A numerical investigation of the void structure of fibrous materials

The void structure of particulate solids has been studied with the aid of a numerical packing algorithm based on the minimisation of an energy potential. This algorithm has been used to form densely packed assemblies of spherical and fibrous particles. The void space within these materials has been characterised using an algorithm that finds chains of voids that pass through the assemblies. The tortuosity (as defined by Carman [P.C. Carman, Fluid flow through granular beds, Trans. Instn. Chem. Engrs., v15 pp 150-166, 1937.]) and mean diameter of these chains have been determined and examined as important parameters that are relevant to the permeability of these materials. Tortuosity was approximately constant in the spherical particle assemblies, while the void size varied with the particle size. In general, the spherical particle assemblies showed much smaller void sizes (relative to the particle diameter) and lower tortuosity than the fibrous materials. The tortuosity of the fibrous materials was found to be a function of both the aspect ratio of the fibres, and the packing efficiency of the assembly.     

Porosity and pore size determination in polysulfone hollow fibers

Average pore sizes and effective porosity of microporous polysulfone hollow fibers were determined by the gas permeability method. Surface structure and porosity were determined by scanning electron microscopy. The values of effective porosity ε/q² (porosity/tortuosity factor) are approximately one order of magnitude lower than those reported previously for flat sheet porous membrane. These lower values are a direct outcome of a higher polymer concentration in the spinning dope. Correlations between the wall void volume, equivalent pore size, and hydraulic permeabilities of the hollow fibers have been determined. Rather low values of ε/q² have been calculated compared to those of the void volume; these effective porosity values indicate either a very high tortuosity factor or a large number of “dead end” pores. Exposure of the fibers to elevated temperature (110°C) for a short period of time drastically reduces the surface pore size and narrows the pore size distributions, whereas overall fiber dimensions are reduced only by 1%, and 85% of the fiber's hydraulic permeability is retained. The scanning electron microscopy study reveals the formation of a relatively dense skin in some spun fibers. For such “skinned” fibers, kinetic (permeability) evaluation of static structure such as mean pore size is not realistic and is further generalized to the term “equivalent pore size.”     

Estimating transport properties of mortars using image analysis on backscattered electron images

The pore structure of two ordinary Portland cement mortars at water-cement ratio of 0.35 and 0.70 was characterised using quantitative backscattered electron imaging. The mortars were cured and conditioned to produce a range of pore structure characteristics. Image analysis was used to characterise the pore structure in terms of simple morphological parameters such as resolvable porosity and the specific surface area. These were found to be correlated to measured transport coefficients (diffusivity, permeability and sorptivity), suggesting the feasibility of image analysis to derive valuable quantitative information describing the pore structure that can be used as input values for a transport prediction model. A simple analytical model incorporating tortuosity and constrictivity was used to predict oxygen diffusivity and a variant of the Kozeny-Carman model was used to predict oxygen permeability. The diffusion model tended to over-predict for the lower w/c ratio mortar, but the general agreement was reasonable, with 90% of the estimated values within a factor of two from the measured values. The modified Kozeny-Carman model, however, over-predicted all permeability values with an error of between half to one order of magnitude.     

Frequency dispersion model of the complex permeability of the epoxy—ferrite composite

The factors that influence the complex permeability of the epoxy—ferrite composite were investigated, and the frequency dispersion behavior model for the complex permeability was proposed. The complex permeability of the composite was measured by an impedance/gain phase analyzer and a network analyzer in the frequency range from 1 MHz to 5 GHz. The permeability of the composite was increased with increasing particle size. The frequency dispersion behavior was found to be dependent on the porosity of the composite at a given particle size and ferrite content. The relaxation curve of the complex permeability became broader and flatter as the porosity increased. The equation proposed in this article coincided with the frequency dispersion behavior of the complex permeability of the composite fairly well. It was also found that the variation of σ and ν had a close relationship with the shape variation of the frequency dispersion curve, and that σ and ν were the parameters related to the porosity, particle size, and particle size distribution. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 477–482, 1997     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally.Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B.Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.     

Determination of the effects of the pore size distribution and pore connectivity distribution on the pore tortuosity and diffusive transport in model porous networks

An efficient computation method to study flow and transport process of small molecules in porous media using a dual site-bond lattice model, DBSM, is described. The microscopic properties of the porous network take into account the influence of local heterogeneities during the simulations. The numerical experiments demonstrated the combined effect of pore size distribution and connectivity distribution on the mass transport properties and the structural tortuosity. The results indicate that the pore size distribution and percolation phenomena related with pore shielding effects, influence significantly the tortuosity and the effective diffusivity of the porous network. Also, the simulations raise the important role of the connectivity distribution among the various pores in the gas diffusive properties of the poorly connected networks.     

低渗透油藏孔隙结构差异与剩余油关系研究

为研究不同低渗油田采收率差异的本质原因,对大庆扶余与长庆长6低渗透岩心分别进行润湿性实验、驱油实验,并利用岩心微观解剖方法求取孔隙参数并计算含油饱和度,找到影响剩余油主要因素,解释两油田采收率差异原因。实验结果表明,低渗透岩心以水湿为主,长庆油田低渗岩心采收率高于大庆油田,其中岩心2-2采收率比岩心1-1高3.9个百分点;同级别低渗岩心大庆油田孔隙表现出形状和连通状况的复杂性与不规则性;相同孔喉比、配位数、迂曲度和形状因子条件下,长庆油田低渗透岩心含剩余油孔隙比例更小,驱油效果更好,该研究为低渗透油藏的进一步开发提供理论支持。     

The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures

Tracer diffusion simulations within random porous structures show that tortuosity factors are independent of diffusion mechanism for all practical void fractions when an equivalent Knudsen diffusivity is correctly defined. Previous studies concluded that tortuosity factors, a geometric property of the void space as defined, increase with increasing Knudsen number, K_n, a measure of the relative number of molecule-surface and intermolecular collisions. The model porous structures in this study consist of random-loose packings of spheres overlapped to achieve a given void fraction and to accurately reflect the void space in practical porous solids. Effective diffusivities were estimated using tracer or flux-based Monte Carlo methods for Knudsen numbers of 10⁻³-10¹⁰; the two methods lead to similar diffusivities for void fractions of 0.06-0.42. Tortuosity factors estimated using the number-averaged distance between collisions, 〈l_p〉, for the characteristic void length scale increased with increasing Knudsen number, even though simulations in infinite cylinders confirmed the accuracy of the Bosanquet equation for all values of K_n. These unexpected changes in a geometric property of the void space become most apparent near the percolation void fraction (∼0.04). For example, the Knudsen tortuosity factor defined in this manner is 1.8 times larger than in the bulk regime for a solid with 0.10 void fraction. Even at high void fractions (∼0.42), the two extreme values of tortuosity factor differ by a factor of ∼1.4. These apparent effects of diffusion mechanism on tortuosities reflect the inaccurate use of number-averaged chord lengths when tracer reflections from random obstacles obey the Knudsen cosine law for diffuse reflection. A corrected length scale, first proposed by Derjaguin, leads to tortuosity factors independent of K_n for void fractions above 0.20; tortuosities differ by only 18% and 4% between Knudsen and bulk regimes even for void fractions of 0.10 and 0.15, respectively. The residual differences at void fractions below 0.10 arise from the increasingly serial nature of the remaining voids. Thus, a long-standing inconsistency between the defined geometric nature of tortuosity factors and their inexplicable dependence on diffusion mechanism is essentially resolved. In practice, these simulations allow the consistent and accurate use of tortuosity factors determined at any value of K_n for all diffusion regimes; they also prescribe, rigorously for void fractions above 0.15 and empirically for lower void fractions, the length scale relevant to diffusion in the Knudsen and transition diffusion regimes.     

Characterization of packing structure of tape cast with non-spherical natural graphite particles

A three-dimensional microstructure of green and pressed tapes cast with graphite particles of non-spherical shape were examined quantitatively on the basis of the distribution of void sizes among the packed particles. The distributions measured over the cross-sections of the tape in three directions were expressed by the theoretical ones deduced for non-spherical particles. Particle shape was characterized by shape indices defined by Fourier analysis of particle outlines measured over the corresponding cross-sections of the green tape. The relationships were totally established between the limiting packing density, characterizing the void size distribution at the same section voidage, and the shape index of particle over the section. As a result, the normalized median void diameter as well as the limiting packing density of the pressed tape was found to increase with the particle shape index, corresponding to wider void size distribution. Therefore, based on developed correlations, the optimization of packing microstructure of the cast tape can be expected to result in high performance battery by using shape-modified graphite particles.     

Influence of inherent particle characteristics on hopper flow rate

The inherent factors influencing the shear strength of particulate materials are also believed to influence the flow rate through a hopper. These inherent particle characteristics include particle size, particle-size distribution, particle shape, angularity, hardness, and surface roughness. To determine the effect of inherent particle characteristics on flow rate and pluviated void ratio, a wide range of materials were tested. These materials ranged from manufactured sands and glass beads to natural sands. Determination of particle size, particle-size distribution, and hardness was achieved by conducting conventional tests such as sieve analyses and specific gravity tests. Quantification of the shape and angularity parameter is more difficult due to the nonavailability of any standard techniques. To achieve the objective of quantifying shape and angularity, a new technique was developed utilizing the image analyzer. Two shape parameters, namely, Shape Factor and Angularity Factor, were determined for various materials. Shape and Angularity Factors were correlated with flow rate as well as the pluviated void ratio. Overall, the results indicate that as shape and angularity of particles increase, the flow rate decreases, and pluviated void ratio increase. A good correlation between drained shear strength properties and the flow rates measured in the cone was also found to exist. Therefore, index tests such as flow rate through a flow cone (hopper) can be used to estimate the drained monotonic strength of particulate materials.     

Compression-Permeability Properties of Compressed Bed of Superabsorbent Hydrogel Particles

The average pore size of the gel network of a superabsorbent hydrogel particle was evaluated based on the data of the permeation rate of water through the compressed bed of gels obtained with the use of a compression-permeability cell (C-P cell). The pore size evaluated based on the Happel's cell model using the C-P cell data was compared with that obtained from the Kozeny-Carman equation in which the Kozeny constant k was assumed to be 5.0. It was clarified that the use of k = 5.0 in Kozeny-Carman equation underestimated the pore size compared to the calculations using the Happel's cell model. Moreover, the effect of bound water in the gel was clarified.     

Analysis and evaluation of permeability techniques for characterizing fine particles Part I. Diffusion and flow through porous media

The specific surface area and particle size can be deduced with speed and simplicity from appropriate measurements and calculations of fluid flow and diffusion in porous media. The interdependence of these two processes is developed in a series of two articles.In Part I, models are presented for molecular and Knudsen diffusion during flow through aggregates of solid particles at both atmospheric and low pressure permeametric conditions. For a randomly packed bed of granular particles, a cell model is developed that takes into account the tortuosity and variations in the cross-sectional area. A new analytical expression for the Kozeny constant is derived in terms of the bed porosity and particle shape. The effect of porosity on surface area measurements using permeability methods is explained.     

On the role of the pore morphology on the electrical conductivity of porous yttria-stabilized zirconia

Yttria Stabilized Zirconia ceramics with well-controlled porosity, pore size and shape were prepared using well-calibrated poly-methyl-methacrylate (PMMA) micro-beads (MB) as a pore-forming agent. The microstructure was observed by Scanning Electron Microscopy. Impedance spectroscopy was used to evaluate the effect of pore morphology (pore size, pore size distribution, pore shape and interconnectivity) on the electrical properties of YSZ ceramics. Archie's law based analyzes to express the dependence of conductivity on porosity have shown that Archie's law is independent of pore size for a pore diameter of between 1 and 7 μm. The Bruggeman model could be used to predict the bulk conductivity if the porosity was less than 25%, thus showing that the impedance response included the effect of sinuousness and constriction induced by pores. Therefore, the tortuosity factor calculated from the bulk conductivity was higher than that predicted by the Bruggeman model for porosities greater than 25% and spherical pores wide (>20 μm). Another point relates to the comparison between tortuosity factors obtained for pore samples fabricated with pore-forming PMMA or by sub-sintering.     

Effect of pore structure on gas permeability constants of porous alumina

Porous alumina was fabricated using different particle size, sintering temperature, and particle size and content of poly (methyl-methacrylate) (PMMA) as pore former. The Forchheimer equation was used to investigate the relationship between porosity and average pore size, and obtain the permeability constants k₁ and k₂ (the viscous effect and the inertial effect, respectively). Compared to Darcy's law, the Forchheimer equation established a more realistic and reliable relationship between fluid pressure and fluid velocity. k₁ and k₂ were found to be more sensitive to the average pore size than to the porosity of alumina. Moreover, reliable relationships were confirmed between the average pore size and k₁, k₂, and their ratio (k₁/k₂).     

Compression-Permeability Properties of Compressed Bed of Superabsorbent Hydrogel Particles

The average pore size of the gel network of a superabsorbent hydrogel particle was evaluated based on the data of the permeation rate of water through the compressed bed of gels obtained with the use of a compression-permeability cell (C-P cell). The pore size evaluated based on the Happel's cell model using the C-P cell data was compared with that obtained from the Kozeny-Carman equation in which the Kozeny constant k was assumed to be 5.0. It was clarified that the use of k = 5.0 in Kozeny-Carman equation underestimated the pore size compared to the calculations using the Happel's cell model. Moreover, the effect of bound water in the gel was clarified.     

A Monte Carlo pore network for the simulation of porous characteristics of functionalized silica: pore size distribution, connectivity distribution and mean tortuosities

The simulation of the random porous network of five samples of functionalized SiO₂ took place using a dual-site-bond model (DSBM) and Monte Carlo techniques for achieving the proper arrangement of the pores into the system. The simulation took place in 7×7×7 lattice. As a starting point of simulation the adsorption branch of N₂ isotherm was considered from which the pore size distribution was estimated. Then as a benchmark of simulation the N₂ desorption branch was considered whose fitting was achieved using the Monte Carlo technique for selecting the proper place of each pore into the 7×7×7 lattice. From the obtained model, it was possible to estimate the distribution of pore connectivities of each system. The mean value of those connectivity distributions tallies with the corresponding mean values estimated using the standard methodology of Seaton. In addition, the mean tortuosity of the porous network was estimated and the results were favorably compared with values of tortuosity estimated recently via the so-called corrugated-pore-structure-model (CPSM) for the same solids. The degree of functionalization of the parent SiO₂ affects both connectivity and tortuosity in a linear way. Some discrepancies observed between the results obtained via this methodology and the ones obtained using the Seaton or the CPSM model are discussed.     

Hybrid‐permeability model evaluation through concepts of tortuosity and resistance rate: Properties of manufactured hybrid laminate

The mechanical properties of composite structures depend on the preform impregnation and a successful impregnation can be achieved using the permeability relation in the case of an infusion process. The objective of this study is to develop an analytical model to predict the permeability K of carbon and glass fabrics through hybrid laminate using different stacking sequence, applying an average‐permeability model. Preforms permeabilities were evaluated through tortuosity and void‐volume fraction. The model allows the analysis of different stacking sequence combinations (interleaved and in block), measuring the contribution of each material type. As a result, hybrid average‐permeability model was validated through experimental permeability tests, dimensionless permeability, and tortuosity results, besides enabling predictions of the flow front behavior with <10% of deviation. Carbon fiber preforms exhibited higher flow resistance, which is explained via tortuosity concept. A combination of carbon/glass preforms presented an increased permeability, which means a synergy that provides higher value of K. In addition, the use of hybrid preforms, especially Hybrid 2 stacking sequence, reduce the injection time and void formation, ensuring composite impregnation quality. POLYM. ENG. SCI., 59:1215–1222 2019. © 2019 Society of Plastics Engineers     

稀释剂对TIPS法等规聚丙烯中空纤维微孔膜孔径及其连通性的影响

热致相分离（TIPS）法制备等规聚丙烯（iPP）中空纤维微孔膜,邻苯二甲酸二丁酯（DBP）与邻苯二甲酸二辛酯（DOP）的混合溶剂作为制膜稀释剂。干/湿氮气流量法测定了α（稀释剂中DBP的质量分数）和β（铸膜液中聚合物的质量分数）对膜样品的平均孔径及其分布的影响,并采用膜孔曲折因子定量表达膜孔连通性。发现全部膜样品均体现窄孔径分布特征。对于相同的β, α增加导致平均孔径及膜孔连通性下降。α=0.20时,β增加,膜的平均孔径先增加后降低,膜孔曲折因子稍下降; α=0.35或0.50时,β增加,膜的平均孔径降低,膜孔曲折因子下降。膜孔连通性体现了膜内部的拓扑结构,共溶剂组成和铸膜液固含量能够调节iPP中空纤维微孔膜的孔径及其连通性。     

A three-parameter Kozeny–Carman generalized equation for fractal porous media

The Kozeny–Carman equation is a traditional permeability–porosity relationship which has been used in many models of real problems related to flows in porous media. In spite of this, some limitations of this well-known equation has motivated the conception of different versions, specialized for particular applications. In the present article, we deduce a three-parameter Kozeny–Carman equation obtained from a fractal structure involving the specific surface and the tortuosity of the porous medium. Here, a theoretical analysis indicates that the new equation is capable to generalize several models existent in the literature. Besides, parameter estimations fitting experimental data of different materials show that the present model can be used to describe the relationship between permeability and porosity of many materials, such as sandstones, sisal fiber mat and glass fiber fabrics.     

The permeability and compressibility of aligned and cross-plied carbon fiber beds during processing of composites

Two of the most important input parameters needed to simulate the processing of continuous fiber laminated composites are the fiber bed permeability and the portion of the autoclave load borne by the consolidating fiber network (compressibility). In this study we have experimentally examined how both these parameter change with resin volume fraction as pressure is applied and consolidation proceeds. For a unidirectional fiber bed, the Kozeny-Carman equation can be used to predict both the transverse (perpendicular to the laminate plies) permeability (Kozeny constant, K′_z = 11) and the axial (parallel to the fibers) permeability (Kozeny constant, K′_X = 0.57). The axial permeability was found to be dependent on the surface tension of the permeant. For a unidirectionally aligned fiber, the measured transverse permeabilities varied from 1.1 × 10^?10 cm² to 12. × 10^?9 cm² while the axial values varied from 2.1 × 10^?9 to 4.4 × 10^?8 cm² for a liquid volume fraction range of 0.25 to 0.5. Axial permeability measurements indicate that the permeability decreases with increasing off-axis angle × (measured from the laminate axial direction). The off-axis permeability behavior can be described by a modified Kozeny-Carman equation. The fiber network compressibility can be described with a logarithmic relation which has been found valid for a large number of consolidated soils.