Asymptotic behavior of densities in diffusion-dominated annihilation reactions
Abstract
We obtain rigorous bounds on the long-time behavior of the densities ρA(t) and ρB(t) of species A and B, which diffuse and annihilate upon meeting, i.e., A+B-->inert. For equal initial densities ρA(0)=ρB(0), the density goes to zero asymptotically as t-d/4 for dimensions d<=4 and as t-1 for d>=4. When ρA(0)<ρB(0), ρA(t)~exp(-λ1 √t ), ρA(t)~exp(-λ2t/logt) for d=1,2, respectively, and ρA(t)~exp(-λdt) for d>=3.
- Publication:
-
Physical Review Letters
- Pub Date:
- November 1988
- DOI:
- 10.1103/PhysRevLett.61.2397
- Bibcode:
- 1988PhRvL..61.2397B
- Keywords:
-
- 05.20.-y;
- 82.20.-w;
- Classical statistical mechanics;
- Chemical kinetics and dynamics