Oxygen Transfer to Blood Flowing in Round Tubes

A mathematical and experimental study of processes for oxygenating through membranes, and the transfer of oxygen to blood flowing through tubes with oxygen permeable walls are presented. The increase in average oxygen saturation of blood is dependent upon the flow rate, the tube length, and the diffusion coefficient and independent of the tube diameter. The solution parametrically depends on the velocity profile, the total hemoglobin in the blood, and the initial oxygen saturation, but not on the shape of the oxyhemoglobin dissociation curve in any appreciable way. The average saturations predicted by the analytic solution were verified by a series of experiments using cattle blood flowing in tubes 2 ft to 6 ft long, with internal diameters ranging from 0.025 in. to 0.25 in. The average diffusivity of blood was found to be 5.3 x 10^-4 cm² per min. The flow rates used in the experiments were between 7.0 cc per min and 0.25 cc per min. Within the normal ranges for adding oxygen and removing carbon dioxide, it was shown that the CO₂ removal does not determine the necessary tube length. Oxygenation requires a longer length than the length required for CO₂ removal.