Download as PowerPoint slide