Time Correlations in Fluid Transport Obtained by Sequential Rephasing Gradient Pulses
✍ Scribed by Siegfried Stapf; Robin A. Damion; Ken J. Packer
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 138 KB
- Volume
- 137
- Category
- Article
- ISSN
- 1090-7807
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✦ Synopsis
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 q 0 , followed by successive rephasing via gradients q 1 and q 2 at times t ؍ ⌬ 1 and t ؍ ⌬ 2 , respectively, where q 0 ؉ q 1 ؉ q 2 ؍ 0. A two-dimensional Fourier transform with respect to q 1 and q 2 gives directly the joint probability density W 2 (R 1 , ⌬ 1 ; R 2 , ⌬ 2 ) for displacements R 1 and R 2 in times ⌬ 1 and ⌬ 2 , respectively. q 1 and q 2 may be in arbitrary directions. Assuming R 1 ʈR 2 , the correlation coefficient R1 ,R2 then reflects the time-history of the fluctuating velocities. The behavior of the cross moment ͗R 1 (⌬ 1 ) ⅐ R 2 (⌬ 2 )͘ 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 ⌬ 1 is appropriately chosen to sample the short-time velocity field within the system, increasing ⌬ 2 clearly shows the loss of correlation when the average fluid element displacement exceeds the bead diameter.
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