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.     

Simulating permeability of 3-D calendered fibrous structures

Many fibrous materials such as nonwoven materials are often consolidated by means of hot calenders, i.e., hot compaction rolls. Hot calendering compresses the fiber assembly and can cause changes in the structure. In nonwovens, calendering has an added function of thermally bonding the fibers at their respective crossovers to form a strong but yet somewhat porous material. Calendering causes a significant increase in the solid volume fraction (SVF) of the media and therefore, affects their permeability. To our knowledge, no work in the literature has been dedicated to modeling the permeability of calendered nonwovens. In this study, virtual nonwoven structures are generated and compressed from top and bottom to resemble the hot calendering process. In agreement with our experimental observations, it was found that the average SVF profile across the material's thickness turns into a U-shape profile after the calendering. In this work, the dimensionless permeability of the calendered media is computed using CFD tools and reported for different compaction ratios. Results of our simulations are compared with the experiment as well as the available empirical and/or analytical permeability models in the literature and good agreement, depending upon the SVF, is observed. We also studied the influence of orientation distribution of the fibers on the dimensionless permeability of the fabric and noticed that permeability decreases by increasing the directionality of the fibers. This is found to be primarily due to the fact that highly oriented uncompressed fiber-webs tend to have a higher SVF. Fiber-webs of identical SVF, however, exhibited almost identical permeabilities regardless of their fiber orientations.     

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.     

A realistic approach for modeling permeability of fibrous media: 3-D imaging coupled with CFD simulation

Determining permeability of fibrous media is of great importance to many industries. While there are several 2-D and 3-D analytical models developed for predicting the permeability of fibrous disordered media, there are not many numerical works that compare the predictions of these models with that of real media. In this work, we present a series of numerical simulations performed on the microstructure of a real fibrous media. An efficient procedure is presented for reconstructing 3-D images from the 2-D images of the real fibrous media and processing them for the purpose of performing fluid flow simulation. Digital volumetric imaging (DVI) of a typical hydroentangled fibrous fabric is obtained, as an example, and its permeability is computed. These results are compared with those obtained from the analytical equations given in the literature. In particular, it was found that permeability of a typical hydroentangled material can be closely predicted by the layered anisotropic models.     

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).     

Numerical investigation on the flow characteristics and permeability of three-dimensional reticulated foam materials

In this paper, a three-dimensional (3D) model was proposed for predicting the flow characteristics and permeability of three-dimensional reticulated foam materials, which were prepared by replication process. Parameters, such as permeability, inertia coefficient, and friction factor, were obtained in order to describe the fluid flow characteristics of porous media. The influence of foam structure on the fluid flow characteristics was elucidated. Three flow regimes in porous media, including Darcy's regime, Forchheimer's regime and Froude's regime, were visualized and discussed. The flow transition from linear (Darcy's regime) to nonlinear (Forchheimer's regime) behavior, which is typical of experiments, was founded in the simulation. The data presented revealed the fact that the numerical results are in agreement with the experimental ones published previously.     

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.     

The contribution of out-of-plane pore dimensions to the pore size distribution of paper and stochastic fibrous materials

Theory is presented for the distribution of the narrowest dimension of voids encountered in a path through a stochastic fibre network from one side of its plane to the other. Using expressions from the literature we show that the mean out-of-plane pore dimension is always less than half the mean in-plane dimension such that out-of-plane pore dimensions have a controlling influence on the measured pore size distribution. An approximate model is derived which predicts that the overall mean pore dimension of a network of fibres with given dimensions is inversely proportional to its areal density and proportional to a simple function of porosity. Good agreement is demonstrated between this model and experimental data. Regression analysis suggests that out-of-plane pore dimensions account for more than 70% of the measured pore size distribution.     

Analysis of the evolution of the pore size distribution and the pore network connectivity of a porous carbon during activation

The development of the microporosity, pore size distribution and pore network connectivity has been studied in the production of activated carbons from lignite char. Grand Canonical Monte Carlo simulation of adsorption was applied to the characterisation of a set of activated carbons produced at a sequence of times. The pore size distributions obtained from nitrogen at 77 K and ethane at 264 K were used as inputs to a method based on percolation theory to study the changing connectivity of the system. The incorporation of percolation concepts in the study of the porosity development gives an insight into the processes involved. The analysis is applied to a particular environmental application, the adsorption of phenanthrene.     

A mixed Weibull model for size reduction of particulate and fibrous materials

This paper describes a simple alternative to the classical population balance breakage model, which characterizes and controls the size distribution of particles submitted to a reduction process. The new approach is based on cumulative distribution functions of mixed random variables. Results indicate that a Weibull mixture distribution function adequately models the size of particles submitted to various breakage processes. The model was further applied to experimental reduction processes with apparently random breakage probability and yielded good estimates of the unbroken particle and fragment distributions. Use of these results for direct and indirect prediction of the size alteration under dimensional reduction processes is discussed.     

Development of a permeability apparatus for concrete and mortar

A simple and straightforward permeability apparatus for concrete or mortar is described. The necessary equations for the calculation of pressure, dynamic viscosity, flow rate and permeability coefficient are given. Methanol vapor was used as the permeating fluid. The test has been found to be sensitive and repeatable. The proposed cell can be manufactured to fit samples of any dimension. The cell may also be used for any other type of solid porous media. The permeability coefficient of the sample run was found to be greatly affected by w/c and initial moist curing periods.     

Three designs for the internal release of sealants, adhesives, and waterproofing chemicals into concrete to reduce permeability

Various types of hazardous wastes need engineered barriers to prevent outflow. Concrete is a brittle and porous material, which changes dramatically over its lifetime. In order to design waste barriers using any type of concrete, the most effective intervention occurs at the time when it is needed during the life of the material and at the location undergoing distress. Internally placed encapsulators containing sealants, adhesives, and waterproofing are designed to release these chemicals where and when they are needed. Optimizing for durability requires an understanding of the timing and location of release. In all of the cases, brittle fibers containing adhesives or sealants release the chemicals where and when the matrix cracks, causing the fiber to crack and release chemicals. Research from over a decade is presented with special emphasis on permeability, cracking, and data and results from field tests.     

Effects of an electrostatic field in pneumatic conveying of granular materials through inclined and vertical pipes

The pneumatic transport of granular materials through an inclined and vertical pipe in the presence of an electrostatic field was studied numerically using the discrete element method (DEM) coupled with computational fluid dynamics (CFD) and a simple electrostatic field model. The simulation outputs corresponded well with previously reported experimental observations and measurements carried out using electrical capacitance tomography and high-speed camera techniques in the present study. The eroding dunes and annular flow regimes, observed experimentally by previous research workers in inclined and vertical pneumatic conveying, respectively, were reproduced computationally by incorporating a simplified electrostatic field model into the CFD-DEM method. The flow behaviours of solid particles in these regimes obtained from the simulations were validated quantitatively by experimental observations and measurements. In the presence of a mild electrostatic field, reversed flow of particles was seen in a dense region close to the bottom wall of the inclined conveying pipe and forward flow in a more dilute region in the space above. At sufficiently high field strengths, complete backflow of solids in the inclined pipe may be observed and a higher inlet gas velocity would be required to sustain a net positive flow along the pipe. However, this may be at the expense of a larger pressure drop over the entire conveying line. In addition, the time required for a steady state to be attained whereby the solids flow rate remains substantially constant with respect to time was also dependent on the amount of electrostatic effects present within the system. The transient period was observed to be longer when the electrostatic field strength was higher. Finally, a flow map or phase diagram was proposed in the present study as a useful reference for designers of inclined pneumatic conveying systems and a means for a better understanding of such systems.     

Experimental measurement of gas permeability through bitumen: results for H2, N2 and O2

This study reports experimental results concerning the transport of permanent gases (H₂, O₂, N₂) through bitumen between 15 and 25 °C. A pressure differential technique, already used in membrane science in order to determine the permeability of gases through dense polymeric films, has been attempted with bitumen samples. It is shown that reproducible permeability data can be obtained thanks to this strategy, providing that bitumen mechanical resistance is improved by a support paper and a low leak module is used. Experimental results are analyzed in terms of permeability value and temperature dependency (activation energy) in comparison with other dense and permeable organic solids (polymers). The limitations of the technique as well as its potential extension to diffusion coefficient determination are discussed.     

Simulation of nitrogen sorption processes in materials with cylindrical mesopores: Hysteresis as a thermodynamic and connectivity phenomenon

A numerical simulation of nitrogen sorption in materials with cylindrical mesopores is proposed. Multilayer formation and capillary condensation-evaporation processes are followed by using the Sonwane and Bhatia's molecular-continuum model, although an empirical expression is used to represent the potential interaction between the adsorbate and the adsorbent. The pore structure of the solid is generated by inscribing 3D cylindrical pores in a 2D square lattice. The connectivity effects on the nitrogen isotherms are studied by using percolation theory. The ability to predict the multilayer thickness and the relative pressure at which phase transition takes place is corroborated with data reported in literature, finding good fittings in this work. On the other hand, we report for the first time a study on the effect that both pore mean diameter and connectivity have on the extent of hysteresis.     

Experimental and numerical investigation of liquid circulation induced by a bubble plume in a baffled tank

Bubble induced liquid circulation is important in applications such as bubble columns and air-lift reactors. In this work, we describe an experimental and numerical investigation of liquid circulation induced by a bubble plume in a tank partitioned by a baffle. The baffle divides the tank into two compartments. Liquid can flow from one compartment to the other through openings at the top and the bottom of the baffle. Gas (air) was injected in the riser section in the form of bubbles at one corner of the tank. The temporal and spatial variation of velocity field in the liquid as a function of the gas flow rate was measured using particle image velocimetry (PIV). At a constant gas flow rate, the liquid flow field is unsteady due to the interaction with the bubbles. The time scales associated with the velocity-time series and the bubble plume thickness variation were calculated. The time averaged-velocity field was used to quantify the variation of the liquid circulation rate with gas flow rate. The turbulence in the liquid was measured in terms of turbulent intensities. These were calculated from the experimental data and were observed to be less than 3 cm/s. A 2-d Euler-Euler two-fluid model with buoyancy and drag as the interaction terms was used to simulate the flow. The parameters chosen for the simulations were selected from literature. It is shown that inclusion of turbulence model such as k-ε is necessary to capture the overall flow behavior. Good agreement was observed between experimentally obtained velocity profiles and the recirculation rates with the simulation results.     

Toward a better comprehension and modeling of hysteresis cycles in the water sorption–desorption process for cement based materials

The aim of this work is to describe a method based on a simple representation of the pore size distribution, which is able to predict hysteresis phenomena encountered in water sorption–desorption isotherms, particularly for cementitious materials. The hysteresis effect due to network constrictivity is taken into account in order to extend models of transfer in porous media to situations involving wetting–drying cycles. This is not achieved in earlier models and their performance in terms of prediction in such conditions is thus limited. The present modeling is based on an idealized pore size distribution. This has three modes, associated with C–S–H pores, medium capillary pores, and large capillary pores including consideration of cracks. The distribution is assessed from the chemical composition of the cement, the formulation of the material, the degree of hydration, the total water porosity and the intrinsic permeability.     

Preparation and characterisation of mesoporous silica–alumina and silica–titania with a narrow pore size distribution

Amorphous mesoporous materials with a different degree of order in the arrangement of pores are outlined. Particularly, the synthesis of a class of mesoporous silica–alumina (MSA) materials with narrow pore size distribution and a disordered arrangement of pores is reported and discussed. Likewise, the preparation of titanium-containing ordered mesoporous silicates (Ti-MCM-41) and disordered mesoporous silica–titania (MST) are also described in detail. The structural properties of the solids are compared by means of X-ray diffraction and UV-Vis diffuse reflectance spectroscopy. The nitrogen adsorption–desorption measurements were performed and the textural properties are evaluated by the BET, DFT, BJH and t-plot methods.

The high specific surface area and pore volume, as well as the acidity, make MSA solids interesting catalysts in several petrochemical transformations, i.e. oligomerisation, alkylation, hydroisomerisation, rearrangement reactions. Besides, thanks to the width of the mesopores of such solids, the catalytic activity of titanium-containing silicates may have a potential application in the epoxidation of bulky unsaturated fine chemical substrates.     

Long-term flux improvement by air sparging and backflushing for a membrane bioreactor, and modeling permeability decline

Fouling remains a major issue for all membrane applications. This study investigated anti-fouling applications for a side-stream membrane bioreactor (MBR) fed with glucose-based synthetic wastewater. Air sparging, backflushing and high cross flow velocity (CFV) were investigated as anti-fouling strategies. For better comparison of longer test runs, an equation to model effects of MLSS and temperature on viscosity was developed. This study showed that for backflushing with a CFV of 5.2 m/s, the permeability is about 3 times higher than for air sparging with CFV of 2 m/s. Long-term investigations of combined air sparging and backflushing compared to conventional membrane filtration at equal CFVs of 2 m/s showed 4 times higher permeability. The long-term permeability decline can be estimated by a power function of the type P= a tⁿ whereby the factor a is related to the initial permeability and the parameter n indicates how rapidly the flux declines. In most cases it was possible to predict the long term flux decline (over a one week or 8 week period) from data for the first two days of filtration with errors of less than 10%.     

Experimental and numerical investigation of supported rhodium catalysts for partial oxidation of methane in exhaust gas diluted reaction mixtures

The partial oxidation of methane/oxygen mixtures with large exhaust gas dilution (46.3 vol% H₂O and 23.1 vol% CO₂) has been investigated experimentally and numerically over Rh/CeO₂-ZrO₂, Rh/ZrO₂ and Rh/α-Al₂O₃ catalysts. Experiments were carried out in a short-contact-time reactor at 5 bar and included exhaust gas analysis, temperature measurements along the reactor, and catalyst characterization. Additional experiments were performed in an optically accessible channel-flow reactor and involved in situ Raman measurements of major gas-phase species concentrations over the catalyst boundary layer and laser-induced fluorescence (LIF) of formaldehyde. A full elliptic two-dimensional numerical code that included elementary hetero-/homogeneous chemical reaction schemes and relevant heat transfer mechanisms in the solid was used in the simulations. The employed heterogeneous reaction mechanism, including only active Rh sites, reproduced the experiments with good accuracy. The ratio of active to geometrical surface area, deduced from hydrogen chemisorption measurements, was the single model parameter needed to account for the effect of different supports. This indicated that water activation occurring on support sites, resulting in inverse OH spillover from the support to the noble metal sites, could be neglected under the present conditions with high water dilution. An evident relationship between noble metal dispersion and catalytic behavior, in terms of methane conversion and synthesis gas yields, could be established. Both measurements and predictions indicated that an increasing Rh dispersion (in the order Rh/α-Al₂O₃, Rh/ZrO₂, and Rh/CeO₂-ZrO₂) resulted in higher methane conversions, lower surface temperatures, and higher synthesis gas yields.