Comparison of diffraction and diffusion measurements in porous media

Abstract

Two manifestations of diffractive behavior in diffusion in a porous medium are reviewed. The measured amplitude, M ( q , t ), in a pulsed field gradient spin echo (PGSE) experiment probes the pore structure using two length scales, the gradient length q −1 and the diffusion length [D(t)t] 1 2 . For a suspension of monosized beads, M ( q , t ) shows a diffraction bump at a wave vector q = 2π 2R , R being the radius of the beads. For large q , M ( q , t ) is shown to be proportional to Γ(t)( S V p )q −4 , in analogy with the Debye-Porod law. Here Γ ( t ) is a time-dependent function that depends on details of the geometry, and S V p is the surface to volume ratio. Experiments on two different suspensions of beads of known sizes in the 500 and 50 μm range, respectively, are used as illustrations. In PGSE, the measured signal amplitude is amplified over that in phase-suppressed magnetic resonance imaging and X-ray diffraction because the sample volume is replaced by the volume enclosed by a diffusion length.