An analysis of oxygen absorption in a tubular membrane oxygenator

Abstract

An analysis of oxygen absorption by blood flowing through a smoll oxygen-permeable fiber in steady state laminar flow is presented. The rigidity and geometry of the fibers eliminate unpredictable shunting and distention, permitting a more detailed analysis o f blood-membrane factors than has previously been undertaken. The mathematical analysis treats the blood as a homogeneous, non-Newtonian fluid with a reversible nonlinear oxygen sink (erythrocytes). The differential equations are solved numerically and the results of the parametric analys'is are presented. The parameters that have a major influence on residence time necessary to obtain a specified oxygen content are the Grashof number, the concentration of hemoglohin in Comparison of the experimental results to the model indicate that mixing due to the heterogeneous nature of blood is minimal and that the major limitation in oxygen absorption i s the blood film. Means of reducing this resistance are discussed.

An Application of the Method of Lines in Biological Mass Transfer

“…Let C denote the total concentration of either oxygen (03 or carbon dioxide (CO,). Then for steady state transfer a simple mass balance yields: ( 1) where J is the diffusive flux, and v is the velocity of the blood.…”

An approximate solution for the Graetz and Lévêque problems from the advancing front theory

“…Assuming steady state conditions, the oxygen balance is given as (Buckles et al, 1968;Dorson, 1970;Spaan, 19i3) Here 4cTs is the concentration of reacted hemoglobin in the form of tetramer. The boundary conditions are…”

Modeling Augmented Oxygen Transfer in Flowing Blood

“…There has been some experimental evidence of increased effective oxygen diffusion coefficients at high fluid shear rates (Colton et at., 1971a;Zander et at., 1972;Dorson et al, 1974;Colton et al, 1971b), although other results are apparently conflicting (Weissman et al, 1967;Villarroel er a/., 1973;Collingham, 1968;Dorson et at., 1971;Buckles et al, 1968). One difficulty is that the effect of the shear-induced red blood cell motion is usually difficult to separate from the larger macroscopic secondary flows (Keller, 1971).…”