Effect of diffusion boundary layers on the initial uptake of O2 by red cells. Theory versus experiment

We have applied theories of mass transfer, in laminar and turbulent flow, to red cells in the stopped-flow apparatus in order to estimate the effect of extracellular diffusion boundary layers on the initial rate of O2 uptake. We compared the theoretical predictions with the results of our previous stopped-flow experiments with suspensions of red cells to which bovine serum albumin (BSA) had been added to decrease O2 solubility and diffusivity (Huxley and Kutchai, 1981). Models of red cells in laminar flow (Friedlander, 1957, 1961; Harriott, 1962) predict a significant retardation of the rate of O2 entry into red cells by diffusion boundary layers. Mixing in the stopped-flow apparatus occurs by convective and turbulent mechanisms in addition to simple molecular diffusion. The more complex theory of mass transfer to particles in turbulent flow (Levich, 1962) shows, because the red cells are highly entrained in the flow, that mixing is not complete on the time scale of initial O2 uptake. The O2 permeability of the diffusion boundary layer, predicted by both laminar and turbulent flow theories, approximates the experimentally obtained value. The theories of mass transfer to particles in laminar flow predict the dependence of the rate of O2 uptake on red cell size observed by other investigators. This suggests that these experimental results may be primarily due to the effect of diffusion boundary layers. Our studies are consistent with the interpretation that red cells in rapid mixing devices may be mixed incompletely with the suspending fluid; thus O2 transfer is limited by molecular diffusion in the immediate vicinity of the erythrocyte. We conclude that the rates of respiratory gas exchange by red cells in flowing systems may be partly limited by diffusion boundary layers.