Novel microscale-macroscale approach to predict permeability of bimodal fibrous media comprised of soft fibers

Abstract

In this study, we utilized a Discrete Element Model (DEM) approach to generate fibrous media comprised of flexible fibers with different diameters. This approach allowed simulations to predict the solid volume fraction (SVF) of the resulting media, which is a unique advantage over previous models reported in the literature, where SVF was used as an input to the fiber generation algorithms. We generated realistic bimodal fibrous media in which coarse and fine fibers of different mass ratios, SVFs, and coarse-to-fine fiber diameter ratios were intimately blended. Permeability of the resulting media were predicted by numerically solving the Stokes equations in the 3-D space between the fibers. To circumvent the need to conduct excessively expensive numerical simulations, we developed a Micro-Macro simulation approach in which the fine fibers were treated as porous matrix engulfing the coarse fibers. The accuracy of our CPU-efficient Micro-Macro simulations was assessed through comparison with the more accurate Micro-Micro (CPU-intensive) simulations, where the actual geometry of both the fine and coarse fibers were resolved. The Micro-Macro simulations were then used to produce a dataset of permeability values to be used in assessing the accuracy of different methods of defining an equivalent unimodal structure that can represent a bimodal fibrous medium for permeability calculation. Our study concluded that the cube-root and area-weighted mean diameter models provide the most accurate predictions for the permeability of bimodal fibrous media. Our theoretical results were compared with experimental data and reasonable agreement was observed.