Oxygen uptake by human erythrocytes has been examined both experimentally and theoretically in terms of the influence of unstirred solvent layers that are adjacent to the cell surface. A one-dimensional plane sheet model has been compared with more complex spherical and cylindrical coordinate schemes. Although simpler and faster, the plane sheet algorithm is an inadequate representation when unstirred solvent layers are considered. The cylindrical disk model most closely represents the physical geometry of human red cells and is required for a quantitative analysis. In our stopped-flow rapid mixing experiments, the thickness of the unstirred solvent layer expands with time as the residual turbulence decays. This phenomenon has been quantified using a formulation based on previously developed hydrodynamic theories. An initial 10(-4) cm unstirred layer is postulated to occur during mixing and expand rapidly with time by a (t)0.5 function when flow stops. This formula, in combination with the three-dimensional cylinder scheme, has been used to describe quantitatively uptake time courses at various oxygen concentrations, two different external solvent viscosities, and two different internal heme concentrations.