Time-dependent velocities in porous media dispersive flow

Applications of optically detected MRI for enhanced contrast and penetration in metal

We report quantitative measurements using optically detected magnetic resonance imaging (MRI) for enhanced pH contrast and flow inside porous metals. Using a gadolinium chelate as the pH contrast agent, we show the response is 0.6s(-1) mM(-1) per pH unit at the ambient magnetic field for the pH range 6-8.5. A stopped flow scheme was used to directly measure T(1) relaxation time to determine the relaxivity. Flow profiles and images were obtained for a series of porous metals with different average pore sizes. The signal amplitudes and spatial distributions were compared. A clogged region in one of the samples was revealed using optically detected MRI but not optical imaging or scanning electron microscopy. These applications will significantly broaden the impact of optically detected MRI in chemical imaging and materials research.

Exchange relaxometry of flow at small Péclet numbers in a glass bead pack

In this paper we consider low Péclet number flow in bead packs. A series of relaxation exchange experiments has been conducted and evaluated by ILT analysis. In the resulting correlation maps, we observed a collapse of the signal and a translation towards smaller relaxation times with increasing flow rates, as well as a signal tilt with respect to the diagonal. In the discussion of the phenomena we present a mathematical theory for relaxation exchange experiments that considers both diffusive and advective transport. We perform simulations based on this theory and discuss them with respect to the conducted experiments.

The displacement correlation tensor: microstructure, ensemble anisotropy and curving fibers

Experiments with multiple diffusion wave vectors are known to carry more information than what is available from standard diffusion experiments. Here we consider a special case of this class of pulse sequences, the double wave vector diffusion experiment, and use the cumulant expansion of the signal to introduce the displacement correlation tensor. We discuss its physical interpretation and properties, noting in particular that its short time behavior allows determination of the surface to volume ratio of the pore space. We present a general expression for the displacement correlation tensor, and provide explicit expressions for a few model geometries. We then show that the scatter matrix characterizing the orientation distribution of an ensemble of cylinders is simply related to the displacement correlation tensor. This result is generalized to ensembles of pores with arbitrary shapes allowing a precise formulation of the influence of microstructural and ensemble anisotropy on the double wave vector diffusion signal in the Gaussian phase approximation. Finally, as a new application of the double wave vector diffusion signal, we analyze its behavior in a curving fiber, and suggest that the displacement correlation tensor may be used to estimate sub-voxel fiber curvature and deflection angle. The theoretical results are corroborated by computer simulations.

From single-pulsed field gradient to double-pulsed field gradient MR: gleaning new microstructural information and developing new forms of contrast in MRI

One of the hallmarks of diffusion NMR and MRI is its ability to utilize restricted diffusion to probe compartments much smaller than the excited volume or the MRI voxel, respectively, and to extract microstructural information from them. Single-pulsed field gradient (s-PFG) MR methodologies have been employed with great success to probe microstructures in various disciplines, ranging from chemistry to neuroscience. However, s-PFG MR also suffers from inherent shortcomings, especially when specimens are characterized by orientation or size distributions: in such cases, the microstructural information available from s-PFG experiments is limited or lost. Double-pulsed field gradient (d-PFG) MR methodology, an extension of s-PFG MR, has attracted attention owing to recent theoretical studies predicting that it can overcome certain inherent limitations of s-PFG MR. In this review, we survey the microstructural features that can be obtained from conventional s-PFG methods in the different q regimes, and highlight its limitations. The experimental aspects of d-PFG methodology are then presented, together with an overview of its theoretical underpinnings and a general framework for relating the MR signal decay and material microstructure, affording new microstructural parameters. We then discuss recent studies that have validated the theory using phantoms in which the ground truth is well known a priori, a crucial step prior to the application of d-PFG methodology in neuronal tissue. The experimental findings are in excellent agreement with the theoretical predictions and reveal, inter alia, zero-crossings of the signal decay, robustness towards size distributions and angular dependences of the signal decay from which accurate microstructural parameters, such as compartment size and even shape, can be extracted. Finally, we show some initial findings in d-PFG MR imaging. This review lays the foundation for future studies, in which accurate and novel microstructural information could be extracted from complex biological specimens, eventually leading to new forms of contrast in MRI.

Detecting diffusion-diffraction patterns in size distribution phantoms using double-pulsed field gradient NMR: Theory and experiments

NMR observable nuclei undergoing restricted diffusion within confining pores are important reporters for microstructural features of porous media including, inter-alia, biological tissues, emulsions and rocks. Diffusion NMR, and especially the single-pulsed field gradient (s-PFG) methodology, is one of the most important noninvasive tools for studying such opaque samples, enabling extraction of important microstructural information from diffusion-diffraction phenomena. However, when the pores are not monodisperse and are characterized by a size distribution, the diffusion-diffraction patterns disappear from the signal decay, and the relevant microstructural information is mostly lost. A recent theoretical study predicted that the diffusion-diffraction patterns in double-PFG (d-PFG) experiments have unique characteristics, such as zero-crossings, that make them more robust with respect to size distributions. In this study, we theoretically compared the signal decay arising from diffusion in isolated cylindrical pores characterized by lognormal size distributions in both s-PFG and d-PFG methodologies using a recently presented general framework for treating diffusion in NMR experiments. We showed the gradual loss of diffusion-diffraction patterns in broadening size distributions in s-PFG and the robustness of the zero-crossings in d-PFG even for very large standard deviations of the size distribution. We then performed s-PFG and d-PFG experiments on well-controlled size distribution phantoms in which the ground-truth is well-known a priori. We showed that the microstructural information, as manifested in the diffusion-diffraction patterns, is lost in the s-PFG experiments, whereas in d-PFG experiments the zero-crossings of the signal persist from which relevant microstructural information can be extracted. This study provides a proof of concept that d-PFG may be useful in obtaining important microstructural features in samples characterized by size distributions.

Measuring small compartmental dimensions with low-q angular double-PGSE NMR: The effect of experimental parameters on signal decay

In confined geometries, the MR signal attenuation obtained from single pulsed gradient spin echo (s-PGSE) experiments reflects the dimension of the compartment, and in some cases, its geometry. However, to measure compartment size, high q-values must be applied, requiring high gradient strengths and/or long pulse durations and diffusion times. The angular double PGSE (d-PGSE) experiment has been proposed as a means to extract dimensions of confined geometries using low q-values. In one realization of the d-PGSE experiment, the first gradient pair is fixed along the x-axis, and the orientation of the second gradient pair is varied in the X-Y plane. Such a measurement is sensitive to microscopic anisotropy induced by the boundaries of the restricting compartment, and allows extraction of the compartment dimension. In this study, we have juxtaposed angular d-PGSE experiments and simulations to extract sizes from well-characterized NMR phantoms consisting of water filled microcapillaries. We are able to accurately extract sizes of small compartments (5mum) using the angular d-PGSE experiment even when the short gradient pulse (SGP) approximation is violated and over a range of mixing and diffusion times. We conclude that the angular d-PGSE experiment may fill an important niche in characterizing compartment sizes in which restricted diffusion occurs.

The effect of experimental parameters on the signal decay in double-PGSE experiments: negative diffractions and enhancement of structural information

Double pulsed gradient spin echo (d-PGSE) experiment has been recently suggested for detecting microscopic anisotropy in macroscopically isotropic samples. This sequence is complex and has many variables, including, intra alia, combinations of directions and amplitudes of the pulsed gradients, diffusion times in each of the encoding periods and the mixing time period. The effect of these experimental parameters of the d-PGSE sequence was studied in an array of water filled microcapillaries of micron diameters. We found that negative diffractions occur, as indeed predicted by recently published simulations. We also found differential effects of prolongation of the mixing time between collinear and orthogonal d-PGSE experiments. The d-PGSE experiment in the collinear direction perpendicular to the long axis of the cylinder exhibited a marked dependence on the mixing time, while the orthogonal d-PGSE experiment exhibited no such dependence at all. Interestingly, one of the most important predictions by the simulations was that the d-PGSE sequence could potentially discriminate between compartments of different sizes better than the single PGSE (s-PGSE) and it seems that our experimental results indeed corroborate these predictions.

Some perspectives on dispersion and the use of ensemble-averaged PGSE NMR

Magnetic resonance methodology has made a significant impact in helping us understand the physics of porous media. Among an important class of experiments is that set of techniques designed to measure fluid dispersion. This paper provides some background on some of the underlying physics of dispersion, and outlines some of the NMR approaches that have proven successful. The local and nonlocal dispersion tensors are described and the prospects for future NMR advances considered.

Spatial dependence of dispersion

The use of Pulsed Gradient Spin Echo (PGSE) NMR to investigate flow in porous media is well established. Using two pairs of position-encoding pulses in the PGSE experiment gives the possibility of examining velocity fluctuations, by comparing displacements, during the two encoding intervals. This method may be used to measure the asymptotic dispersion coefficient as well as the Velocity Auto-Correlation Function (VACF) in porous media flow. Some examples of two-dimensional maps of density and velocity distributions are accompanied by the first attempt to perform localized measurements of flow dispersion in porous media.

Use of the second dimension in PGSE NMR studies of porous media

2-dimensional methods based on PGSE NMR may be used to correlate or separate molecular dynamical properties, or to elucidate fluctuations. These may utilize either the gradient (q-vector) domain, in which molecular displacements are measured, or the time domain, in which relaxation is measured, and may be analyzed by combinations of inverse Fourier or Laplace transforms. Existing methodologies are reviewed and new experiments proposed. In particular the use of diffusion-diffusion exchange and correlation analysis is demonstrated using the case of water diffusion in a lamellar phase liquid crystal.

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.