Dispersion in Porous Bead Packs Studied by Velocity Exchange Spectroscopy
The use of Pulsed Gradient Spin Echo (PGSE) NMR to investigate flow in porous media is well established [1,2]. In particular, the Fourier Transformation of the echo attenuation with respect to the encoding wave vector yields the probability density of displacements, or the propagator. The shape of the propagator depends on the encoding time Δ, during which dispersion processes allow a sampling of different portions of the flow field by a given fluid particle. Using two pairs of gradient pulses in the PGSE experiment, separated by a mixing time τm, allows the examination of velocity fluctuations by comparing displacements during the two encoding intervals. In particular, Velocity Exchange Spectroscopy (VEXSY) [3–5] experiments can reveal the gradual transition to asymptotic behavior as the ratio of the exchange time to the correlation time is increased. Furthermore, the VEXSY results can be employed to calculate the conditional probabilities of velocities, a representation which is suitable to visualize the loss of correlations with increasing τm.
KeywordsConditional Probability Correlation Time Transverse Magnetization Gradient Pulse Bead Diameter
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