Theory and Simulation Framework for the Relaxation of Nuclear Spin Order in Porous Media

The theory of nuclear spin relaxation in a liquid permeating a solid structure of irregular geometry is examined. The effects of restricted diffusion and the demagnetizing field generated by an inhomogeneous distribution of magnetic susceptibility in the system are explored. A framework comprising Brownian Dynamics, average Hamiltonian theory, and Liouville-space spin dynamics is proposed for simulating nuclear spin relaxation in 3D models of random structures obtained from CT scans of actual samples. Simulations results are compared with experimental data. An analytical solution valid within approximation is also reported.