A theoretical model is developed for the motion of a human red blood cell in a shear field. The model consists of a tank-treading ellipsoidal membrane encapsulating an incompressible Newtonian liquid immersed in a plane shear flow of another incom- pressible Newtonian liquid. Equilibrium and energy considerations lead to a solution for the motion of the particle that depends on the ellipsoidal-axis ratios and the ratio of the inner- to outer-liquid viscosities. The effect of variation in these parameters is explored and it is shown that, depending on their values, one of two types of overall motion is exhibited: a steady stationary-orientation motion or an unsteady flipping motion. A qualitative agreement of the predicted behaviour of the model with experi- mental observations on red blood cells is found.

A fluid-mechanical model is developed for representing the mechanism of propulsion of a h i t e ciliated micro-organism having a prolate-spheroidal shape. The basic concept is the representation of the micro-organism by a prolate-spheroidal control surface upon which certain boundary conditions on the tangential and normal fluid velocities are prescribed. Expressions are obtained for the velocity of propulsion, the rate of energy dissipation in the fluid exterior to the cilia layer, and the stream function of the motion. The effect of the shape of the organism upon its locomotion is explored. Experimental streak photographs of the flow around both freely swimming and inert sedimenting Paramecia are presented and good agreement with the theoretical prediction of the streamlines is found.

The historical development of the mechanics of blood flow can be traced from ancient times, to Leonardo da Vinci and Leonhard Euler and up to the present times with increasing biological knowledge and mathematical analysis. In the last two decades, quantitative and numerical methods have steadily given more complete and precise understanding. In the arterial system wave propagation computations based on nonlinear one-dimensional modeling have given the best representation of pulse wave propagation. In the veins, the theory of unsteady flow in collapsible tubes has recently been extensively developed. In the last decade, progress has been made in describing the blood flow at junctions, through stenoses, in bends and in capillary blood vessels. The rheological behavior of individual red blood cells has been explored. A working model consists of an elastic membrane filled with viscous fluid. This model forms a basis for understanding the viscous and viscoelastic behavior of blood.