An analysis of oxygen absorption by blood flowing through a small 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 of 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 analysis 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 hemoglobin in the blood, and wall Nusselt number, γ: γ = DLαL/DMαM In [1 + tm/R] where D = diffusion coefficient, α = Bunsen solubility coefficient, subscript L = liquid in tube, subscript M = tube material, R = inner radius of tube, tm = tube wall thickness.
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 is the blood film. Means of reducing this resistance are discussed.