Diffusion and reaction in heterogeneous media: Pore size distribution, relaxation times, and mean survival time

Journal Article · Fri Nov 01 04:00:00 EST 1991 · Journal of Chemical Physics; (United States)

DOI:https://doi.org/10.1063/1.461519· OSTI ID:5053796

Torquato, S; Avellaneda, M ^[1]

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1. Courant Institute of Mathematical Sciences, New York University, New York, New York (USA)

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 {ital T}{sub {ital n}} ({ital n}=1,2,...) and the mean survival time {tau} is considered for diffusion and reaction among {ital partially} absorbing traps with dimensionless surface rate constant {bar {kappa}}. The limits {bar {kappa}}={infinity} and {bar {kappa}}=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 {ital T}{sub 1} and mean survival time {tau} for arbitrary {bar {kappa}} are derived in terms of the {ital pore} {ital size} {ital distribution} {ital P}({delta}). Here {ital P}({delta}){ital d}{delta} is the probability that a randomly chosen point in the pore region lies at a distance {delta} and {delta}+{ital d}{delta} from the {ital nearest} point on the pore--trap interface. The aforementioned moments and hence the bounds on {ital T}{sub 1} and {tau} are evaluated for distributions of interpenetrable spherical traps. The length scales {l angle}{delta}{r angle} and {l angle}{delta}{sup 2}{r angle}{sup 1/2}, under certain conditions, can yield useful information about the times {ital T}{sub 1} and {tau}, underscoring the importance of experimentally measuring or theoretically determining the pore size distribution {ital P}({delta}). Moreover, rigorous relations between the relaxation times {ital T}{sub {ital n}} and the mean survival time are proved. One states that {tau} is a certain weighted sum over the {ital T}{sub {ital n}}, while another bounds {tau} from above and below in terms of the principal relaxation time {ital T}{sub 1}. Consequences of these relationships are examined for diffusion interior and exterior to distributions of spheres.

• OSTI ID: 5053796
• Journal Information: Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 95:9; ISSN JCPSA; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
BIOLOGY
CHEMICAL REACTIONS
DIFFUSION
DISTRIBUTION
FLUIDS
HETEROGENEOUS EFFECTS
MAGNETIC RESONANCE
MATERIALS
MOLECULES
NUCLEAR MAGNETIC RESONANCE
PHYSICS
POROSITY
POROUS MATERIALS
PROBABILITY
RANDOMNESS
RELAXATION
RESONANCE
SATURATION
SIZE