corner
corner
APS » Journals » Phys. Rev. E » Volume 77 » Issue 4
< Previous Article | Next Article >

Phys. Rev. E 77, 046103 (2008) [6 pages]

Exponential temporal asymptotics of the A+B→0 reaction-diffusion process with initially separated reactants

Download: PDF (378 kB) Buy this article Export: BibTeX or EndNote (RIS)

S. Kisilevich*
Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel

M. Sinder and J. Pelleg
Department of Materials Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel

V. Sokolovsky
Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel

Received 31 May 2007; revised 5 February 2008; published 2 April 2008

We study theoretically and numerically the irreversible A+B→0 reaction-diffusion process of initially separated reactants occupying the regions of lengths LA, LB comparable with the diffusion length (LA,LB∼√Dt, here D is the diffusion coefficient of the reactants). It is shown that the process can be divided into two stages in time. For t⪡L2∕D the front characteristics are described by the well-known power-law dependencies on time, whereas for t>L2∕D these are well-approximated by exponential laws. The reaction-diffusion process of about 0.5 of initial quantities of reactants is described by the obtained exponential laws. Our theoretical predictions show good agreement with numerical simulations.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.77.046103
DOI:
10.1103/PhysRevE.77.046103
PACS:
82.20.−w, 68.35.Fx

*Present address: Department of Information System Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel.

 
< Previous Article | Next Article >