### 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 q_{0}, followed by successive rephasing via gradients q_{1} and q_{2} at times t = Δ_{1} and t = Δ_{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}, Δ_{1}; R_{2}, Δ_{2}) for displacements R_{1} and R_{2} in times Δ_{1} and Δ_{2}, respectively. q_{1} and q_{2} may be in arbitrary directions. Assuming R_{1}∥R_{2}, the correlation coefficient ρ_{R1,R2} then reflects the time-history of the fluctuating velocities. The behavior of the cross moment 〈R_{1}(Δ_{1}) · R_{2}(Δ_{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 Δ_{1} is appropriately chosen to sample the short-time velocity field within the system, increasing Δ_{2} clearly shows the loss of correlation when the average fluid element displacement exceeds the bead diameter.

Original language | English |
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Pages (from-to) | 316-323 |

Number of pages | 8 |

Journal | Journal of Magnetic Resonance |

Volume | 137 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1999 |

### Keywords

- Flow
- Multiple rephasing
- Porous media
- Time correlation
- Two-dimensional propagators

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## Cite this

*Journal of Magnetic Resonance*,

*137*(2), 316-323. https://doi.org/10.1006/jmre.1998.1685