Short-time behavior of the diffusion coefficient as a geometrical probe of porous media

Mitra, P. P., Sen, P. N., Schwartz, L. M. (1993) Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Physical Review B, 47 (14). pp. 8565-8574. ISSN 01631829 (ISSN)

URL: https://www.ncbi.nlm.nih.gov/pubmed/10004895
DOI: 10.1103/PhysRevB.47.8565

Abstract

We investigate the time-dependent diffusion coefficient, D(t)=r2(t)/(6t), of random walkers in porous media with piecewise-smooth pore-grain interfaces. D(t) is measured in pulsed-field-gradient spin-echo (PFGSE) experiments on fluid-saturated porous media. For reflecting boundary conditions at the interface we show that for short times D(t)/D0 =1-A0(D0t)1/2+B0D0t+O[(D0t)3/2], where A0=4S/(9 π VP) and B0=-HS/(12VP)-tsumi(Li/VP)f(φi). Here D0 is the diffusion constant of the bulk fluid, S/VP is the surface area to pore volume ratio, H is the mean curvature of the smooth portions of the surface, Li is the length of a wedge of angle φi, and the function f(φ) is defined below. More generally, we consider partially absorbing boundary conditions, where the absorption strength is controlled by a surface-relaxivity parameter ρ. Here, the density of walkers (i.e., the net magnetization) decays as M(t)=1-ρSt/VP+..., and D(t) is defined as r2(t)s/(6t), where r2(t)s is the mean-square displacement of surviving walkers. When ρ0 we find that the coefficient A0 of the D0t term in the above equation is unchanged, while the coefficient of the linear term changes to B0+ρS/(6VP). Thus, data on D(t) and M(t) at short times may be used simultaneously to determine S/VP and ρ. The limiting behavior of D(t) as ρ→ is also discussed. © 1993 The American Physical Society.

Item Type: Paper
Subjects: physics > biophysics
physics > biophysics > membrane dynamics
physics
physics > biophysics > pore dynamics
CSHL Authors:
Communities: CSHL labs > Mitra lab
Depositing User: CSHL Librarian
Date: 1993
Date Deposited: 02 Apr 2012 20:20
Last Modified: 10 Feb 2017 20:44
Related URLs:
URI: http://repository.cshl.edu/id/eprint/25864

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