Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the $x$ direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter $(α)$⁠, pulsation amplitude $(A)$⁠, and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure $O2$ and air. The flow and concentration fields were computed for Re=5, 10, and 40, $0≤A≤0.75$⁠, $α=0.25$⁠, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as $A$ and $α$ are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure $O2$ feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small $A$⁠) for both feed-gas mixtures. The time averaged Sherwood number, $Sh̿$⁠, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with $A$⁠. Little change is observed with varying $α$ for the ranges investigated. The effect of pulsatility on $Sh̿$ is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.