Under-sampling and compressed sensing of 3D spatially-resolved displacement propagators in porous media using APGSTE-RARE MRI.

A method for under-sampling and compressed sensing of 3D spatially-resolved propagators is presented and demonstrated for flow in a packed bed and a heterogeneous carbonate rock. By sampling only 12.5% of q,k-space, the experimental acquisition time was reduced by almost an order of magnitude. In particular, for both systems studied, a 3D image was acquired at 1 mm isotropic spatial resolution such that 134,400 local propagators were obtained. Data were acquired in ~1 h and ~11 h for the packed bed and rock, respectively. It is shown that spatial resolution and under-sampling using this implementation retains the quantitative nature of the propagator measurement, and differences between implementation of this measurement in two and three dimensions are identified. The potential for 3D spatially-resolved propagators to provide new insights into transport processes in porous media by characterisation of the statistical moments of the propagators is discussed.

Fast spatially-resolved T2 measurements with constant-gradient CPMG.

Speed of acquisition is paramount for the application of magnetic resonance to flow experiments through porous rocks. One popular method for imaging core floods is the spatially resolved T2 experiment which can separate fluids either by their viscosity contrast or by doping one fluid with a relaxation agent. Existing techniques for spatial-T2 may suffer from long acquisition times and eddy currents due to the pulsing of magnetic field gradients. Here, we propose a constant gradient method for 1d spatially-resolved T2 which embraces the speed of frequency encoding techniques and avoids eddy currents by the absence of any gradient ramps during the radio frequency (r.f.) pulse train. We provide the operating envelope for this kind of experiment, which is restricted due to the slice selectivity of the r.f. pulses in the presence of the magnetic field gradient. Additionally, we show that the effects of self-diffusion and the mixing of T1 and T2 contributions are manageable. As an illustration, we have applied this technique to an enhanced oil recovery experiment. The two fluid phases were tracked without any doping and with a time resolution of 40 s. In this case, the increased time resolution allowed us to observe dynamic flow phenomena such as fluid fingering and the calculation of the velocity of the fluid displacement fronts.

Heterogeneity of Network Structures and Water Dynamics in κ-Carrageenan Gels Probed by Nanoparticle Diffusometry.

A set of functionalized nanoparticles (PEGylated dendrimers, d = 2.8-11 nm) was used to probe the structural heterogeneity in Na+/K+ induced κ-carrageenan gels. The self-diffusion behavior of these nanoparticles as observed by 1H pulsed-field gradient NMR, fluorescence recovery after photobleaching, and raster image correlation spectroscopy revealed a fast and a slow component, pointing toward microstructural heterogeneity in the gel network. The self-diffusion behavior of the faster nanoparticles could be modeled with obstruction by a coarse network (average mesh size <100 nm), while the slower-diffusing nanoparticles are trapped in a dense network (lower mesh size limit of 4.6 nm). Overhauser dynamic nuclear polarization-enhanced NMR relaxometry revealed a reduced local solvent water diffusivity near 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO)-labeled nanoparticles trapped in the dense network, showing that heterogeneity in the physical network is also reflected in heterogeneous self-diffusivity of water. The observed heterogeneity in mesh sizes and in water self-diffusivity is of interest for understanding and modeling of transport through and release of solutes from heterogeneous biopolymer gels.

Acquisition of spatially-resolved displacement propagators using compressed sensing APGSTE-RARE MRI.

A method is presented for accelerating the acquisition of spatially-resolved displacement propagators via under-sampling of an Alternating Pulsed Gradient Stimulated Echo - Rapid Acquisition with Relaxation Enhancement (APGSTE-RARE) data acquisition with compressed sensing image reconstruction. The method was demonstrated with respect to the acquisition of 2D spatially-resolved displacement propagators of water flowing through a packed bed of hollow cylinders. The q,k-space was under-sampled according to variable-density pseudo-random sampling patterns. The quality of compressed sensing reconstructions of spatially-resolved propagators at a range of sampling fractions was assessed using the peak signal-to-noise ratio (PSNR) as a quality metric. Propagators of good quality (PSNR 33.2 dB) were reconstructed from only 6.25% of all data points in q,k-space, resulting in a reduction in the data acquisition time from 4 h to 14 min. The spatially-resolved propagators were reconstructed using both the total variation and nuclear norm sparsifying transforms; use of total variation resulted in a slightly higher quality of the reconstructed image in most cases. To illustrate the power of this method to characterise heterogeneous flow in porous media, the method is applied to the characterisation of flow in a vuggy carbonate rock.

Yielding and flow of cellulose microfibril dispersions in the presence of a charged polymer.

The shear flow of microfibrillated cellulose dispersions is still not wholly understood as a consequence of their multi-length-scale heterogeneity. We added carboxymethyl cellulose, a charged polymer, that makes cellulose microfibril dispersions more homogeneous at the submicron and macro scales. We then compared the yielding and flow behavior of these dispersions to that of typical thixotropic yield-stress fluids. Despite the apparent homogeneity of the dispersions, their flow velocity profiles in cone-plate geometry, as measured by rheo-MRI velocimetry, differ strongly from those observed for typical thixotropic model systems: the viscosity across the gap is not uniform, despite a flat stress field across the gap. We describe these velocity profiles with a nonlocal model, and attribute the non-locality to persistent micron-scale structural heterogeneity.

Complex Coacervate Core Micelles with Spectroscopic Labels for Diffusometric Probing of Biopolymer Networks.

We present the design, preparation, and characterization of two types of complex coacervate core micelles (C3Ms) with cross-linked cores and spectroscopic labels and demonstrate their use as diffusional probes to investigate the microstructure of percolating biopolymer networks. The first type consists of poly(allylamine hydrochloride) (PAH) and poly(ethylene oxide)-poly(methacrylic acid) (PEO-b-PMAA), labeled with ATTO 488 fluorescent dyes. We show that the size of these probes can be tuned by choosing the length of the PEO-PMAA chains. ATTO 488-labeled PEO113-PMAA15 micelles are very bright with 18 dye molecules incorporated into their cores. The second type is a (19)F-labeled micelle, for which we used PAH and a (19)F-labeled diblock copolymer tailor-made from poly(ethylene oxide)-poly(acrylic acid) (mPEO79-b-PAA14). These micelles contain approximately 4 wt % of (19)F and can be detected by (19)F NMR. The (19)F labels are placed at the end of a small spacer to allow for the necessary rotational mobility. We used these ATTO- and (19)F-labeled micelles to probe the microstructures of a transient gel (xanthan gum) and a cross-linked, heterogeneous gel (κ-carrageenan). For the transient gel, sensitive optical diffusometry methods, including fluorescence correlation spectroscopy, fluorescence recovery after photobleaching, and super-resolution single nanoparticle tracking, allowed us to measure the diffusion coefficient in networks with increasing density. From these measurements, we determined the diameters of the constituent xanthan fibers. In the heterogeneous κ-carrageenan gels, bimodal nanoparticle diffusion was observed, which is a signpost of microstructural heterogeneity of the network.

Reversible Temperature-Switching of Hydrogel Stiffness of Coassembled, Silk-Collagen-Like Hydrogels.

Recombinant protein polymers, which can combine different bioinspired self-assembly motifs in a well-defined block sequence, have large potential as building blocks for making complex, hierarchically structured materials. In this paper we demonstrate the stepwise formation of thermosensitive hydrogels by combination of two distinct, orthogonal self-assembly mechanisms. In the first step, fibers are coassembled from two recombinant protein polymers: (a) a symmetric silk-like block copolymer consisting of a central silk-like block flanked by two soluble random coil blocks and (b) an asymmetric silk-collagen-like block copolymer consisting of a central random-coil block flanked on one side by a silk-like block and on the other side a collagen-like block. In the second step, induced by cooling, the collagen-like blocks form triple helices and thereby cross-link the fibers, leading to hydrogels with a thermo-reversibly switchable stiffness. Our work demonstrates how complex self-assembled materials can be formed through careful control of the self-assembly pathway.

NMR nanoparticle diffusometry in hydrogels: enhancing sensitivity and selectivity.

From the diffusional behavior of nanoparticles in heterogeneous hydrogels, quantitative information about submicron structural features of the polymer matrix can be derived. Pulsed-gradient spin-echo NMR is often the method of choice because it measures diffusion of the whole ensemble of nanoparticles. However, in (1)H diffusion-ordered spectroscopy (DOSY), low-intensity nanoparticle signals have to be separated from a highly protonated background. To circumvent this, we prepared (19)F labeled, PEGylated, water-soluble dendritic nanoparticles with a (19)F loading of ~7 wt % to enable background free (19)F DOSY experiments. (19)F nanoparticle diffusometry was benchmarked against (1)H diffusion-T2 correlation spectroscopy (DRCOSY), which has a stronger signal separation potential than the commonly used (1)H DOSY experiment. We used bootstrap data resampling to estimate confidence intervals and stabilize 2D-Laplace inversion of DRCOSY data with high noise levels and artifacts, allowing quantitative diffusometry even at low magnetic field strengths (30 MHz). The employed methods offer significant advantages in terms of sensitivity and selectivity.