EXTENDED CHARACTERIZATION OF COMBUSTION-GENERATED AGGREGATES - SELF-AFFINITY AND LACUNARITIES

A large population of combustion-generated soot aggregates (more than 3000 samples) was thermophoretically extracted from a variety of lamin ar and turbulent flames and analyzed by using transmission electron mi croscopy (TEM). It was shown that the scaling structural properties of these fractal aggregates cannot be exclusively characterized by a sin gle mass fractal dimension. Asymmetric properties of the aggregates we re considered here by first assuming and then demonstrating their self -affinity via affinity exponents reflecting different scaling with res pect to the length and width of the aggregate projections. In addition to the conventional fractal dimension, D-f, determined by using the g eometrical mean of the longitudinal and transverse sizes as the charac teristic length, the affinity exponent, H, and two complementary fract al dimensions, one longitudinal, D-L = [(1 + H)/2]D-f, and one transve rse, D-w = [(1 + H)/2H]D-f, were introduced. By fitting the TEM data f or the entire population of aggregates, the values of D-f = 1.75 and H = 0.91 were obtained. To classify the density and crossover scales of aggregates having the same fractal dimensions, lacunarities of the fi rst and second order were also defined as prefactors in the scaling re lationships among aggregate mean mass, rms mass and linear sizes. Anal ysis of the second moment of the mass-size distribution confirmed that the scaling properties of flame-generated aggregates cannot be consum mately characterized by a single fractal dimension; it is necessary to introduce a set of scaling exponents. This more precise description o f aggregate morphologies in terms of self-affine scaling and lacunarit ies is not captured by previous idealized cluster-cluster aggregation models. Current investigations of the reasons for this are expected to lead to a deeper understanding of the coagulation dynamics, transport properties, and restructuring kinetics of flame-generated aggregates. (C) 1996 Academic Press, Inc.