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Self-Affinity of Combustion-Generated Aggregates

Published online by Cambridge University Press:  10 February 2011

A. V. Neimark,
Ü. Ö. Köylü and
D. E. Rosner
A. V. Neimark
Affiliation:
Department of Chemical Engineering, Yale University, New Haven CT 06520–8286
Ü. Ö. Köylü
Affiliation:
Department of Chemical Engineering, Yale University, New Haven CT 06520–8286
D. E. Rosner
Affiliation:
Department of Chemical Engineering, Yale University, New Haven CT 06520–8286
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Abstract

A large population of combustion-generated soot aggregates (more than 3,000 samples) was thermophoretically extracted from a variety of laminar and turbulent flames and analyzed using transmission electron microscopy (TEM). It was shown that the scaling structural properties of these fractal aggregates cannot be exclusively characterized by a single mass fractal dimension. Asymmetric properties of the aggregates were considered here by first assuming and then demonstrating their self-affinity via. an affinity exponent reflecting scaling with respect to the length and width of the aggregate projections. In addition to the conventional fractal dimension, D f , determined by using the geometrical mean of the longitudinal and transverse sizes as the characteristic length, the affinity exponent, H, and two complementary fractal dimensions, one longitudinal, D L =[(1+H)/2 ]D f , and one transverse, D W =[(1+H)/2H]D f , were introduced. By fitting TEM data for the entire population of aggregates, the values D f = 1.75 and H = 0.91 were obtained. This more complete description of aggregate morphologies in terms of the self-affine scaling is expected to lead to a better understanding of the transport properties and restructuring kinetics of flame-generated aggregates.

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