A Fractal Model for Kozeny–carman Constant and Dimensionless Permeability of Fibrous Porous Media With Roughened Surfaces

Abstract

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 Sustainable Recycling Alternative: Electrospun PET-Membranes for Air Nanofiltration

“…Material elongation was performed at a speed of 700 µm/min from 0 to 10,000 µm at room temperature (25 °C) in air. The permeability is an important transport property, which is connected to the geometric structure of porous fibrous materials because can influence the flow of fluids through these materials [ 45 ], so the arrangement of the fibers can be challenging or favorable to the airflow passing through the filter. Thus, permeability is the estimation of the easiness of the flow of fluids in fibrous materials.…”

“…The permeability constant (K 1 ) was obtained using Darcy’s Equation (Equation (1)) (tested in duplicates) and the volumetric flow rate was varied from 100 to 2000 mL/min for a filtration area of 5.2 cm 2 : ∆P/L = (μ/K 1 ) × (v s ) where μ is the gas viscosity, L is the thickness of the filter media, v s is the filtration superficial velocity and ∆P is the pressure drop; this last parameter was measured using a digital manometer (VelociCalc Model 3A-181WP09, TSI, Shoreview, MN, USA) connected to the filtration apparatus, as described by Bortolassi et al [ 31 , 32 ]. Thus, the permeability is explicitly related to the microstructural parameters of fibrous porous media [ 45 , 46 ]. The empirical porosity (ε) of the filter media was calculated as proposed by Ergun’s Equation in 1952, as presented follow (Equation (2)): ∆P/L = (150(1 − ε) 2 μv s )/(ε 3 ·d f 2 ) + (1.75(1 − ε) ρ g v s 2 )/(ε 3 d f ) where ρ g is the gas density and d f is the average diameter of the fiber.…”

CeO2 Nanoparticle-Containing Polymers for Biomedical Applications: A Review

“…Transport phenomena and mass transfer in polymers are very complex problems to understand and require consideration of both porous media and filler properties, along with the nature of permeant and interface effects. Some advances in the permeability of porous fibrous media have been discussed elsewhere [ 159 , 160 , 161 ] but there is a strong need for further progress in regard to composite materials containing CeNPs.…”

Cotton Wastes Functionalized Biomaterials from Micro to Nano: A Cleaner Approach for a Sustainable Environmental Application

“…Synthesis of these waste fibres have created potentials and a wide application due to their intrinsic properties. The functionalization of polymers for improved surface properties such as adhesion, surface properties including porosity roughness, surface adsorption, and wettability potentials through active functional groups determines its applicability [ 2 , 5 ]. The recycling of wastes into functional materials and application for water treatment, food packaging, biomedical applications, and textiles have been reviewed by Reference [ 35 ].…”

“…The demand for textile materials is increasing globally due to population growth and economic development [ 1 ]. Textile materials have been widely used in many fields of life [ 2 ]. Reference [ 3 ] stated that, among world fibre consumption, cotton is the most consumed fibre after polyester.…”