Time Correlations in Fluid Transport Obtained by Sequential Rephasing Gradient Pulses

Stapf, Siegfried; Damion, Robin A.; Packer, Ken J.

Abstract

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 = Δ1 and t = Δ2, 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, Δ1; R2, Δ2) for displacements R1 and R2 in times Δ1 and Δ2, respectively. q1 and q2 may be in arbitrary directions. Assuming R1∥R2, the correlation coefficient ρR1,R2 then reflects the time-history of the fluctuating velocities. The behavior of the cross moment 〈R1(Δ1) · R2(Δ2)〉 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 Δ1 is appropriately chosen to sample the short-time velocity field within the system, increasing Δ2 clearly shows the loss of correlation when the average fluid element displacement exceeds the bead diameter. © 1999 Academic Press.

Citation

Stapf, S., Damion, R. A., & Packer, K. J. (1999). Time Correlations in Fluid Transport Obtained by Sequential Rephasing Gradient Pulses. Journal of Magnetic Resonance, 137(2), 316-323. https://doi.org/10.1006/jmre.1998.1685

• Journal Article Type: Article
• Online Publication Date: May 25, 2002
• Publication Date: Apr 1, 1999
• Deposit Date: Dec 8, 2022
• Journal: Journal of Magnetic Resonance
• Print ISSN: 1090-7807
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 137
• Issue: 2
• Pages: 316-323
• DOI: https://doi.org/10.1006/jmre.1998.1685
• Public URL: https://nottingham-repository.worktribe.com/output/14321169
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S1090780798916858?via%3Dihub