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.     

Application of F NMR relaxometry to the determination of porosity and pore size distribution in hydrated cements and other porous materials

The potential to determine the porosity of cements and other porous materials by employing ¹⁹F NMR relaxometry was explored for samples of hydrated Portland cement, white cement and calcium aluminate, filled with Freon 11. The dependence of ¹⁹F signal amplitudes on the content of Freon in samples with completely filled pores was linear with a small (< 6%) intercept thus allowing a direct determination of total porosity. Additionally it was found that magnetic susceptibility (hence the content of paramagnetic compounds) of the solid can be evaluated from ¹⁹F NMR spectra of samples containing exterior liquid. Information concerning pore size distribution can be obtained from the analysis of multiexponential relaxation of ¹⁹F nuclei in samples with completely filled pores. Mathematical models employing sets of distributions of relaxation rates have been developed for this purpose. Distributions were assumed to be of a (fixed) square/triangular type allowing for the calculation of moments of any order from the estimated initial value, width of distribution and asymmetry factor. Longitudinal and transverse relaxation were characterised by either single or several continuous distributions of relaxation rates. One of the relaxating phases (assigned to fluid occupying throats connecting the pores) was found to selectively disappear when Freon was evaporated from samples. Another approach is to analyse the dependencies of means and variances of relaxation rates on Freon content. This has been done by employing the two-site relaxation model with a permanent adsorption layer and pore-dependent relaxation enhancement. Simultaneous fitting of dependencies of means and variances of relaxation rates on Freon content yields parameters of pore size distribution and of the dependence of relaxation enhancement on the pore radius. Analysis of experimental data shows agreement between these two approaches.     

Theoretical consideration of the effect of porosity on thermal conductivity of porous materials

The thermal conductivity of porous materials is theoretically studied in connection with nanoporous materials used in recent semiconductor devices. The effects of porosity and pore size on the thermal conductivity are discussed. The thermal conductivity of insulating materials is determined by the heat capacity of phonons, the average phonon velocity and the phonon mean free path. We investigate the porosity dependence of these quantities, especially by taking into account phonon scatterings by pores, and present an expression for the thermal conductivity as a function of porosity. Our model consideration predicts that the thermal conductivity of nanoporous materials depends on the ratio of the pore size R_p to the phonon mean free path for zero-porosity, l₀. The thermal conductivity for l₀/R_p > 1 decreases steeply with increasing porosity because of effective phonon scatterings by pores. On the other hand, the thermal conductivity for l₀/R_p < 0.1 decreases moderately with increasing porosity because phonon scatterings by pores are no longer effective. On the basis of the present theoretical consideration, we discuss the principal factor dominating the porosity dependence of thermal conductivity in nanoporous materials. We also discuss how one can design nanoporous materials with lower or higher thermal conductivity.     

Prediction of the relative permeability to gas flow of cement-based materials

The macroscopic physical modeling of coupled air and water transport in unsaturated porous material requires transport coefficients for the two phases along with the diffusion coefficient of vapor in air.As their experimental determination is often difficult and time consuming, relations have been proposed for a long time to allow the calculation of all the needed parameters, starting from experimental properties that are easier to obtain, such as water pressure head as a function of the degree of saturation or isothermal sorption curves.These relations, validated for soils, are also used for cement, mortars or concrete, although they have not been really justified in these cases.The aim of this study is to determine if soil physics principles can be applied to unsaturated moisture movement in concrete.We measured the air permeability of concrete specimens from which we obtained the relative permeability. Evidently, the parameters introduced in the relations given by Van Genuchten [Ann. Geophys. 3 (1985) 615] have to be revised. New values are proposed for the parameters for the concrete studied. These values are justified by the good reproduction of the experimental air permeability and airflow evolution observed during experiments.     

Relationship of threshold diameter and Darcean permeability in unconsolidated porous structures

Experiment was conducted on the threshold pressure for atmospheric air through unconsolidated narrow size distributed mini sphere and sand particles at low flow rates. The threshold diameter calculated from measured threshold pressure showed that it does not follow the traditional similarity theory. This is consistent with our experiment on accurate permeability measurement, and can be explained as a result of gas slip flow within such micro pore structure. Our current work tend to find the method to predict the permeability-threshold pressure relationship for unconsolidated porous structures.     

Setting time determination of cementitious materials based on measurements of the hydraulic pressure variations

An experimental investigation was carried out to determine the setting time of cement based materials (cement paste, mortar, concrete, etc.). An original method based on measurements of both total lateral pressure and hydraulic pressure has been investigated. An original device has been engineered to measure the pressure kinetics. Just after mixing and filling of the device, a simultaneous drop and an equal value of the both hydraulic and total lateral pressures has been recorded. A definitive cessation of total lateral pressure and negative hydraulic pressures are then observed. The proposed setting time was defined as the elapsed time between the end of mixing and the time at which the hydraulic pressure becomes zero. In addition to the usual W / C parameter, the influence of the vibration and the height of the material tested on the pressure based method were studied. Comparing to other classical methods (Vicat, calorimetry, ultrasonic pulse-echo …), the presented device is efficient with major types of cement based materials (concrete, SCC …) and was able to give a simple and direct information about the mechanical state of the material.     

Effects of nano-alumina content on the formation of interconnected pores in porous purging plug materials

The physical properties and microstructure of porous purging plug materials added with different nano-alumina contents and firing temperatures were investigated by means of X-ray diffraction, scanning electron microscopy, air permeability, pore size distribution, mean pore size, apparent porosity, bulk density, and cold crushing strength (CCS) tests. The results showed that the addition of nano-alumina had a great effect on the physical properties and microstructure of the porous purging plug materials. With increasing nano-alumina content in the composition, the main phase was α-Al₂O₃ in all compositions and the mean pore size, apparent porosity and air permeability all increased due to the increased number of pores and pore size of the specimens which facilitated the formation of interconnected pores. When the sintering temperature was changed from 1550 °C to 1650 °C, some of the smaller pores vanished due to solid phase sintering, which reduced the apparent porosity, and some open pores connected to form interconnected pores, which promoted increased air permeability. In addition, the strength and porosity were found to follow the relationship σ = σ₀ exp (-b P). When the apparent porosity increased, the CCS decreased, and vice versa.     

Permeability of the porous Al2O3 ceramic with bimodal pore size distribution

Porous Al₂O₃ ceramics with bimodal pore size distribution were fabricated by partial sintering with monodispersed PMMA micro balls as pore agent. The porosity of the fabricated porous Al₂O₃ is increased with content of the pore agent increase, the bulk density and bending strength are decreased, accordingly. Relations between pressure drop and flow velocity of the air through the porous Al₂O₃ fit the Forchheimer's equation well for compressible fluid. Due to pores introduced by the pore agent, the Darcy permeability and inertial permeability of the porous Al₂O₃ are increased obviously. For given flow velocity, with increase of the PMMA content, the Forchheimer's number of the fluid through the porous Al₂O₃ is decreased, which results in decrease of the inertial resistance ratio to the total pressure drop. The porous Al₂O₃ ceramics with pores introduced by the monodispersed PMMA micro balls show higher permeability while the filtration selectivity is not deteriorated.     

Role of Fiber Length and Pore Former on the Porous Network of Carbon Paper Electrode and its Performance in PEMFC

Porous conducting carbon paper has been recognized as one of the ideal materials to be used as an electrode backing in a fuel cell assembly. Carbon paper is prepared by the combined process of papermaking followed by composite formation. Two different studies, i.e. (i) using chopped carbon fiber of different lengths in the papermaking process, and (ii) introducing pore formers (blowing agents) in the sample during the resin impregnation/composite formation step, were adopted separately to control the porosity of the paper. The effect of the above processes on the various properties of the carbon paper electrode affecting its performance in a unit polymer electrolyte membrane fuel cell has been discussed. A maximum power density of 766 mW cm^–2 has been achieved for carbon paper with 0.6 cm fiber length, an increase of nearly 12% as compared to 684 mW cm^–2 for sample with 1.0 cm fiber length and tested under similar conditions. The introduction of pore former demonstrates increased performance of the fuel cell at high current densities.     

Microstructure and permeability of porous Si3N4 supports prepared via SHS

Porous Si₃N₄ ceramics with tailored pore structures were fabricated via self-propagating high temperature synthesis (SHS) using Polymethylmethacrylate (PMMA) as pore forming agent. The pore structures, mechanical properties and permeation performance of porous Si₃N₄ ceramics were investigated by altering the particle sizes and amount of PMMA. With the increasing content of PMMA, the flexural strength of samples decreased from 102.5 MPa to 9.4 MPa. The tortuosity which showed irregular variation affected gas permeability directly. The samples with 20 wt% content of PMMA exhibited the maximum Darcian and non-Darcian constants with the smallest tortuosity. Moreover, the comparison of permeability coefficients with other ceramics via different pore forming methods in literature was presented. The specimens exhibited great permeability due to the large pore sizes created by the elongated and coarsened β-Si₃N₄ grains during the SHS process, providing a low-cost and environmentally friendly method for preparing high permeability porous Si₃N₄ supports.     

Reactive synthesis for porous TiVAlC ceramics by TiH2,V,Al and graphite powders

Using the mixed powder of TiH₂, graphite, aluminum and vanadium as starting materials, porous TiVAlC ceramics were fabricated by the reactive synthesis technology at 1300 °C. The chemical steadiness of porous TiVAlC along with the effects of sintering temperature on the viscous permeability coefficient, strength, porosity, pore size and volume expansion rate of the porous TiVAlC were explored, and the mechanism of pore formation was also revealed. The preparation process includes five steps as follows: (i) the complete decomposition of stearic acid at 500 °C; (ii) the pyrolysis of TiH₂ at 700 °C, converting TiH₂ into hydrogen and titanium (iii) The solid-liquid chemical reaction of solid vanadium, titanium and molten aluminum at 700 °C, converting the mixture into V–Al and Ti–Al compounds; (iv) At 900–1100 °C, Surplus V and Ti interact with graphite to synthesize carbides of TiVC₂, VC, and TiC; (v) Reactive synthesized carbides (TiVC₂, VC, and TiC), Ti₂AlC, V–Al and Ti–Al compounds that yield porous TiVAlC at 1300 °C.     

Analytical expressions for predicting permeability of bimodal fibrous porous media

Pressure drop is one of the most important characteristics of a fibrous media. While numerous analytical, numerical, and experimental published works are available for predicting the permeability of media made up of fibers with a unimodal fiber diameter distribution (referred to as unimodal media here), there are almost no easy-to-use expressions available for media with a bimodal fiber diameter distribution (referred to as bimodal media). In the present work, the permeability of bimodal media is calculated by solving the Stokes flow governing equations in a series of 3-D virtual geometries that mimic the microstructure of fibrous materials. These simulations are designed to establish a unimodal equivalent diameter for the bimodal media thereby taking advantage of the existing expressions of unimodal materials for permeability prediction. We evaluated eight different methods of defining an equivalent diameter for bimodal media and concluded that the area-weighted average diameter of Brown and Thorpe [2001. Glass-fiber filters with bimodal fiber size distributions. Powder Technology 118, 3-9], volume-weighted resistivity model of Clague and Phillips [1997. A numerical calculation of the hydraulic permeability of three dimensional disordered fibrous media. Physics of Fluids 9 (6), 1562-1572], and the cube root relation of the current paper offer the best predictions for the entire range of mass (number) fractions, 0?n_c?1, with fiber diameter ratios, 1?R_cf?5, and solidities, 5?α?15.     

Particulate clusters and permeability in porous media

The permeability of particulate colloidal titanium dioxide, P25, was investigated during sedimentation, permeation and filtration when suspended in water at a consistent ionic strength similar to tap water. Happel's cell model of permeability was used to determine the apparent particle size during these processes, and compared with the size of particle clusters measured using laser diffraction under identical ionic conditions and varying degree of shear. The primary particle size of the P25 was determined to be 28 nm, from consideration of the surface area and density of the particles, and the cluster size during permeation and filtration was close to 100 nm. During sedimentation the cluster size was determined to be close to 10 μm, which is the same size obtained by laser diffraction when measuring under conditions of low shear. Using the above two sizes (28 nm and 10 μm) as limits in Happel's permeability model it was possible to determine an ‘operating envelope’ of permeability that matched the experimentally measured values for the sedimentation, permeation and filtration processes.     

Compression-dependent permeability measurement for random soft porous media and its implications to lift generation

In the past decade, foundations have been laid for understanding the lift generation in a soft porous medium under rapid compaction (Feng and Weinbaum, 2000. Journal of Fluid Mechanics 422, 282–317; Wu et al., 2005b. Journal of Fluid Mechanics 542, 281–304; Wu et al., 2004a. Physical Review Letters 93(19), 194501; Barabadi et al., 2009. Journal of Heat Transfer 131(10), 101006-1–101006-12; Al-Chidiac et al., 2009. Journal of Porous Media 12(11), 1019–1035). One of the key parameters that affects the lift generation is the variation of the Darcy permeability as a function of compression. This critical problem is investigated in the current study using a novel experimental setup, namely a permeameter. Three different, soft, synthetic, fibrous, porous materials were chosen for the study. Their microstructures were characterized using a scanning electron microscope and a stereomicroscope. Their porosities were precisely measured using a water displacement method. By carefully controlling the air flow through the materials contained in a long Plexiglas tube of the permeameter, one obtained consistent results for the Darcy permeability of the tested material as a function of its porosity. Fluffing the porous materials caused disturbance of their microstructures thus variations in the permeability, especially in the high porosity range. The experimental data was curve-fitted and compared to established expressions. It showed that the Nogai Expression (Nogai and Ihara, 1978. Journal of Textile Machinery Society of Japan 31(12), T166–T170) provided the best fit for the change of permeability as a function of compression for the fibrous materials studied herein. The Carman–Kozeny equation, however, is only applicable for one of the fibrous materials. This finding is consistent with the theoretical predictions by Barabadi et al. (2009).     

Experimental study of gas and liquid permeability of a mortar

Eight samples cored from the same mortar were used to investigate their respective gas, ethanol and water permeability. Two gas and liquid permeability cells, using special devices for measuring the injected flow under steady conditions, were designed and presented in this paper. The obtained results showed that water permeability was systematically lower (in an order of magnitude from 1 to 2) than gas permeability whereas ethanol permeability was intermediate between these two values. Nevertheless, ethanol and gas permeabilities were found of the same order and, when gas permeability is corrected from the Klinkenberg (or slippage) effect, the results given by these two fluids are virtually identical and can be considered to be the intrinsic permeability value. Thus, the differences observed between water and gas permeability values have to be explained by other phenomena such as rehydration, dissolution and migration of fine elements or water adsorption in the thinnest pores.     

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).     

Porosity features and gas permeability analysis of bi-modal porous alumina and mullite for filtration applications

Bimodal porous structures were prepared by combining conventional sacrificial template and partial sintering methods. These porous structures were analysed by comparing pore characteristics and gas permeation properties of alumina/mullite specimens sintered at different temperatures. The pore characteristics were investigated by SEM, mercury porosimetry, and capillary flow porosimetry. A bimodal pore structure was observed. One type of pore was induced by starch, which acted as a sacrificial template. The other pore type was due to partial sintering. The pores produced by starch were between 2 and 10 µm whereas those produced by partial sintering exhibited pore size of 0.1–0.5 µm. The effects of sintering temperature on porosity, gas permeability, and mullite phase formation were studied. The formation of the mullite phase was confirmed by XRD. Compressive strengths of 37.9 MPa and 12.4 MPa with porosities of 65.3% and 70% were achieved in alumina and mullite specimens sintered at 1600 °C.     

A review of bioceramic porous scaffolds for hard tissue applications: Effects of structural features

Tissue engineering has acquired remarkable attention as an alternative strategy to treat and restore bone defects during recent years. A scaffold is a fundamental component for tissue engineering, on which cells attach, proliferate and differentiate to form new desirable functional tissue. The composition, and structural features of scaffolds, including porosity and pore size, play a fundamental role in the success of tissue-engineered construct. This review summarizes the effect of porosity and pore size of bioceramic-based scaffolds on their mechanical properties and biological performances. The focus of this review is on scaffolds with porosities 40% and above. From the mechanical point of view, the degree of porosity is a more important factor than pore size and scaffolds with porosities greater than 40% were more likely to substitute trabecular bones. While for in vitro and in vivo performances, pore size appeared more influential feature and co-existence of macropores and micropores led to better bone formation.     

Different synthesis methods allow to tune the permeability and permselectivity of dopamine–melanin films to electrochemical probes

Different methods to prepare melanin films by dopamine oxidation are compared with respect to their permeability to electrochemical probes being either neutral or carrying a positive or a negative charge. To examine charge-dependence of the permeability differently charged probes of similar size (hexaamineruthenium, ferrocenemethanol and hexacyanoferrate) are employed. We deliberately not investigated the permeability of metal cations through the melanin films owing to their possible complexation by the catechol groups of melanin. The films prepared by solution oxydation methods (O₂ or Cu²⁺ as oxidants) are impermeable to hexacyanoferrate as soon as their thickness reaches 5–10 nm but remain permeable to hexaamineruthenium and ferrocenemethanol up to thickness reaching 25–40 nm before becoming also impermeable. The melanin films prepared by electrochemical deposition display a marked difference; they remain permeable to hexacyanoferrate up to 35 nm in thickness and to hexaamineruthenium and ferrocenemethanol up to the maximal thickness that can be reached by this deposition method. When the maximal film thickness of 45 nm is reached the film becomes also impermeable to these two redox probes. These results are explained on the basis of structural differences of the melanin films at the molecular level. The permselectivity of the melanin coatings is related to their negative surface charge density at the working pH of 7.5.