Diffusion and Magnetic Relaxation in Computer Generated Model Porous Media

Abstract

Understanding various physical processes occurring inside porous media and how they are influenced by the geometry and disorder has attracted unabated attention for last several decades. Examples of porous media are naturally occurring rocks, biological cells, zeolites, intercalate compounds, and more recently discovered nano and meso tubes like MCM-4 1. Measurement of magnetic relaxation and diffusivity has been routinely used to extract information about the geometry and connectivity of these porous media. Many of the earlier work on porous media have dealt with models of highly consolidated structures ofnaturallyoccurringsandstonesandrocks1 whoseporositiescan beextremelylow. In this paper we have explored diffusion and magnetic relaxation in a class of two dimensional model porous media of relatively larger porosities with varying degree of nonuniformity and connectivity. One of the key features of these computer generated model porous media is that for a fixed porosity it is possible to generate structures with very different surface morphologies. These structures have very marked effect on the long time diffusion constant, These morphologies can be changed in a controlled manner which enables us to study transport and relaxation in a very systematic way. Nuclear magnetic relaxation has been widely used to extract information about the fluid saturated porous media. In a proton NMR experiment the rate of decay of magnetization depends on the characteristic length scales of the pore space and on the interactions at the pore grain interface. The additional interaction of protons with paramagnetic impurities located on the grain surface enhances the relaxation process. The continuum description of this process has traditionally been described through diffusion equation. The effect of the surface relaxers are taken into account through boundary condition at the pore surface. Long time ago Brownstein and Tarr2 made a very important observation that for very small pores the decay was multiexponential, the geometry of the pore being the decisive factor