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.

Rheo-NMR studies of the behavior of a nematic liquid crystal in a low-shear-rate regime: the transition from director alignment to reorientation.

Deuterium NMR spectroscopy has been used to study the director dynamics of the nematic liquid-crystal system cetyl trimethylammonium bromide/D2O under the action of applied viscous torques. Shear forces were applied using a custom-built Couette cell that was introduced into an NMR superconducting magnet, so that its rotational axis was parallel to the magnetic field direction, along which the liquid-crystal director originally aligned. Subsequently, the inner cylinder of the cell was rotated continuously at different rates using a stepper motor. The resulting time evolution and ultimate steady-state orientation of the director, governed by the competition between the applied viscous torque with elastic and magnetic terms, was measured via observed changes in the deuterium spectrum. Using a simple gearbox allowed unprecedented access to a low-shear-rate regime in which, above a threshold shear rate, the director of part of the sample was observed to reorient, while the remaining part still aligned with the magnetic field. Subsequent increases in the applied rotational rate were found to increase the relative proportion of the orienting fraction. Spatially resolved NMR spectra showed that the orienting and field-aligned fractions formed separated bands across the gap of the Couette cell, with director reorientation being initiated at the moving inner wall. The behavior was found to be consistent with the often ignored variation in velocity gradient manifest across the gap of a cylindrical cell, so that as the angular frequency of the inner cylinder was increased the radial location of the critical shear rate required for reorientation traversed the gap. Once the applied rotational rate was sufficient to reorient the director of the entire sample, the dependence of the exhibited steady-state orientation on the average applied shear rate was measured. These results could be fitted to an analytical solution of the force-balance equation, made tractable by the assumption that the elasticity term was of minor significance and could be ignored. Additionally, the use of a numerical solution of the full force-balance equation, which explicitly includes elasticity and secondary flow and additionally allows the time evolution of the director orientation to be calculated, was investigated.

Pore characterization through propagator-resolved transverse relaxation exchange.

We use the propagator-resolved transverse relaxation exchange experiment to characterize the pore space and fluid behavior of water saturated, tight-packed quartz sand. The experiment uses T2 exchange plots to observe the number of molecules that shift their environment for a range of mixing times. The propagator dimension allows us to determine how far the molecules have moved. The peak intensities are integrated and then plotted as a function of displacement and mixing time. We also model our system using both a probabilistic pore-hopping simulation and a spreading Gaussian model. We use the results of these simulations to interpret the peak intensity plots. From this, we can estimate pore features such as characteristic time, pore radii, and interpore spacing. The tortuosity of the different pore sizes can then be calculated from these values.

The dependence on magnetic field strength of correlated internal gradient relaxation time distributions in heterogeneous materials.

Magnetic susceptibility differences in porous media produce local gradients within the pore space. At high magnetic fields, these inhomogeneities have the potential to greatly affect nuclear magnetic resonance measurements. We undertake a study using a new NMR technique to measure the internal gradients present in highly heterogeneous samples over a wide range of magnetic field strengths. Our results show that even at ultra-high fields there can exist signal at internal gradient strengths sufficiently small that techniques for suppressing unwanted side effects have the possibility to be used. Our findings encourage the use of these high and ultra-high field strengths for a broader range of samples. Our results also give experimental evidence to support the theory of internal gradient scaling as a function of field strength within pores.

Aging, yielding, and shear banding in soft colloidal glasses.

Soft colloidal interactions in colloidal glasses are modeled using suspensions of multiarm star polymers. Using a preshearing protocol that ensures a reproducible initial state ("rejuvenation" of the system), we report here the evolution of the flow curve from monotonically increasing to one dominated by a stress plateau, demonstrating a corresponding shear-banded state. Phenomenological understanding is provided through a scalar model that describes the free-energy landscape.

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.

Shear deformation of polymer melt observed via proton NMR: theory and experiment.

We here develop a theory for the effect of shearing flow on residual proton dipole-dipole interactions for polymer melts. The model is based on the use of correlation functions which derive from the return to origin probability for polymers reptating in the tube of surrounding constraints. Using Doi-Edwards theory we calculate the spin-echo response under equilibrium conditions and then consider the effect of a shearing flow which deforms the tube, finding that there exists a strong dependence of transverse relaxation on Weissenberg number. The results are compared with NMR measurements of shear-perturbed proton T2 relaxation in 494kDa poly (dimethylsiloxane).

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.

NMR measurement of nonlocal dispersion in complex flows.

The flow and diffusion driven separation of initially adjacent liquid molecules is known as dispersion. The primary physical quantity describing this process, the nonlocal dispersion tensor, provides insight regarding both the spatial and temporal correlations of molecular velocity fluctuations in complex flows. We here propose and demonstrate a nuclear magnetic resonance method for the measurement of this tensor, validating its implementation for the case of cylindrical Couette flow, and demonstrating its application to the study of fluid dispersion in a random bead pack.

Tracking pore to pore exchange using relaxation exchange spectroscopy.

We observe the movement of water over time between pores of differing sizes in Castlegate sandstone. To achieve this, we perform an NMR transverse relaxation exchange experiment for several mixing times. The resulting data are converted to 2D T2 distributions using a 2D inverse Laplace transform (ILT). We show for the first time that quantitative analysis of ILT distributions enables one to extract characteristic times for different pores sizes. This information is potentially useful for permeability determination as well as better understanding of exchange between specific pore subpopulations.

A mobile one-sided NMR sensor with a homogeneous magnetic field: the NMR-MOLE.

A new portable NMR sensor with a novel one-sided access magnet design, termed NMR-MOLE (MObile Lateral Explorer), has been characterised in terms of sensitivity and depth penetration. The magnet has been designed to be portable and create a volume with a relatively homogeneous magnetic field, 15,000 ppm over a region from 4 to 16 mm away from the probe, with maximum sensitivity at a depth of 10 mm. The proton NMR frequency is 3.3 MHz. We have demonstrated that with this approach a highly sensitive, portable, unilateral NMR sensor can be built. Such a design is especially suited for the characterisation of liquids in situations where unilateral or portable access is required.

Undulations and fluctuations in a lamellar phase lyotropic liquid crystal and their suppression by weak shear flow.

Using multi-echo pulsed gradient nuclear magnetic resonance (NMR) we measure the anisotropic diffusion of water molecules in the lamellar phase of lyotropic system composed of cetylpyridinium chloride/hexanol diluted in brine. The technique reveals the Fourier spectrum of the molecular velocity autocorrelation function, and its repetitive compensating nature permits effective measurement in the presence of shear flow. We show that under zero shear the phase is highly oriented and that both the amplitude and fluctuation correlation time of lamellar undulations can be measured. The suppression of undulations by weak shear is apparent. We further measure transverse lamellae permeability arising from defects.

Measurement of diffusion in the presence of shear flow.

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.

Rheo-NMR phenomena of wormlike micelles.

Using a combination of rheology and nuclear magnetic resonance (NMR) spectroscopy/velocimetry we demonstrate the existence of shear banding fluctuations under Couette flow of the micellar system 10% w/v cetylpyridinium chloride and sodium salicylate (CPyCl-NaSal) molar ratio 2 : 1 in 0.5 M NaCl in either HO or HO, using both time-averaged and real-time measurements. These shear banding fluctuations are consistent not only with the shear stress fluctuations observed in rheological measurements but also with fluctuations in the change of the constrained fraction of the amphiphile chain (Δ) observed in H-NMR spectroscopy experiments. Using H-NMR spectroscopy on a deuterated probe molecule (-decane) located in the wormlike micellar interior, direct measurement of the shear-induced nematic phase transition is reported.

NMR velocimetry studies of the steady-shear rheology of a concentrated hard-sphere colloidal system.

NMR velocimetry has been used to observe the steady-shear rheological behaviour of a concentrated suspension of hard-sphere like 370 nm diameter PMMA core-shell latex particles at the volume fraction phi = 0.46, the liquid core of the spheres rendering possible NMR observation of the particles themselves. Rheological measurements in a cone-and-plate geometry indicate that when aged (i.e. left at rest for two weeks), the material exhibits yield stress behaviour at very low shear rates. For shear rates greater than 1 s(-1) a transition to liquid-like behaviour was observed, leading to a rejuvenated fluid state which exhibits shear-thinning behaviour over a wide range of shear rates. A similar yield stress behaviour was reflected in NMR velocimetry measurements in a Couette geometry, where the solid-to liquid transition could be clearly observed. Under steady-state flow, the fluid state inside the radius at which yield stress was observed, exhibited shear-thinning behaviour with a power law exponent n slowly approaching unity with increasing shear rate. This behaviour has some similarities with a model of Derec et al. in which aging and rejuvenation effects compete. Substantial wall slip was observed both at the inner and at the outer wall, an effect which disappeared as the shear rate was increased. No radial particle migration from the high-shear region at the inner wall was observed.

Diffusion correlation NMR spectroscopic study of anisotropic diffusion of water in plant tissues.

The anisotropic diffusion of water in chive (Allium schoenoprasum) tissues has been investigated using two-dimensional nuclear magnetic resonance methods: diffusion-diffusion correlation spectroscopy and diffusion-relaxation correlation spectroscopy. Corresponding one-dimensional T2 and diffusion measurements confirm independently the results of the two-dimensional investigations. In particular the diffusion-diffusion correlation spectroscopy method proves to be very powerful in resolving the different components of the diffusion tensor at different sites in the sample.

Diffusion exchange NMR spectroscopic study of dextran exchange through polyelectrolyte multilayer capsules.

Diffusion exchange of dextran with molecular weights 4.4 and 77 kDa through polyelectrolyte multilayer (PEM) hollow capsules consisting of four bilayers of polystyrene sulfonate/polydiallyldimethylammonium chloride has been investigated using two-dimensional nuclear-magnetic-resonance methods: diffusion-diffusion exchange spectroscopy (DEXSY) and diffusion-relaxation correlation spectroscopy (DRCOSY). Results obtained in DRCOSY experiments show that the diffusion process of dextran 77 kDa exhibits an observation time dependence suggesting a diffusion behavior restricted by confinement. We find evidence for both single capsule and capsule aggregate states, with a partitioning of the 77-kDa dextran between the free and capsule states much larger than that suggested by volume fraction alone. Results from DEXSY experiments show that dextran 77 kDa is in diffusive exchange through the capsules with an exchange time of around 1 s. In contrast, the capsules have no detectable influence on the diffusion process of the dextran 4.4 kDa. This quantitative information may be used in designing PEM capsules as drug carriers.

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.

Diffusion-diffusion correlation and exchange as a signature for local order and dynamics.

We demonstrate the use of new two-dimensional nuclear magnetic resonance experiments in the examination of local diffusional anisotropy under conditions of global isotropy. The methods, known as diffusion-diffusion correlation spectroscopy and diffusion exchange spectroscopy, employ successive pairs of magnetic field gradient pulses, with signal analysis using two-dimensional inverse Laplace transformation. Diffusional anisotropy is measured for water molecules in a polydomain lamellar phase lyotropic liquid crystal, 40 wt % nonionic surfactant C10E3 (C10H21O(CH2CH2O)6H) in H2O.

Shear banding fluctuations and nematic order in wormlike micelles.

Using rapid NMR velocimetry we demonstrate the existence of shear band fluctuations in the Couette flow of the wormlike micelle system, 10% w/v cetylpyridinium chloride and sodium salicylate (molar ratio 2:1) in 0.5 M 2H2O NaCl brine. We show that the fluctuations may be either quasirandom or periodic, the fluctuation spectrum being similar to that observed in the stress. Despite the equilibrium fluid being far from an isotropic-nematic transition, deuterium NMR shows that the onset of shear banding is associated with a nematic micellar state whose order parameter depends on shear rate.