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

Stapf, Siegfried; Han, Song-I; Heine, Christian; Blümich, Bernhard

doi:10.1002/cmr.10021

Cited by 20 publications

(14 citation statements)

References 82 publications

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“…Finally, we would like to note that it may be possible to obtain more information from the signal attenuation curves by transforming the signal decay profiles into higher-dimensional joint probability density functions [23,18], which could suggest an alternative explanation to the origins of the predicted diffraction patterns by illustrating the correlations of molecular motion between the separate encoding intervals.…”

Section: Discussionmentioning

confidence: 99%

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MR diffusion–“diffraction” phenomenon in multi-pulse-field-gradient experiments

Özarslan

Basser

2007

Journal of Magnetic Resonance

142

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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.

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Section: Discussionmentioning

confidence: 99%

“…For a review of the more general N-PFG experiments and techniques of obtaining the features of spatiotemporal correlations of molecular motion, see[18].…”

mentioning

confidence: 99%

MR diffusion–“diffraction” phenomenon in multi-pulse-field-gradient experiments

Özarslan

Basser

2007

Journal of Magnetic Resonance

142

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“…Variants of this pulse sequence have been considered for and found useful in various applications. [3][4][5][6][7][8][9][10] The simplest version of such sequences employs only two pairs of gradients; a spin-echo version of this double-PFG sequence is shown in Fig. 1͑a͒.…”

Section: Introductionmentioning

confidence: 99%

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

Özarslan

Basser

2008

The Journal of Chemical Physics

128

206

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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.

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“…Multiple gradient methods provide the ability to determine multiple displacement directional correlations [16,57], velocity time and directional correlations [58], frequency dependent dispersion [59] and velocity autocorrelation functions [60,61]. In addition rapid 'single shot' techniques for the measurement of effective diffusion and flow provide the means to acquire complete data in the millisecond time scale to study transient behavior [62,63].…”

Section: Advanced Techniquesmentioning

confidence: 99%

Finla Technical Report DE-FG02-03ER63576

Seymour¹

2007

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The magnetic resonance microscopy (MRM) work at Montana State University has extended the imaging of a single biofilm in a 1 mm capillary reactor to correlate T 2 magnetic relaxation maps displaying biofilm structure with the corresponding velocity patterns in three dimensions in a Staphylococcus epidermidis biofilm fouled square capillary. A square duct geometry is chosen to provide correlation with existing experiments and simulations, as research bioreactors tend to be of square or rectangular cross section for optical or microelectrode access. The spatially resolved velocity data provide details on the impact of biofilm induced advection on mass transport from the bulk fluid to the biofilm and through the capillary bioreactor. These issues are of significant importance in biosensor and bioseparations applications based on microfluidics or 'lab on a chip' technology, as well as a model for a flow in fractured geological media. Extension of published work in Journal of Magnetic Resonance applied concepts from the theory of fluid mixing to quantify the secondary flows induced by the spatially heterogeneous biofilm. The secondary flows are measured to be 20% of the axial velocity and indicate a significant alteration of transport from the bulk fluid to the biomass from diffusive to convective dominated. A paper has been published in Biotechnology and Bioengineering detailing the experimental results and analysis. The impact of microbial activity, particularly surface attached biofilms, on the transport of fluids in porous systems is relevant to fields as seemingly diverse as geophysics and medicine. Few direct experimental data on the impact of bioactivity on transport dynamics in three-dimensional media are available due to sample opacity. Non-invasive magnetic resonance microscopy (MRM) directly measures length and time scale dependent dynamics in porous media. Our research demonstrates by direct measurement of the propagator, i.e. the displacement conditional probability or van Hove scattering function, the transition from normal to anomalous hydrodynamic dispersion as a function of bioactivity. The microbial activity transforms the porous media from a homogeneous to heterogeneous structure, increasing system complexity as defined in terms of dynamics. Continuous time random walk (CTRW) based fractional advection-diffusion equation (ADE) models which generate anomalous or fractional dynamics are compared to the measured dynamics in both the propagator displacement space and the Fourier reciprocal displacement wavelength space. The data provide insight into the application and development of fractional calculus based models and indicates their direct applicability to biofilm impacted porous media transport. A manuscript reporting these results was published in Physical Review Letters. Unsaturated flow in porous media has been analyzed using magnetic resonance (MR) propagator measurements of scale dependent displacement. The data show a change in dynamics from Gaussian to non-Gaussian. Velocity and pore distrib...

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

Cited by 20 publications

References 82 publications

MR diffusion–“diffraction” phenomenon in multi-pulse-field-gradient experiments

MR diffusion–“diffraction” phenomenon in multi-pulse-field-gradient experiments

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

Finla Technical Report DE-FG02-03ER63576

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