Time Correlations in Fluid Transport Obtained by Sequential Rephasing Gradient Pulses

We present a basic experiment by which the evolution of the displacement probability density (propagator) of static or flowing fluid in N successive time intervals is obtained by single labeling, coupled with multiple rephasing events during the course of a pulsed field-gradient sequence. We term this type of sequence SERPENT: SEquential Rephasing by Pulsed field-gradients Encoding N Time-intervals. Realizations of the SERPENT experiment for the case N = 2 which include spin echo, stimulated echo, and Carr-Purcell pulse sequences are suggested. They have in common a spatial spin-labeling of the initial magnetization by a gradient of area q0, followed by successive rephasing via gradients q1 and q2 at times t = Delta1 and t = Delta2, respectively, where q0 + q1 + q2 = 0. A two-dimensional Fourier transform with respect to q1 and q2 gives directly the joint probability density W2(R1, Delta1; R2, Delta2) for displacements R1 and R2 in times Delta1 and Delta2, respectively. q1 and q2 may be in arbitrary directions. Assuming R1 ||R2, the correlation coefficient rhoR1,R2 then reflects the time-history of the fluctuating velocities. The behavior of the cross moment can be obtained from either a full two-dimensional or a set of one-dimensional SERPENT measurements. Experimental results are presented for water flowing through a bed of packed glass beads. While Delta1 is appropriately chosen to sample the short-time velocity field within the system, increasing Delta2 clearly shows the loss of correlation when the average fluid element displacement exceeds the bead diameter. Copyright 1999 Academic Press.