Time correlations in fluid transport obtained by sequential rephasing gradient pulses

We present a basic experiment by which the evolution of the displacement pr obability density (propagator) of static or flowing fluid in N successive t ime intervals is obtained by single labeling, coupled with multiple rephasi ng events during the course of a pulsed field-gradient sequence. We term th is type of sequence SERPENT: SEquential Rephasing by Pulsed held-gradients Encoding N Time-intervals. Realizations of the SERPENT experiment for the c ase 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 q(0), followed by successive r ephasing via gradients q(1) and q(2) at times t = Delta(1) and t = Delta(2) , respectively, where q(0) + q(1) + q(2) = 0. A two-dimensional Fourier tra nsform with respect to q(1) and q(2) gives directly the joint probability d ensity W-2(R-1, Delta(1); R-2, Delta(2)) for displacements R-1 and R-2 in t imes Delta(1) and Delta(2), respectively. q(1) and q(2) may be in arbitrary directions. Assuming R(1)parallel to R-2, the correlation coefficient rho( R1,R2) then reflects the time-history of the fluctuating velocities. The be havior of the cross moment [R-1(Delta(1)).R-2(Delta(2))] can be obtained fr om either a full two-dimensional or a set of one-dimensional SERPENT measur ements. Experimental results are presented for water flowing through a bed of packed glass beads. While Delta(1) is appropriately chosen to sample the short-time velocity field within the system, increasing Delta(2) clearly s hows the loss of correlation when the average fluid element displacement ex ceeds the bead diameter. (C) 1999 Academic Press.