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.     

Time-dependence of nuclear magnetic resonance quadrupole interactions for polymers under shear

We consider the problem of performing NMR spectroscopy under conditions of flow, a central issue in Rheo-NMR. By way of example, the effects of rotational motion on the deuterium NMR spectrum are considered for Couette cell experiments involving deformation of polymers under shearing conditions. The polymer was modelled as a power law fluid and for each streamline, the spin Hamiltonian evolved to allow for flow reorientation. The gap-integral spectra are compared with the 'ideal' spectra for a polymer under shear, but without reorientation. It is found that flow does affect the shape of the deuterium spectra, as well as slightly perturbing the splittings.     

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.     

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.     

Propagator resolved transverse relaxation exchange spectroscopy

We present in this communication a novel propagator-resolved transverse relaxation exchange experiment. This experiment enhances the previous technique of transverse relaxation exchange by enabling spatial resolution. Hence, we are able to obtain separate, and remarkably different, T2-T2 exchange plots, corresponding to different spatial displacement of the spin bearing water molecules in a porous sand matrix. This experiment is the first to combine two inverse Laplace dimensions with a Fourier dimension, opening the door to a host of new experiments combining Fourier and inverse Laplace spectroscopy.     

Measurement of multilamellar onion dimensions under shear using frequency domain pulsed gradient NMR

We present a simple method by which the dimensions of shear-induced multilamellar vesicles (MLVs), also known as onions, can be measured during the shearing process itself. This approach is based on the use of a closely spaced train of magnetic field gradient pulses applied during a CPMG echo sequence. The CPMG train compensates flow effects while the frequency-dependence of apparent diffusion can reveal the onion size. We present here a simple phenomenological model for restricted diffusion in multilamellar vesicles, which may be used to interpret the resulting diffusion spectrum. We demonstrate this approach with MLVs formed from the lamellar phase of sodium dodecyl sulfate (SDS) in water and octanol.     

Effect of shear on an onion texture

Lamellar systems are self-assemblies of surfactant molecules forming planar bilayers separated by layers of solvent. At sufficiently high shear rates, they are known to form spherical objects often referred to as onions. In this paper, we are concerned with the effect of shear on those multi-lamellar vesicles. We measure solvent diffusion by nuclear magnetic resonance (NMR) using a method which is sensitive to the time dependence of mean-squared displacements. This method, combined with NMR velocimetry, allows us to infer onion structure as a function of shear rate, identifying different regimes in which local viscosity is related to the onion size. The role of slip is examined and the stress dependence of wall slip velocities is determined.     

Transient wave behaviour over an underwater sliding hump from experiments and analytical and numerical modelling

Flume measurements of a one-dimensional sliding hump starting from rest in quiescence fresh water indicate that when the hump travels at speed less than the shallow-water wave celerity, three waves emerge, travelling in two directions. One wave travels in the opposite direction to the sliding hump at approximately the shallow-water wave celerity (backward free wave). Another wave travels approximately in step with the hump (forced wave), and the remaining wave travels in the direction of the hump at approximately the shallow-water wave celerity (forward free wave). These experiments were completed for a range of sliding hump speed relative to the shallow-water wave celerity, up to unity of this ratio, to investigate possible derivation from solutions of the Euler equation with non-linear and non-hydrostatic terms being included or excluded. For the experimental arrangements tested, the forced waves were negative (depression or reduced water surface elevation) waves while the free waves were positive (bulges or increased water surface elevation). For experiments where the sliding hump travelled at less than 80% of the shallow-water wave celerity did not include transient behaviour measurements (i.e. when the three waves still overlapped). The three wave framework was partially supported by these measurements in that the separated forward and forced waves were compared to measurements. For the laboratory scale experiments, the forward free wave height was predicted reasonably by the long-wave equation (ignoring non-linear and non-hydrostatic terms) when the sliding hump speed was less than 80% of the shallow-water wave celerity. The forced wave depression magnitude required the Euler equations for all hump speed tested. The long-wave solution, while being valid in a limited parameter range, does predict the existence of the three waves as found in these experiments (forward travelling waves measured quantitatively while the backward travelling waves visually by video). Nevertheless, the forced wave transient development required non-linear and non-hydrostatic terms for higher sliding hump speeds. The forward free wave, controversially, does not need non-linear and non-hydrostatic terms until much higher hump speeds, suggesting that the forward free wave falls in the parameter space where long-wave equations apply whereas the forced wave more often falls into the parameter space requiring non-linear and non-hydrostatic terms. It does raise the question of why the forced wave transient dynamics does not impact on the initial transient dynamics where the forward free wave is in the long-wave theory, escaping the forced wave (at least for speeds less than 80% of the shallow-water wave celerity).     

Two-dimensional NMR spectroscopy in Earth's magnetic field

We demonstrate the first two-dimensional correlation NMR (COSY) spectra obtained at ultra low frequencies (ULF) using the Earth's magnetic field. Using a specially developed spectrometer with multiple audio-frequency pulses under controlled pulse phase, we observe magnetisation transfer arising from heteronuclear J-couplings in trifluoroethanol and para-difluorobenzene. The 2D COSY spectra exhibit all diagonal and off-diagonal multiplets consistent with known J-couplings in these molecules.