Abstract
We examine the long-time behavior of A+B→0 reaction-diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constantsD A andD B and initial concentrationsa 0 andb 0 of A's and B's. We divide the domain of the partial differential equations describing the problem into several regions in which they can be reduced to simpler, solvable equations, and we merge the solutions. Thus we derive general formulas for the concentration profiles outside the reaction zone, the location of the reaction zone center, and the total reaction rate. An asymptotic condition for the reaction front to be stationary is also derived. The properties of the reaction layer are studied in the mean-field approximation, and we show that not only the scaling exponents, but also the scaling functions are independent ofD A,D B,a 0 andb 0.
Similar content being viewed by others
References
Proceedings of the NIH Meeting on Models of Non-Classical Reaction Rates,J. Stat. Phys. 65(5/6) (1991).
L. Gálfi and Z. Rácz,Phys. Rev. A 38:3151 (1988).
Y. L. Koo and R. Kopelman,J. Stat. Phys. 65:893 (1991).
H. Taitelbaum, Y. E. L. Koo, S. Havlin, R. Kopelman, and G. H. WeissPhys. Rev. A 46:2151 (1992).
H. Taitelbaum, InDiffusion Processes: Experiment, Theory and Simulations, Andrzej Pękalski, ed. (Springer-Verlag, Berlin, 1994).
Z. Jiang and C. Ebner,Phys. Rev. A 42:7483 (1990).
S. Cornell,Phys. Rev. E 51:4055 (1995).
S. Cornell, M. Droz, and B. Chopard,Physica A 188:322 (1992).
S. Cornell, M. Droz, and B. Chopard,Phys. Rev. A 44:4826 (1991).
B. P. Lee and J. Cardy,Phys. Rev. E 50:R3287 (1994).
M. Howard and J. Cardy,J. Phys. A: Math. Gen. 28:3599 (1995).
B. P. Lee and J. Cardy,J. Stat. Phys. 80:971 (1995).
H. Taitelbaum, S. Havlin, J. E. Kiefer, B. Trus, and G. H. Weiss,J. Stat. Phys. 65:873 (1991).
H. Larralde, M. Araujo, S. Havlin, and H. E. Stanley,Phys. Rev. A 46: R6121 (1992).
H. Larralde, M. Araujo, S. Havlin, and H. E. Stanley,Phys. Rev. A 46:855 (1992).
S. Cornell and M. Droz,Phys. Rev. Lett. 70:3824 (1993).
S. Cornell, Z. Koza, and M. Droz,Phys. Rev. E 52:3500 (1995).
P. L. Krapivsky,Phys. Rev. E 51:4774 (1995).
E. Ben-Naim and S. Redner,J. Phys. A: Math. Gen. 28:L575 (1992).
S. Havlin, M. Araujo, H. Larralde, A Shehter, H. E. Stanley and P. Trunfio inDiffusion Processes: Experiment Theory and Simulations, Andrzej Pękalski, ed. (Springer-Verlag, Berlin, 1994).
Z. Koza and H. Taitelbaum, In preparation.
Y. L. Luke,Integrals of Bessel Functions (McGraw-Hill, New York, 1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koza, Z. The long-time behavior of initially separated A+B→0 reaction-diffusion systems with arbitrary diffusion constants. J Stat Phys 85, 179–191 (1996). https://doi.org/10.1007/BF02175561
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02175561