Pulsatile Flow in Small Blood Vessels: I. Casson Theory.
The Casson model of printing ink flow has been shown to represent the steady flow of blood [in vitro]. This study extends the Casson model of fluid with yield stress, shear-dependent viscosity, and a power law of one half, to the pulsatile flow in arterioles, venules, and capillaries. The bloodstream is modeled as a Casson core with a much less viscous Newtonian wall layer. Velocity profiles are calculated over time for various physiologically representative cases. In the small vessels considered, inertial effects are negligible, pulsatile flow phenomena are quasi-steady, and viscous stress and pressure gradient forces are in instantaneous balance. These conclusions agree qualitatively with observations by Bugliarello and Sevilla. The plasma layer has a surprisingly large lubricating effect during periods when the effective shear viscosity is significantly higher than the ultimate high shear viscosity. These effects may be important throughout the circulation in cases of hemorrhagic shock. (See also R-768, R-769, RM-6214.) 30 pp. Ref.