Diffusion and reaction among traps: some theoretical and simulation results

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Abstract

Diffusion and reaction in heterogeneous media arise in a host of phenomena in the physical and biological sciences. The determination of the mean survival time τ (i.e., inverse trapping rate) and relaxation times Tn, n=1,2,3,... (i.e., inverse eigenvalues), associated with diffusion among partially absorbing, static traps with surface rate constant k are problems of long-standing interest. The limits k=∞ and k=0 correspond to the diffusion-controlled case (i.e., perfect absorbers) and reaction-controlled case (i.e., perfect reflectors), respectively. This paper reviews progress we have made on several basic aspects of this problem: (i) the formulation of rigorous bonding techniques and computational methodologies that enable one to estimate the mean survival time τ and principal relaxation time T1 (ii) the quantitative characterization of the microstructure of nontrivial continuum (i.e., off-lattice) models of heterogeneous media; and (iii) evaluation of τ and T1 for the same models. We also describe a rigorous link between the mean survival time t and a different effective parameter of the system, namely the fluid permeability tensor k associated with Stokes flow through the same porous medium.

Original languageEnglish (US)
Pages (from-to)1173-1206
Number of pages34
JournalJournal of Statistical Physics
Volume65
Issue number5-6
DOIs
StatePublished - Dec 1 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Diffusion
  • traps

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