The Mathematics of Pulsatile Flow in Small Vessels: I. Casson Theory.

by Jerry Aroesty, Joseph Francis Gross

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Primarily a mathematical analysis of the Casson model of blood rheology, in which the fluid possesses finite yield stress and shear-dependent viscosity when it is subjected to a periodic pressure gradient in a long, rigid tube. In this report, the fluid is applied under pulsatile pressure conditions, assuming a low-viscosity plasma wall layer and a Casson core. The coupled nonlinear equations of motion and constitutive relations are nondimensionalized, and solutions valid for small tubes are derived by perturbation analysis. The inertial or time effects are shown to be negligible for conditions of physiological relevance. Thus, blood flow in the larger arterioles and capillaries can be accurately approximated by the quasi-steady solution, despite its pulsatility. (See also R-767, R-769, RM-6214.) 32 pp. Ref.

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