Pore Scale Modeling of Non Newtonian Shear Thinning Fluids in Blood Oxygenator Design

Abstract

This paper reviews and further develops porescale computational flow modeling techniques used for creeping flow through orthotropic fiber bundles used in blood oxygenators. Porous model significantly reduces geometrical complexity by taking a homogenization approach to model the fiber bundles. This significantly simplifies meshing and can avoid large timeconsuming simulations. Analytical relationships between permeability and porosity exist for Newtonian flow through regular arrangements of fibers and are commonly used in macroscale porous models by introducing a Darcy viscous term in the flow momentum equations. To this extent, verification of analytical Newtonian permeability–porosity relationships has been conducted for parallel and transverse flow through square and staggered arrangements of fibers. Similar procedures are then used to determine the permeability–porosity relationship for nonNewtonian blood. The results demonstrate that modeling nonNewtonian shearthinning fluids in porous media can be performed via a generalized Darcy equation with a porous medium viscosity decomposed into a constant term and a directional expression through least squares fitting. This concept is then investigated for various nonNewtonian blood viscosity models. The proposed methodology is conducted with two different porous model approaches, homogeneous and heterogeneous, and validated against a highfidelity model. The results of the heterogeneous porous model approach yield improved pressure and velocity distribution which highlights the importance of wall effects.