Effect of micropolar fluid properties on the hydraulic permeability of fibrous biomaterials

Abstract

Background and objective: In this work, the effect of the micropolar fluid parameters on the hydraulic permeability of fibrous biomaterials comprised of square arrays of undirectional fibrils is investigated.

Methods: Simulations are carried out in three dimensional geometries consisting of 9 unidirectional fibers regularly placed in a square lattice within a unit cell. Fiber arrays with volume fraction from 0.1 to 0.6 are considered. The effect of each of the micropolar parameters, namely the vortex viscosity (m), spin gradient viscosity (N) and microinertia constant (J) on the hydraulic permeability is analysed and the differences from Newtonian fluid flow are presented.

Results: Among the micropolar parameters, the vortex viscosity and the spin gradient viscosity affect the hydraulic permeability, while the effect of the micro inertia constant seems to be insignificant. A relationship that connects the difference in the hydraulic permeability between the micropolar and the Newtonian case (ΔK) and the vortex and spin gradient viscosity is presented, the main finding being that ΔK is proportional to the product m · N.

Conclusions: The effects of the micropolar parameters are found to decrease as the volume fraction of the fiber arrays increases; this is due to the reduction in available flow area and the corresponding decrease in microrotation.

Keywords: Computational fluid dynamics; Hydraulic permeability; Micropolar fluid; Micropolar parameters; Square fiber arrays.