NMR Velocity Mapping of Couette Flow Using Oscillating Magnetic Field Gradients

Abstract

A method for obtaining spin-density distributions of selected layers in annular shear flow is introduced. A transverse rotating magnetic field gradient is generated by oscillating orthogonal gradients in quadrature. The equivalence of the frames of reference of a rotating sample with a fixed magnetic field gradient and a rotating magnetic field gradient with a fixed sample is demonstrated with modulation sideband patterns. When the magnetic field gradient and sample rotation frequency differ, sidebands appear at integer multiples of thedifferencebetween the two rotation frequencies. When the gradient is synchronized with the sample rotation, the spectrum is a spin-density projection of the sample onto the gradient. When the sample and gradient are counterrotating, high audio-frequency sidebands appear with consequent spectral simplification. When the orthogonal components used to generate the rotating gradient are imperfectly matched, sidebands appear at integer multiples of the sum and difference frequencies of Ωsand Ωg. A novel, low-cost electronic system is described to create the rotating gradient on a standard high-resolution spectrometer. Spectra of layers of fluid moving at a chosen angular frequency in a sample undergoing Couette flow shearing are shown. The radial fluid layer is selected by stroboscopically sampling with a Hahn-echo refocusing pulse applied at integer multiples of the rotation period. A two-dimensional analysis is given that separates the signal arising from the layer that is synchronized with the rotating gradient from the signals arising from the rest of the sample. Complex phase distortions occur when the echo delays do not match the rotation period. A radial frequency map of the Couette streamline flow is generated using the 2D technique which compares favorably with the calculated flow field.