Diffraction-like effects in NMR diffusion studies of fluids in porous solids

THE transport of fluids in porous media is of importance in a wide range of areas, such as oil recovery, heterogeneous catalysis and biological perfusion. The pulsed gradient spin-echo (PGSE) NMR technique has been used for many years to characterize diffusion and flow in such systems. The analogy between NMR measurements in a field gradient and diffraction has been pointed out in the context of NMR imaging and, more recently, diffraction-like effects in the PGSE experiment have been discussed for diffusion in both impermeable and connected structures. The gradient pulse area plays the role of a wavevector, q, which can probe the structure in which the fluid diffuses. Here we report experimental confirmation of these predicted effects from proton NMR studies of a water-saturated, orientationally disordered, loosely packed array of monodisperse polystyrene spheres. The PGSE-NMR experiments may thus be used to provide an indirect, averaged image of the internal structure of porous solids at a resolution higher than that achievable with conventional NMR imaging. This is particularly advantageous for measurements on large samples, as the resolution available with the PGSE method depends only on the available range of gradient pulse amplitude and duration and is unconstrained by the factors determining resolution in conventional NMR imaging

Pore shapes, volume distribution and orientations in monodisperse granular assemblies

The complex mechanical behaviour of granular materials is commonly studied by considering the evolving particle contact network. An often overlooked feature is the influence of micro-scale geometric configuration of pores on the macroscopic response. This paper presents a series of tools to quantify the shape, volume distribution and orientation characteristics of the pore space. The proposed approach is compared against data extracted from physical and numerical experiments with monodisperse assemblies of spheres. Individual pores are represented by polyhedral pore unit cells obtained by combining the Delaunay tessellation with an algorithm for merging Delaunay cells based on the concept of maximal inscribed sphere, after Al-Raoush et al. (Soil Sci Soc Am J 67(6):1687–1700, 2003). A pore shape parameter is proposed that considers pore volume and surface, and is analytically related to the void ratio and the number of edges forming the polyhedral pore unit cell. The pore volume distribution is shown to be uniquely described by the analytical k-gamma distribution proposed by Aste and Di Matteo (Phys Rev E 77(2):021309, 2008). A pore orientation tensor is introduced to define the principal orientation of individual pore units. This is subsequently used to define a global orientation tensor that reveals an isotropic pore network for the reference monodisperse assemblies. The global orientation tensor is analytically expressed in terms of the parameters defining the pore volume distribution.Australian Research Council (Grant DP150104123