The diffusion-limited reaction A+B→0 on a fractal substrate

LM Sander — 2007-08-16T19:17:42-00:00

Journal of Stat. Phys., Vol. 65 (December 1991), pp. 919-924.

We show in this paper how the segregation of reactants in the diffusion-limited reaction A+B→0 on a fractal substrate arises. For spectral dimensions d s ⩽ 2 we obtain segregation controlled by the source and/or the intrinsic lifetime of the particles.

Steady-state diffusion-controlled A+A-->0 reaction in Euclidean and fractal dimensions: Rate laws and particle self-ordering

Eric Clément — 2007-08-16T18:04:22-00:00

Physical Review A, Vol. 39, No. 12. (15 June 1989), 6472.

For diffusion-limited reactions of the type A+A→0; we present a theory for the pair correlation function and the macroscopic reaction law for the Euclidean dimensions d =1; 2; 3 and for self-similar fractal structures with spectral dimension such that 1≤ d s ≤2. In any dimension we define a length Λ ; which is the typical size of the depletion zone around each particle. Λ is expressed as a function of a fundamental size ξ= √ρD/R ; where ρ is the steady-state density; R the external source rate; and D the microscopic diffusion constant. For d s ≤2; we obtain the ‘‘fractal’’ reaction order X=1+2/ d s and a mesoscopic; density-dependent depletion zone around each particle. We give an interpretation of the particle self-ordering and anomalous rate laws in terms of the random-walk topological properties.

CiteULike: kopelman's Clément

The diffusion-limited reaction A+B→0 on a fractal substrate

Steady-state diffusion-controlled A+A-->0 reaction in Euclidean and fractal dimensions: Rate laws and particle self-ordering