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The several widely different values of the elastic modulus of the human red blood cell membrane which have been reported in the literature are incorporated into a single strain energy function consisting of two terms. One term gives the small stresses and low elastic modulus which is observed when the red cell membrane is deformed at constant area. The second term contributes a large isotropic stress dependent on the change of area. The strain energy function is applied to the process of sphering of red blood cells in a hypotonic solution. It is shown that a nearly perfect sphere can result even though the red blood cell membrane is homogeneous in all areas of the cell. Results pertinent to sieving and micropipette experiments are also explored.

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.

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Flow of red blood cells along narrow cylindrical vessels, with inside diameters up to 8 μm, is modelled theoretically. Axisymmetric cell shapes are assumed, and lubrication theory is used to describe the flow of the suspending fluid in the gaps between the cells and the vessel wall. The models take into account the elastic properties of the red blood cell membrane, including its responses to shear and bending. At moderate or high cell velocities, about 1 mm/s or more, the membrane stress may be approximated by an isotropic tension which is maximal at the nose of the cell and falls to zero at the rear. Cell shape and apparent viscosity are then independent of flow rate. At lower flow velocities, membrane shear and bending stresses become increasingly important, and models are developed to take these into account. Apparent viscosity is shown to increase with decreasing flow rate, in agreement with previous experimental and theoretical studies.

A new parallel plate flow chamber that has a linear variation of shear stress, starting from a predetermined maximum value at the entrance and falling to zero at the exit, has been designed and tested. This is in contrast to the usual rectangular channel plan which produces a constant shear stress over the entire length. The new design is based on the theory of Hele-Shaw flow between parallel plates. To verify the efficacy of the flow channel, the effect of fluid shear stress on platelet adhesion to a fibrinogen-coated glass surface was tested. The percentage of attached platelets after 5 min of shear stress is shown to be a function of shear stress. With this new flow chamber, cell-cell interactions can be studied efficiently over a wide range of shear stress using a single run at constant discharge.