Abstract
Irreversible coagulation (or aggregation) processes are described first by equations, for which a scaling theory is described. It is then argued that the range of validity of this description does not necessarily include the case where diffusion is the rate-limiting step. A simplified model to simulate this latter case is then described and shown to deviate from the predictions of the rate equations if the space dimension d (or the spectral dimension d s for fractal substrates) is less than or equal to two. Finally, some open problems in the treatment of more realistic models are discussed.
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References
For a recent presentation of the subject, see e.g. On Growth and Form ,H. E. Stanley and N. Ostrowski eds., M. Nijhoff, Dordrecht (1986)
H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and Precipitation ,Reidel, Dordrecht (1978)
S. K. Friedlander, Smoke, Dust and Haze ,Wiley, New-York (1977)
P. J. Flory, Principles of Polymer Chemistry ,Cornell University, Ithaca, New-York (1953)
W. H. Stockmayer, J. Chem. Phys. 11, 45 (1043)
G. B. Field and W. C. Saslow, Astrophys. J. 142, 568 (1065)
J. Silk and S. D. White, Astrophys. J. 223, L59 (1978)
F. W. Wiegel and A. S. Perelson, J. Stat. Phys. 29, 813 (1982)
P. Meakin, Phys. Rev. Lett. 51, 1119 (1983)
M. Kolb, R. Botet and R. Jul lien, Phys. Rev. Lett. 51. 1123 (1983)
R. Jullien and M. Kolb, J. Phys. A: Math. Gen. 17, L639 (1984)
D. Weitz and M.Oliveira, Phys. Rev. Lett. 52, 1433 (1084)
D. W. Schaefer, J. Martin, P. Wiltzius and D. S. Cannell, Phys. Rev. Lett. 52, 2371 (1984)
D. Weitz, J. S. Huang, M. Y. Lin and J. Sung, Phys. Rev. Lett. 54, 1416 (1085)
K. Kang and S. Redner, Phys. Rev. A30, 2833 (1984)
K. Kang and S. Redner, Phys. Rev. A32, 435 (1985)
P. G. J. van Dongen and M. H. Ernst, Phys. Rev. Lett. 54, 1306 (1085)
S. K. Friedlander, J. Meteor. 17, 373 (1060)
S. K. Friedlander, J. Meteor. 17, 470 (1060)
T. Vicsek and F. Family, Phys. Rev. Lett. 52, 1660 (1084)
F. Leyvraz and H. R. Tschudi, J. Phys. A: Math. Gen. 14, 3380 (1081)
F. Leyvraz and H. R. Tschudi, J. Phys. A: Math. Gen. 15, 1951 (1082)
F. Leyvraz, J. Phys. A: Math. Gen. 16, 2661 (1983)
E. H. Hendriks, M. H. Ernst and R. M. Ziff, J. Stat. Phys. 31, 519 (1983)
P. G. J. van Dongen, J. Stat. Phys. 44, 785 (1086)
M. v. Smoluchowski, Phys. Z. 17, 593 (1016)
R. Jullien, M. Kolb and R. Botet in Kinetics of Aggregation and Gelation ,F. Family and D. P. Landau eds., Elsevier, North Holland, Amsterdam (1084)
W. D. Brown and R. C. Ball, J. Phys. A: Math. Gen. 18, L517 (1985)
R. C. Ball, D. Weitz, T. Witten and F. Leyvraz, Phys. Rev. Lett. 58, 274 (1087)
L. Peliti, J. Phys. A: Math. Gen. 19, 973 (1986)
K. Kang, S. Redner, P. Meakin and F. Leyvraz, Phys. Rev. A31, 1171 (1986)
R. Kopelman, P. W. Klymko, J. S. Newhouse and L. W. Anacker, Phys. Rev. B 29, 3747 (1984)
P. Meakin and H. E. Stanley, J. Phys. A: Math. Gen. 17, L173 (1984)
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© 1988 Kluwer Academic Publishers
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Leyvraz, F. (1988). Reaction Kinetics for Diffusion Controlled Aggregation. In: Amann, A., Cederbaum, L.S., Gans, W. (eds) Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics. NATO ASI Series, vol 235. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3005-6_4
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DOI: https://doi.org/10.1007/978-94-009-3005-6_4
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