Measurement of in-plane permeability of anisotropic fiber reinforcements

Three of the most common methods (two with parallel flow and one with radial flow) for determination of the in-plane permeability tensor are studied both theoretically and experimentally. An error analysis shows that the difference between the methods is negligible if the error levels are equal. However, the radial flow method is found to be susceptible to large errors from mold deflection in an experimental comparison between the methods. Additional experiments with the radial flow method in a stiffer mold show that the method gives the same values for the permeability tensor as the other two methods. A new method with multiple cavities in parallel is proposed that combines the simplicity of the radial flow method with the stiff mold of the parallel flow method. Only mass and time need to be measured in one experiment and it eliminates the need to measure fluid viscosity, temperature, and injection pressure. The method depends on the availability of a reference material with known permeability.     

Calibration of one‐dimensional flow setup used for estimating fabric permeability using three different reference media

Experimental estimation of the permeability of reinforcement fabrics is very important in conducting accurate mold‐filling simulations for liquid composite molding (LCM) processes employed to manufacture polymer matrix composites. In this study, the one‐dimensional (1D) flow based permeability measuring setup was calibrated for the first time using three different reference media: an aluminum block with drilled parallel holes, a lattice of 3D unit cells created using rapid prototyping, and carbon fabric used in the recently concluded permeability bench‐mark study [Vernet N, et al. Compos Part A, 61, 172 (2014)]. The steady‐state permeability was estimated for all the three cases while the transient permeability was estimated only for the lattice‐type and carbon fabric media. The carbon‐fabric results were presented as the transient and steady‐state permeabilities for three different directions of 0°, 45°, and 90°, and the in‐plane principal permeability components were calculated using the correlations for anisotropic fabrics. The results for the aluminum‐plate and lattice‐like media were compared with the previous numerical and experimental studies and good agreement was observed. To validating the carbon‐fabric results, the experimental permeability was compared with two different analytical permeabilities for dual‐scale porous media [Papathanasiou, Int. J. Multiphase Flow, 27 ( 8 ), 1451 (2001) and K.M. Pillai and S.G. Advani, Transport Porous Med., 21 ( 1 ), 1 (1995)], and a good agreement with experimental results established the accuracy of our 1D flow setup. The study raises some important questions on the permeability benchmark study conducted recently [Vernet N, et al. Compos Part A, 61, 172 (2014)]. POLYM. COMPOS., 37:925–935, 2016. © 2014 Society of Plastics Engineers     

A study on the determination of in-plane permeability of fiber preforms

One of the parameters most frequently used in modeling and designing the mold filling process is the permeability of fibrous preforms. To obtain radial propagation of a viscous polymer into a homogeneous orthotropic porous medium, an approximate solution is derived and its results are compared with numerical ones obtained from boundary element method (BEM). A simple and direct procedure incorporating approximate solution with experimental data has been proposed to determine the principal in-plane permeabilities of the reinforcements. A scheme is also suggested in order to increase the accuracy in the determination of degree of anisotropy. The effect of resin injection type on permeability is investigated through the experiments.     

The permeability of fibrous porous media

The literature was searched for experiments and theories related to low-Reynolds-number flow through fibrous porous media, particularly highly porous structures. Experimental data were found for a wide range of materials, from polymer chains to fiberglass, and the results collapse reasonably well when the appropriate dimensionless co-ordinates are employed. Of the theories, accurate solutions of Stokes equation are available for regular arrays of parallel rods, either aligned with or normal to the flow. For irregular arrays and three-dimensional media, approximate permeabilities can be calculated from several flow models.     

Visualization and quantification of forced in-plane flow through deformed porous media

Fluid flow in liquid molding processes and in other applications involving porous media is often characterized with a permeability tensor and modeled by d'Arcy's law. The permeability is a sensitive function of pore structure, which, in deformable materials, is influenced by compression and extension. The majority of previous permeability measurements on composite reinforcement fabrics did not account for deformations imposed on them by corners and curves in the mold. In the present study, transparent molds were designed with a single 90° bend in which the gap between plates was held constant throughout the flow path. Thus, the effects of fabric curvature on permeability were investigated independently of the effects of fabric compression in the thickness direction. A new experimental system was developed to visualize and quantify fluid flow in fabrics mounted in transparent molds. The reported measurements were conducted with fluid flowing through a (vertical) flat region of fabric, around the 90° curve, and then along a second (horizontal) flat region. Permeability was found to be reduced by the imposed curvature for a nonwoven polyester and three-dimensional woven glass fabric. We were able to quantify the effect of curvature on permeability for the former, but not for the latter because of an enduring, dominant nonlinear entrance resistance. For the glass, comparison of two flow rates indicates that the faster flow is characterized by a two stage filling process, whereas, at the slower rate, the liquid front fills all pores at the same time.     

三维织物厚度方向渗透率研究

复合材料的液体成型特点是树脂需在复杂结构纤维预制体中流经较长的距离,故探讨树脂在纤维织物中的流动行为尤为重要。研究了三维织物厚度、纤维细度以及纤维体积分数对类树脂液体在厚度方向渗透行为的影响,并分析了相关的流动行为规律。研究结果表明:当织物厚度较小时,树脂的渗透率随织物厚度增加而迅速下降;当织物厚度达到阈值时,渗透率因织物中孔隙减少而趋于定值。当织物的纱线细度降低时,纤维束间孔隙增大,使纤维束形状和结构发生改变,故渗透率增大;当织物厚度方向的压缩量增加时,纤维束间孔隙减少,孔隙形状趋于扁平,流动通道减少,故渗透率降低。     

Anisotropic in-plane spin splitting in an asymmetric (001) GaAs/AlGaAs quantum well

The in-plane spin splitting of conduction-band electron has been investigated in an asymmetric (001) GaAs/Al_xGa_1-xAs quantum well by time-resolved Kerr rotation technique under a transverse magnetic field. The distinctive anisotropy of the spin splitting was observed while the temperature is below approximately 200 K. This anisotropy emerges from the combined effect of Dresselhaus spin-orbit coupling plus asymmetric potential gradients. We also exploit the temperature dependence of spin-splitting energy. Both the anisotropy of spin splitting and the in-plane effective g-factor decrease with increasing temperature.PACS: 78.47.jm, 71.70.Ej, 75.75.+a, 72.25.Fe,     

Measurement of in-plane effective thermal conductivity in PEM fuel cell diffusion media

Gas diffusion media used in polymer electrolyte membrane (PEM) fuel cells are highly anisotropic with significantly different transport property values in the through- and in-plane directions. In this study, experimental measurements of the in-plane effective thermal conductivity k for gas diffusion media used in PEM fuel cells have been carried out using a parallel thermal conductance technique. Conductivity values are measured at a mean sample temperature of 70 °C for six different material types and two different orientations in order to quantify the effect of PTFE content on thermal conductivity and to reveal any anisotropic behavior. The results vary from a minimum of k = 3.54 W/(m °C) to a maximum value of 15.1 W/(m °C) for various samples and configurations tested in this study, with an uncertainty between 1% and 2% for all the cases investigated.     

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.     

Anisotropic continuum damage model for prediction of failure in flax/polypropylene fabric composites

An anisotropic continuum damage modeling approach was applied to model failure of a composite of unidirectional flax in a polypropylene matrix under quasi‐static tensile loading. Tensile, compressive and shear stiffness, and strength values of the composite were characterized according to ASTM standards, and the damage was quantified by optical microscopy. Based on the experimental strength and damage values, an anisotropic strain‐dependent material damage model was developed and implemented in the finite element program ABAQUS. This was combined with geometric models of the fabric composites incorporating the yarn geometry. Good agreement was observed between the experimental and numerical stress–strain curves, and the failure strength prediction by the model was within 3.1% of the experimental value. This study shows that combining a geometric model closely incorporating the actual geometry of a fabric composite with an experimentally determined material degradation model can yield good predictions of the mechanical behaviour of the composite. POLYM. COMPOS., 37:2588–2597, 2016. © 2015 Society of Plastics Engineers     

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.     

Simultaneous measurements of permeability and capillary pressure of thermosetting matrices in woven fabric reinforcements

A simple apparatus was designed and constructed capable of measuring the unsteady-state permeability and the capillary pressure simultaneously in a simulated composite impregnation experiment. It was found that the Kozeny-Carman equation used to describe the permeability of composites during impregnation adequately described experimental results for woven fabric preform up to porosity values of 0.5. Above this value, observed deviations were attributed to interfacial effects between adjacent woven fabric layers. For woven fabric preforms made of T-300 carbon fibers, a maximum capillary pressure of 3.7 × 10⁴ Pa (=5.4 psi) was observed at low porosity values. Thus, the capillary pressure may compete with other pressure sources in low pressure processes, such as the prepregging process. The woven fabric preform used in this study is observed to have a permeability similar to a unidirectional fibrous preform along the transverse direction. Furthermore, an existing modeling methodology capable of predicting permeability and capillary pressure through different preforms was found to be valid for fibrous preforms of complex orientation.     

Permeability characterization. Part 1: A proposed standard reference fabric for permeability

A three-dimensionally woven fabric is proposed as a standard reference material for permeability characterization. The 3-D woven fabric requires care in cutting and handling, although it is more robust than 2-D woven or braided fabrics. If prepared carefully, the permeability of the 3-D woven fabric can be measured reproducibly within 15% in either radial flow or saturated 1-D flow geometries. The material was characterized for permeability in radial, unsaturated and saturated 1-D, and through-thickness flow geometries. The transient results demonstrated the importance of structural heterogeneity on the unsaturated flow behavior, and agree qualitatively with a simplistic model of flow in heterogeneous unsaturated porous media. The effects of heterogeneity were manifested in the proposed SRM by an increasing trend in the “unsaturated permeability.” Experiments were also conducted with a random mat that displayed transient flows dominated by wicking. The effects of wicking on the macroscopic flow behavior were manifested by transients in the “unsaturated permeability” in which a decreasing trend was observed.     

A unified approach to determine principal permeability of fibrous porous media

This paper presents a unified approach (UA) to determining permeability in liquid composite molding. The UA applies both to the channel flow and the radial flow experiment and it unifies the data processing of almost all known permeability measurement methods. It permits principal permeability to be calculated from experimental measurements which are carried out in an arbitrary co-ordinate system. This paper describes the UA and its main features. Further, the UA is applied to a number of experimental results for radial flow and channel flow measurements to demonstrate its validity. In addition, the algorithms of current permeability measurement methods are classified according to the UA, and, where necessary, differences are discussed. Some data processing algorithms were found to contain weaknesses or shortcomings.     

Modeling permeability of 3-D nanofiber media in slip flow regime

Over the last few decades, numerous analytical and/or numerical expressions have been developed for predicting the permeability of a fibrous medium. These expressions, however, are not accurate in predicting the permeability of media made up of nanofibers. This is because the previous expressions were mostly developed for coarse fibers, where using the so-called no-slip velocity boundary condition at the fiber surface is quite justified. Removing the no-slip velocity restriction in this work, we study the effect of slip flow on the permeability of fibrous materials made up of nanofibers. This has been accomplished by generating a large series of 3-D virtual geometries that resemble the microstructure of a nanofiber (e.g., electrospun) material. Stokes flow equations are solved numerically in the void space between the nanofibers, with the slip flow boundary condition developed based on the Maxwell first order model. The influence of fiber diameter and solid volume fraction (SVF) on the media's permeability is studied, and used to establish a correction factor for the existing permeability expressions when used for nanofiber media.     

Control of the permeability of a porous media using a thermally sensitive polymer

Experiments explore the reduction in permeability of a porous bead pack when a suspension of thermally responsive polymer is injected and the temperature then increased above the thermal activation temperature. The change in permeability is greater with higher polymer concentration, provided that the ionic concentration of the solution is sufficient for floc formation. The time for activation of the blocking effect is within tens of seconds to minutes of when the polymer solution is heated. This is consistent with the timescale for diffusion‐limited aggregation, although the detailed value depends on the geometry and polymer concentration. Dynamical experiments demonstrate that once the porous media is blocked, adding additional polymer has no effect. The mechanism for permeability reduction may be modeled in the context of a pore‐network model, and we build a simple model to illustrate the permeability reduction as a function of the fraction of pores links which are blocked. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1193–1201, 2014     

Effect of the fibre diameter polydispersity on the permeability of nonwoven filter media

This paper studies the permeability values of air filter media obtained by 3-D simulations using the GeoDict® code. 3-D fibrous structures with different specific characteristics that can be encountered in air filtration (0.03 ≤ solid volume fraction [α] ≤ 0.25, monodisperse fibres [1 μm ≤ df ≤8 μm], or polydisperse fibres) were generated. For monodisperse fibres, the permeability values obtained were compared with various correlations identified in the literature. After confirming that Davies' or Jackson and James' relations allowed a good estimate of the permeability, it is shown that the modified Happel's correlation provides a better prediction. In the case of normal (standard deviation: σ ≤ 1.5) or lognormal fibre size distribution (geometric standard deviation: σ_G ≤ 2), this modified Happel's correlation, in which the fibre diameter is replaced by an equivalent fibre diameter, leads to a relative deviation of less than ±8% and ±4% for lognormal and normal fibre distributions, respectively. The comparison with experimental permeability values obtained on real media provides quite encouraging results.