Modeling fluid polarization during flow in a non-uniform polarization field - Rutger Tromp; Leo Pel; David Smeulders (Journal of Magnetic Resonance Open, 2021)
A sample will undergo T1 relaxation at continuously changing applied magnetic field strengths when flowing from the Earth magnetic field outside an NMR instrument to the much stronger applied magnetic field inside an NMR instrument. The interaction between fluid flow, T1 relaxation and magnetic field distributions in the case of negligible T1 dispersion can be described by considering two length scales involved: the characteristic polarization length vT1, and the effective polarization magnet length Lm⁎. By comparing water flow experiments on a 0.9 m long Halbach magnet array with simulations using the Bloch-Torrey equation, we determined that Lm⁎ is given by the integral along flow direction x of the normalized axial polarization field distribution, p(x) = B0(x)/B0(xROI), in which xROI is the center of the polarization magnet. The fluid magnetization level Mz in a region-of-interest located at xROI is a function of the ratio s = vT1/Lm⁎ and can be generally expressed as Mz,ROI = M0⁎(s)[1–exp(-1/2 s)]. The effective equilibrium magnetization function M0⁎(s) was found to have both a sample independent contribution from the axial polarization field p(x) and a sample dependent contribution from the flow velocity profile at a given flow rate. In our experiments, the axial Halbach field was found to contribute with a weight of approximately 1/3 to M0⁎(s) and the remaining 2/3 wt is contributed by the flow velocity distribution. Based on this analysis, a set of general principles for magnetization build up modeling and online NMR instrument design has been derived.