Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-02T20:23:32.011Z Has data issue: false hasContentIssue false

Self-Affinity of Combustion-Generated Aggregates

Published online by Cambridge University Press:  10 February 2011

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
Get access

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, Df, 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, DL =[(1+H)/2 ]Df, and one transverse, DW =[(1+H)/2H]Df, were introduced. By fitting TEM data for the entire population of aggregates, the values Df = 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.

Type
Research Article
Copyright
Copyright © Materials Research Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Mandelbrot, B. B., The Fractal Geometry of Nature, Freeman & Co., New York, 1983.Google Scholar
2. Jullien, R. and Botet, R., Aggregation and Fractal Aggregates, World Scientific, Singapore, 1987.Google Scholar
3. Vicsek, T., Fractal Growth Phenomena, World Scientific, Singapore, 1992.Google Scholar
4. Weitz, D. A. and Huang, J. S., in Kinetics of Aggregation and Gelation, edited by Family, F. and Landau, D. P., p. 19, Elsevier Science, Amsterdam, 1984.Google Scholar
5. Botet, R. and Jullien, R., J. Phys. A: Math. Gen. 19, L907 (1986).Google Scholar
6. Lindsay, H. M., Klein, R., Weitz, D. A., Lin, M. Y. and Meakin, P., Phys. Rev. A 39, 3112 (1989).Google Scholar
7. Köylü, Ü. Ö. and Faeth, G. M., Combust. Flame 89, 140 (1992).Google Scholar
8. Köylü, Ü. Ö. and Faeth, G. M., ASME J. Heat Trans. 116, 971 (1994).Google Scholar
9. Sunderland, P. B., Köylü, Ü. Ö. and Faeth, G. M.,Combust. Flame 100, 310 (1995).Google Scholar
10. Dobbins, R. A. and Megaridis, C. M., Langmuir 3, 254 (1987).Google Scholar
11. Rosner, D. E., Mackowski, D. W. and Garcia-Ybarra, P., Combust. Sci. Tech. 80, 87 (1991).Google Scholar
12. Köylü, Ü. Ö., Xing, Y. and Rosner, D. E., Langmuir, in press (1995).Google Scholar
13. Mandelbrot, B. B., Phys. Scr. 32, 257 (1985).Google Scholar
14. Mandelbrot, B. B., in Fractals in Physics, edited by Pietronero, L. and Tosatti, E., Elsevier, Amsterdam, 1986.Google Scholar
15. Neimark, A. V., Phys. Rev. B 50, 15435 (1994).Google Scholar
16. Rosner, D. E. and Tandon, P., AIChE J. 40, 1167 (1994).Google Scholar
17. Tandon, P. and Rosner, D. E., I&EC Research 34, 3265 (1995).Google Scholar
18. Garcia-Ybarra, P. and Rosner, D. E., AIChE J. 35, 139 (1989).Google Scholar
19. Tandon, P. and Rosner, D. E., Chem. Eng. Comm., in press (1995).Google Scholar