### Abstract

Diffusion and reaction in heterogeneous media plays an important role in a variety of processes arising in the physical and biological sciences. The determination of the relaxation times T_{n} (n = 1,2,...) and the mean survival time τ is considered for diffusion and reaction among partially absorbing traps with dimensionless surface rate constant κ̄. The limits κ̄= ∞ and κ̄ = 0 correspond to the diffusion-controlled case (i.e., perfect absorbers) and reaction-controlled case (i.e., perfect reflectors), respectively. Rigorous lower bounds on the principal (or largest) relaxation time T_{1} and mean survival time τ for arbitrary κ̄ are derived in terms of the pore size distribution P(δ). Here P(δ)dδ is the probability that a randomly chosen point in the pore region lies at a distance δ and δ + dδ from the nearest point on the pore-trap interface. The aforementioned moments and hence the bounds on T_{1} and τ are evaluated for distributions of interpenetrable spherical traps. The length scales 〈δ〉 and 〈δ^{2}〉^{1/2}, under certain conditions, can yield useful information about the times T_{1} and τ, underscoring the importance of experimentally measuring or theoretically determining the pore size distribution P(δ). Moreover, rigorous relations between the relaxation times T_{n} and the mean survival time are proved. One states that τ is a certain weighted sum over the T_{n}, while another bounds τ from above and below in terms of the principal relaxation time T_{1}. Consequences of these relationships are examined for diffusion interior and exterior to distributions of spheres. Finally, we note the connection between the times T_{1} and τ and the fluid permeability for flow through porous media, in light of a previously proved theorem, and nuclear magnetic resonance (NMR) relaxation in fluid-saturated porous media.

Original language | English (US) |
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Pages (from-to) | 6477-6489 |

Number of pages | 13 |

Journal | The Journal of Chemical Physics |

Volume | 95 |

Issue number | 9 |

DOIs | |

State | Published - 1991 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry