Abstract
We investigate the time-dependent diffusion coefficient, D(t)=〈(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)/ =1-(t+t+O[(t], where =4S/(9 √π ) and =-HS/(12)-(/)f(). Here is the diffusion constant of the bulk fluid, S/ is the surface area to pore volume ratio, H is the mean curvature of the smooth portions of the surface, is the length of a wedge of angle , 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/+..., and D(t) is defined as 〈(t)/(6t), where 〈(t) is the mean-square displacement of surviving walkers. When ρ≠0 we find that the coefficient of the √t term in the above equation is unchanged, while the coefficient of the linear term changes to +ρS/(6). Thus, data on D(t) and M(t) at short times may be used simultaneously to determine S/ and ρ. The limiting behavior of D(t) as ρ→∞ is also discussed.
- Received 17 November 1992
DOI:https://doi.org/10.1103/PhysRevB.47.8565
©1993 American Physical Society