Abstract
We study some properties of the A+B→C reaction-diffusion system with initially separated components, first analyzed by means of an asymptotic scaling argument by Gàlfi and Ràcz. We show that, in contrast to the asymptotic result that predicts that the rate of production of C goes liket −1, at early times it is shown to increase ast 1/2. Deviations from this behavior appear at times inversely proportional to the reaction constant. Analogous crossover properties appear in the kinetic behavior of the reaction front. A second part of the study is concerned with the same chemical reaction on a fractal surface. When the substrate is a percolation cluster at criticality, both the maximum production rate and the width of the reaction zone differ considerably from those for the homogeneous space.
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References
M. v. Smoluchowski,Z. Phys. Chem. 92:129 (1917).
S. A. Rice,Diffusion-Limited Reactions (Elsevier, Amsterdam, 1985).
A. A. Ovchinnikov and Ya. B. Zeldovich,Chem. Phys. 28:215 (1978).
D. Toussaint and F. Wilczek,J. Chem. Phys. 78:2642 (1983).
K. Kang and S. Redner,Phys. Rev. Lett. 52:955 (1984).
P. Meakin and H. E. Stanley,J. Phys. A 17:L173 (1984).
R. Kopelman,J. Stat. Phys. 42:201 (1986).
Y. L. Koo and R. Kopelman,J. Stat. Phys., this issue.
D. Avnir and M. Kagan,Nature 307:717 (1984), and references cited therein.
G. T. Dee,Phys. Rev. Lett. 57:275 (1986).
B. Heidel, C. M. Knobler, R. Hilfer, and R. Bruinsma,Phys. Rev. Lett. 60:2492 (1986).
R. E. Liesegang,Naturwiss. Wochensch. 11:353 (1896).
T. A. Witten and L. M. Sander,Phys. Rev. Lett. 47:1400 (1981).
K. F. Mueller,Science 225:1021 (1984).
R. A. Ball,Aust. Gemmol. 12:89 (1974).
L. Gàlfi and Z. Ràcz,Phys. Rev. A 38:3151 (1988).
Y. E. Koo, L. Li, and R. Kopelman,Mol. Cryst. Liq. Cryst. 183:187 (1990).
Z. Jiang and C. Ebner,Phys. Rev. A 42:7483 (1990).
D. Ben-Avraham and S. Havlin,J. Phys. A 15:L691 (1982).
S. Havlin, M. Dishon, J. E. Kiefer, and G. H. Weiss,Phys. Rev. Lett. 53:407 (1984).
S. Havlin and D. Ben-Avraham,Adv. Phys. 36:695 (1987).
F. J. Muzzio and J. M. Ottino,Phys. Rev. Lett. 63:47 (1989).
F. J. Muzzio and J. M. Ottino,Phys. Rev. A 40:7182 (1989).
F. J. Muzzio and J. M. Ottino,Phys. Rev. A 42:5873 (1990).
G. H. Weiss, R. Kopelman, and S. Havlin,Phys. Rev. A 39:466 (1989).
H. Taitelbaum, R. Kopelman, G. H. Weiss, and S. Havlin,Phys. Rev. A 41:3116 (1990).
R. Schoonover, D. Ben-Avraham, S. Havlin, R. Kopelman, and G. H. Weiss,Physica A 171:232 (1991).
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Taitelbaum, H., Havlin, S., Kiefer, J.E. et al. Some properties of the a+b → C reaction-diffusion system with initially separated components. J Stat Phys 65, 873–891 (1991). https://doi.org/10.1007/BF01049587
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DOI: https://doi.org/10.1007/BF01049587