Position Displacement Correlations in Fluids from Magnetic-Resonance Gradient-Echo Shapes

A nuclear magnetic resonance technique providing slice-selected spatial distribution of fluid displacements is introduced and exemplified. This echo-shape analysis method exploits the fact that, in a pulsed-gradient spin-echo sequence, the phase encoding of the echo evolves from a position dependence at the start of this pulse to a displacement dependence at the echo peak. The shape of the forming echo is therefore determined by the joint probability distribution correlating initial particle positions with displacements occurring between the first and the second gradient pulses. This distribution may be directly extracted by Fourier analysis of the echo shape as a function of gradient level. This procedure provides efficient access to Lagrangian flow statistics, as is illustrated by application to Taylor-Couette flow. Agreement between experimental results and simulations demonstrates the suitability of this method for examining spatially heterogeneous flow and molecular transport processes.