Modeling fluid polarization during flow in a non-uniform polarization field

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 L_m^⁎. By comparing water flow experiments on a 0.9 m long Halbach magnet array with simulations using the Bloch-Torrey equation, we determined that L_m^⁎ is given by the integral along flow direction x of the normalized axial polarization field distribution, p(x) = B₀(x)/B₀(x_ROI), in which x_ROI is the center of the polarization magnet. The fluid magnetization level M_z in a region-of-interest located at xROI is a function of the ratio s = vT₁/L_m^⁎ and can be generally expressed as M_z,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.