Spatiotemporal correlations in transport processes determined by multiple pulsed field gradient experiments

PGSE NMR measurement of the non-local dispersion tensor for flow in porous media

The non-local dispersion tensor provides a fundamental description of velocity correlations and displacement information in a pre-asymptotic dispersive system. Here we describe in detail how PGSE NMR may be used to measure this tensor, outlining the pulse sequences needed for signal superposition, as well as the data analysis procedures. The sequence is inherently two-dimensional, the first dimension giving the displacement resolution, the second giving correlation information. The technique is verified against simulated echo attenuation data from a lattice-Boltzmann simulation.

Compartment shape anisotropy (CSA) revealed by double pulsed field gradient MR

The multiple scattering extensions of the pulsed field gradient (PFG) experiments can be used to characterize restriction-induced anisotropy at different length scales. In double-PFG acquisitions that involve two pairs of diffusion gradient pulses, the dependence of the MR signal attenuation on the angle between the two gradients is a signature of restriction that can be observed even at low gradient strengths. In this article, a comprehensive theoretical treatment of the double-PFG observation of restricted diffusion is presented. In the first part of the article, the problem is treated for arbitrarily shaped pores under idealized experimental conditions, comprising infinitesimally narrow gradient pulses with long separation times and long or vanishing mixing times. New insights are obtained when the treatment is applied to simple pore shapes of spheres, ellipsoids, and capped cylinders. The capped cylinder geometry is considered in the second part of the article where the solution for a double-PFG experiment with arbitrary experimental parameters is introduced. Although compartment shape anisotropy (CSA) is emphasized here, the findings of this article can be used in gleaning the volume, eccentricity, and orientation distribution function associated with ensembles of anisotropic compartments using double-PFG acquisitions with arbitrary experimental parameters.

Compartment size estimation with double wave vector diffusion-weighted imaging

Double wave vector diffusion weighting uses gradients along two different directions between excitation and acquisition. It has been shown theoretically that for restricted diffusion the signal amplitude in such an experiment can depend on the angle between the two gradient vectors. The highest amplitude is obtained with antiparallel orientation, and the amplitude difference between parallel and antiparallel gradient orientations depends on the compartment size. The validity of this description is experimentally tested for water between polymer beads, for radish, and for porcine spinal cord, using a clinical MR system with limited gradient strength. The results indicate that the phenomenon is observable; however, the size of the signal difference is considerably diminished when compared with theory. This is attributed to violations of the approximating conditions underlying the theoretical description and to free diffusion contributions. It is concluded that the effect could successfully be used as a basis for developing a new noninvasive method for assessing cell size.

Microscopic anisotropy revealed by NMR double pulsed field gradient experiments with arbitrary timing parameters

We consider a general double pulsed field gradient experiment with arbitrary experimental parameters and calculate an exact expression for the NMR signal attenuation from restricted geometries, which is valid at long wavelengths, i.e., when the product of the gyromagnetic ratio of the spins, the pulsed gradients' duration, and their magnitude is small compared to the reciprocal of the pore size. It is possible to observe microscopic anisotropy within the pore space induced by the boundaries of the pore, which can be used to differentiate restricted from free or multicompartmental diffusion and to estimate a characteristic pore dimension in the former case. Explicit solutions for diffusion taking place between parallel plates as well as in cylindrical and spherical pores are provided. In coherently packed cylindrical pores, it is possible to measure simultaneously the cylinders' orientation and diameter using small gradient strengths. The presence of orientational heterogeneity of cylinders is addressed, and a scheme for differentiating microscopic from ensemble anisotropy is proposed.

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.

A PGSE study of propane gas flow through model porous bead packs

We present a study of the probability density for molecular displacements of gas flowing through bead packs. The three bead packs to be described are composed of polydispersed porous PVC particles, 500 microm glass spheres, and 300 microm polystyrene spheres. A range of velocities (1 cm s(-1) to 1 m s(-1)) and observation times (3-500 ms), hence transport distances, are presented. For comparison we also measure the propagators for water flow in the polystyrene sphere pack. The exchange time between the moving and the stagnant portions of the flow is a strong function of the diffusion coefficient of the fluid. Comparing the propagators between water and propane flowing in similar porous media makes this clear. The gas propagators, for flowing and diffusing molecules, consistently show a feature at the average pore diameter. This feature has previously been observed for similar Peclet number studies in smaller monodispersed bead packs using liquids, but is now demonstrated for larger beads with gas. We analyze and discuss these propagators in the physically intuitive propagator space and also in the well-understood Fourier q space. The extension of NMR PGSE experiments to gas systems allows flow and diffusion information to be obtained over a wider range of length and time scales than with liquids, and also for a new range of physical environments and systems. Interactions between stochastic and deterministic motion are fundamental to the theoretical description of transport in porous media, and the time and length scale dependences are central to an understanding of the resultant dispersive motion.

Applications of controlled-flow laser-polarized xenon gas to porous and granular media study

We report initial NMR studies of continuous flow laser-polarized xenon gas, both in unrestricted tubing, and in a model porous media. The study uses Pulsed Gradient Spin Echo-based techniques in the gas-phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients. Pulsed Gradient Echo studies of continuous flow laser-polarized xenon gas in unrestricted tubing indicate clear diffraction minima resulting from a wide distribution of velocities in the flow field. The maximum velocity experienced in the flow can be calculated from this minimum, and is seen to agree with the information from the complete velocity spectrum, or motion propagator, as well as previously published images. The susceptibility of gas flows to parameters such as gas mixture content, and hence viscosity, are observed in experiments aimed at identifying clear structural features from echo attenuation plots of gas flow in porous media. Gas-phase NMR scattering, or position correlation flow-diffraction, previously clearly seen in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack is not so clear in experiments using a different gas mixture. A propagator analysis shows most gas in the sample remains close to static, while a small portion moves through a presumably near-unimpeded path at high velocities.

NMR visualization of displacement correlations for flow in porous media

The temporal correlations of velocities for both water and a water-glycerol mixture flowing through a random packings of monodisperse spherical particles have been investigated using two-dimensional nuclear magnetic resonance methods. By combining various flow rates, fluid viscosities, and bead sizes, a wide range of flow parameters has been covered, the dimensionless Peclet number ranging from 100 to 100 000. The velocity exchange spectroscopy (VEXSY) technique has been employed to measure the correlation between velocities during two intervals separated from each other by a mixing time tau(m). This time is made both large and small compared with the time constant tau(c), required for a fluid element possessing the average flow velocity to cover a distance equal to the characteristic size in the system, the bead diameter. The two-dimensional conditional probability of displacement resulting from the VEXSY method reveals the existence of different "subensembles" of molecules, including a slow moving pool whose displacement is dominated by Brownian motion, an intermediate ensemble whose velocities change little over the mixing time, and a fast flowing ensemble which loses correlation due to mechanical dispersion. We find that that the approach to asymptotic dispersion, as tau(c)/tau(m) increases, depends strongly on the Peclet number, the deviation of the velocity autocorrelation function from a monoexponential Ornstein-Uhlenbeck process becoming more pronounced with increasing Peclet number.