Properties of the reaction front in a reversible A+B<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mo>⇌</mo></mrow><mrow><mi mathvariant="italic">g</mi></mrow><mrow><mi mathvariant="italic">k</mi></mrow></msubsup></mrow></math>C reaction-diffusion process

Bastien Chopard; Michel Droz; Theo Karapiperis; Zoltán Rácz

doi:10.1103/PhysRevE.47.R40

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Properties of the reaction front in a reversible A+B $⇌_{g}^{k}$ C reaction-diffusion process

Group for Parallel Computing, University of Geneva, 1211 Genève 4, Switzerland

Département de Physique Théorique, Université de Genève, 1211 Genève 4, Switzerland

Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland

Physics Department, Clarkson University, Potsdam, N.Y. 13676

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Phys. Rev. E 47, R40(R) – Published 1 January, 1993

DOI: https://doi.org/10.1103/PhysRevE.47.R40

Abstract

We study the properties of the reaction front formed in a reversible reaction-diffusion process, A+B $?_{g}^{k}$ C, with initially separated reagents. It is shown that the dynamics of the front can be described in terms of a crossover between ‘‘irreversible’’ scaling at short times (t≪ $g^{- 1}$ ) and ‘‘reversible’’ scaling at long times (t≫ $g^{- 1}$ ). The reversible regime is dominated by diffusion and the critical exponents characterizing the properties of the front are independent of dimension.

References (18)

L. Gálfi and Z. Rácz, Phys. Rev. A 38, 3151 (1988).
Y. E. Lee Koo, L. Li and R. Kopelman, Mol. Cryst. Liq. Cryst. 183, 187 (1990).
Z. Jiang and C. Ebner, Phys. Rev. A 42, 7483 (1990).
Y. E. Lee Koo and R. Kopelman, J. Stat. Phys. 65, 893 (1991).
B. Chopard and M. Droz, Europhys. Lett. 15, 459 (1991).
S. Cornell, B. Chopard and M. Droz, Phys. Rev. A 44, 4826 (1991).
H. Taitelbaum, S. Havlin, J. E. Kiefer, B. Trus and G. H. Weiss, J. Stat. Phys. 65, 873 (1991).
F. Leyvraz and S. Redner, Phys. Rev. Lett. 66, 2168 (1991); J. Stat. Phys. 65, 1043 (1991).
E. Ben-Naim and S. Redner, J. Phys. A 25, L575 (1992).
M. Araujo, S. Havlin, H. Larralde and H. E. Stanley, Phys. Rev. Lett. 68, 1791 (1992).
H. Larralde, M. Araujo, S. Havlin and H. E. Stanley, Phys. Rev. A 46, 855 (1992).
H. Taitelbaum, Y. E. Lee Koo, S. Havlin, R. Kopelman and G. H. Weiss, Phys. Rev. A 46, 2151 (1992).
J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).
G. T. Dee, J. Stat. Phys. 39, 705 (1985); Phys. Rev. Lett. 57, 275 (1986).
R. Kopelman, S. J. Parus and J. Prasad, Chem. Phys. 128, 209 (1988).
C. R. Doering and D. ben-Avraham, Phys. Rev. A 38, 3035 (1988); D. ben-Avraham and C. R. Doering, Phys. Rev. Lett. 62, 2563 (1989).
K. Lindenberg, B. J. West and R. Kopelman, Phys. Rev. A 42, 890 (1990).
B. Chopard and M. Droz, J. Stat. Phys. 64, 859 (1991).

[c1] L. Gálfi and Z. Rácz, Phys. Rev. A 38, 3151 (1988).

[c2] Y. E. Lee Koo, L. Li and R. Kopelman, Mol. Cryst. Liq. Cryst. 183, 187 (1990).

[c3] Z. Jiang and C. Ebner, Phys. Rev. A 42, 7483 (1990).

[c4] Y. E. Lee Koo and R. Kopelman, J. Stat. Phys. 65, 893 (1991).

[c5] B. Chopard and M. Droz, Europhys. Lett. 15, 459 (1991).

[c6] S. Cornell, B. Chopard and M. Droz, Phys. Rev. A 44, 4826 (1991).

[c7] H. Taitelbaum, S. Havlin, J. E. Kiefer, B. Trus and G. H. Weiss, J. Stat. Phys. 65, 873 (1991).

[c8] F. Leyvraz and S. Redner, Phys. Rev. Lett. 66, 2168 (1991); J. Stat. Phys. 65, 1043 (1991).

[c9] E. Ben-Naim and S. Redner, J. Phys. A 25, L575 (1992).

[c10] M. Araujo, S. Havlin, H. Larralde and H. E. Stanley, Phys. Rev. Lett. 68, 1791 (1992).

[c11] H. Larralde, M. Araujo, S. Havlin and H. E. Stanley, Phys. Rev. A 46, 855 (1992).

[c12] H. Taitelbaum, Y. E. Lee Koo, S. Havlin, R. Kopelman and G. H. Weiss, Phys. Rev. A 46, 2151 (1992).

[c13] J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).

[c14] G. T. Dee, J. Stat. Phys. 39, 705 (1985); Phys. Rev. Lett. 57, 275 (1986).

[c15] R. Kopelman, S. J. Parus and J. Prasad, Chem. Phys. 128, 209 (1988).

[c16] C. R. Doering and D. ben-Avraham, Phys. Rev. A 38, 3035 (1988); D. ben-Avraham and C. R. Doering, Phys. Rev. Lett. 62, 2563 (1989).

[c17] K. Lindenberg, B. J. West and R. Kopelman, Phys. Rev. A 42, 890 (1990).

[c18] B. Chopard and M. Droz, J. Stat. Phys. 64, 859 (1991).

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Properties of the reaction front in a reversible A+B $⇌_{g}^{k}$ C reaction-diffusion process

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Properties of the reaction front in a reversible A+B⇌gkC reaction-diffusion process

Abstract

References (18)

Properties of the reaction front in a reversible A+B $⇌_{g}^{k}$ C reaction-diffusion process