Permeability of microscale fibrous porous media using the lattice Boltzmann method

- **Objective**

The permeability of fibrous porous media have been characterized. The modeled fibrous porous media are:

(a) simple cubic; (b) body-centered cubic

(a) skewed simple cubic; (b) skewed body-centered cubic

The skewed models are introduced for eliminating the overlapping region to accurately model the actual fibrous porous media. Also, the non-overlapping skewed fibrous models allow accurate calculation of the effective diameter of the inclusions, which is used to nondimensionalize the permeability *K*.

- **Method**

The D3Q15 (three-dimensional, 15-velocity) LB model is used to calculate the flow field and the permeability of the given porous media. Multiple-relaxation-time (MRT) model is adopted for stable and viscous independent permeability calculation. The governing equation is

where **f** and **m** are the vectors of the particle distribution functions and the kinetic parameters, respectively. The matrices on the RHS of the governing equation control the collision of the particle distribution functions.

The effect of the slip flow is investigated by introducing local Knudsen number as

- **Results**

Contours of various flow variables for the simple cubic model are obtained: (a) u, (b) v, (c) w, (d) p

Skewed simple cubic model resulted in three distinct regions for the dimensionless permeability. When the fiber diameter is large, the fibrous porous media acts as a granular porous media. As the fiber diameter decreases, the dimensionless permeability tends to diverge from the correlation for the granular porous media.

The correlations for the dimensionless permeability of the given four models are obtained. The overlapping fibers resulted in about 2.5 times larger permeability than that of the non-overlapping fibers.

The effect of slip flow is investigated in the range of . The dimensionless permeability generally increases as the Knudsen number increases, especially when the porosity is low.