Abstract
A general qualitative theory for the mean-field rate equation describing aggregation processes is described. Various exponents describing the cluster-size distribution and its time evolution are derived. It is found that this theory frequently gives a good account of systems with more realistic kinetics, such as cluster-cluster aggregation, but that considerable caution must be exercised to ensure being in the actual asymptotic regime, since very long crossovers are sometimes observed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
S. K. Friedlander, Smoke, Dust and Haze ( Wiley-Interscience, New York, 1977 ).
G. B. Field, W. C. Saslaw, Astrophys. J. 142, 568 (1965); G. B. Field and J. Hutchins, Astrophys. J. 155, 737 (19xx).
R. L. Drake, in Topics in Current Aerosol Research, vol. 3, eds. G. M. Midy and J. R. Brock.
W. H. Stockmayer, J. Chem. Phys. 11, 45 (1943).
F. Leyvraz and H. R. Tschudi, J. Phys. A 15, 1951 (1982).
E. M. Hendriks, M. H. Ernst and R. M. Ziff, J. Stat. Phys. 31, 519 (1983); Phys. Rev. Lett. 49, 593 (1982).
E. M. Hendriks, J. Phys. A 17, 2299 (1984).
W. White, J. Coll. Interface Sci. 87, 204 (1982).
A. A. Lushnikov and V. N. Piskunov, Dolklady Phys. Chem. 231, 1166 (1976).
T. Vicsek and F. Family, Phys. Rev. Lett. 52, 1669 (1984).
M. v. Smoluchowski, Phys. Z. 17, 585 (1916).
A. M. Golvin, Izv. Geophys. Ser. 1963, 783 (1963) [English translation: Bull Acad. Sci. USSR, Geophys. Ser. No. 5, 482 (1963).
R. M. Ziff, J. Stat. Phys. 23, 241 (1980).
F. Leyvraz and H. R. Tschudi, J. Phys. A 14, 3389 (1981).
P. van Dongen and M. H. Ernst (preprint).
P. Meakin, Phys. Rev. Lett. 51, 1119 (1983).
M. Kolb, R. Botet and R. Jullien, Phys. Rev. Lett. 51, 1123 (1983).
P. Meakin, T. Vicsek and F. Family, Phys. Rev. B 31, 564 (1985).
M. Kolb, Phys. Rev. Lett. 53, 1653 (1984).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Leyvraz, F. (1986). Rate Equation Approach to Aggregation Phenomena. In: Stanley, H.E., Ostrowsky, N. (eds) On Growth and Form. NATO ASI Series, vol 100. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5165-5_8
Download citation
DOI: https://doi.org/10.1007/978-94-009-5165-5_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-89838-850-3
Online ISBN: 978-94-009-5165-5
eBook Packages: Springer Book Archive