Engineering the fractal-like porous architecture of fibrous materials

Abstract

Porous fibrous materials have wide applications in many different fields including textile fabric, fiber reinforced composite, fuel cells, filtration, thermal insulation, paper products, and tissue scaffold. In most of these applications, it is essential to optimize the transport properties. For example, permeability, diffusivity and thermal conductivity are the key parameters to affect the optimization of fibrous materials such as minimum permeability for wind proof and minimum effective thermal conductivity for clothing insulation. The transport phenomena in fibrous porous media are complex processes. The understanding and modeling of these processes can lead to the optimization and innovation of fibrous materials. However, the geometric structure of fibrous materials is very complex and difficult to determine. The transport properties of fibrous materials have been studied for many years, but the effects of the geometric parameters of the fibrous materials on the heat and mass transfer are still to be fully elucidated. Therefore, the current studies are aimed at elucidating the relationship between the transport properties (viz. permeability, diffusivity and thermal conductivity) and the geometric parameters of fibrous materials, obtaining the optimization of the fractal like architecture of porous fibrous materials related to total effective thermal conductivity, effective diffusivity, and effective permeability based on the established theoretical models, and predicting the optimized structure of porous fibrous materials for different applications. The first part of this work was aimed at studying the relative permeability with the effect of capillary pressure based on fractal geometry and the Monte Carlo simulations in the unsaturated porous material. The relative permeability was expressed as a function of porosity, the fractal dimension of tortuous capillaries, the area fractal dimension of pore, saturation and capillary pressure. It was found that the capillary pressure increased with decreasing saturation, and the capillary pressure increased sharply with decreasing saturation at small saturation. In addition, it was shown that the fractal dimensions of wetting phase and non-wetting strongly depended on the porosity of the unsaturated porous material. The predicted relative permeability obtained by the present Monte Carlo simulation was shown to have a good agreement with the available experimental result. Thus the proposed model improved the understanding of physical mechanisms of the liquid transport through the unsaturated porous material. The second part obtained a novel analytical model for the permeabilities of the fibrous gas diffusion layer in proton exchange membrane fuel cells. In this model, the geometry structure of fibrous gas diffusion layer was characterized in the light of the water and gas fractal dimensions, the porosity, the tortuosity fractal dimension, and the pore area fractal dimension. It was shown that the water and gas relative permeabilities have no relationship with the porosity and were a function of the water saturation of fibrous gas diffusion layer only. Besides, it was found that the dimensionless permeability decreased markedly with increasing tortuosity fractal dimension. However, there was only a small decrease in the water and gas relative permeabilities when tortuosity fractal dimension increased. The model calculations were compared with the available experimental results and past models results, and good agreement was found. One advantage of the proposed analytical model was that it contained no empirical constant, which was normally required in past models. In the third part, the optimization of the fractal like architecture of porous fibrous materials related to permeability, diffusivity, and thermal conductivity was analyzed by applying the established theoretical models. In this analysis, the geometrical structure of porous fibrous materials was characterized in the light of the fractal dimension of pore area, the porosity, and the tortuosity fractal dimension. It was observed that the ratio of dimensionless permeability over dimensionless effective diffusivity (Y3=(K/D2f)/(De/Db)) of the fractal like architecture of porous fibrous materials decreased with the decrease of porosity and tortuosity fractal dimension, respectively, which implied that lower porosity and tortuosity fractal dimension were beneficial to wind/water resistant fabric, as it reduced the ratio of dimensionless permeability over dimensionless effective diffusivity (Y3=(K/D2f)/(De/Db)), resulting in lower permeability and higher diffusivity. Besides, it was shown that the ratio of dimensionless total effective thermal conductivity over dimensionless effective diffusivity (Y5=(keff/kg)/(De/Db)) of the fractal like architecture of porous fibrous materials decreased with the increase of porosity when porosity was lower than 0.92. On the other hand, it was found that the ratio of dimensionless total effective thermal conductivity over dimensionless effective diffusivity (Y5=(keff/kg)/(De/Db)) increased with porosity when porosity was greater than 0.92. In addition, it was found that the ratio of the dimensionless total effective thermal conductivity over dimensionless effective diffusivity (Y5=(keff/kg)/(De/Db)) increased with tortuosity fractal dimension, which implied lower tortuosity fractal dimension was beneficial to clothing insulation, as it reduced the ratio of dimensionless total effective thermal conductivity over dimensionless effective diffusivity (Y5=(keff/kg)/(De/Db)). The optimization results indicated that fabrics with more aligned fibers were preferred for protective clothing, as the low tortuosity fractal dimension implied fibers in the fibrous materials should be more aligned. Based on above findings and models, further investigations may be directed towards modifying and improving the established theoretical models for the optimization of the fractal like architecture of porous fibrous materials wherever necessary, fabricating electronspun nano- and micro fibrous membranes for the validation of established theoretical models, and fabricating prototypes of the optimized heterogeneous fibrous materials for clothing, and filters.