Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-19T11:51:37.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling of Reaction Fronts in the Presence of Disorder

Published online by Cambridge University Press:  15 February 2011

Mariela Araujo
Mariela Araujo*
Affiliation:
Intevep S.A. Apartado 76343, Caracas 1070A. Venezuela
Get access

Abstract

A study of the dynamics of the reaction front that appears in diffusion-reaction systems of the form A + B → C with initially separated reactants in the presence of quenched disorder is presented. The scaling of the width of the front w is analyzed as a function of the “disorder strength” and the dimensionality of the system. It is shown that disorder strongly affects the width exponent α, ω tα even for d ≥ 2, where the mean field approximation is known to be valid. The scaling of the nearest neighbor distance, midpoint fluctuations and concentration profiles near the center of the front, are also studied.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 366: Symposium N – Dynamics in Small Confining Systems , 1994 , 403
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Gálfi, L. and Rácz, Z., Phys. Rev. A 38, 3151 (1988).Google Scholar
[2] Jiang, Z. and Ebner, C., Phys. Rev. A 42, 7483 (1990).Google Scholar
[3] Ben-Naim, E. and Redner, S., J. Phys. A 25, L575 (1992).Google Scholar
[4] Laxralde, H., Araujo, M., Havlin, S., and Stanley, H.E., Phys. Rev. A 46, 855 (1992).Google Scholar
[5] Taitelbaum, H., Havlin, S., Kiefer, J., Trus, B.L., and Weiss, G.H., J. Stat. Phys. 65, 873 (1991).Google Scholar
[6] Koo, Y.E., Li, L., and Kopelman, R., Mol. Cryst. Liq. Cryst. 183, 187 (1990); Y.E. Koo and R. Kopelman, J. Stat. Phys. 65, 893 (1991).Google Scholar
[7] Larralde, H., Araujo, M., Havlin, S. and Stanley, H.E., Phys. Rev. A 46, R6121 (1992).Google Scholar
[8] Cornell, S., Droz, M., and Chopard, B., Phys. Rev. A 44, 4826 (1991).Google Scholar
[9] Chopard, B., Droz, M., Kaxapiperis, T., and R~cz, Z., Phys. Rev. E 47, 40 (1993).Google Scholar
[10] Havlin, S., Araujo, M., Laxralde, H., Shehter, A. and Stanley, H.E., Fractals 1, 475 (1993).Google Scholar
[11] Araujo, M., Larralde, H., Havlin, S. and Stanley, H.E., Phys. Rev. Lett. 71 3592 (1993).Google Scholar
[12] Redner, S. and Leyvraz, F., J. Stat. Phys. 65, 1043 (1991); F. Leyvraz and S. Redner, Phys. Rev. A 46, 3132 (1992).Google Scholar
[13] Burlastsky, S. F.. Teor. Eskp. Kim. 14, 483 (1978); P. Meakin and H.E. Stanley, J. Phys. A 17, L173 (1984); K. Kang and S. Redner, Phys. Rev. Lett. 52, 955 (1984).Google Scholar
[14] Cornell, S., preprint 1994.Google Scholar
[15] Lee, B.P. and Cardy, J., preprint 1994.Google Scholar
[16] Avnir, D. and Kagan, M., Nature 307, 717 (1984); 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. Witten and L. Sander, Phys. Rev. Lett. 47, 1400 (1981); R. A Ball, Ausr. Gemmol. 12, 89 (1984).Google Scholar
[17] Havlin, S. and Ben-Avraham, D., Adv. in Phys. 36, 695 214 (1987).Google Scholar
[18] Taitelbaum, H. and Weiss, G.H., Phys. Rev. E, 50, 2357 (1994).Google Scholar