The physics of arteriole blood flow: I. General theory

A continuum physics theory of arteriole blood flow is presented based on the observed behaviour of blood using high-speed photography. The theory highlights the importance of time scales as well as length scales in constructing a physical theory of blood flow. Arteriole flow viewed at 8000 frames s-1 reveals a highly complicated cellular motion; however the same flow viewed at the same spatial magnification by the human sensor, the eye, reveals only a pinkish column of fluid. The eye 'smoothes out' the microscopic cellular behaviour. This principle is used in the continuum theory, where averages are taken over space and time, to explain how the observed collisions of the erythrocytes with themselves, plasma molecules and the arteriole wall determine blood, mass-averaged velocity profiles and mass flow rates. A new dimensionless similarity parameter arises from the continuum mixture. Its magnitude provides a measure of the relative importance of the viscous drag of a constituent and the frictional force experienced by one constituent due to the presence of another constituent in the mixture during arteriole blood flow. (The second paper in a series.)