Transport through random bimodal and multimodal fiber structures

Abstract

Random walk simulation results are reported for the transport and structural properties of random bimodal fibrous media for a range of values of the porosity, relative fiber size, and relative fiber density. Analytical expressions are derived for the mean intercept length of random bimodal and multimodal fiber structures, and are validated through simulations. A fiber dispersity factor emerges from the derivations, accounting for the deviation of the mean intercept length of such structures from that of unimodal fiber beds of the same porosity. Tortuosity factors in all diffusion regimes for in-plane and transverse flow through bimodal fibrous media of moderate or high porosity are practically independent of the relative fiber size and density and equal to those reported earlier for beds of unimodal fibers. The same holds for the formation factor of such structures, accounting for the dimensionless effective bulk diffusivity, thermal and electrical conductivity, magnetic permeability, dielectric constant and refractive index. The dimensionless viscous permeability of bimodal and multimodal fiber structures of moderate or high porosity may be obtained from that of unimodal fiber structures through simple multiplication by the square of the dispersity factor. This result is in line with a multitude of experimental data of the literature.