Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

Abstract

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.