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A theoretical model is developed to investigate the role played by the particulate (two-phase) nature of blood on oxygen (O₂) release in capillary-size vessels. Red cells flowing in single-file suspension through capillaries are modelled as evenly spaced, hemoglobin (Hb)-containing circular particles in a rectangular channel (two-dimensional case) or axisymmetric spheres in a circular tube (three-dimensional case). The model includes the free and Hb-facilitated transport of O₂ and HbO₂ kinetics inside the particles, diffusion of free O₂ in the suspending phase, and a specified O₂ tension at the capillary wall that drives the release of O₂ from the particles as they traverse the capillary. The results are expressed in the form of a capillary mass transfer coefficient, an inverse resistance, that relates the spatial average flux of O₂ out of the capillary to a driving force for O₂ release. The results indicate that this coefficient …