Transport Properties Of Porous Materials Research Articles

Porosity-permeability tensor relationship of closely and randomly packed fibrous biomaterials and biological tissues: Application to the brain white matter

The constitutive model for the porosity-permeability relationship is a powerful tool to estimate and design the transport properties of porous materials, which has attracted significant attention for the advancement of novel materials. However, in comparison with other materials, biomaterials, especially natural and artificial tissues, have more complex microstructures e.g. high anisotropy, high randomness of cell/fibre dimensions/position and very low porosity. Consequently, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive. To fill this gap, we start a mathematical derivation from the fundamental brain white matter (WM) formed by nerve fibres. This is augmented by a numerical characterisation and experimental validations to obtain an anisotropic permeability tensor of the brain WM as a function of the tissue porosity. A versatile microstructure generation software (MicroFiM) for fibrous biomaterial with complex microstructure and low porosity was built accordingly and made freely accessible here. Moreover, we propose an anisotropic poro-hyperelastic model enhanced by the newly defined porosity-permeability tensor relationship which precisely captures the tissues macro-scale permeability changes due to the microstructural deformation in an infusion scenario. The constitutive model, theories and protocols established in this study will both provide improved design strategies to tailor the transport properties of fibrous biomaterials and enable the non-invasive characterisation of the transport properties of biological tissues. This will lead to the provision of better patient-specific medical treatments, such as drug delivery. Statement of significanceDue to the microstructural complexity, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive, which hinders our way of tuning the fluid transport property of the biomaterials by directly programming their microstructure. The same problem hinders non-invasive characterisations of fluid transport properties in biological tissues, which can significantly improve the efficiency of treatments e.g. drug delivery, directly from the tissues accessible microstructural information, e.g. porosity. Here, we developed a validated mathematical formulation to link the random microstructure to a fibrous material’s macroscale permeability tensor. This will advance our capability to design complex biomaterials and make it possible to non-invasively characterise the permeability of living tissues for precise treatment planning. The newly established theory and protocol can be easily adapted to various types of fibrous biomaterials.

Discrete modelling of hydro-chemo-mechanical performance of clay materials

The truncated octahedron cellular assemblies are used to represent the clay materials which align with experimentally characterised microstructures. The cellular assembly is divided into two interacting graphs: one is the mechanical graph which is developed to describe the deformation behaviour of the material, and the other is physical/chemical graph which is developed to demonstrate the reactive transport in the material. This setting is realistic especially when the mechanically-driven cracking has an impact on the transport pathways. Both graphs can represent the anisotropy and heterogeneity of the materials. The model performance is demonstrated using experimental data on the diffusion of species through Opalinus clay (OPA) – a complex process that involves elastic response, diffusion and anionic exclusion. The accuracy of the model is validated by the simulating the confining pressure and reactions dependency of different species transport through OPA. The model improves the understanding of the microstructure influence on the macroscopic transport properties of porous materials. The developed model can be applied to a variety of scientific and engineering problems, such as hydraulic cracking of gas-bearing shale, radioactive nuclear waste geo-disposal, contaminated soil remediation and geological carbon storage.

The influence of activator type and quantity on the transport properties of class F fly ash geopolymer

It is known that transport properties of porous materials were important in terms of its durability aspect. In this paper, the effect of activator type, Na amount on the transport properties of geopolymer mortar made with class F fly ash were explored. Two different class F fly ash were employed in producing geopolymer that activated alkaline solutions. As alkali activator, sodium hydroxide solution, and combination of sodium silicate with sodium hydroxide were used. Activator contained 6%, 9%, 12% and 15% of fly ash weight as Na amount. Heat curing regimes were imposed to specimens at 100 °C temperature for 24 h duration. Tests were carried out on the geopolymer samples including water absorption, volume of permeable voids, sorptivity, depth of penetration of water under pressure, chloride ion penetration and accelerated corrosion. It is found that the transport properties of geopolymer samples are improved by increasing the Na amounts of mortar mixtures from 6% to 15%. In general, better results were obtained with 15% Na ratio. The mortars produced with only sodium hydroxide have shown better transport properties than mortars made with combination of sodium hydroxide-sodium silicate mixture.

A Mass Transport Model for Flows in Channels and Porous Media of Fuel Cells

Low-temperature fuel cells are a promising alternative technology to conventional energy systems such as internal combustion engines. However, their large-scale commercialization is still limited due to several challenges, such as mass transport losses at high power densities [1]. Estimation of gas transport properties in porous materials of fuel cells, such as gas diffusion layers (GDLs), is therefore critical. Several experimental studies in literature estimated the permeability of different GDL samples using a one-dimensional model, which does not account for channel effects [1-6]. Some authors in literature have assumed that the flow is incompressible in their numerical studies [7-10]. This hypothesis is not justified because the error in permeability estimation with an incompressible fluid flow model compared to the estimation with a compressible fluid flow model can be as high as 20% [2]. Numerical models for channels and porous media require volume-averaged formulations, and an in-depth discussion on the physical meaning of density and velocity in these models is seldom found in literature. Also, most of the existing numerical studies neglect the anisotropic nature of GDLs.In this work, a volume-averaged form of the steady-state, compressible, and isothermal Navier-Stokes equations for flows in channels and porous materials is developed and implemented in the open-source framework OpenFCST [11]. Particular attention is given to flows in channels and GDLs of polymer electrolyte fuel cells. The fluid flow model in porous materials is derived by means of the method of volume averaging [12]. A continuous Galerkin finite element method is used to discretize and numerically solve the resulting system of governing equations in the framework of a single domain approach. The coupling boundary conditions at the internal interface between channels and porous media are discussed and a stable non-oscillatory pair of solution variables in the porous domain is obtained. The study reveals that for volume-averaged formulations, the permeability obtained in experiments has to be corrected with the sample porosity. The model is used to estimate in-plane and through-plane permeabilities of fuel cell diffusion media, which is compared to experimental data. Three-dimensional simulations show that channel effects cannot be neglected and therefore one-dimensional models for permeability estimation are limited. Assuming that the fluid is incompressible is only valid for through-plane permeability, and a compressible formulation should be used for in-plane simulations, even at moderate gas flow rates. The suitability of the mathematical model for fuel cell applications is illustrated by estimating the change in pressure drop in a serpentine channel in contact with either a solid wall or a gas diffusion media. An interdigitated channel design is also considered in order to compare the pressure drop and the velocity in the GDL with the results observed with a serpentine channel.

A Permeability–Throat Diameter Correlation for a Medium Generated with Delaunay Tessellation and Voronoi Algorithm

Describing different transport phenomena through porous media at micro- and mesoscale represents a convenient pre-step in experimental characterization for materials. A detailed study of transport properties in porous materials is required to find suitable microstructural configurations which allow a better performance into mechanic/hydraulic system. Porous media are widely used in several fields of application such as in fuel cells (different layers inside the device) and geological sciences (soil properties). The purpose of the present work is to propose a permeability correlation for digitally created three-dimensional (3D) pore media considering the diameter of the throats connecting the pores within the domain. The 3D samples are generated by means of the Delaunay tessellation and Voronoi algorithm for pore position and throat characteristics, respectively. The model implementation is carried out by using OpenPNM, an open-source pore network modeling package, which has proven to be a powerful tool to compute several transport phenomena for porous media applications. Several samples have been created keeping the pore diameter as a constant, while the throat diameter connecting the pores is changing for a selected range of values in order to analyze the impact of the throat diameter on the permeability. A correlation to compute the permeability as a function of the throat diameter with a coefficient of determination of 95% has been proposed.

Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media

AbstractWe statistically infer fluid flow and transport properties of porous materials based on their geometry and connectivity, without the need for detailed We summarize structure by persistent homology and then determines the similarity of structures using image analysis and statistics. Longer term, this may enable quick and automated categorization of rocks into known archetypes. We first compute persistent homology of binarized 3D images of material subvolume samples. The persistence parameter is the signed Euclidean distance from inferred material interfaces, which captures the distribution of sizes of pores and grains. Each persistence diagram is converted into an image vector. We infer structural similarity by calculating image similarity. For each image vector, we compute principal components to extract features. We fit statistical models to features estimates material permeability, tortuosity, and anisotropy. We develop a Structural SIMilarity index to determine statistical representative elementary volumes.

Theoretical framework for percolation threshold, tortuosity and transport properties of porous materials containing 3D non-spherical pores

Understanding the effects of porous network characteristics including the percolation and tortuosity on transport properties of porous materials is of great importance for the design and optimization of such materials, e.g., for superior resistance to degradation due to the transfer of corrosive fluids. Meanwhile, the percolation and tortuosity of porous networks are strongly affected by the geometrical shape of pores. In this work, we devise a generic theoretical framework for the accurate predictions of the percolation threshold and tortuosity of porous networks and a variety of transport properties of two-phase porous materials composed of three-dimensional (3D) interpenetrating non-spherical pores randomly distributed in a homogeneous solid matrix. Our framework contains three major components: (1) a coupled scheme of Monte Carlo simulations and a rigorous excluded-volume percolation model for determining of the percolation threshold of porous networks; (2) a continuum percolation-based tortuosity model (CPTM) for deriving the geometrical tortuosity of porous networks near the percolation threshold and above; and (3) a continuum percolation-based generalized effective medium theory (CP-GEMT) for predicting various effective transport properties including the effective diffusivity, permeability, electrical and thermal conductivity of porous materials over the entire range of porosities. The theoretical framework yields accurate predictions of the percolation threshold, tortuosity and various effective transport properties, which are verified and validated using extensive experimental, numerical and analytical data for a wide spectrum of different porous materials reported in literature. Our framework is readily applicable to other non-spherical percolating networks composed of interpenetrating discrete objects like cracks, particles, interfaces, capsules and tunneling networks though 3D spherocylindrical porous networks are used as an introductory example in this work. Finally, we utilize the framework to explore the influences of the pore geometrical configurations on the tortuosity and effective diffusivity of porous materials. The results shed light on the intrinsic and complex interplay of components, structures and transport properties in porous materials, which in turn can provide novel insights for understanding degradation of porous materials in practical applications.

Laser-induced alteration of microstructural and microscopic transport properties in porous materials: Experiment, modeling and analysis

Porous materials are of great importance in various industrial applications. Microscopic modifications in the pore structures of these materials can change their functional behavior. We treat Indiana limestone by lasers to modify its pore structures microscopically. Microcomputed tomography (micro-CT) of the treated samples reveal that pulsed Nd:YAG laser with energy 330 mJ increases open porosity of limestone by 15% and almost doubles the total porosity. This laser increases the limestone pore connectivity by 460%. High power CO2 laser increases the open porosity by 20% but it reduces the pore connectivity of limestone. Our findings show that pulsed laser beams induce high increase in porosity and connectivity. 3D pore scale modeling using Cascaded lattice Boltzmann method (CLBM) on a D3Q27 model shows that regions treated by pulsed Nd:YAG lasers exhibit enhanced fluid transport efficiency compared to untreated regions. The obtained results successfully demonstrate that lasers can be used to induce a well controlled heat transfer in porous materials directly enhancing their morphometric characteristics and microscopic fluid transport behavior.

Relation between the porosity and tortuosity of a membrane formed by disconnected irregular pores and the spatial diffusion coefficient of the Fick-Jacobs model.

In this work, we provide a theoretical relationship between the spatial-dependent diffusion coefficient derived in the Fick-Jacobs (FJ) approximation and the macroscopic diffusion coefficient of a membrane that depends on the porosity, tortuosity, and the constriction factors. Based on simple mass conservation arguments under equilibrium as well as in nonequilibrium conditions, we generalize previous expressions for the effective diffusion coefficient of an irregular pore, originally obtained by Festa and d'Agliano for horizontal and periodic pores, and then extended by Bradley for tortuous periodic pores, to the case of pores with arbitrary geometry. Through a formal definition of the constrictivity factor in terms of the geometry of the pore, our results provide very clear physical interpretation of experimental measurements since they link the local properties of the flow with macroscopic quantities of experimental relevance in the design and optimization of porous materials. The macroscopic diffusion coefficient as well as the spatiotemporal evolution of the concentration profiles inside a pore have been recently measured by using pulse field gradient NMR techniques. The advantage of using the FJ approach is that the spatiotemporal concentration profile inside a pore of irregular geometry is directly related to the pore's shape and, therefore, that the macroscopic diffusion coefficient can be obtained by comparing the spatiotemporal concentration profiles from such experiments with those of the theoretical model. Hence, the present study is relevant for the understanding of the transport properties of porous materials where the shape and arrangement of pores can be controlled at will.

Effect of capillary condensation on gas transport properties in porous materials

Effect of capillary condensation on gas transport properties in porous materials

Three‐dimensional pore structure and ion conductivity of porous ceramic diaphragms

The ion conductivity of two series of porous ceramic diaphragms impregnated with caustic potash was investigated by electrochemical impedance spectroscopy. To understand the impact of the pore structure on ion conductivity, the three‐dimensional (3‐D) pore geometry of the diaphragms was characterized with synchrotron x‐ray absorption tomography. Ion migration was calculated based on an extended pore structure model, which includes the electrolyte conductivity and geometric pore parameters, for example, tortuosity (τ) and constriction factor (β), but no fitting parameters. The calculated ion conductivities are in agreement with the data obtained from electrochemical measurements on the diaphragms. The geometric tortuosity was found to be nearly independent of porosity. Pore path constrictions diminish with increasing porosity. The lower constrictivity provides more pore space that can effectively be used for mass transport. Direct measurements from tomographs of tortuosity and constrictivity opens new possibilities to study pore structures and transport properties of porous materials.

Numerical estimation of transport properties of cementitious materials using 3D digital images

A multi-scale characterisation of the transport process within cementitious microstructure possesses a great challenge in terms of modelling and schematization. In this paper a numerical method is proposed to mitigate the resolution problems in numerical methods for calculating effective transport properties of porous materials using 3D digital images. The method up-scales sub-voxel information from the fractional occupancy level of the interface voxels, i.e. voxels containing phaseboundary, to increase the accuracy of the pore schematization and hence the accuracy of the numerical transport calculation as well. The numerical identification of the subvoxels that is associated with their level of occupancy by each phase is obtained by increasing the pre-processing resolution. The proposed method is presented and employed for hydrated cement paste microstructures obtained from Hymostruc, a numerical model for cement hydration and microstructure simulation. The new method significantly reduces computational efforts, is relatively easy to implement, and improves the accuracy of the estimation of the effective transport property.

The influence of constrictivity on the effective transport properties of porous layers in electrolysis and fuel cells

The aim of the present investigation is to define microstructure parameters, which control the effective transport properties in porous materials for energy technology. Recent improvements in 3D-imaging (FIB-nanotomography, synchrotron X-ray tomography) and image analysis (skeletonization and graph analysis, transport simulations) open new possibilities for the study of microstructure effects. In this study, we describe novel procedures for a quantitative analysis of constrictivity, which characterizes the so-called bottleneck effect. In a first experimental part, methodological tests are performed using a porous (La,Sr)CoO3 material (SOFC cathode). The tests indicate that the proposed procedure for quantitative analysis of constrictivity gives reproducible results even for samples with inhomogeneous microstructures (cracks, gradient of porosity). In the second part, 3D analyses are combined with measurements of ionic conductivity by impedance spectroscopy. The investigations are preformed on membranes of electrolysis cells with porosities between 0.27 and 0.8. Surprisingly, the tortuosities remain nearly constant (1.6) for the entire range of porosity. In contrast, the constrictivities vary strongly and correlate well with the measured transport resistances. Hence, constrictivity represents the dominant microstructure parameter, which controls the effective transport properties in the analysed membrane materials. An empirical relationship is then derived for the calculation of effective transport properties based on phase volume fraction, tortuosity, and constrictivity.

Determination of Material Properties of Gas Diffusion Layers: Experiments and Simulations Using Phase Contrast Tomographic Microscopy

Understanding the transport properties of porous materials plays an important role in the development and optimization of polymer electrolyte fuel cells (PEFCs). In this study numerical simulations of different transport properties are compared and validated with data obtained using recently developed experimental techniques. The study is based on a Toray TGP-H-060 carbon paper, a common gas diffusion layer (GDL) material in PEFC. Diffusivity, permeability, and electric conductivity of the anisotropic, porous material are measured experimentally under various levels of compression. A sample of the GDL is imaged with synchrotron-based X-ray tomography under three different compression levels. Based on these three-dimensional images, diffusivity, permeability, and conductivity are calculated numerically. Experimental and numerical results agree in general. Deviations are observed for the through-plane conductivity. An explanation for the discrepancy is presented and affirmed by numerical simulations on a virtually created structure model. This proves that numerical simulation based on tomography data is a versatile tool for the investigation and development of porous structures used in PEFCs.

New insights into the relationship between internal phase level of emulsion templates and gas–liquid permeability of interconnected macroporous polymers

Interconnected macroporous polymers can be made by polymerisation of emulsion templates consisting of an aqueous phase and a monomer phase (typically styrene and divinylbenzene) in which the aqueous (internal) phase is in the form of drops and the monomer phase is the continuous phase between the drops. Until recently it was thought that interconnected macroporous polymers could only be produced from the polymerisation of high internal phase emulsion (HIPE) templates with an internal phase level exceeding 74 vol%. Improvement of the poor mechanical performance, characteristic of such macroporous polymers, was achieved simply by increasing the material density of the macroporous polymer. However, this required a reduction in the internal phase volume of the emulsion template. Polymerisation of the continuous organic phase of emulsion templates with an internal phase volume ranging from 84 vol% to 70 vol% resulted in the production of poly(merised)HIPEs, polymerisation of medium internal phase emulsions with internal phase volume ranging from 70 vol% to 30 vol% in polyMIPEs and polymerisation of a low internal phase emulsion with an internal phase volume of 25 vol% in a polyLIPE. The resulting macroporous polymers were characterised in terms of mechanical and structural properties as well as gas and mercury permeability. Compression tests show that mechanical properties improved as the material density was increased. Gas and mercury permeability measurements show that as the internal phase volume of the emulsion template is reduced, the permeability of the resultant macroporous polymer is also reduced. However, surprisingly even macroporous polymers produced from low internal phase emulsion templates (25 vol%) were permeable with a gas permeability of 2.6 × 10−14m2 indicating that polyLIPEs are still interconnected macroporous polymers. Reconstruction modelling of the transport properties of porous materials shows that the permeability of a porous material with similar structures to that of the macroporous polymers increases exponentially with the porosity.

Investigation of transport phenomena in porous structures containing three fluid phases

The spatial distribution of three fluid phases inside pore structures is determined through the minimization of total interfacial energy. A modified simulated annealing scheme is used for the determination of the optimal configuration rendering the method efficient at low saturations. The study in a further step of the distributions of the fluid phases in single and multipore domains indicates that the combination of the digital reconstruction with the annealing-based technique can adequately represent those multiphase systems. The proposed method provides the basis for the future prediction of sorption and transport properties of porous materials filled with more than two fluid phases. In order to testify the method, the tracer diffusion in a random sphere packing filled by three fluid phases as well as the creeping flow of a fluid phase through the same porous structure when the pore space is occupied by two immobile fluid phases, are investigated. The effective diffusivities are computed by a random walk method. The relative permeabilities are determined through the solution of Stokes equations using a finite-difference scheme in conjunction with the artificial compressibility relaxation algorithm. It is found that the aforementioned transport properties of the wetting and the non-wetting phases are in a good agreement with pertinent literature data and also are independent of whether the pore space is occupied by two or three fluid phases. The former reinforces the reliability of the proposed fluid-phase distribution technique. For both effective diffusivities and relative permeabilities, a number of very useful empirical equations, when only one fluid phase is conducting, are generated.

Characterisation of the gas transport properties of porous materials by determining the radon diffusion coefficient

A method for the determination of the diffusion coefficient of materials by using the radioactive gas radon is presented. This gas is inert and extremely low concentrations can be detected because of the radioactive decay. The method was applied to mortars and concretes in order to optimise their composition with respect to a low radon diffusion rate. These optimised materials are to be used for concrete slabs in buildings. Compared to regular concrete, a reduction of the radon diffusion rate by more than 90% could be achieved.

Capillary water migration in rock: process and material properties examined by NMR imaging

We report the application of proton nuclear magnetic resonance (NMR) imaging to the measurement of water content distributions in Lepine limestone, a typical constructional stone. The method is used to observe the kinetics of the absorption of water into this material by capillarity. The water content distributions are consistent with the predictions of unsaturated flow theory. The hydraulic diffusivity of Lepine stone is found to be an approximately exponential function of the water content, in agreement with experimental data on other porous materials. The best estimate of the diffusivity function is D (m2s−1) = 6.3 × 10−9 exp (4.90θr), whereθr is the normalized volumetric water content. The sorptivity estimated from NMR data is in close agreement with the directly measured value (1.00 mm min−1/2). NMR imaging methods appear promising as a non-destructive and rapid laboratory means of determining moisture distributions, especially for the purpose of accurate measurement of the capillary transport properties of porous materials.

Analysis of the one-dimensional moisture migration caused by temperature gradients in a porous medium

An analytical solution is obtained for the one-dimensional moisture migration in a slab of porous material under the influence of temperature gradients. The solution is relevant to such problems as the moisture redistribution in soil under the influence of solar heat, the moisture migration in the vicinity of earth sheltered structures, the measurement of transport properties of porous materials and others.