Permeability Of Fibrous Porous Media Research Articles

Corrigendum to “On the examination of the Darcy permeability of fibrous porous media; New correlations” [Chem. Eng. Sci. 173 (2017) 525–536

Corrigendum to “On the examination of the Darcy permeability of fibrous porous media; New correlations” [Chem. Eng. Sci. 173 (2017) 525–536

A study for the longitudinal permeability of fibrous porous media with consideration of electroviscous effects

We investigate theoretically the longitudinal permeability for the electroviscous flow through one-dimensional (1D) fibrous porous media with orderly and disorderly fiber arrays. The structures of fibrous porous media are idealized as circular unit cells. In the cell, the dimensionless net charge density is given by solving the linearized Poisson-Boltzmann equation, and is approximated as 1 by detailed discussions. Based on the approximate value of the net charge density, circular unit cell and Voronoi Tessellation method, we propose mathematical models for the longitudinal permeability with considering electroviscous effects. The effects of the fiber volume fraction, fiber radius and electroviscous resistance number on the longitudinal permeability are analyzed in detail. Moreover, there are good agreements between the present predictions and these results from the literatures.

A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

A novel fractal solution for permeability and Kozeny-Carman constant of fibrous porous media made up of solid particles and porous fibers

This paper presents a novel fractal solution to investigate the permeability and the Kozeny-Carman (KC) constant of fibrous porous media made up of solid particles and porous fibers. The proposed model has been verified with satisfying agreements of the permeability and KC constant of fibrous porous media obtained by our model and those obtained by experimental data, analytical solution, and numerical simulation reported in literature. The results demonstrate that 1) an increase in particle diameter leads to an increase in the absolute permeability; 2) an increase in the tortuosity fractal dimension leads to an increase in the KC constant and decreases in the dimensionless permeability and absolute permeability; 3) an increase in the porosity results in increases in the dimensionless permeability and absolute permeability of the fibrous porous media; 4) increases in the fiber diameter yields an increase in the absolute permeability of fibrous porous media. The proposed fractal model explicitly relates the KC constant and the permeability to the microstructural parameters of the fibrous porous media, and consequently facilitating the understanding of the detailed physical mechanisms for fluids transport through fibrous porous media.

On the examination of the Darcy permeability of soft fibrous porous media; new correlations

In this paper, we report a novel experimental approach to investigate the compression-dependent Darcy permeability of soft porous media. Especially, we are proposing new correlations that describe the change of the permeability of random fibrous porous media as a function of its compression. A special device was developed that consisted of a rectangular flow channel with adjustable gap thickness ranging from 3mm to 20mm. Air was forced through the thin gap filled with testing fibrous materials. By measuring the flow rate and the pressure gradient, we have successfully obtained the Darcy permeability of different fibrous porous materials at different compression ratios. Theoretical or semi-empirical models have been compared with the experimental results, indicating various degrees of disagreement. The new correlations were then proposed which fit with experimental data very well. The study presented herein provides a useful approach to evaluate the change of the permeability of fibrous porous media as a function of its compression. It will be valuable for examining fluid flow in fibrous porous media where the permeability is difficult to be measured directly. This kind of porous media widely exists in biological systems.

Microstructural Effects on the Fluid Transport in Fibrous Media

A numerical approach is presented for computing the macroscopic permeability of fibrous porous media taking into account for various fiber types in hexagonal arrangement. A model based on Lattice Boltzmann Method(LBM) for viscous, incompressible flow through a regular array of fibers is employed for predicting the permeability of this media. The effect of porosity on the macroscopic permeability is studied. Such microstructure parameter as fiber shape is varied. The results show that the fiber shape significantly affects the permeability of this media in different porosity.

Permeability and compression of fibrous porous media generated from dilute suspensions of fiberglass debris during a loss of coolant accident

Permeability of fibrous porous media has been studied for decades in various engineering applications, including liquid purifications, air filters, and textiles. In nuclear engineering, fiberglass has been found to be a hazard during a Loss-of-Coolant Accident. The high energy steam jet from a break impinges on surrounding fiberglass insulation materials, producing a large amount of fibrous debris. The fibrous debris is then transported through the reactor containment and reaches the sump strainers. Accumulation of such debris on the surface of the strainers produces a fibrous bed, which is a fibrous porous medium that can undermine reactor core cooling. The present study investigated the buildup of fibrous porous media on two types of perforated plate and the pressure drop through the fibrous porous media without chemical effect. The development of the fibrous bed was visually recorded in order to correlate the pressure drop, the approach velocity, and the thickness of the fibrous porous media. The experimental results were compared to semi-theoretical models and theoretical models proposed by other researchers. Additionally, a compression model was developed to predict the thickness and the local porosity of a fibrous bed as a function of pressure.

RECENT ADVANCES ON FRACTAL MODELING OF PERMEABILITY FOR FIBROUS POROUS MEDIA

Permeability is an important hydraulic parameter for characterizing heat and mass transfer properties of fibrous porous media. However, it is difficult to be quantitatively predicted due to the complex and irregular pore structure of fibrous porous media. Fractal geometry has been verified to be an effective method for determining the permeability of fibrous porous media. In this study, recent works on the permeability of fibrous porous media by means of fractal geometry are reviewed, the advances for each presented fractal model are analyzed and summarized, parameter equations used in available fractal permeability models are also briefly compared and reviewed. Future work for more generalized permeability model of fibrous porous media need to conducted by considering the special characters of fibrous materials, uniform pore structure parameter model and the influence factor of capillary pressure, electrokinetic phenomena, etc.

Analytical determination of the effect of compression on the permeability of fibrous porous media

An existing geometric pore-scale model is geometrically adapted from an isotropic to an anisotropic structure in order to determine the effects of compression on permeability. In this analysis, streamwise compression is accounted for by incorporating the compression–porosity relationship into the analytical model, while permeability is expressed in terms of the fiber diameter and the pore-scale linear dimensions of the geometric model. The linear dimensions are determined from several required input characteristics, namely, the measured hydraulic pore diameters, the porosity, and the compression ratios. The proposed model is applied to determine the airflow through a compressed non-woven glass fiber filter, with results that are corroborated with experimental permeability data. The model is further validated against experimental permeability data for glass and nylon fibers as well as for airflow through a soft fibrous porous medium. Despite the simple model geometry, permeability predictions of the correct order of magnitude are obtained, with the significant effects of compression on permeability observed in the experimental data verified by these analytic permeability predictions.

Analytical determination of the effect of compression on the permeability of fibrous porous media

Analytical determination of the effect of compression on the permeability of fibrous porous media

An Air Permeability Study of Anisotropic Glass Wool Fibrous Products

This article reports an experimental study of the permeability of fibrous porous media based on air flow. Two glass wools have been analyzed in three different flow directions to evaluate their anisotropic structure. The usual flow theories such as Darcy’s law, valid for granular materials, have been shown to apply also to these fibrous media which is a more complex structure (fiber arrangement, high porous media,…). The intrinsic permeabilities and the anisotropic factors have been determined from an air permeability measurement based on a standard test for industrial fabrics. The experimental results have been compared to different models, showing the limits of some simplistic models when applied to our highly porous structures. One model, Kyan’s model based on the flow around submerged objects, was, however, found to agree with our experimental data. This study also demonstrates the interesting use of an experimental technique, which is air permeability measurement (water permeability is not adapted), in the investigation of flow phenomena in a fibrous medium.

Effect of 3D fiber orientation distribution on transverse air permeability of fibrous porous media

In the recent past years, there was a resurgence of interest to study the air permeability of fibrous porous media, but the results reported on the effect of 3D fiber orientation on the transverse permeability of fibrous porous media appeared to be contradictory. While Stylianopoulos et al. [Physics of Fluids 20, 123601 (2008)] observed that the highly aligned network was more permeable than the moderately aligned network, which, in turn, was more permeable than the isotropic fiber network, but Tahir and Tafreshi [Physics of Fluids, 21, 083604 (2009)] found that the transverse permeability was increased with the increase in the deviations of the fibers through-plane angle from zero. In order to resolve this contradiction, in this work, a series of virtual fibrous structures were generated on computer by varying the degree of anisotropy of 3D fiber orientation and the transverse permeability of such structures was obtained by solving stokes equation. It was observed that the transverse permeability of the fibrous porous media was increased with the increase in degree of anisotropy of 3D fiber orientation.

Microstructural effects on the permeability of periodic fibrous porous media

An analytical–numerical approach is presented for computing the macroscopic permeability of fibrous porous media taking into account their microstructure. A finite element (FE) based model for viscous, incompressible flow through a regular array of cylinders/fibers is employed for predicting the permeability associated with this type of media. High resolution data, obtained from our simulations, are utilized for validating the commonly used semi-analytical models of drag relations from which the permeability is often derived. The effect of porosity, or volume fraction, on the macroscopic permeability is studied. Also microstructure parameters like particle shape, orientation and unit cell staggered angle are varied. The results are compared with the Carman–Kozeny (CK) equation and the Kozeny factor (often assumed to be constant) dependence on the microstructural parameters is reported and used as an attempt to predict a closed form relation for the permeability in a variety of structures, shapes and wide range of porosities.

Hydraulic permeability of fibrous porous media

In this study, the hydraulic permeability for viscous flow through fibrous media of high porosity is investigated theoretically. Fibrous media in one-dimensional (1D), two-dimensional (2D) or three-dimensional (3D) structure are approximated as consisting of repetitive unit cells based on Voronoi Tessellation approximation and volume averaging method. In the new model, the hydraulic permeability of fibrous media is described as a function of porosity and fiber radius as well as geometrical formation factors including the degree of randomness (viz. randomness of fiber distribution) and fiber orientation. In particular, the slip effect for flow through superfine fibrous media is analytically studied. The prediction of the new model for fibrous media with porosity greater than 0.7 is highly consistent with the analytical, experimental and numerical results found in the literature. It is further demonstrated that randomly packed fibrous media have larger permeability than regular ones, the hydraulic permeability of fibrous media increases with increasing of through-plane orientation, but is less dependent on in-plane fiber orientation, and the slip effect on the longitudinal hydraulic permeability is greater than the perpendicular one.

Transverse permeability of fibrous porous media

In this study, the transverse permeability of fibrous porous media is studied both experimentally and theoretically. A scale analysis technique is employed for determining the transverse permeability of various fibrous matrices including square, staggered, and hexagonal arrangements of unidirectionally aligned fibers, as well as simple two-directional mats and simple cubic structures. In the present approach, the permeability is related to the porosity, fiber diameter, and tortuosity of the medium. In addition, the pressure drop in several samples of tube banks of different arrangements and metal foams are measured in the creeping flow regime. The pressure-drop results are then used to calculate the permeability of the samples. The developed compact relationships are successfully verified through comparison with these experimental results and the data reported by others. Our results suggest that fiber orientation has an important effect on the permeability; however, these effects are more pronounced in low porosities, i.e., ɛ<0.7.

Transverse mobility prediction of non-Newtonian fluids across fibrous porous media

This work is an extension of our previous work [Wang JF and Hwang WR. Permeability prediction of fibrous porous media in a bi-periodic domain. J Compos Mater 2007; 42: 909—929], in which a finite-element fictitious-domain mortar-element technique was developed to investigate the permeability of fibrous porous media in the bi-periodic domain, to non-Newtonian shear-thinning fluid. Considering the amount of shear-thinning, the pressure drop, the fiber microstructure, and the porosity as parameters, we investigate (i) the (normalized) mobility and its dependence on both the amount of shear-thinning and the given pressure drop; (ii) mechanisms leading to the main flow path in a highly shear-thinning fluid in randomly distributed fiber problems, and (iii) inter-tow and intra-tow non-Newtonian flow characteristics in a fiber bundle problem. The dependence of the mobility on shear-thinning has been found to appear completely opposite according to given pressure drop values.

A difference-fractal model for the permeability of fibrous porous media

In this Letter, a difference-fractal model for the permeability of viscous flow through fibrous porous media is proposed. Since fractal objects have well-defined geometric properties, and are discrete and discontinuous, we apply the difference approach to developing the fractal model. The model of non-dimensional permeability is expressed as a function of porosity and fractal dimension. To verify the validity of the proposed model, the predicted permeability values are compared with those of experimental measurements. A good agreement between the prediction of the fractal model and the existing experimental data from the literature is found.

A Method to Estimate the Accuracy of Radial Flow—Based Permeability Measuring Devices

Radial flow experiment is often used to measure the permeability of fibrous porous media by the composites processing community. However, very little work has been done to calibrate the radial flow set-up with media of known permeability. This article presents a new method for calibrating the permeability measuring set-ups based on radial flows. A reference medium in the form of two concentric annular slits is created for the radial flow mold whose permeability is estimated analytically and numerically. It is observed that the experimentally measured permeability deviates from the theoretical and numerical permeabilities with an increase in the flow rate for an injection setup using a gear pump as well as a piston-cylinder pump. The deviation can be attributed to two possible reasons: one is the leakage between the calibration device and mold plate surfaces because of a slight mold deformation at higher flow rates, the other one is the increase in the gap clearance of the reference medium because of the higher gap pressures at higher flow rates. No such deviation is observed while measuring the permeability of a fiber mat at different flow rates. Hence, the proposed reference medium can calibrate a conventional radial flow-based permeability measuring setups at low flow rates; the accuracy thus obtained can be extended to higher flow rates as well if permeability of a fiber mat can be shown to remain constant with the flow rate.

A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method

Fluid flow analyses for porous media are of great importance in a wide range of industrial applications including, but not limited to, resin transfer moulding, filter analysis, transport of underground water and pollutants, and hydrocarbon recovery. Permeability is perhaps the most important property that characterizes porous media; however, its determination for different types of porous media is challenging due its complex dependence on the pore-level structure of the media. In the present work, fluid flow in three-dimensional random fibrous media is simulated using the lattice Boltzmann method. We determine the permeability of the medium using the Darcy law across a wide range of void fractions (0.08 ⩽ ϕ ⩽ 0.99) and find that the values for the permeability that we obtain are consistent with available experimental data. We use our numerical data to develop a semi-empirical constitutive model for the permeability of fibrous media as a function of their porosity and of the fibre diameter. The model, which is underpinned by the theoretical analysis of flow through cylinder arrays presented by [Gebart BR. Permeability of unidirectional reinforcements for RTM. J Compos Mater 1992; 26(8): 1100–33], gives an excellent fit to these data across the range of ϕ. We perform further simulations to determine the impact of the curvature and aspect ratio of the fibres on the permeability. We find that curvature has a negligible effect, and that aspect ratio is only important for fibres with aspect ratio smaller than 6:1, in which case the permeability increases with increasing aspect ratio. Finally, we calculate the permeability tensor for the fibrous media studied and confirm numerically that, for an isotropic medium, the permeability tensor reduces to a scalar value.

A Method to Estimate the Accuracy of Radial Flow-Based Permeability Measuring Devices

Radial flow experiment is often used to measure the permeability of fibrous porous media by the composites processing community. However, very little work has been done to calibrate the radial flow set-up with media of known permeability. This article presents a new method for calibrating the permeability measuring set-ups based on radial flows. A reference medium in the form of two concentric annular slits is created for the radial flow mold whose permeability is estimated analytically and numerically. It is observed that the experimentally measured permeability deviates from the theoretical and numerical permeabilities with an increase in the flow rate for an injection setup using a gear pump as well as a piston-cylinder pump. The deviation can be attributed to two possible reasons: one is the leakage between the calibration device and mold plate surfaces because of a slight mold deformation at higher flow rates, the other one is the increase in the gap clearance of the reference medium because of the higher gap pressures at higher flow rates. No such deviation is observed while measuring the permeability of a fiber mat at different flow rates. Hence, the proposed reference medium can calibrate a conventional radial flow-based permeability measuring setups at low flow rates; the accuracy thus obtained can be extended to higher flow rates as well if permeability of a fiber mat can be shown to remain constant with the flow rate.