Heterogeneous diffusion in aerobic granular sludge

Aerobic granular sludge (AGS) technology allows simultaneous nitrogen, phosphorus, and carbon removal in compact wastewater treatment processes. To operate, design, and model AGS reactors, it is essential to properly understand the diffusive transport within the granules. In this study, diffusive mass transfer within full‐scale and lab‐scale AGS was characterized with nuclear magnetic resonance (NMR) methods. Self‐diffusion coefficients of water inside the granules were determined with pulsed‐field gradient NMR, while the granule structure was visualized with NMR imaging. A reaction‐diffusion granule‐scale model was set up to evaluate the impact of heterogeneous diffusion on granule performance. The self‐diffusion coefficient of water in AGS was ∼70% of the self‐diffusion coefficient of free water. There was no significant difference between self‐diffusion in AGS from full‐scale treatment plants and from lab‐scale reactors. The results of the model showed that diffusional heterogeneity did not lead to a major change of flux into the granule (<1%). This study shows that differences between granular sludges and heterogeneity within granules have little impact on the kinetic properties of AGS. Thus, a relatively simple approach is sufficient to describe mass transport by diffusion into the granules.

Characterizing the structure of aerobic granular sludge using ultra-high field magnetic resonance

Despite aerobic granular sludge wastewater treatment plants operating around the world, our understanding of internal granule structure and its relation to treatment efficiency remains limited. This can be attributed in part to the drawbacks of time-consuming, labor-intensive, and invasive microscopy protocols which effectively restrict samples sizes and may introduce artefacts. Time-domain nuclear magnetic resonance (NMR) allows non-invasive measurements which describe internal structural features of opaque, complex materials like biofilms. NMR was used to image aerobic granules collected from five full-scale wastewater treatment plants in the Netherlands and United States, as well as laboratory granules and control beads. T₁ and T₂ relaxation-weighted images reveal heterogeneous structures that include high- and low-density biofilm regions, water-like voids, and solid-like inclusions. Channels larger than approximately 50 μm and connected to the bulk fluid were not visible. Both cluster and ring-like structures were observed with each granule source having a characteristic structural type. These structures, and their NMR relaxation behavior, were stable over several months of storage. These observations reveal the complex structures within aerobic granules from a range of sources and highlight the need for non-invasive characterization methods like NMR to be applied in the ongoing effort to correlate structure and function.

Microbial growth rates and local external mass transfer coefficients in a porous bed biofilm system measured by 19 F magnetic resonance imaging of structure, oxygen concentration, and flow velocity

¹⁹ F nuclear magnetic resonance (NMR) oximetry and ¹ H NMR velocimetry were used to noninvasively map oxygen concentrations and hydrodynamics in space and time in a model packed bed biofilm system in the presence and absence of flow. The development of a local oxygen sink associated with a single gel bead inoculated with respiring Escherichia coli was analyzed with a phenomenological model to determine the specific growth rate of the bacteria in situ, returning a value (0.66 hr^-1 ) that was close to that measured independently in planktonic culture (0.62 hr^-1 ). The decay of oxygen concentration in and around the microbiologically active bead was delayed and slower in experiments conducted under continuous flow in comparison to no-flow experiments. Concentration boundary layer thicknesses were determined and Sherwood numbers calculated to quantify external mass transfer resistance. Boundary layers were thicker in no-flow experiments compared to experiments with flow. Whereas the oxygen concentration profile across a reactive biofilm particle was symmetric in no-flow experiments, it was asymmetric with respect to flow direction in flow experiments with Sherwood numbers on the leading edge (Sh = 7) being larger than the trailing edge (Sh = 3.5). The magnitude of the experimental Sh was comparable to values predicted by a variety of correlations. These spatially resolved measurements of oxygen distribution in a geometrically complex model reveal in innovative detail the local coupling between microbial growth, oxygen consumption, and external mass transfer.

A two-region transport model for interpreting T1-T2 measurements in complex systems

A 1D two region coupled pore model with discrete pore coupling is developed to elucidate the eigenmode interactions in regions with different surface relaxivity. Numerical solution of the model and simulation of the correlation experiment for varying surface relaxivity, pore connectivity and pore size ratio indicate the role of negative eigenmodes and overlap of T₁ and T₂ eigenmodes in generating a time domain signal increase with inversion recovery time, t₁. The eigenmodes and eigenfunctions are considered in detail providing connection between the mathematical model and the diffusion dynamics and spin physics of the system. Physical systems, i.e. a microporous glass bead pack, a cyclopentane/water hydrate former, and beeswax, showing experimentally measured T₁-T₂ time domain signal rise are considered within the limitations of the model.

Non-invasive imaging of oxygen concentration in a complex in vitro biofilm infection model using 19 F MRI: Persistence of an oxygen sink despite prolonged antibiotic therapy

PURPOSE

Oxygen availability is a critical determinant of microbial biofilm activity and antibiotic susceptibility. However, measuring oxygen gradients in these systems remains difficult, with the standard microelectrode approach being both invasive and limited to single-point measurement. The goal of the study was to develop a ¹⁹ F MRI approach for 2D oxygen mapping in biofilm systems and to visualize oxygen consumption behavior in real time during antibiotic therapy.

METHODS

Oxygen-sensing beads were created by encapsulating an emulsion of oxygen-sensing fluorocarbon into alginate gel. Escherichia coli biofilms were grown in and on the alginate matrix, which was contained inside a packed bed column subjected to nutrient flow, mimicking the complex porous structure of human wound tissue, and subjected to antibiotic challenge.

RESULTS

The linear relationship between ¹⁹ F spin-lattice relaxation rate R₁ and local oxygen concentration permitted noninvasive spatial mapping of oxygen distribution in real time over the course of biofilm growth and subsequent antibiotic challenge. This technique was used to visualize persistence of microbial oxygen respiration during continuous gentamicin administration, providing a time series of complete spatial maps detailing the continued bacterial utilization of oxygen during prolonged chemotherapy in an in vitro biofilm model with complex spatial structure.

CONCLUSIONS

Antibiotic exposure temporarily causes oxygen consumption to enter a pseudosteady state wherein oxygen distribution becomes fixed; oxygen sink expansion resumes quickly after antibiotic clearance. This technique may provide valuable information for future investigations of biofilms by permitting the study of complex geometries (typical of in vivo biofilms) and facilitating noninvasive oxygen measurement.

Probing diffusion dynamics during hydrate formation by high field NMR relaxometry and diffusometry

High-field nuclear magnetic resonance (NMR) relaxometry and diffusometry along with magnetic resonance imaging were used to monitor phase transition molecular dynamics during hydrate formation occurring in water droplets dispersed in liquid cyclopentane. 1D T₂ relaxation measurements indicate the extent of hydrate formation as well as a reduction in water droplet size with progression of hydrate growth. MRI intensity maps and T₂ relaxation maps indicate spatially dependent hydrate formation rates due to the heterogeneity of the system. Spectrally resolved diffusion measurements indicate a reduction in the porosity of the hydrate agglomerate as the hydrate shell increases in thickness. A novel signal rise observed in two dimensional T₁-T₂ relaxation correlation experiments indicates complex diffusion dynamics due to coupling between regions with varying relaxation and diffusion. These results indicate the ability to monitor hydrate growth and phase transition molecular dynamics due to evolution of the porous hydrate agglomerate by means of high-field NMR.

Glass Dynamics and Domain Size in a Solvent-Polymer Weak Gel Measured by Multidimensional Magnetic Resonance Relaxometry and Diffusometry

Nuclear magnetic resonance measurements of rotational and translational molecular dynamics are applied to characterize the nanoscale dynamic heterogeneity of a physically cross-linked solvent-polymer system above and below the glass transition temperature. Measured rotational dynamics identify domains associated with regions of solidlike and liquidlike dynamics. Translational dynamics provide quantitative length and timescales of nanoscale heterogeneity due to polymer network cross-link density. Mean squared displacement measurements of the solvent provide microrheological characterization of the system and indicate glasslike caging dynamics both above and below the glass transition temperature.

Flow velocity maps measured by nuclear magnetic resonance in medical intravenous catheter needleless connectors

This work explains the motivation, advantages, and novel approach of using velocity magnetic resonance imaging (MRI) for studying the hydrodynamics in a complicated structural biomedical device such as an intravenous catheter needleless connector (NC). MRI was applied as a non-invasive and non-destructive technique to evaluate the fluid dynamics associated with various internal designs of the NC. Spatial velocity maps of fluid flow at specific locations within these medical devices were acquired. Dynamic MRI is demonstrated as an effective method to quantify flow patterns and fluid dynamic dependence on structural features of NCs. These spatial velocity maps could be used as a basis for groundtruthing computational fluid dynamics (CFD) methods that could impact the design of NCs.

NMR investigation of water diffusion in different biofilm structures

Mass transfer in biofilms is determined by diffusion. Different mostly invasive approaches have been used to measure diffusion coefficients in biofilms, however, data on heterogeneous biomass under realistic conditions is still missing. To non-invasively elucidate fluid-structure interactions in complex multispecies biofilms pulsed field gradient-nuclear magnetic resonance (PFG-NMR) was applied to measure the water diffusion in five different types of biomass aggregates: one type of sludge flocs, two types of biofilm, and two types of granules. Data analysis is an important issue when measuring heterogeneous systems and is shown to significantly influence the interpretation and understanding of water diffusion. With respect to numerical reproducibility and physico-chemical interpretation, different data processing methods were explored: (bi)-exponential data analysis and the Γ distribution model. Furthermore, the diffusion coefficient distribution in relation to relaxation was studied by D-T₂ maps obtained by 2D inverse Laplace transform (2D ILT). The results show that the effective diffusion coefficients for all biofilm samples ranged from 0.36 to 0.96 relative to that of water. NMR diffusion was linked to biofilm structure (e.g., biomass density, organic and inorganic matter) as observed by magnetic resonance imaging and to traditional biofilm parameters: diffusion was most restricted in granules with compact structures, and fast diffusion was found in heterotrophic biofilms with fluffy structures. The effective diffusion coefficients in the biomass were found to be broadly distributed because of internal biomass heterogeneities, such as gas bubbles, precipitates, and locally changing biofilm densities. Thus, estimations based on biofilm bulk properties in multispecies systems can be overestimated and mean diffusion coefficients might not be sufficiently informative to describe mass transport in biofilms and the near bulk.

Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation

We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference ([Formula: see text]) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold ([Formula: see text]), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop ([Formula: see text]). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.

Impact of Mineral Precipitation on Flow and Mixing in Porous Media Determined by Microcomputed Tomography and MRI

Precipitation reactions influence transport properties in porous media and can be coupled to advective and dispersive transport. For example, in subsurface environments, mixing of groundwater and injected solutions can induce mineral supersaturation of constituents and drive precipitation reactions. Magnetic resonance imaging (MRI) and microcomputed tomography (μ-CT) were employed as complementary techniques to evaluate advection, dispersion, and formation of precipitate in a 3D porous media flow cell. Two parallel fluids were flowed concentrically through packed glass beads under two relative flow rates with Na₂CO₃ and CaCl₂ in the inner and outer fluids, respectively. CaCO₃ became supersaturated and formed a precipitate at the mixing interface between the two solutions. Spatial maps of changing local velocity fields and dispersion in the flow cell were generated from MRI, while high resolution μ-CT imaging visualized the precipitate formed in the porous media. Formation of a precipitate minimized dispersive and advective transport between the two fluids and the shape of the precipitation front was influenced by the relative flow rates. This work demonstrates that the combined use of MRI and μ-CT can be highly complementary in the study of reactive transport processes in porous media.

Detecting Microbially Induced Calcite Precipitation in a Model Well-Bore Using Downhole Low-Field NMR

Microbially induced calcite precipitation (MICP) has been widely researched recently due to its relevance for subsurface engineering applications including sealing leakage pathways and permeability modification. These applications of MICP are inherently difficult to monitor nondestructively in time and space. Nuclear magnetic resonance (NMR) can characterize the pore size distributions, porosity, and permeability of subsurface formations. This investigation used a low-field NMR well-logging probe to monitor MICP in a sand-filled bioreactor, measuring NMR signal amplitude and T₂ relaxation over an 8 day experimental period. Following inoculation with the ureolytic bacteria, Sporosarcina pasteurii, and pulsed injections of urea and calcium substrate, the NMR measured water content in the reactor decreased to 76% of its initial value. T₂ relaxation distributions bifurcated from a single mode centered about approximately 650 ms into a fast decaying population (T₂ less than 10 ms) and a larger population with T₂ greater than 1000 ms. The combination of changes in pore volume and surface minerology accounts for the changes in the T₂ distributions. Destructive sampling confirmed final porosity was approximately 88% of the original value. These results indicate the low-field NMR well-logging probe is sensitive to the physical and chemical changes caused by MICP in a laboratory bioreactor.

In Situ Detection of Subsurface Biofilm Using Low-Field NMR: A Field Study

Subsurface biofilms are central to bioremediation of chemical contaminants in soil and groundwater whereby micro-organisms degrade or sequester environmental pollutants like nitrate, hydrocarbons, chlorinated solvents and heavy metals. Current methods to monitor subsurface biofilm growth in situ are indirect. Previous laboratory research conducted at MSU has indicated that low-field nuclear magnetic resonance (NMR) is sensitive to biofilm growth in porous media, where biofilm contributes a polymer gel-like phase and enhances T2 relaxation. Here we show that a small diameter NMR well logging tool can detect biofilm accumulation in the subsurface using the change in T2 relaxation behavior over time. T2 relaxation distributions were measured over an 18 day experimental period by two NMR probes, operating at approximately 275 kHz and 400 kHz, installed in 10.2 cm wells in an engineered field testing site. The mean log T2 relaxation times were reduced by 62% and 43%, respectively, while biofilm was cultivated in the soil surrounding each well. Biofilm growth was confirmed by bleaching and flushing the wells and observing the NMR signal's return to baseline. This result provides a direct and noninvasive method to spatiotemporally monitor biofilm accumulation in the subsurface.

Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry

Nuclear magnetic resonance (NMR) relaxometry is commonly used to provide lithology-independent porosity and pore-size estimates for petroleum resource evaluation based on fluid-phase signals. However in shales, substantial hydrogen content is associated with solid and fluid signals and both may be detected. Depending on the motional regime, the signal from the solids may be best described using either exponential or Gaussian decay functions. When the inverse Laplace transform, the standard method for analysis of NMR relaxometry results, is applied to data containing Gaussian decays, this can lead to physically unrealistic responses such as signal or porosity overcall and relaxation times that are too short to be determined using the applied instrument settings. We apply a new simultaneous Gaussian-Exponential (SGE) inversion method to simulated data and measured results obtained on a variety of oil shale samples. The SGE inversion produces more physically realistic results than the inverse Laplace transform and displays more consistent relaxation behavior at high magnetic field strengths. Residuals for the SGE inversion are consistently lower than for the inverse Laplace method and signal overcall at short T2 times is mitigated. Beyond geological samples, the method can also be applied in other fields where the sample relaxation consists of both Gaussian and exponential decays, for example in material, medical and food sciences.

Recrystallization inhibition in ice due to ice binding protein activity detected by nuclear magnetic resonance

Liquid water present in polycrystalline ice at the interstices between ice crystals results in a network of liquid-filled veins and nodes within a solid ice matrix, making ice a low porosity porous media. Here we used nuclear magnetic resonance (NMR) relaxation and time dependent self-diffusion measurements developed for porous media applications to monitor three dimensional changes to the vein network in ices with and without a bacterial ice binding protein (IBP). Shorter effective diffusion distances were detected as a function of increased irreversible ice binding activity, indicating inhibition of ice recrystallization and persistent small crystal structure. The modification of ice structure by the IBP demonstrates a potential mechanism for the microorganism to enhance survivability in ice. These results highlight the potential of NMR techniques in evaluation of the impact of IBPs on vein network structure and recrystallization processes; information useful for continued development of ice-interacting proteins for biotechnology applications.

Anomalous preasymptotic colloid transport by hydrodynamic dispersion in microfluidic capillary flow

The anomalous preasymptotic transport of colloids in a microfluidic capillary flow due to hydrodynamic dispersion is measured by noninvasive nuclear magnetic resonance (NMR). The data indicate a reduced scaling of mean squared displacement with time from the 〈z(t)(2)〉(c) ∼ t(3) behavior for the interaction of a normal diffusion process with a simple shear flow. This nonequilibrium steady-state system is shown to be modeled by a continuous time random walk (CTRW) on a moving fluid. The full propagator of the motion is measured by NMR, providing verification of the assumption of Gaussian jump length distributions in the CTRW model. The connection of the data to microrheology measurements by NMR, in which every particle in a suspension contributes information, is established.

Biofilm detection in natural unconsolidated porous media using a low-field magnetic resonance system

The extent to which T(2) relaxation measurements can be used to determine biofouling in several natural geological sand media using a low-field (275 kHz, 6.5 mT) NMR system has been demonstrated. It has been previously shown that, at high laboratory strength fields (300 MHz, 7 T), T(2) techniques can be used as a bioassay to confirm the growth of biofilm inside opaque porous media with low magnetic susceptibilities such as borosilicate or soda lime glass beads. Additionally decreases in T(2) can be associated with intact biofilm as opposed to degraded biofilm material. However, in natural geological media, the strong susceptibility gradients generated at high fields dominated the T(2) relaxation time distributions and biofilm growth could not be reliably detected. Samples studied included Bacillus mojavensis biofilm in several sand types, as well as alginate solution and alginate gel in several sand types. One of the sand types was highly magnetic. Data was collected with a low-field (275 kHz, 6.5 mT) benchtop NMR system using a CPMG sequence with an echo time of 1.25 ms providing the ability to detect signals with T(2) greater than 1 ms. Data presented here clearly demonstrate that biofilm can be reliably detected and monitored in highly magnetically susceptible geological samples using a low-field NMR spectrometer indicating that low-field NMR could be viable as a biofilm sensor at bioremedation sites.

Magnetic resonance diffusion and relaxation characterization of water in the unfrozen vein network in polycrystalline ice and its response to microbial metabolic products

Polycrystalline ice, as found in glaciers and the ice sheets of Antarctica, is a low porosity porous media consisting of a complicated and dynamic pore structure of liquid-filled intercrystalline veins within a solid ice matrix. In this work, Nuclear Magnetic Resonance measurements of relaxation rates and molecular diffusion, useful for probing pore structure and transport dynamics in porous systems, were used to physically characterize the unfrozen vein network structure in ice and its response to the presence of metabolic products produced by V3519-10, a cold tolerant microorganism isolated from the Vostok ice core. Recent research has found microorganisms that can remain viable and even metabolically active within icy environments at sub-zero temperatures. One potential mechanism of survival for V3519-10 is secretion of an extracellular ice binding protein that binds to the prism face of ice crystals and inhibits ice recrystallization, a coarsening process resulting in crystal growth with ice aging. Understanding the impact of ice binding activity on the bulk vein network structure in ice is important to modeling of frozen geophysical systems and in development of ice interacting proteins for biotechnology applications, such as cryopreservation of cell lines, and manufacturing processes in food sciences. Here, we present the first observations of recrystallization inhibition in low porosity ice containing V3519-10 extracellular protein extract as measured with Nuclear Magnetic Resonance and Magnetic Resonance Imaging.

Microbial and algal alginate gelation characterized by magnetic resonance

Advanced magnetic resonance (MR) relaxation and diffusion correlation measurements and imaging provide a means to non-invasively monitor gelation for biotechnology applications. In this study, MR is used to characterize physical gelation of three alginates with distinct chemical structures; an algal alginate, which is not O-acetylated but contains poly guluronate (G) blocks, bacterial alginate from Pseudomonas aeruginosa, which does not have poly-G blocks, but is O-acetylated at the C2 and/or C3 of the mannuronate residues, and alginate from a P. aeruginosa mutant that lacks O-acetyl groups. The MR data indicate that diffusion-reaction front gelation with Ca(2+) ions generates gels of different bulk homogeneities dependent on the alginate structure. Shorter spin-spin T(2) magnetic relaxation times in the alginate gels that lack O-acetyl groups indicate stronger molecular interaction between the water and biopolymer. The data characterize gel differences over a hierarchy of scales from molecular to system size.

Preasymptotic hydrodynamic dispersion as a quantitative probe of permeability

We interpret a generalized short-time expansion of stochastic hydrodynamic dispersion dynamics in the case of small Reynolds number flow through macroscopically homogenous permeable porous media to directly determine hydrodynamic permeability. The approach allows determination of hydrodynamic permeability from pulsed field gradient spin-echo nuclear magnetic resonance measurement of the short-time effective hydrodynamic dispersion coefficient. The analytical expansion of asymptotic dynamics agrees with experimental NMR data and lattice Boltzmann simulation of hydrodynamic dispersion in consolidated random sphere pack media.

MR measurement of critical phase transition dynamics and supercritical fluid dynamics in capillary and porous media flow

Supercritical fluids (SCF) are useful solvents in green chemistry and oil recovery and are of great current interest in the context of carbon sequestration. Magnetic resonance techniques were applied to study near critical and supercritical dynamics for pump driven flow through a capillary and a packed bed porous media. Velocity maps and displacement propagators measure the dynamics of C(2)F(6) at pressures below, at, and above the critical pressure and at temperatures below and above the critical temperature. Displacement propagators were measured at various displacement observation times to quantify the time evolution of dynamics. In capillary flow, the critical phase transition fluid C(2)F(6) showed increased compressibility compared to the near critical gas and supercritical fluid. These flows exhibit large variations in buoyancy arising from large changes in density due to very small changes in temperature.

Magnetic resonance analysis of capillary formation reaction front dynamics in alginate gels

The formation of heterogeneous structures in biopolymer gels is of current interest for biomedical applications and is of fundamental interest to understanding the molecular level origins of structures generated from disordered solutions by reactions. The cation-mediated physical gelation of alginate by calcium and copper is analyzed using magnetic resonance measurements of spatially resolved molecular dynamics during gel front propagation. Relaxation time and pulse-field gradient methods are applied to determine the impact of ion front motion on molecular translational dynamics. The formation of capillaries in alginate copper gels is correlated to changes in translational dynamics.

Erratum to: Hydrodynamic dispersion in β-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through β-lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

NMR measurement of hydrodynamic dispersion in porous media subject to biofilm mediated precipitation reactions

Noninvasive measurements of hydrodynamic dispersion by nuclear magnetic resonance (NMR) are made in a model porous system before and after a biologically mediated precipitation reaction. Traditional magnetic resonance imaging (MRI) was unable to detect the small scale changes in pore structure visualized during light microscopy analysis after destructive sampling of the porous medium. However, pulse gradient spin echo nuclear magnetic resonance (PGSE NMR) measurements clearly indicated a change in hydrodynamics including increased pore scale mixing. These changes were detected through time-dependent measurement of the propagator by PGSE NMR. The dynamics indicate an increased pore scale mixing which alters the preasymptotic approach to asymptotic Gaussian dynamics governed by the advection diffusion equation. The methods described here can be used in the future to directly measure the transport of solutes in biomineral-affected porous media and contribute towards reactive transport models, which take into account the influence of pore scale changes in hydrodynamics.

Hydrodynamic dispersion in β-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through [Formula: see text] -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

Dynamic length-scale characterization and nonequilibrium statistical mechanics of transport in open-cell foams

Nuclear magnetic resonance measurements of scale dependent dynamics in a random solid open-cell foam reveal a characteristic length scale for transport processes in this novel type of porous medium. These measurements and lattice Boltzmann simulations for a model foam structure indicate dynamical behavior analogous to lower porosity consolidated granular porous media, despite extremely high porosity in solid cellular foams. Scaling by the measured characteristic length collapses data for different foam structures as well as consolidated granular media. The nonequilibrium statistical mechanics theory of preasymptotic dispersion, developed for hierarchical porous media, is shown to model the hydrodynamic dispersive transport in a foam structure.

Secondary flow mixing due to biofilm growth in capillaries of varying dimensions

Using a magnetic resonance microscopy (MRM) technique, velocity perturbations due to biofouling in capillaries were detected in 3D velocity maps. The velocity images in each of the three square capillary sizes (2, 0.9, and 0.5 mm i.d.) tested indicate secondary flow in both the x- and y-directions for the biofouled capillaries. Similar flow maps generated in a clean square capillary show only an axial component. Investigation of these secondary flows and their geometric and dynamic similarity is the focus of this study. The results showed significant secondary flows present in the 0.9 mm i.d. capillary, on the scale of 20% of the bulk fluid flow. Since this is the "standard 1 mm" size capillary used in confocal microscopy laboratory bioreactors to investigate biofilm properties, it is important to understand how these enhanced flows impact bioreactor transport.

Biopolymer and water dynamics in microbial biofilm extracellular polymeric substance

Nuclear magnetic resonance (NMR) is a noninvasive and nondestructive tool able to access several observable quantities in biofilms such as chemical composition, diffusion, and macroscale structure and transport. Pulsed gradient spin echo (PGSE) NMR techniques were used to measure spectrally resolved biomacromolecular diffusion in biofilm biomass, extending previous research on spectrally resolved diffusion in biofilms. The dominant free water signal was nulled using an inversion recovery modification of the traditional PGSE technique in which the signal from free water is minimized in order to view the spectra of components such as the rotationally mobile carbohydrates, DNA, and proteins. Diffusion data for the major constituents obtained from each of these spectral peaks demonstrate that the biomass of the biofilm contains both a fast and slow diffusion component. The dependence of diffusion on antimicrobial and environmental challenges suggests the polymer molecular dynamics measured by NMR are a sensitive indicator of biofilm function.

Dynamics of the solid and liquid phases in dilute sheared Brownian suspensions: irreversibility and particle migration

Magnetic resonance measurements of migration and irreversible dynamics in the capillary shear flow of a Brownian suspension are presented. The results demonstrate the presence of phenomena typically associated with concentrated noncolloidal systems and indicate the role of many body hydrodynamics in dilute Brownian suspension transport. The application of concepts from chaos theory and nonequilibrium statistical mechanics is demonstrated.

Magnetic resonance microscopy determined velocity and hematocrit distributions in a Couette viscometer

Magnetic resonance microscopy is used to non-invasively measure the radial velocity distribution in Couette flow of erythrocyte suspensions of varying aggregation behavior at a nominal shear rate of 2.20 s(-1) in a 1 mm gap. Suspensions of red blood cells in albumin-saline, plasma and 1.48% Dextran added plasma at average hematocrits near 0.40 are studied, providing a range of aggregation ability. The spatial distribution of the red blood cell volume fraction, hematocrit, is calculated from the velocity distribution. The hematocrit profiles provide direct measure of the thickness of the aggregation and shear rate dependent red blood cell depletion at the Couette surfaces. At the nominal shear rate studied hematocrit distributions for the red blood cells in plasma show a depletion zone near the inner Couette wall but not the outer wall. The red blood cells in plasma with Dextran show cell depletion regions of approximately 100 mum at both the inner and outer Couette surfaces, with greater depletion at the inner wall, but approach the normal blood hematocrit distribution with a doubling of shear rate due to decreased aggregation. The material response of the blood is spatially dependent with the shear rate and the hematocrit distribution non-uniform across the gap.

Magnetic resonance microscopy analysis of advective transport in a biofilm reactor

In this article we present magnetic resonance microscopy (MRM) characterization of the advective transport in a biofilm capillary reactor. The biofilm generates non-axial flows that are up to 20% of the maximum axial velocity. The presence of secondary velocities of this magnitude alters the mass transport in the bioreactor relative to non-biofilm fouled reactors and questions the applicability of empirical mass transfer coefficient approaches. The data are discussed in the context of simulations and models of biofilm transport and conceptual aspects of transport modeling in complex flows are also discussed. The variation in the residence time distribution due to biofilm growth is calculated from the measured propagator of the motion. Dynamical systems methods applied to model fluid mixing in complex flows are indicated as a template for extending mass transport theory to quantitatively incorporate microscale data on the advection field into macroscale mass transfer models.

Anomalous fluid transport in porous media induced by biofilm growth

Magnetic resonance measurements of the transition from normal to anomalous hydrodynamic dispersion in porous media due to biological activity are presented. Fractional advection-diffusion equations are shown to provide models for the measured impact of biofilm growth on porous media transport dynamics.

Magnetic resonance microscopy of biofilm structure and impact on transport in a capillary bioreactor

Microorganisms that colonize surfaces, biofilms, are of significant importance due to their role in medical infections, subsurface contaminant remediation, and industrial processing. Spatially resolved data on the distribution of biomass within a capillary bioreactor, the heterogeneity of the biofilm itself and the impact on transport dynamics for a Staphylococcus epidermidis biofilm in the natural growth state are presented. The data demonstrate the ability of magnetic resonance microscopy to study spatially resolved processes in bacterial biofilms, thus providing a basis for future studies of spatially resolved metabolism and in vivo clinical detection.

A PGSE study of propane gas flow through model porous bead packs

We present a study of the probability density for molecular displacements of gas flowing through bead packs. The three bead packs to be described are composed of polydispersed porous PVC particles, 500 microm glass spheres, and 300 microm polystyrene spheres. A range of velocities (1 cm s(-1) to 1 m s(-1)) and observation times (3-500 ms), hence transport distances, are presented. For comparison we also measure the propagators for water flow in the polystyrene sphere pack. The exchange time between the moving and the stagnant portions of the flow is a strong function of the diffusion coefficient of the fluid. Comparing the propagators between water and propane flowing in similar porous media makes this clear. The gas propagators, for flowing and diffusing molecules, consistently show a feature at the average pore diameter. This feature has previously been observed for similar Peclet number studies in smaller monodispersed bead packs using liquids, but is now demonstrated for larger beads with gas. We analyze and discuss these propagators in the physically intuitive propagator space and also in the well-understood Fourier q space. The extension of NMR PGSE experiments to gas systems allows flow and diffusion information to be obtained over a wider range of length and time scales than with liquids, and also for a new range of physical environments and systems. Interactions between stochastic and deterministic motion are fundamental to the theoretical description of transport in porous media, and the time and length scale dependences are central to an understanding of the resultant dispersive motion.

Studies of porous media by thermally polarized gas NMR: current status

Three examples of thermally polarized gas NMR performed at New Mexico Resonance are presented to demonstrate its unique advantages in porous media studies. 1) In-vivo animal lung imaging by Kuethe et al., in which useful quality 3D images of rat lungs were obtained in 30 min. It is conjectured that comparable human lung images would take much less time to make, possibly by the ratio of body weights, a factor of several hundred. 2) The success of the lung imaging suggested other porous media as candidates for thermally polarized gas NMR. Caprihan and coworkers obtained excellent images from partially sintered ceramics and Vycor glass. Since then, Beyea has developed the technique of spatially resolved BET curves for ceramics and other nanoporous solids. In this way, surface area, pore size, and porosity, averaged over an image voxel, can be spatially resolved. This greatly aids in the characterization of such materials, especially with regards to spatial heterogeneities. 3) Finally, we describe Codd's propagator experiments on propane gas flowing through a packed bed of 300 microm beads. In order to increase signal-to-noise ratio, the flowing gas was pressurized to 170 kPa. Excellent quality propagators showing the discrete nature of the bead pack were obtained. This type of information is not available in comparable liquid studies because most spins will not diffuse far enough to sample the walls in the time available.

Taylor dispersion and molecular displacements in Poiseuille flow

We have used pulsed gradient spin echo (PGSE) NMR to measure longitudinal displacements of octane molecules undergoing Poiseuille flow in a 150 microm diameter pipe, accessing time scales which approach the Taylor dispersion limit. We monitor the change in displacement distribution which occurs as molecules undergoing Brownian motion sample an increasing proportion of the ensemble of streamlines, observing the effects of wall collisions and the gradual transition of the propagator from Poiseuille to Taylor-Aris behavior. The further use of a double PGSE sequence allows the direct measurement of the stochastic part of the motion alone.

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson. 129, 74-84 (1997)], and based on the multiple propagator approach of Caprihan et al. [J. Magn. Reson. A 118, 94-102 (1996)], allows for the calculation of the echo attenuation, E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid-surface interactions. In particular, the q-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (delta approximately a2/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry. Copyright 1999 Academic Press.

Generalised calculation of NMR imaging edge effects arising from restricted diffusion in porous media

The theoretical problem of how to describe apparent image spin density under conditions of restricted diffusion, given any general gradient sequence, is intrinsically complex. Here we demonstrate a simple approach to calculating the signal and the corresponding density in nuclear magnetic resonance (NMR) imaging experiments by means of an impulse-propagator method based on matrix multiplication. The multiplication scheme bears a natural and straightforward relationship to the k-space sampling, while the matrices themselves are calculated from the eigenmodes of the pore diffusion equation. Good agreement is found between theoretical predictions and the results of micro-imaging experiments on water trapped in rectangular pores whose walls are spaced by 100 microns along the read direction.

A three-dimensional NMR imaging scheme utilizing doubly resonant gradient coils

A 3DFT gradient-echo technique has been developed which, in conjunction with series-resonant gradient-coil circuits, can produce three-dimensional NMR images with an echo time of less than 100 microseconds. The method involves a read-gradient waveform composed of two sinusoids of different frequencies. This is an improvement on previous imaging sequences using a single sinusoid where only half of k space was sampled and where the second half was calculated using conjugate symmetry. The inaccuracies involved in the necessary "cut and paste" of k space inevitably lead to artifacts in the final image. The important features of the new method are that with suitable phase encoding all octants of k space are sampled, the RF pulse is applied when the gradients are all zero, and the echo forms when the gradient is essentially constant. This method will allow more extensive application of solid imaging techniques to biological samples in vivo.

Physical determinants of bronchial mucosal folding

It has recently been proposed, on the basis of a theoretical analysis, that the folding of the mucosa provides a significant component of airway stiffness. The model predicted that the stiffness of an airway was directly related to the number of epithelial folds that developed. In this study we examine the possibility that the folding pattern is determined by the physical requirements that the folding membrane must stay within the boundary of the smooth muscle wall, that the submucosal mass is constant, and that the strain energy of the folding membrane is the minimum possible within the geometric constraints. Model predictions are compared with morphometric data from the noncartilaginous airways of 17 sheep lungs. The data are in agreement with our predictions, which are based on the assumption that the folding membrane thickness is proportional to the submucosal thickness (in a fully dilated airway). The outcome of this analysis is that the increase in intrinsic stiffness of the folding membrane resulting from the increased thickness outweighs the decrease in stiffness conferred by the fewer folds required by the thicker submucosa. It is suggested that the increase in folding membrane thickness observed in asthma could be viewed as a protective mechanism that tends to reduce hyperresponsiveness.