We investigate the time-dependent diffusion coefficient, D(t)=〈${\mathit{r}}^2$(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)/${\mathit{D}}_0$ =1-${\mathit{A}}_0$(${\mathit{D}}_0$t${)}^{1/2}$+${\mathit{B}}_0$${\mathit{D}}_0$t+O[(${\mathit{D}}_0$t${)}^{3/2}$], where ${\mathit{A}}_0$=4S/(9 √π ${\mathit{V}}_{\mathit{P}}$) and ${\mathit{B}}_0$=-HS/(12${\mathit{V}}_{\mathit{P}}$)-${\mathit{tsum}}_{\mathit{i}}$(${\mathit{L}}_{\mathit{i}}$/${\mathit{V}}_{\mathit{P}}$)f(${\mathrm{\phi }}_{\mathit{i}}$). Here ${\mathit{D}}_0$ is the diffusion constant of the bulk fluid, S/${\mathit{V}}_{\mathit{P}}$ is the surface area to pore volume ratio, H is the mean curvature of the smooth portions of the surface, ${\mathit{L}}_{\mathit{i}}$ is the length of a wedge of angle ${\mathrm{\phi }}_{\mathit{i}}$, 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/${\mathit{V}}_{\mathit{P}}$+..., and D(t) is defined as 〈${\mathit{r}}^2$(t)${\mathrm{〉}}_{\mathit{s}}$/(6t), where 〈${\mathit{r}}^2$(t)${\mathrm{〉}}_{\mathit{s}}$ is the mean-square displacement of surviving walkers. When ρ≠0 we find that the coefficient ${\mathit{A}}_0$ of the √${\mathit{D}}_0$t term in the above equation is unchanged, while the coefficient of the linear term changes to ${\mathit{B}}_0$+ρS/(6${\mathit{V}}_{\mathit{P}}$). Thus, data on D(t) and M(t) at short times may be used simultaneously to determine S/${\mathit{V}}_{\mathit{P}}$ 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