Geometric and Topological Analysis of Three-Dimensional Porous Media: Pore Space Partitioning Based on Morphological Skeletonization

This article presents a versatile, rigorous, and efficient methodology for extracting various geometric and topological parameters of 3D discrete porous media. The new approach takes advantage of the morphological skeleton of the pore structure-a lower dimensional representation of the pore space akin to the topological "deformation retract". The skeleton is derived by a fully parallel thinning algorithm that fulfils two essential requirements: it generates a medial axis and preserves the connectivity of the pore space. Topological analysis is accomplished by classifying all skeleton points as node or link (branch) points according to the concept of lambda-adjacency in 3D discrete space. In this manner, node coordination number and link length distributions are directly obtained from the skeleton. Pore necks (throats) are identified through a search for minima in the hydraulic radius of individual pore space channels outlined by skeleton links. In addition to the determination of the size distribution of the constrictions (pore necks) that control nonwetting phase invasion, improved estimates of the distributions of effective hydraulic and electric conductivity of individual pore space channels are obtained. Furthermore, erection of planes at the location of pore necks results in partitioning of the pore space into its constituent pores. This enables the characterization of the pore space in terms of a pore volume distribution. The new methodology is illustrated by application to a regular cubic pore network and irregularly shaped 2D and 3D pore networks generated by stochastic simulation. In the latter case, important new results are obtained concerning the sensitivity of geometric and topological properties of the microstructure to the parameters of stochastic simulation, namely, the porosity and correlation function. It is found that model porous media reconstructed from the same porosity and correlation function can exhibit marked differences in geometry and connectivity, which correlate with differences in specific surface area. Copyright 2000 Academic Press.     

Structural and Transport Properties of Alumina Porous Membranes from Process-Based and Statistical Reconstruction Techniques

We study the structural and transport properties of two model porous membranes made by compaction of spherical monosize gamma-alumina particles. A ballistic deposition process of spherical particles has been employed as a process-based representation method for accurately simulating the pore structure of the membranes. Comparison between the computed and experimental permeability values obtained in the Knudsen regime shows very good agreement for both membranes and indicates that sufficient representation of the original pore structure is achieved with the random sphere packs. In a further step, a medium with the same porosity and autocorrelation function as the sphere pack has been stochastically reconstructed. Comparison between the structural properties of the random sphere pack system (process-based model) and the stochastically reconstructed medium (statistical model) shows nearly identical correlation functions and pore chord length distributions but widely different mass chord length distributions. This is reflected to a significant difference in the prediction of a dynamic property like the Knudsen permeability by a factor of about 4. The results suggest that matching of the porosity and the two-point correlation function alone is not always adequate when pursuing an accurate representation of the structure of a porous material. In such cases, higher order statistical properties of the material contained in the chord length distribution of both pore and solid phase should be satisfied as well. It is also found that proper account of the formation process in the reconstruction of a porous material (process-based model) leads to representations of its structure more accurate than those of statistical reconstruction models. Copyright 2000 Academic Press.     

Modeling liquid porosimetry in modeled and imaged 3-D fibrous microstructures

In this paper, an analysis to distinguish the geometric and porosimetric pore size distributions of a fibrous material is presented. The work is based on simulating the intrusion of nonwetting fluid in a series of 3-D fibrous microstructures obtained from 3-D image reconstruction or virtual geometries mathematically generated according to the properties of the media. We start our study by computing the pore size distribution of two typical hydroentangled nonwoven materials and present a theoretical model for their geometric pore size distributions based on Poisson line network model of the fibrous media. It is shown that the probability density function of the geometric pore size distribution can be approximated by a two-parametric Gamma distribution. We also study connectivity of the pore space in fibrous media by computing and comparing the accessible and allowed pore volumes in the form access function graphs. It is shown that the so-called ink-bottle effect can significantly influence the fluid intrusion in a porous material. The pore space connectivity of a homogeneous fibrous media is observed to be a function of thickness, solid volume fraction (SVF), and fiber diameter. It is shown that increasing the materials' thickness or SVF, while other properties are kept constant, reduces the pore space connectivity. On the other hand, increasing the fiber diameter enhances the connectivity of the pores if all other parameters are fixed. Moreover, modeling layered fibrous microstructures; it is shown that the access function graphs can be used to detect the location of the bottle neck pores in a layered/composite porous material.     

A statistical model for the heterogeneous structure of porous catalyst pellets

The complex structures of the void space of porous media are often characterised by parameters such as pore network connectivity and lattice size. This paper presents a comparison of the estimates of these parameters obtained from two previous methods based on nitrogen sorption and mercury porosimetry, and also from a new, completely independent approach based on pulsed-gradient spin-echo nuclear magnetic resonance (PGSE NMR). It was found that the new PGSE NMR technique obtains estimates of connectivity and lattice size in agreement with nitrogen sorption but different to mercury porosimetry. This difference was attributed to the various physical processes involved actually probing different aspects of the pore space geometry. It was further suggested that the representation of the pore structure derived from either nitrogen sorption or PGSE NMR is really a mapping of the real pore space onto an equivalent abstract, random pore bond network. However, it has been shown that this mapping does capture some of the characteristic properties of the pore space that control transport over mesoscopic ( < 10 microm) length scales. For materials which additionally possessed macroscopic (> 10 microm) structural heterogeneity, it was found that the model could also be adapted to predict the macroscopic transport properties of the porous medium.     

Simulation of electrical-conduction and filtration processes in porous media

Results of simulation of electrical-conduction and filtration processes in porous media have been reported. For better visualization and simplification of the analysis of the results obtained, simple model distributions of pore sizes with the patterns of a triangle, rectangle, semiellipse, etc., have been used. The porous medium has been simulated in terms of a capillary lattice model, which represents a three dimensional cubic lattice of capillaries the sizes and number of which are selected according to a preset pore size distribution. The data obtained reflect the general regularities of the influence of the pore structure on the transfer processes, show the interrelation between the parameters characterizing these processes, and illustrate the potential of the capillary-lattice model for describing the properties of porous media.     

Electrical conductivity of porous media with two-phase saturation

Relations are derived for calculating the electrical conductivity of porous media with two-phase saturation. The considered calculations are based on a capillary-lattice model of a porous medium, the model being composed of several unequally scaled three-dimensional cubic lattices of capillaries. Each lattice may be represented as a large number of analogous cubic cells with the same structure of pore space and a preset pore size distribution over the cells. The distribution of porosity over pore sizes serves as a starting datum for the calculation of all model parameters. The number and scale of lattices are determined by the peculiarities of this distribution. The possibilities of practical use of the considered model are shown by the example of experimental data on samples of porous rocks. The results obtained, in particular, suggest that the model is applicable to solving problems of applied geophysics relevant to determining the saturation of rocks with water and hydrocarbons.     

The Potentials of Pulsed Field Gradient NMR for Investigation of Porous Media

PFG NMR self-diffusion studies provide information on the translational mobility of fluid molecules. Since in porous media the diffusion path of fluid molecules in the pore space is affected by interaction with the pore wall, PFG NMR measurements are sensitive to structural peculiarities of the confining porous medium. The pore space properties which can be investigated depend on length scales set by the PFG NMR experiment in respect to the typical size of the structural feature studied. Based upon these length scales, an interpretation pattern for PFG NMR self-diffusion studies in porous media is given. PFG NMR self-diffusion studies in macro- and microporous systems such as sedimentary rocks and zeolite crystallites, respectively, are reviewed.     

Construction by molecular dynamics modeling and simulations of the porous structures formed by dextran polymer chains attached on the surface of the pores of a base matrix: characterization of porous structures

Significant increases in the separation of bioactive molecules by using ion-exchange chromatography are realized by utilizing porous adsorbent particles in which the affinity group/ligand is linked to the base matrix of the porous particle via a polymeric extender. To study and understand the behavior of such systems, the M3B model is modified and used in molecular dynamics (MD) simulation studies to construct porous dextran layers on the surface of a base matrix, where the dextran polymer chains and the surface are covered by water. Two different porous polymer layers having 25 and 40 monomers per main polymer chain of dextran, respectively, are constructed, and their three-dimensional (3D) porous structures are characterized with respect to porosity, pore size distribution, and number of conducting pathways along the direction of net transport. It is found that the more desirable practical implications with respect to structural properties exhibited by the porous polymer layer having 40 monomers per main polymer chain, are mainly due to the higher flexibility of the polymer chains of this system, especially in the upper region of the porous structure. The characterization and analysis of the porous structures have suggested a useful definition for the physical meaning and implications of the pore connectivity of a real porous medium that is significantly different than the artificial physical meaning associated with the pore connectivity parameter employed in pore network models and whose physical limitations are discussed; furthermore, the methodology developed for the characterization of the three-dimensional structures of real porous media could be used to analyze the experimental data obtained from high-resolution noninvasive three-dimensional methods like high-resolution optical microscopy. The MD modeling and simulations methodology presented here could be used, considering that the type and size of affinity group/ligand as well as the size of the biomolecule to be adsorbed onto the affinity group/ligand are known, to construct different porous dextran layers by varying the length of the polymeric chain of dextran, the number of attachment points to the base matrix, the degree of side branching, and the number of main polymeric chains immobilized per unit surface area of base matrix. After the characterization of the porous structures of the different porous dextran layers is performed, then only a few promising structures would be selected for studying the immobilization of adsorption sites on the pore surfaces and the subsequent adsorption of the bioactive molecules onto the immobilized affinity groups/ligands.     

聚乙烯醇多孔膜的制备

以醋酸乙烯酯微乳液聚合所得的微乳粒子为占孔物质,通过辅助倒相法制备了聚乙烯醇多孔膜,其中部分孔的尺寸与占孔微乳粒子的大小相近（小于300nm)。利用透射电镜观测微乳粒子的大小和形态并且在扫描电镜下观察PVA多孔膜的孔形态,探讨了通过控制微乳粒子粒径以实现多孔膜孔径调节的可行性。     

Comparison of the Adsorption Behavior and Porosity of Clay and Various Porous Clays

Recently, microporous materials,displaying zeolite-type properties, have attracted much interest^[1]. As one of the most interesting synthetic molecular sieves^[2],the porosity of porous clays plays a very important role on the application of microporous materials. Here we investigate the adsorption behavior and the pore size distributions of several porous clays materials by using N₂ adsorption at low temperature (77 K),and discuss the influences of different crosslinking agents on resulting porosity of porous clays.     

Nanoporous metals with controlled multimodal pore size distribution

A simple two-step dealloying strategy is described to make free-standing metal membranes with hierarchical porous architecture. This structure has a bimodal pore size distribution composed of large porosity channels and small porosity channel walls, where each pore size can be tailored independently of the others. A new gas-phase electroless plating technique was also developed here that could be used to uniformly fill porous structures with pore size as small as 10 nm.     

Pore structure of the packing of fine particles

This paper presents a numerical study of the pore structure of fine particles. By means of granular dynamics simulation, packings of mono-sized particles ranging from 1 to 1000 microm are constructed. Our results show that packing density varies with particle size due to the effect of the cohesive van der Waals force. Pores and their connectivity are then analysed in terms of Delaunay tessellation. The geometries of the pores are represented by the size and shape of Delaunay cells and quantified as a function of packing density or particle size. It shows that the cell size decreases and the cell shape becomes more spherical with increasing packing density. A general correlation exists between the size and shape of cells: the larger the cell size relative to particle size, the more spherical the cell shape. This correlation, however, becomes weaker as packing density decreases. The connectivity between pores is represented by throat size and channel length. With decreasing packing density, the throat size increases and the channel length decreases. The pore scale information would be useful to understand and model the transport and mechanical properties of porous media.     

Single- and two-phase flow in microfluidic porous media analogs based on Voronoi tessellation

The objective of this study was to create a microfluidic model of complex porous media for studying single and multiphase flows. Most experimental porous media models consist of periodic geometries that lend themselves to comparison with well-developed theoretical predictions. However, many real porous media such as geological formations and biological tissues contain a degree of randomness and complexity at certain length scales that is not adequately represented in periodic geometries. To design an experimental tool to study these complex geometries, we created microfluidic models of random homogeneous and heterogeneous networks based on Voronoi tessellations. These networks consisted of approximately 600 grains separated by a highly connected network of channels with an overall porosity of 0.11-0.20. We found that introducing heterogeneities in the form of large cavities within the network changed the permeability in a way that cannot be predicted by the classical porosity-permeability relationship known as the Kozeny equation. The values of permeability found in experiments were in excellent agreement with those calculated from three-dimensional lattice Boltzmann simulations. In two-phase flow experiments of oil displacement with water we found that the wettability of channel walls determined the pattern of water invasion, while the network topology determined the residual oil saturation. The presence of cavities increased the microscopic sweeping efficiency in water-oil displacement. These results suggest that complex network topologies lead to fluid flow behavior that is difficult to predict based solely on porosity. The novelty of this approach is a unique geometry generation algorithm coupled with microfabrication techniques to produce pore scale models of stochastic homogeneous and heterogeneous porous media. The ability to perform and visualize multiphase flow experiments within these geometries will be useful in measuring the mechanism(s) of displacement within micro- and nanoscale pores.     

Pore Modification in Porous Ceramic Membranes With Sol-Gel Process and Determination of Gas Permeability and Selectivity

Summary: The aim of the study was to investigate the variation in total surface area, porosity, pore size, Knudsen and surface diffusion coefficients, gas permeability and selectivity before and after the application of sol-gel process to porous ceramic membrane in order to determine the effect of pore modification. In this study, three different sol-gel process were applied to the ceramic support separately; one was the silica sol-gel process which was applied to increase porosity, others were silica-sol dip coating and silica-sol processing methods which were applied to decrease pore size. As a result of this, total surface area, pore size and porosity of ceramic support and membranes were determined by using BET instrument. In addition to this, Knudsen and surface diffusion coefficients were also calculated. After then, ceramic support and membranes were exposed to gas permeation experiments by using the CO₂ gas with different flow rates. Gas permeability and selectivity of those membranes were measured according to the data obtained. Thus, pore surface area, porosity, pore size and Knudsen diffusion coefficient of membrane treated with silica sol-gel process increased while total surface area was decreasing. Therefore, permeability of ceramic support and membrane treated with silica sol-gel process increased, and selectivity decreased with increasing the gas flow rate. Also, surface area, porosity, pore size, permeability, selectivity, Knudsen and surface diffusion coefficients of membranes treated with silica-sol dip coating and silica-sol processing methods were determined. As a result of this, porosity, pore size, Knudsen and surface diffusion coefficients decreased, total surface area increased in both methods. However, viscous flow and Knudsen flow permeability were detected as a consequence of gas permeability test and Knudsen flow was found to be a dominant transport mechanism in addition to surface diffusive flow owing to the small pore diameter in both methods. It was observed that silica-sol processing method had lower pore diameter and higher surface diffusion coefficient than silica-sol dip coating method.     

Morphological analysis of physically reconstructed capillary hybrid silica monoliths and correlation with separation efficiency

We report an experimental study on the structural (especially radial) heterogeneity of eleven 100 μm i.d. capillary tetramethoxysilane-methyltrimethoxysilane hybrid silica monoliths with different pore and skeleton sizes, which were imaged by an optimized confocal laser scanning microscopy method. This method allows the optical sectioning of the monoliths, which is a prerequisite for quantitative morphological image analysis. Both radial porosity profiles and chord length distributions were calculated in the macropore domain for each column from at least 100 complete cross-sectional views along the column axis. The statistical approach visualized radial heterogeneities on different length scales in the monolithic structures. Chord length distributions followed a simplified k-gamma function, and a structural parameter obtained from this function is introduced to provide a scalar measure of column heterogeneity. It enables the comparison of monoliths with different pore sizes and helps to establish correlations between the microscopic properties of a column, eddy dispersion, and its separation efficiency.     

Colloid-templated multisectional porous polymeric fibers

A fabrication method for porous polymeric fibers (PPFs) is reported. We show that a multisectional colloidal crystal can be assembled within a microcapillary by alternating dipping into colloidal solutions of varying size. Subsequent infiltration with curable polymer and washing with suitable solvents results in porous fibers with a cylindrical cross section. Along the length of the fiber, alternating sections of controlled length, pore size, and pore size distribution exist. These fibers present interesting materials for neural scaffolding, catalysis, and possibly photonics if produced with a high degree of crystallinity. The surface pores and bulk porosity of the fibers are characterized by variable-pressure scanning electron microscopy (vp-SEM). Careful analysis shows that the surface pores vary with the colloidal template diameter and polymer infiltration time.     

Chemico-electromechanical coupling in microporous media

We determine the macroscopic transport properties of isotropic microporous media by volume-averaging the local Nernst-Planck and Navier-Stokes equations in nonisothermal conditions. In such media, the excess of charge that counterbalances the charge deficiency of the surface of the minerals is partitioned between the Gouy-Chapman layer and the Stern layer. The Stern layer of sorbed counterions is attached to the solid phase, while the Gouy-Chapman diffuse layer is assumed to have a thickness comparable to the size of the pores. Rather than using Poisson-Boltzmann distributions to describe the ionic concentrations in the pore space of the medium, we rely on Donnan distributions obtained by equating the chemical potentials of the water molecules and ions between a reservoir of ions and the pore space of the medium. The macroscopic Maxwell equations and the macroscopic linear constitutive transport equations are derived in the vicinity of equilibrium, assuming that the porous material is deformable. In the vicinity of thermodynamic equilibrium, the cross-coupling phenomena of the macroscopic constitutive equations of transport follow Onsager reciprocity. In addition, all the material properties entering the constitutive equations depend only on two textural properties, the permeability and the electrical formation factor.     

Sintering effects related to filtration properties of porous continuously gradient ceramic structures

A single-step processing method has been previously established to prepare porous alumina microstructures by a controlled sedimentation technique whereby fine powder from an aqueous suspension consolidates over a casting slab. Metastable surface chemical control of the suspension properties was able to produce a highly porous flat disc structure with a continuously increasing mean pore size from top to bottom. Formation of this gradient structure was facilitated by using a relatively broad particle size distribution. Top layer pore sizes less than 50 nm have been achieved. Without modification, these structures are suitable for use as ultrafiltration media.The present work presents a comparison of properties and performance data for samples made with the above mentioned functionally gradient characteristics, to samples made with a more uniform microstructure. The effects of sintering time and temperature were analysed in view of overall porosity, pore size distribution and the extent of densification from the green state. These results are presented along with permeation measurements from a filtration test module.