A fractal permeability model for the gas diffusion layer of PEM fuel cells

In this paper a fractal permeability model for the gas diffusion layer (GDL) of PEM fuel cells (PEMFCs) is presented. The model accounts for the actual microstructures of the GDL in terms of two fractal dimensions, one relating the size of the capillary flow pathways to their population and the other describing the tortuosity of the capillary pathways. In addition, the gas molecule effect is considered by using the Adzumi equation. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of pore and the effective porosity of porous medium without any empirical constants. mercury-intrusion porosimetry was used to measure the microstructures of the GDL. Based on scanning electron microscope (SEM) images, two fractal dimensions are determined by the box-counting method. To verify the validity of the model, the predicted permeability data of the present fractal model were compared with the experimental data supplied by Toray Inc. It is found that the permeability prediction of the model was in accordance with experimental data. This verifies the validity of the present fractal permeability model for the GDL.     

Permeability of fractal porous media by Monte Carlo simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.     

Analysis of seepage characters in fractal porous media

In this paper, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The obtained expressions are the functions of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the expressions. The pressure distribution equations for plane-radial and plane-parallel flows in fractal porous media are also derived. The pressure and velocity distributions in plane-radial reservoirs are calculated and discussed.     

A fractal model for determining oxygen effective diffusivity of gas diffusion layer under the dry and wet conditions

In this paper, we propose a new fractal model to determine the oxygen effective diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cell for both the dry and wet conditions. The model considers the GDL structure in terms of tortuosity and area fractal dimensions and also takes the Knudsen effect into account, which has no empirical constant but parameters with physical meanings. The fractal model is verified by the fair agreement with the experimental data and the results obtained from existing models. It is revealed that the Knudsen effect is essential for the understanding of the oxygen transport through the GDL. Under the dry condition, the oxygen effective diffusivity increases with higher area fractal dimension and lower tortuosity fractal dimension. For the wet condition, the water condensation in the GDL of mixed wettability is considered; and it is found that the behavior of oxygen effective diffusivity with liquid saturation depends on the GDL wettability. It is further revealed that for a given liquid saturation, the oxygen effective diffusivity increases with greater area fractal dimension; with the decrease of tortuosity fractal dimension, it also increases, except for the hydrophilic case at high liquid saturation.     

A fractal model for predicting permeability and liquid water relative permeability in the gas diffusion layer (GDL) of PEMFCs

In this study, a fractal model is developed to predict the permeability and liquid water relative permeability of the GDL (TGP-H-120 carbon paper) in proton exchange membrane fuel cells (PEMFCs), based on the micrographs (by SEM, i.e. scanning electron microscope) of the TGP-H-120. Pore size distribution (PSD), maximum pore size, porosity, diameter of the carbon fiber, pore tortuosity, area dimension, hydrophilicity or hydrophobicity, the thickness of GDL and saturation are involved in this model. The model was validated by comparison between the predicted results and experimental data. The results indicate that the water relative permeability in the hydrophobicity case is much higher than in the hydrophilicity case. So, a hydrophobic carbon paper is preferred for efficient removal of liquid water from the cathode of PEMFCs.     

A fractal resistance model for flow through porous media

A fractal model for resistance of flow through porous media is developed based on the fractal characters of porous media and on the pore–throat model for capillary. The proposed model is expressed as a function of the pore–throat ratio, porosity, property of fluid, pore/capillary and particle sizes, fluid velocity (or Reynolds number) and fractal dimensions of porous media. There is no empirical constant and every parameter has clear physical meaning in the proposed model. The model predictions are compared with experiment data, and good agreement is found between them.     

Analysis of effective thermal conductivity for circular tubes made with porous media based on fractal theory

Accurately evaluating the relation between heat transfer performance and the complex structure of porous media is still a difficult task. Most previous fractal models of effective thermal conductivity (ETC) are developed to describe the heat-conducting characteristics of a unit cell or a representative elementary volume in porous media, and few models have paid attentions to the ETC for practical circular tubes made with a porous structure based on fractal theory. This paper proposes a new ETC model for a circular tube made with porous media based on fractals, and the validity of the present model is proved by previous models and testing data in the literature, then the effects of intrinsic thermo-physical properties of each component and pore structures on the ETC are discussed. The analysis results indicate that a circular tube made with porous media can improve its heat-insulating performance by about 25% compared with a common parallel circular tube. This can supply an alternative scheme for pipe insulation design in cold/hot fluid supplying systems or air conditioning systems.     

Fractal model for predicting the effective binary oxygen diffusivity of the gas diffusion layer in proton exchange membrane fuel cells

We propose an analytical model to predict the effective binary oxygen diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs). In this study, we consider the fractal characteristics of the porous GDL as well as its general microstructure, and we adopt the Bosanquet equation to derive effective diffusivity. The fractal characterization of GDL enables us to model effective diffusivity in a continuous manner while taking into account the effect of pore size distribution. Comparison to two other theoretical models that are generally accepted in the simulation of PEMFCs shows similar trends in all three models, indicating that our proposed model is well founded. Furthermore, the predicted effective binary oxygen diffusivities of two samples show that after treatment with polytetrafluoroethylene (PTFE), the effective binary diffusivity of the GDL decreases. Based on the parametric effect analysis, we conclude that effective binary diffusivity is negatively correlated with tortuosity fractal dimension but positively correlated with the fractal dimension of pore area, porosity, or mean pore diameter. The proposed model facilitates fast prediction of effective diffusivity as well as multi-scale modeling of PEMFCs and thus facilitates the design of the GDLs and of PEMFCs.     

A fractal model for the coupled heat and mass transfer in porous fibrous media

This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory.     

A fractal analysis of dropwise condensation heat transfer

In this paper, a fractal model for dropwise condensation heat transfer is developed based on the fractal characteristics of drop size distributions on condensing surfaces. Expressions for the fractal dimension and area fraction of drop sizes are derived, which are shown to be a function of temperature difference between condensing surface and saturated vapor. The condensation heat transfer is found to be a function of the fractal dimension for drop sizes, maximum and minimum drop radii, the temperature difference, and physical properties of fluid. The predicted total heat flux from a condensing surface based on the present fractal model is compared with existing experimental data. Good agreement between the model predictions and experimental data is found, which verifies the validity of the present model.     

A fractal model for gas permeation through porous membranes

Macro and micro porous membranes have been used in many industrial areas. The disordered nature of pore structures in these membranes suggests the existence of a fractal structure formed by the pores. Fractal theory is employed to build the permeation model through these porous membranes. The fractal dimensions for surface pore area and tortuosity of membrane is obtained by box-counting method. Contrary to previous studies which consider only the Poiseulle flow in pores, in this research, the model reflects two gas diffusion mechanisms simultaneously: when the Knudsen number is less than 0.01, the Poiseulle flow is dominant; while when the Knudsen number is greater than 10, the Knudsen flow is dominant; and when the Knudsen number is from 0.01 to 10, the two mechanisms coexist. Contact gas permeation experiments with three porous hydrophobic PVDF membranes are conducted to validate the model. Comparisons between the current model and those from references are made.     

Study on effective thermal conductivity for porous media using fractal techniques

In this paper, the geometric structure of porous media is described using fractal techniques, and a section particle area fractal dimension d of a porous medium with various porosities is considered with a simplified model. Also an expression of the effective thermal conductivity for soil is presented via a fractal dimension and a model of heat transfer in soil. The results obtained in this paper indicate the effectiveness of the method for determining the effective thermal conductivity by using the section area dimension. © 2000 Scripta Technica, Heat Trans Asian Res, 29(6): 491–497, 2000     

Determination of Effective Thermal Conductivity ForReal Porous Media Using Fractal Theory

INTRODUCTIONPorousmediaisacompositemediathatincludessolidframeandfluidandexistedwidelyintheeajrthbiosphere.Heatandmasstransferinporousmediaisbothanaturalphenomenoninearthbiosphereandaphysicalchemistryprocessinindustries,agricultureandhumanlife.Thusthestudyonheatandmasstransferinporousmediahasbecomeanimportanttasktoscielltistsandengineers.Heatandmasstransferinporousmediaisaverycomplexobject.Therearestillmanydifficultiestodescribethecoupledheatandmasstransferphenomena.Amongthesedifficultie…     

含甲烷水合物的石英砂渗透率实验和分形模型对比研究

含水合物的多孔介质渗透率是影响水合物开采的关键参数,多孔介质渗透率与水合物的饱和度密切相关。定量研究多孔介质渗透率随水合物饱和度的变化,对自然界中天然气水合物藏内渗流场的研究具有重要的理论价值。本文以平均粒径为139.612 μm的石英砂为多孔介质,采用稳态注水法测量在不同甲烷水合物饱和度（0 ~ 28.56%）下的石英砂渗透率,将实验数据与两种不同水合物赋存形式（颗粒包裹、孔隙填充）下的石英砂渗透率二维分形模型进行了对比。结果表明,石英砂渗透率比K_r随甲烷水合物饱和度S_h的增大呈现指数减小的趋势。当水合物饱和度低于11.83%时,渗透率比下降缓慢。而当水合物饱和度高于11.83%时,渗透率比下降迅速;当饱和度指数n = 12时,渗透率分形模型与实验数据吻合良好。通过分形模型与实验数据对比,发现当水合物饱和度低于11.83%时,甲烷水合物的赋存形式为颗粒包裹型。在11.83% ~ 28.56%水合物饱和度范围内,甲烷水合物的赋存形式为孔隙填充型。本研究成果量化了石英砂渗透率与甲烷水合物饱和度的关系,确定了含甲烷水合物的石英砂的渗透率分形模型的参数取值。     

多孔介质导热的分形模型

多孔介质中热量传递与多孔介质内部的几何结构有密切的关系，讨论了多孔介质的分形结构和相关的分形维数，利用能量方程，导出了分形维数为D的有限尺度多孔介质中的广义热传导方程，在此基础上，假定热量在多孔介质中的传导路线也是一种分形结构，提出了一个筒化的多孔介质并联通道分形导热模型，求出了基于分形理论的多孔介质有效导热系数表达式。     

Differential spontaneous capillary flow through heterogeneous porous media

Engineered heterogeneous porous materials with aeolotropic liquid transport properties can have many applications. In this work, spontaneous flow of liquids through layered heterogeneous porous materials is analyzed based on fractal theory. Both capillary pressure and hydraulic resistance are expressed in terms of microscopic variables such as minimum and maximum pore sizes and fractal dimensions. The transplanar liquid flow in terms of the mass absorbed by the different layers against time is computed. The effect of layer configuration and pore size, fractal dimension and porosity in each layer are numerically investigated. It is found that different combinations of porous layers of different porosity and pore size distribution create different absorption patterns, and differential liquid transport properties can be achieved by having a gradient of porosity and pore size across the thickness.     

Fractal analysis of Herschel–Bulkley fluid flow in porous media

The Herschel–Bulkley (HB) fluid is the representative fluid which may be reduced to the power-law fluid, Bingham and Newtonian fluids in appropriate conditions. In this paper, fractal models for velocity and the starting pressure gradient for HB fluid in porous media are derived based on fractal characteristics of porous media and capillary model. The proposed models are expressed as a function of fractal dimensions, porosity, maximum pore size and representative length of porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of HB fluid to the structural parameters of porous media. The variation trends of fractal velocity and starting pressure gradient versus different impact factors are shown, and the analytical expressions reveal the physical principles for flow velocity and starting pressure gradient in porous media.     

Fractal description of microstructures and properties of dynamically evolving porous media

Transport through porous media is encountered in several engineering and biological applications. The porous media can be subjected to changes in structure owing to deposition, erosion, swelling or shrinkage which, in turn, affects the transport properties of the media. A dynamic fractal model (DFM) is developed to describe the evolution in pore structure undergoing deposition using fractal dimensions and to predict the changes in the effective diffusivity in terms of the dynamic fractal dimensions. Evolving microstructures undergoing deposition are analyzed at various saturation levels to determine the effective diffusivity using the dynamic fractal model. The effective diffusivity values of the evolving porous media are compared against existing data in the literature.     

Fractal model for prediction of effective hydrogen diffusivity of gas diffusion layer in proton exchange membrane fuel cell

This paper presents a novel prediction model of the effective hydrogen diffusivity for the gas diffusion layer (GDL) in proton exchange membrane fuel cell (PEMFC) by using fractal theory to characterize microstructure. With the consideration of pore-size distribution and Knudsen diffusion effect, a relationship between micro-structural parameters and effective hydrogen diffusivity of GDL is deduced. The prediction of effective hydrogen diffusivities of two samples shows that Knudsen diffusion effect makes the effective diffusivity value decrease, and after being treated with polytetrafluoroethylene (PTFE), carbon paper, a basal material of the GDL, exhibits a lower effective diffusivity value due to the decrease in the pore space and porosity. From the parametric effect study, it can be concluded that effective diffusivity has a positive correlation with pore area fractal dimension D_p or porosity ?, whereas it has a negative correlation with tortuosity fractal dimension D_t.