NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

Abstract

We consider analytical and numerical solution of NMR relaxation under the condition of surface relaxation in an equilateral triangular geometry. We present an analytical expression for the Green's function in this geometry. We calculate the transverse magnetic relaxation without magnetic gradients present, single-phase, both analytically and numerically. There is a very good match between the analytical and numerical results. We also show that the magnetic signal from an equilateral triangular geometry is qualitatively different from the known solution: plate, cylinder, and sphere, in the case of a nonuniform initial magnetization. Nonuniform magnetization close to the sharp corners makes the magnetic signal very fast multiexponential. This type of initial configuration fits qualitatively with the experimental results by Song (Phys.

Local boundary conditions for NMR-relaxation in digitized porous media

“…For random walk simulations to converge with high accuracy, the number of trajectories needs to be large, and the step-size (∆r) needs to be small, see [17,23] for details. However, as we illustrate here for digitized media, the way the true geometry is mapped onto for example a computed tomography (CT) digital image is of additional importance.…”

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A lattice Boltzmann‐BGK algorithm for a diffusion equation with Robin boundary condition—application to NMR relaxation

“…We have chosen an equilateral triangle [21], see Appendix A, for this purpose. The Robin boundary condition is a boundary value problem where only the combination of the flux and field is known at the surface.…”

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“…For an equilateral triangle, the calculation is a bit more involved, but the result can be expressed [21] as…”