Diffusion and Reaction among Traps: Some Theoretical and Simulation Results

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 z (i.e., inverse trapping rate) and relaxation times T,, 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 ~c = oc and tc = 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 z 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 z and T I for the same models. We also describe a rigorous link between the mean survival time r and a different effective parameter of the system, namely the fluid permeability tensor k associated with Stokes flow through the same porous medium.