Tortuosity Values Research Articles

(Invited) Understanding Fuel Cell Catalyst Layer Morphology and Its Transport Properties Via Advanced Diagnostics, Imaging and Modeling

Optimizing activity and morphology of the cathode catalyst layer is one of the major challenges to overcome cost and durability of polymer electrolyte fuel cells (PEFCs). The PEFC performance is primarily determined by the losses in the catalyst layer. These are kinetic and mass-transport overpotentials associated with the sluggish oxygen reduction reaction (ORR), transport of oxygen and water flooding at high current densities. A combination of characterization, modeling and multi-modal imaging techniques is used to understand morphology and to decouple the transport processes that limit electrocatalsyt utilization and mass transport within the catalyst layer. Hydrogen pump technique is used to measure ionic conductivity of the catalyst layers without Pt. The technique is a modified version of that previously reported [1], where a pseudo-catalyst layer is fabricated with an ionomer and carbon. The interlayer thickness is varied to plot the catalyst layer ionic resistance as a function of the layers thickness (Figure 1). The slope of the curve produces an inverse of ionic conductivity, whereas the intercept with y-axis is due to membrane and contact resistances. We varied the inter-layer thickness (three to four thicknesses), ratio of ionomer to carbon (I/C) content and the type of ionomer within the carbon black support (Vulcan XC-72). We observed an increase in ionic conductivity with increase in I/C ratio, and also PFIA ionomer at low RH showed higher conductivity compared to PFSA ionomer for the same I/C ratios. Increased ionic conductivity of PFIA ionomer explained some of the improvements in the polarization behavior of the PEFC with PFIA-containing ionomer. Hydrogen pump “DC” method is also compared to the electrochemical impedance spectroscopy (EIS) method to explain some of the differences observed in literature with DC vs AC methods [2]. To probe local ionomer interaction with the electrocatalyst a CO-displacement experiment [3] is performed on the catalyst layers with varied ionomers, I/C ratios and carbon supports. A combined rotating disc electrode (RDE) and membrane electrode assembly (MEA) studies are performed. Electrochemical studies for ionic conductivity measurements are compared to direct imaging of ionomer distribution in the catalyst layers using nano X-ray computed tomography (CT) and spectroscopy. Current methods to image ionomer rely on staining it with heavy Cesium ions to enhance the absorption contrast imaging. However, distinguishing between the Cs- stained ionomer and Pt is challenging because of similar X-ray attenuation coefficients. We use X-ray absorption near edge spectroscopy (XANES) to image samples at Cs and Pt K-edges, enabling distinction between these two phases. Figure 1 shows images above and below Pt L3-edge, as well as volume-rendered representation of Pt and ionomer-phases. Ionomer tortuosity values obtained with imaging and hydrogen pump technique show good agreement. Lastly, direct imaging of water formation within the catalyst layer is still challenging due to either resolution, ambient environment or field of view limitations of the imaging techniques. Over the last two years we have been developing operando nano X-ray computed tomography PEFC hardware to enable imaging with 30-60 nm resolution and 80 um field of view. Challenges of X-ray beam damage to membrane at low energies were solved by using synchrotron beamline ID 16B at ESRF with higher X-ray energy (17.5 keV) and Kirkpatrick-Baez optics. We observed no beam damage to the MEAs at these operating conditions. Complementary continuum and pore-network model bridging was conducted to explain water distributions in catalyst layers. Acknowledgement: This material is based upon work supported by the Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE), under Award Number DE-EE0007270

Method to Determine in-Plane Tortuosity of Battery Electrodes and Its Dependence on Particle Shape, Binder Content, and Porosity

One of the critical parameters that affect the performance of a commercial lithium-ion battery is the through-plane tortuosity. The shape and size distribution of electrode particles, binder content, and preparation method, may affect the tortuosity of an electrode. The design optimization of novel 3-dimensional battery architectures like patterned electrodes1-4—where the transport of lithium-ions within the electrode is not restricted to the through-plane direction alone—will require quantitative values for both the in-plane and the through-plane tortuosity.5 While methods to determine through-plane tortuosity are established in the literature and summarized by Landesfeind et al.,6, 7 in-plane tortuosity values are rarely reported and so far are only accessible by modeling the transport in 3D reconstructed electrodes.8 In this presentation, we outline an experimental setup that enables us to extract the in-plane tortuosity of a battery electrode. The mathematical analysis is performed using the blocking-conditionransmission line model. The precise measurements of in-plane tortuosity along with the through-plane tortuosity will be very critical for simulating and optimizing the above mentioned 3-dimensional electrode architectures and for gaining insights into the quality of electrode preparation methods. The combined use of through-plane and in-plane tortuosity will act as an indispensable tool to design better electrodes and validate numerical models for electrodes.9 Figure 1 shows comparison of through-plane (\U0001d70fT-P) and in-plane (\U0001d70fI-P) tortuosity of two different electrodes consisting of mesoporous carbon microbeads MCMB (spherical) and flake-like graphite materials obtained using the proposed method. Figure 1: and of MCMB based electrodes (MCMB 97%wt, PVDF 3%wt, porosity ~48%) and Flake-like graphite based electrode (Graphite 94%wt, PVDF 6%wt, porosity ~55%). The error bars represent the standard deviation from 2 measurements. SEM images of MCMB and flake-like graphite based electrodes are also shown. After having outlined our method to determine the in-plane tortuosity of electrodes, we will also show its dependence on various factors, such as particle shape, binder content, binder layer thickness, and electrode porosity. Acknowledgements: This work is supported by the BMBF (Federal Ministry of Education and Research, Germany) for its financial support under the auspices of the ExZellTUM II project (grant number 03XP0081).

Ion transport limitations in all-solid-state lithium battery electrodes containing a sulfide-based electrolyte

We study ion transport limitations in composite electrodes for all-solid-state lithium batteries. These electrodes are composed of variable volume fractions of active material particles (Li4Ti5O12) and of a sulfide-based solid electrolyte, while the volume fraction of carbon black acting as conductive additive is held constant. The ion transport limitations are characterized by impedance spectroscopic measurements on different types of symmetrical solid-state cells. Ion transport resistances are calculated either based on a transmission line model or from the Li+ ion current under electron-blocking conditions. In addition, we demonstrate a cell setup, for which both types of measurements can be carried out on the same composite electrodes. Effective ion transport tortuosities τeff are then derived from the resistance values and analyzed in dependence on the volume fraction of the solid electrolyte in the composite electrodes, ε . We show that for ε≥0.4, both methods yield very similar tortuosity values, while discrepancies between the results obtained from the two methods are found for ε<0.4. Our results give strong indication that the power density of solid-state batteries with volume fractions ε around 0.4 of the best solid Li+ electrolytes should be at least equal that of commercial liquid electrolyte-based Li-ion batteries.

Characterizing Pores and Pore-Scale Flow Properties in Middle Bakken Cores

Summary To understand the flow and transport mechanisms in shale reservoirs, we needed reliable core-measured data that were not available to us. Thus, in 2014, we conducted a series of diverse experiments to characterize pores and determine the flow properties of 12 Middle Bakken cores that served as representatives for unconventional low-permeability reservoirs. The experiments included centrifuge, mercury-intrusion capillary pressure (MICP), nitrogen adsorption, nuclear magnetic resonance (NMR), and resistivity. From the centrifuge measurements, we determined the mobile-fluid-saturation range for water displacing oil and gas displacing oil in addition to irreducible fluid saturations. From MICP and nitrogen adsorption, we determined pore-size distribution (PSD). Finally, from resistivity measurements, we determined tortuosity. In addition to flow characterization, these data provided key parameters that shed light on the mechanisms involved in primary production and the enhanced-oil-recovery (EOR) technique. The cores were in three conditions: clean, preserved, and uncleaned. The hydrocarbon included Bakken dead oil and decane, and the brine included Bakken produced water and synthetic brine. After saturating the cores with brine or oil, a set of drainage and imbibition experiments was performed. NMR measurements were conducted before and after each saturation/desaturation step. After cleaning, PSD was determined for four cores using MICP and nitrogen-adsorption tests. Finally, resistivity was measured for five of the brine-saturated cores. The most significant results include the following: Centrifuge capillary pressure in Bakken cores was on the order of hundreds of psi, both in positive and negative range. Mobile-oil-saturation range for water displacing oil was very narrow [approximately 12% pore volume (PV)] and much wider (approximately 40% PV) for gas displacing oil. In Bakken cores, oil production by spontaneous imbibition of high-salinity brine was small unless low-salinity brine was used for spontaneous imbibition. Resistivity measurements yielded unexpectedly large tortuosity values (12 to 19), indicating that molecules and bulk fluids have great difficulty to travel from one point to another in shale reservoirs.

Application of electrical resistivity method in estimating geohydraulic properties of a sandy hydrolithofacies: a case study of Ajali Sandstone in Ninth Mile, Enugu State, Nigeria

Geoelectric investigation using vertical electrical sounding (VES) (Schlumberger electrode configuration) was carried out in 14 locations at Ninth Mile area, southeastern Nigeria to determine the variations and interrelationship of some geoelectric and geohydraulic parameters of a sandstone hydrolithofacies. The measured resistivity data were interpreted using manual and computer software packages, which gave the resistivity, depth, and thickness for each layer within the maximum current electrodes separation. The aquifer resistivity values range from 86.56 to 4753.0 Ωm with 1669.40 Ωm average value. The values of water resistivity from borehole locations close to the sounding points range from 79.49 to 454 .55 Ωm and averaging about 264.7 Ωm. Porosity values of the sandy aquifer range from 30.19 to 34.20%. Fractional porosity values range from 0.3019 to 0.3292, while the tortuosity values vary between 2.91 and 22.85. The geohydraulic parameters estimated vary across the study area. Formation factor ranges from 0.28 to 15.29, hydraulic conductivity ranges from 1.21 to 66.54 m/day which, however, influences the natural flow of water in the aquifer while tortuosity values range from 2.91 to 23.27. The contour maps clearly show the variation of these parameters in the subsurface and the plots show their relationship and high correlation coefficients with one another. The results of this study have revealed the geological characteristics of the subsurface aquifer, established the influence on the amount of groundwater, and proposed a strategy for the management and exploitation of groundwater resources in the area and other aquiferous formations.

Thick Binder-Free Electrodes for Li-Ion Battery Fabricated Using Templating Approach and Spark Plasma Sintering Reveals High Areal Capacity

The templating approach is a powerful method for preparing porous electrodes with interconnected well-controlled pore sizes and morphologies. The optimization of the pore architecture design facilitates electrolyte penetration and provides a rapid diffusion path for lithium ion, which becomes even more crucial for thick porous electrodes. In the present work, we used NaCl micro-size particles as templating agent for the fabrication of 1 mm-thick porous LiFePO4 (LFP) and Li4Ti5O12 (LTO) composite electrodes using Spark Plasma Sintering (SPS) technique. These sintered binder-free electrodes are self-supported and present a large porosity (40%) with relatively uniform pores. The electrochemical performances of half and full batteries reveals a remarkable specific areal capacity (20 mAh/cm2), which is four times higher than those of 100 µm thick electrodes present in conventional tape-casted Li-ion batteries (5 mAh/cm2). 3D morphological study of both electrode types was carried out using µCT full field TXM technique to obtain tortuosity values and pore size distributions leading to a strong correlation with their electrochemical properties. These results also demonstrate that the coupling between salt templating method and SPS technique turn out to be a promising way to reach the ultimate goal in the fabrication of thick electrodes with high energy density.

Analysis of Iliac Artery Geometric Properties in Fenestrated Aortic Stent Graft Rotation.

A complication of fenestrated endovascular aneurysm repair is the potential for stent graft rotation during deployment causing fenestration misalignment and branch artery occlusion. The objective of this study is to demonstrate that this rotation is caused by a buildup of rotational energy as the device is delivered through the iliac arteries and to quantify iliac artery geometric properties associated with device rotation. A retrospective clinical study was undertaken in which iliac artery geometric properties were assessed from preoperative imaging for 42 cases divided into 2 groups: 27 in the nonrotation group and 15 in the rotation group. Preoperative computed tomography scans were segmented, and the iliac artery centerlines were determined. Iliac artery tortuosity, curvature, torsion, and diameter were calculated from the centerline and the segmented vessel geometry. The total iliac artery net torsion was found to be higher in the rotation group compared to the nonrotation group (23.5 ± 14.7 vs 14.6 ± 12.8 mm-1; P = .05). No statistically significant differences were found for the mean values of tortuosity, curvature, torsion, or diameter between the 2 groups. Stent graft rotation occurred in 36% of the cases considered in this study. Cases with high iliac artery total net torsion were found to be more likely to have stent graft rotation upon deployment. This retrospective study provides a framework for prospectively studying the influence of iliac artery geometric properties on fenestrated stent graft rotation.

Thick Binder‐Free Electrodes for Li–Ion Battery Fabricated Using Templating Approach and Spark Plasma Sintering Reveals High Areal Capacity

AbstractThe templating approach is a powerful method for preparing porous electrodes with interconnected well‐controlled pore sizes and morphologies. The optimization of the pore architecture design facilitates electrolyte penetration and provides a rapid diffusion path for lithium ions, which becomes even more crucial for thick porous electrodes. Here, NaCl microsize particles are used as a templating agent for the fabrication of 1 mm thick porous LiFePO4 and Li4Ti5O12 composite electrodes using spark plasma sintering technique. These sintered binder‐free electrodes are self‐supported and present a large porosity (40%) with relatively uniform pores. The electrochemical performances of half and full batteries reveal a remarkable specific areal capacity (20 mA h cm−2), which is 4 times higher than those of 100 µm thick electrodes present in conventional tape‐casted Li–ion batteries (5 mA h cm−2). The 3D morphological study is carried out using full field transmission X‐ray microscopy in microcomputed tomography mode to obtain tortuosity values and pore size distributions leading to a strong correlation with their electrochemical properties. These results also demonstrate that the coupling between the salt templating method and the spark plasma sintering technique turns out to be a promising way to fabricate thick electrodes with high energy density.

Tortuosity of Battery Electrodes: Validation of Impedance-Derived Values and Critical Comparison with 3D Tomography

Tortuosity values of porous battery electrodes determined using electrochemical impedance spectroscopy in symmetric cells with a non-intercalating electrolyte are typically higher than those values based on numerical analysis of 3D tomographic reconstructions. The electrochemical approach assumes that the electronic resistance in the porous coating is negligible and that the tortuosity of the porous electrode can be calculated from the ionic resistance determined by fitting a transmission line equivalent circuit model to the experimental data. In this work, we validate the assumptions behind the electrochemical approach. First, we experimentally and theoretically investigate the influence of the electronic resistance of the porous electrode on the extracted ionic resistances using a general transmission line model, and provide a convenient method to determine whether the electronic resistance is sufficiently low for the model to be correctly applied. Second, using a macroscopic setup with known tortuosity, we prove that the ionic resistance quantified by the transmission line model indeed yields the true tortuosity of a porous medium. Based on our findings, we analyze the tortuosities of porous electrodes using both X-ray tomography and electrochemical impedance spectroscopy on electrodes from the same coating and conclude that the distribution of the polymeric binder phase, which is not imaged in most tomographic experiments, is a key reason for the underestimated tortuosity values calculated from 3D reconstructions of electrode microstructures.

Reconstruction–Simulation Approach Verifies Impedance-Derived Ion Transport Tortuosity of a Graphite Battery Electrode

The performance of a composite battery electrode depends strongly on the morphology of its liquid electrolyte-filled pore space, where ion transport takes place. Ion transport limitations within the pore space are quantified by the tortuosity, which can be determined from diffusion simulations in the reconstructed pore space or through electrochemical impedance spectroscopy (EIS) using, for example, the transmission line model. Although rarely directly compared, the tortuosities determined by the two approaches have so far been lacking in agreement, raising doubts about the validity of each method. In this study, we use a graphite composite electrode to demonstrate that the two methods deliver comparable tortuosity values under two conditions: (i) The pore space is reconstructed by focused ion-beam scanning electron microscopy using an osmium-based contrast agent for positive staining. (ii) The dimensions of the reconstructed volume are sufficient to represent the electrode microstructure and to prevent finite-size effects in the diffusion simulations. Fulfillment of these conditions is proven by a comprehensive morphological analysis, comprising porosity profiles, chord length distributions of solid phase and pore space, and the geometrical tortuosity. Our results confirm EIS as a reliable method for assessing the ion transport tortuosity of battery electrodes.

Experimental characterization of rigid porous material via the first ultrasonic reflected waves at oblique incidence

Enhanced ultrasonic method for the evaluation of acoustic parameters of air-saturated porous material is presented. This method is based on the direct and inverse problem of the reflection of an oblique incident wave from the surface of the porous medium with rigid frame. The interaction of the sound pulse with the porous material is described by the equivalent fluid model using the Johnson-Champoux-Allard approach (JCA) to describe the visco-inertial dissipative effects and the thermal effects inside the porous media. Four parameters are involved in the calculation of the dynamic density and the bulk modulus at high frequencies, namely the porosity ϕ, the high frequency limit of tortuosity α∞, the viscous and thermal characteristic lengths Λ and Λ′. The sensitivity of each parameter on reflected waves from the surface of the porous medium is studied for different oblique angles of incidence. The advantage of the proposed method is that the inverted values of porosity, tortuosity, viscous and thermal characteristic lengths are simultaneously obtained by minimizing between the experimental and simulated reflected signals. Moreover, no relationship is assumed between the viscous and thermal characteristic lengths. The numerical and experimental validation of this method is presented and compared to the theoretical prediction.

Electrical prediction of tortuosity in porous media

The fluid transport phenomena in porous materials such as concrete, is one of the main actions involved in the degradation of the structures lying in aggressive areas. This transport is governed by several physical and chemical parameters such as porosity, tortuosity, diffusion coefficient or concentration of chemical species. The main objective of this work is to quantify the tortuosity parameter by a non-destructive method. Tortuosity is a parameter with significant inflluence on the transfer and diffusion of particles in porous media. Indeed it takes account of the irregularity and sinuous transport paths in the pore structure of the material. The experimental program focuses on applying a non-destructive method for measuring the electrical conductivity of materials as glass beads and sand with different classes, saturated with NaCl solution at different concentration. The material is placed in a PVC cell of 50 mm diameter, equipped with two stainless steel electrodes connected to the measuring circuit. The tortuosity values obtained in this work are less than unity. This accords considerably with the values found in the literature, we also note that the variation of this parameter depends on the nature of the medium but also according to its geometrical properties.

Influence of the Design of High-Energy-Density Graphite Negative Electrodes on the Electrochemical Performance

Energy density of current Li-ion cells still need improvement for wide-spreading sales of electric vehicles. One can increase energy density of cells based on state-of-the-art active materials, such as graphite, by using thicker and/or lower-porosity electrodes, which contain a higher active-material loading. A downside of this approach is that in addition to enhancing the cell energy density, these thick/dense porous electrodes suffer lower cell power capability because of higher electrolyte transport limitations across the electrode. Large concentration and potential gradients develop across the electrode, leading to significant polarization increase and the possible occurrence of side reactions, such as Li plating. Active particle shape may also contribute to electrolyte transport limitations; Anisotropic particles may stack in a preferred direction that likely impede ionic transport. When studying high-energy-density porous electrodes, it is then essential to correlate the electrochemical performance with design parameters. Physics-based models, such as the Newman porous electrode model [1], prove effective to attempt such a correlation. In this work, industry-grade graphite porous electrodes with different thicknesses and porosities are studied by a variety of electrochemical techniques such as rate-capability tests, pulse tests and electrochemical impedance spectroscopy. Electrode tortuosities are estimated with a model analysis of impedance diagrams of symmetric graphite/graphite cells. Tortuosity values lie well above what is predicted by the Bruggeman relation possibly because the graphite particles have a platelet-like shape that promotes a stacking perpendicular to ionic pathways. Cycling and rate performance as well as electrochemical impedance of several high-loading-electrode designs are compared. [1] T.F. Fuller, M. Doyle, J. Newman, Simulation and Optimization of the Dual Lithium Ion Insertion Cell, J. Electrochem. Soc. 141 (1994). Figure 1

Self-diffusion of electrolyte species in model battery electrodes using Magic Angle Spinning and Pulsed Field Gradient Nuclear Magnetic Resonance

Lithium-ion batteries are electrochemical storage devices using the electrochemical activity of the lithium ion in relation to intercalation compounds owing to mass transport phenomena through diffusion. Diffusion of the lithium ion in the electrode pores has been poorly understood due to the lack of experimental techniques for measuring its self-diffusion coefficient in porous media. Magic-Angle Spinning, Pulsed Field Gradient, Stimulated-Echo Nuclear Magnetic Resonance (MAS-PFG-STE NMR) was used here for the first time to measure the self-diffusion coefficients of the electrolyte species in the LP30 battery electrolyte (i.e. a 1 M solution of LiPF6 dissolved in 1:1 Ethylene Carbonate - Dimethyl Carbonate) in model composites. These composite electrodes were made of alumina, carbon black and PVdF-HFP. Alumina's magnetic susceptibility is close to the measured magnetic susceptibility of the LP30 electrolyte thereby limiting undesirable internal field gradients. Interestingly, the self-diffusion coefficient of lithium ions decreases with increasing carbon content. FIB-SEM was used to describe the 3D geometry of the samples. The comparison between the reduction of self-diffusion coefficients as measured by PFG-NMR and as geometrically derived from FIB/SEM tortuosity values highlights the contribution of specific interactions at the material/electrolyte interface on the lithium transport properties.

TORT3D: A MATLAB code to compute geometric tortuosity from 3D images of unconsolidated porous media

Tortuosity is a parameter that plays a significant role in the characterization of complex porous media systems and it has a significant impact on many engineering and environmental processes and applications. Flow in porous media, diffusion of gases in complex pore structures and membrane flux in water desalination are examples of the application of this important micro-scale parameter. In this paper, an algorithm was developed and implemented as a MATLAB code to compute tortuosity from three-dimensional images. The code reads a segmented image and finds all possible tortuous paths required to compute tortuosity. The code is user-friendly, easy to use and computationally efficient, as it requires a relatively short time to identify all possible connected paths between two boundaries of large images. The main idea of the developed algorithm is that it conducts a guided search for connected paths in the void space of the image utilizing the medial surface of the void space. Once all connected paths are identified in a specific direction, the average of all connected paths in that direction is used to compute tortuosity.Three-dimensional images of sand systems acquired using X-ray computed tomography were used to validate the algorithm. Tortuosity values were computed from three-dimensional images of nine different natural sand systems using the developed algorithm and compared with predicted values by models available in the literature. Findings indicate that the code can successfully compute tortuosity for any unconsolidated porous system irrespective of the shape (i.e., geometry) of particles.

Preparation of Poly(vinylidene fluoride) Lithium-Ion Battery Separators and Their Compatibilization with Ionic Liquid - A Green Solvent Approach

Battery separator membranes for lithium-ion batteries have been developed based on poly(vinylidene fluoride), PVDF, and using the “green solvent” - N,N’-dimethylpropyleneurea (DMPU). This separator presents a porous microstructure with a degree of porosity of 20 % and pore size below 1 μm, showing excellent mechanical properties. Further, its ionic conductivity, tortuosity and MacMullin number values are 0.1 mS.cm−1, 4 and 82, respectively. This PVDF separator membrane was evaluated in Li/C–LiFePO4 half-cells with electrolyte solution showing good cyclability and rate capability, with a discharge value after 50 cycles of 56 mAh.g−1 at C, corresponding to 50 % of the capacity retention. Its electrochemical performance soaked in ionic liquid presents a discharge capacity of 45 mAh.g−1 at C/5-rate and capacity retention of 60%, respectively. Thus, this separator is an appropriate candidate for environmentally friendlier and safer lithium-ion batteries.

Tortuosity of mesoporous alumina catalyst supports: Influence of the pore network organization

Inverse liquid chromatography experiments were performed on five mesoporous alumina catalyst supports with similar porosity and different pore size distributions. By varying the size of the molecular tracer, it was shown that the diffusion regime in our conditions is molecular diffusion. Hindered diffusion was not observed even for squalane, a C30 molecule. Using the slope of the Van Deemter equation, the tortuosity of each alumina support was determined. The results are in disagreement with literature correlations: although all alumina supports had similar total porosities, the measured tortuosity values are really different and much higher than those predicted by these theoretical models. This discrepancy has been resolved by assuming a two–level pore network organization, whose characteristics can be entirely estimated from a classical nitrogen adsorption isotherm. This simple methodology allows to evaluate the mass transfer in mesoporous alumina supports knowing their textural properties, which is an important issue for the design and optimization of numerous catalytic processes.

Pore-scale simulation of transport properties of carbonate rocks using FIB-SEM 3D microstructure: Implications for field scale solute transport simulations

Pore-scale simulations using a nanoscale FIB-SEM three dimensional microstructure have been used to estimate the absolute permeability and diffusive tortuosity of a representative limestone sample collected from the Arab Formation (Jurassic) carbonate gas reservoir of Abu Dhabi, United Arab Emirates. Estimated absolute permeability (k) values are in excellent agreement with reported experimental permeability values. However, estimated diffusive tortuosity (τd) values required to calculate effective diffusivity (Deff) values of multiple species involved in thermochemical sulfate reduction (TSR) are unrealistically larger than hydraulic tortuosity (τh) values. Widely employed empirical correlations (e.g. τd = φ Dm/Deff) which include only porosity as the factor affecting τd of natural porous media yield unrealistically smaller values than 1.0. Realistic τd values were only obtained if a constrictivity factor (δ) was included in the estimation of τd. Given the difficulty in estimating both δ and τd values simultaneously, it is proposed that Deff values for reactive transport simulations of TSR, which are commonly calculated as function of φ and τd (e.g. Deff = (φ/τd)Dm), should be instead estimated as function of a formation factor (F) (Deff = FDm). In the proposed expression F accounts for the combined effect of porosity, tortuosity and constrictivity (F = δφ/τd). Our pore-scale simulation results shows that F can be accurately estimated from pore-scale simulations using FIB-SEM 3D images.

A clinical correlation of conjunctival microangiopathy with grades of retinopathy in type 2 diabetes mellitus

BackgroundConjunctival microangiopathy has been described among diabetics similar to retinal vessel angiopathy. Correlation of these conjunctival microangiopathy changes with retinopathy may form the basis of screening by external examination without expert fundus evaluation. MethodsConjunctival vessels widths and tortuous segment length of conjunctival vessels of 96 patients with type 2 diabetes mellitus were photographed and measured by the Zeiss Fundus camera Visupac software. The measurements were correlated with retinopathy grade in those eyes. ResultsThe mean conjunctival vessel width was 40.61μ (SD 17.25) with a uniform increase from 34.4μ (SD 8.70) in mild NPDR to 53.50μ (SD 33.45) in the PDR group which was statistically significant (p<0.01). The tortuous conjunctival vessel segment length increased from 711.51μ (SD 83.90) in the mild NPDR group to 921.94μ (SD 129.26) in those with PDR (p<0.01). Vessel width greater than 80μ was seen only in PDR and tortuosity values greater than 900μ were seen in severe grades (severe NPDR and PDR). Both conjunctival vessel width and tortuosity showed a positive statistical correlation with increasing severity of retinopathy (r=0.386, r2=0.149 and r=0.645, r2=0.415). ConclusionA positive correlation was seen between conjunctival vessel width and tortuosity with severity of retinopathy. Widths over 80μ and tortuous segment length over 900μ are suggestive of severe grades of retinopathy.

An Ensemble Modeling Approach for Estimating Diffusive Tortuosity for Saturated Soils From Porosity

Apparent diffusion constants in soil are generally estimated by dividing molecular diffusion coefficient for a solute with soil tortuosity (τ) values. Several models have been proposed to estimate τ from soil porosity (ϕ) alone, but most of these models fail when the variability in observed τ-ϕ pairs increases. Pedotransfer functions can be used to predict τ from easy-to-measure soil properties such soil texture, organic carbon contents, and ϕ, but such an approach requires more measurements to be performed than just measuring ϕ. Here, we show that τ may be estimated from ϕ alone using the ensemble averaging approach. We examined seven different analytical expressions for τ-ϕ and seven different ensemble-modeling approaches to estimate τ for 100 pairs of τ-ϕ collected from a wide geographical area. Modeling results showed that the Bayesian model averaging method was the best ensemble-modeling approach for estimating τ from ϕ. Of 119 different combinations of τ (ϕ) models, three models derived considering (1) packing of square-shaped particles, (2) fractal geometry with particles of different sizes, and (3) percolation theory were identified as the best individual models for ensemble modeling. The coefficient of determination (0.67), root-mean-squared error (0.23), and the Akaike information criterion (94.37) values for this ensemble model were better than those when a single model was used for prediction. Inclusion of these three models that are based on both fractal and regular geometrical shapes for particles of different sizes may be a reason for improved performance of the ensemble approach. These results suggest that τ may be estimated from ϕ using the ensemble approach without the need for additional soil data, as is done in a pedotransfer function approach.