Diffusion exchange NMR spectroscopy in inhomogeneous magnetic fields

Two-dimensional diffusion exchange experiments in the presence of a strong, static magnetic field gradient are presented. The experiments are performed in the stray field of a single sided NMR sensor with a proton Larmor frequency of 11.7 MHz. As a consequence of the strong and static magnetic field gradient the magnetization has contributions from different coherence pathways. In order to select the desired coherence pathways, a suitable phase cycling scheme is introduced. The pulse sequence is applied to study diffusion as well as the molecular exchange properties of organic solvents embedded in a mesoporous matrix consisting of a sieve of zeolites with a pore size of 0.8 nm and grain size of 2 μm. This pulse sequence extends the possibilities of the study of transport properties in porous media, with satisfying sensitivity in measurement times of a few hours, in a new generation of relatively inexpensive low-field NMR mobile devices.     

On the use of 2D correlation and exchange NMR spectroscopy in organic porous materials

Two-dimensional (2D) nuclear magnetic resonance (NMR) methods for the investigation of correlation and exchange have been introduced in recent years and have been applied to a range of different systems. Here, we report on the use of 2D NMR diffusion-diffusion correlation spectroscopy for the investigation of diffusion anisotropy in cellular plant tissues and of diffusion-diffusion exchange spectroscopy for the study of the diffusive exchange of dextran in a dispersion of polyelectrolyte multilayer hollow capsules. Furthermore, diffusion-relaxation correlation spectroscopy was applied to both systems.     

Initially linear echo-spacing dependence of 1/T2 measurements in many porous media with pore-scale inhomogeneous fields

For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, the increase R in R2=1/T2 for CPMG measurements is 1/3(taugammag)2D, where gamma is magnetogyric ratio, tau is the half the echo spacing TE, and D is the diffusion constant. For measurements on samples of porous media with pore fluids and without externally applied gradients there may still be significant pore-scale local inhomogeneous fields due to susceptibility differences, whose contributions to R2 depend on tau. Here, diffusion is not unrestricted nor is the field gradient constant. One class of approaches to this problem is to use an "effective gradient" or some kind of average gradient. Then, R2 is often plotted against tau2, with the effective gradient determined from the slope of some of the early points. In many cases, a replot of R2 against tau instead of tau2 shows a substantial straight-line interval, often including the earliest available points. In earlier work [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104; R.J.S. Brown, P. Fantazzini, Phys. Rev. B 47 (1993) 14823] these features were noted, and attention was called to the fact that very large changes in field and gradient are likely for a small part of the pore fluid over distances very much smaller than pore dimensions. A truncated Cauchy-Lorentz (C-L) distribution of local fields in the pore space was used to explain observations, giving reduced effects of diffusion because of the averaging properties of the C-L distribution, the truncation being at approximately +/-1/2chiB0, where chi is the susceptibility difference. It was also noted that, when there is a narrow range of pore size a, over a range of about 40 of the parameter xi=1/3chinua2/D, where nu is the frequency, R2 does not depend much on pore size a nor on diffusion constant D. Examples are shown where plots of R2 vs tau show better linear fits to the data for small tau values than do plots vs tau2. The present work shows that, if both grain-scale and sample-scale gradients are present for samples with narrow ranges of T2, it may be possible to identify the separate effects with the linear and quadratic coefficients in a second-order polynomial fit to the early data points. Of course, many porous media have wide pore size and T2 distributions and hence wide ranges of xi. For some of these wide distributions we have plotted R2 vs tau for signal percentiles, normalized to total signal for shortest tau, again showing initially linear tau-dependence even when available data do not cover the longest and/or shortest T2 values for alltau values. For the examples presented, both the intercepts and the initial slopes of the plots of R2 vs tau increase systematically with signal percentile, starting at smallest R2.     

Velocity autocorrelation spectra of fluid in porous media measured by the CPMG sequence and constant magnetic field gradient

Carr-Purcell-Meiboom-Gill (CPMG) train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency domain instead of in the time domain as with the two-pulse gradient spin echo. The frequency range of this novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO2) and provides comprehensive information about the molecular restricted motion as well as about the structure of the medium.     

Interactions between butterfly-shaped pulses in the inhomogeneous media

Pulse interactions affect pulse qualities during the propagation. Interactions between butterfly-shaped pulses are investigated to improve pulse qualities in the inhomogeneous media. In order to describe the interactions between butterfly-shaped pulses, analytic two-soliton solutions are derived. Based on those solutions, influences of corresponding parameters on pulse interactions are discussed. Methods to control the pulse interactions are suggested.     

Special features of the functional dependences of magnetic susceptibility of magnetic colloids in porous media

The frequency and temperature dependences of the magnetic susceptibility of magnetic colloids with large particle sizes placed in porous media have been found to be different from the similar dependences for bulk samples. The observed peculiarities can be explained by the influence of surface phenomena on the processes of relaxation of the magnetic moment of colloidal particles.     

A random field model for anomalous diffusion in heterogeneous porous media

Heterogeneity, as it occurs in porous media, is characterized in terms of a scaling exponent, or fractal dimension. A feature of primary interest for two-phase flow is the mixing length. This paper determines the relation between the scaling exponent for the heterogeneity and the scaling exponent which governs the mixing length. The analysis assumes a linear transport equation and uses random fields first in the characterization of the heterogeneity and second in the solution of the flow problem, in order to determine the mixing exponents. The scaling behavior changes from long-length-scale dominated to short-length-scale dominated at a critical value of the scaling exponent of the rock heterogeneity. The long-length-scale-dominated diffusion is anomalous.     

Imaging water fluxes in porous media by magnetic resonance imaging using D(2)O as a tracer

In this study, we investigate the usefulness of D(2)O as a conservative tracer for monitoring water flux by MRI in a heterogeneous sand column. The column consisted of a cylindrical 3x9-cm packing of fine sand in which an 8-mm diameter cylindrical obstacle was placed. Constant steady-state flux densities between J(w)=0.07 and 0.28 cm min(-1) corresponding to mean pore flow velocities between 0.20 and 0.79 cm min(-1) were imposed at the top of the sand column, and a constant hydraulic head of -39 cm was maintained at the lower boundary. We injected pulses of 0.01 M NiCl(2) and 55% D(2)O and monitored the motion of the tracer plumes by MRI using a fast spin echo sequence over a period of 20 min. We observed that the center of gravity of all plumes moved with the mean pore flow velocity, which showed that D(2)O behaves as a conservative tracer. The motion of the tracer plume at J(w)=0.14 cm min(-1) was validated by a numerical simulation using HYDRUS2D, which reproduced the experimentally observed behavior very satisfactorily.     

Single-scan 2D DOSY NMR spectroscopy

Spatial encoding is a particular kind of spin manipulation that enables the acquisition of multidimensional NMR spectra within a single scan. This encoding has been shown to possess a general applicability and to enable the completion of arbitrary nD NMR acquisitions within a single transient. The present study explores its potential towards the acquisition of 2D DOSY spectra, where the indirect dimension is meant to encode molecular displacements rather than a coherent spin evolution. We find that in its simplest form this extension shows similarities with methods that have been recently discussed for the single-scan acquisition of this kind of traces; still, a number of advantageous features are also evidenced by the “ultrafast” modality hereby introduced. The principles underlying the operation of this new single-scan 2D DOSY approach are discussed, its use is illustrated with a variety of sequences and of samples, the limitations of this new experiment are noted, and potential extensions of the methodology are mentioned.     

Extracting intergranular exchange coupling in perpendicular magnetic recording media

A micromagnetic numerical technique has been used to demonstrate how intergranular exchange coupling and intrinsic anisotropy field dispersion can be extracted from measuring two types of M-H curves. A realistic grain configuration formed by planar Voronoi cells is used to simulate perpendicular magnetic media. This technique effectively separates the effects of intergranular exchange coupling and anisotropy dispersion by finding their correlation to differentiated M-H curves with different initial magnetization states, even in the presence of thermal fluctuation. The validity of this method is investigated with a series of intergranular exchange couplings and anisotropy dispersions for different media thickness. A relationship between the auto-correlation function of an ac-erased sample and dispersion of the exchange interaction is demonstrated. Utilizing magnetization auto-correlation functions, the magnetic intergranular exchange coupling statistics show a correlation with the auto-correlation function shape in terms of zero-cross and undershoot values.     

Transition in the propagation mechanism during flame acceleration in porous media

The combustion of stoichiometric hydrogen-air at various initial pressures was investigated in a 7.62 cm square cross-section channel filled with 1.27 cm diameter beads. The flame time-of-arrival and pressure time history along the channel were obtained by ionization probes and piezoelectric pressure transducers. Flame acceleration was found to be very rapid, e.g. at an initial pressure of 45 kPa the flame achieves a velocity of over 600 m/s in roughly 0.3 m. It was determined that at this high speed a well defined planar shock wave precedes a thick reaction zone. It was also shown that there is a transition in the flame propagation mechanism, similar to that observed in an obstacle laden channel [G. Ciccarelli and C. Johansen, The role of shock-flame interactions on flame acceleration in an obstacle laden channel, Proc. 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems, Minsk, 2009]. By varying the initial pressure of the mixture, changes in the axial location of the transition between combustion propagation regimes was also observed. A soot foil technique was used to identify the transition in the propagation mechanism, as well as to provide information concerning the local flow field around the beads and the overall average flow direction.     

Thermodynamic and magnetic properties of the electron gas in the inhomogeneous magnetic field Hr−1

The nonrelativistic and relativistic energy eigenvalues of the electron in the inhomogeneous magnetic fieldH _z =Hr ⁻¹,r=(x ² +y ²)^1/2 are derived in a form displaying the explicit spin dependence. The possibility of magnetic hydrogen atom formation and the spontaneouse ⁺ e ⁻ pair creation following from these eigenvalues is mentioned. The expressions for pressure, energy, particle number and magnetic moment of an electron gas in this IMF are calculated in the degenerate limit. The possibility of spontaneous magnetisation,i.e., ferromagnetic behaviour, is established. Further, the pressure of the electron gas in the same type of fields is an order of magnitude higher than those in a homogeneous magnetic field and crossed homogeneous electric and magnetic fields for comparable field strengths.     

A heteronuclear intermolecular single-quantum coherence scheme for high-resolution 2D J-resolved 1H NMR spectra in inhomogeneous magnetic fields

Based on heteronuclear intermolecular single-quantum coherences between proton (¹H) and quadrupolar nuclei (i.e. deuterium ²H), a three-dimensional nuclear magnetic resonance (NMR) pulse sequence is proposed for recovering high-resolution two-dimensional J-resolved NMR spectra from samples mixed with a deuterated solvent in the presence of large magnetic field inhomogeneities. Benefitting from excitation of spins via two different radio frequency (RF) transmit channels, this sequence is suitable for applications in randomly large inhomogeneous fields and the solvent suppression generally required in homonuclear intermolecular multiple-quantum coherence approaches is no longer necessary. Systematic theoretical analyses are given based on the distant dipolar field treatment. Experiment on a sample of corn oil in deuterated acetone and ethyl 3-bromopropionate and acetone dissolved in DMSO-d₆ in a deshimmed field with severe inhomogeneous broadening is performed to show the feasibility and applicability of this sequence.     

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot’s system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space–time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.     

In situ observations by magnetic resonance imaging for formation and dissociation of tetrahydrofuran hydrate in porous media

Tetrahydrofuran (THF) hydrate has long been used as a substitute for methane hydrate in laboratory studies. This article investigated the formation and dissociation characteristics of THF hydrate in porous media simulated by various-sized quartz glass beads. The formation and dissociation processes of THF hydrate are observed using magnetic resonance imaging (MRI) technology. The hydrate saturation during the formation is obtained based on the MRI data. The experimental result suggests that the third surface has an effect on hydrate formation. THF hydrate crystals lean to form on the glass beads and in their adjacent area as well as from the wall of the sample container firstly. Furthermore, as the pore size diminishes, or as the formation temperature decreases, the nucleation gets easier and the formation processes faster. However, the dissociation rate is mostly dependent on the dissociation temperature rather than on the pore size.     

The heterogeneous distribution of the liquid phase in partially filled porous glasses and its effect on self-diffusion

The spatial distribution of the liquid phase in a typical, partially filled, porous glass (VitraPor #5) has been examined with the aid of magnetic resonance microscopy and field gradient nuclear magnetic resonance diffusometry techniques. The correlation length of the material turned out to be long enough to permit the visualization of the microscopic heterogeneity of the material by magnetic resonance imaging. Contrasts are dominated by transverse relaxation depending on local filling degree, which in turn depends on local microstructure. The bimodal heterogeneity of the latter was also visualized by scanning electron microscopy. The effect of heterogeneity on an effective diffusion coefficient has been examined for polar (water) and nonpolar (cyclohexane) molecules.     

Diffusion of oriented particles in porous media

Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.     

Theoretical analysis of porous radiant burners under 2-D radiation field using discrete ordinates method

This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners (PRBs). In the present work, a 2-D rectangular model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. The gas and the solid phases are considered in non-local thermal equilibrium and combustion in the porous medium is modeled by considering a non-uniform heat generation zone. The homogeneous porous media, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. The radiation effect in the gas flow is neglected but the conductive heat transfer is taken into account. In order to analyze the thermal characteristics of porous burners, the coupled energy equations for the gas and porous medium in steady condition are solved numerically and the discrete ordinates method (DOM) is used to obtain the distribution of radiative heat flux in the porous media. Finally, the effects of various parameters on the performance of porous radiant burners are examined. The present results are compared with some reported theoretical and experimental results by other investigators and good agreement is found.     

The effect of the properties of porous media on light scattering

Numerical wave-optical methods for light scattering simulations are used to asses the effect of porosity on the optical properties of paper coating. Both constant porosity profile and media with porosity contrast between layers at different depths are considered. We can predict optimal paper coating structures for both brightness and gloss from the results.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.