Formulation of Time Dependent Bloch NMR Equations for Computational Analyses of Nano Particles in Porous Media

Nuclear Magnetic Resonance (NMR) has been very useful in the study of pore size distribution of porous materials and in molecular recognition. Important properties of the porous media have been shown to be very much dependent on the T1 and T2 relaxation times. The NMR transverse magnetization carries information on the pores’ properties. This has been demonstrated by many experiments on porous media but analytical expressions showing the direct relationships between the pore features and the NMR parameters have been quite scarce in literature. In this study, formulation of time dependent Bloch NMR equation for computational analyses of nano particles in porous media has been presented. Since the nano particle is expected to be imaged in a nano-porous medium, we apply the transformation that makes the NMR transverse magnetization My (t) expressible in term of My (p) with porosity p(t) . Two new parameters which validate the transformation are properly defined in terms of the porosity, T1 and T2 relaxation parameters. The results obtained in this study can have applications in functional magnetic resonance imaging (fMRI), Petroleum exploration and well design, geological engineering and could be a frontier towards a very robust way of describing porousity and permeability in systems transporting particles of specific shape and form.