Propagator-resolved 2D exchange in porous media in the inhomogeneous magnetic field

We present a propagator-resolved 2D exchange spectroscopy technique for observing fluid motion in a porous medium. The susceptibility difference between the matrix and the fluid is exploited to produce an inhomogeneous internal magnetic field, causing the Larmor frequency to change as molecules migrate. We test our method using a randomly packed monodisperse 100 μm diameter glass bead matrix saturated with distilled water. Building upon previous 2D exchange spectroscopy work we add a displacement dimension which allows us to obtain 2D exchange spectra that are defined by both mixing time and spatial displacement rather than by mixing time alone. We also simulate our system using a Monte Carlo process in a random nonpenetrating monodisperse bead pack, finding good agreement with experiment. A simple analytic model is used to interpret the NMR data in terms of a characteristic length scale over which molecules must diffuse to sample the inhomogeneous field distribution.