The transverse permeability of disordered fiber arrays: a statistical correlation in terms of the mean nearest interfiber spacing

Abstract

In the porous media literature, unidirectional fibrous systems are broadly categorized as ordered or disordered. The former class, easily tractable for analysis purposes but limited in its relation to reality, involves square, hexagonal and various staggered arrays. The latter class involves everything else. While the dimensionless hydraulic permeability of ordered fibrous media is known to be a deterministic function of their porosity φ, the parameters affecting the permeability of disordered fiber arrays are not very well understood. The objective of this study is to computationally investigate flow across many unidirectional arrays of randomly placed fibers and derive a correlation between K and some measure of their microstructure. In the process, we explain the wide scatter in permeability values observed computationally as well as experimentally. This task is achieved using a parallel implementation of the Boundary Element Method (BEM). Over 600 simulations are carried out in twodimensional geometries consisting of 576 fiber cross-sections placed within a square unit cell by a Monte Carlo procedure. The porosity varies from 0.45 to 0.90. The computed permeabilities are compared with earlier theoretical results and experimental data. Analysis of the computational results reveals that the permeability of disordered arrays with φ < 0.7 is reduced as the non-uniformity of the fiber distribution increases. This reduction can be substantial at low porosities. The key finding of this study is a direct correlation between K and the mean nearest inter-fiber spacingδ 1 , the latter depending on the microstructure of the fibrous medium.

Darcy’s Law for Flow in a Periodic Thin Porous Medium Confined Between Two Parallel Plates

“…More precisely, we consider pressure-driven flow through a periodic array of vertical cylinders confined between two parallel plates. The parallel plates make the geometry different from those studied in Chen and Papathanasiou (2008), Gebart (1992), , Hwang and Advani (2010), Jourak et al (2013), Koch and Ladd (1997), , Lundström and Gebart (1995), Sangani and Yao (1988). A representative elementary volume for such TPM is a cube of lateral length ε and vertical length δ.…”

Numerical Simulation and Experimental Validation for the Filtration Performance of Fibrous Air Filter Media with LB Method

“…For the case where inter-space between fibers is large, air flow channels will be formed through these spaces and the average velocity through the channel is comparatively large. This was also discovered by Chen and Papathanasiou (2008).…”

Flow through a Two‐Scale Porosity Material

“…In addition, the mean nearest fibre spacing δ 1 is included, to account for the degree of uniformity in the fibre placement. It has been established by Chen and Papathanasiou [5,6] that as the degree of heterogeneity in the fibre distribution increases, δ 1 decreases. These fibre distributions can be generated by a Monte Carlo process.…”

“…The constant C and the maximum f , f max are dependent on the arrangement of the fibres. Due to its efficiency in very complex geometries (in the BEM only boundaries need to be meshed), the BEM can resolve every fibre and thus model the detailed microscale flow within the bundles [5,6]. While in this approach the small scale can be perfectly modelled, it can be difficult to implement 3D effects on the fibre bundle scale as done with CFD.…”