NMR for Equilateral Triangular Geometry under Conditions of Surface Relaxivity - Analytical and Random Walk Solution

TL;DR

This paper develops analytical and numerical solutions for NMR relaxation in an equilateral triangular geometry with surface relaxivity, revealing unique magnetic signal behaviors and potential applications in chemical absorption modeling.

Contribution

It provides the first analytical Green's function for NMR relaxation in an equilateral triangle and compares it with numerical results, highlighting differences from other geometries.

Findings

Analytical Green's function derived for the triangular geometry.

Good agreement between analytical and numerical solutions.

Nonuniform initial magnetization causes rapid multi-exponential decay.

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. Non uniform magnetization close to the sharp corners makes the magnetic signal very fast multi exponential. This type of initial configuration fits qualitatively with the experimental results by Song et al.[1]. It should also be noted that the solution presented here can be used to describe absorption of a chemical substance in an equilateral triangular geometry (for a stationary fluid).