We saw in Chapter 1 how real materials, in particular fluids, can be regarded as continuous if the distances over which their gross properties (like density) change is much larger than the molecular spacing. They can then be split up into small elements, to each of which the laws of particle mechanics can be applied. We have also set down those laws. Before applying them, however, we must know what forces act on such an element. As with the body sliding along the table (Fig. 2.7), the forces experienced by a representative fluid element are of two kinds: long-range and short-range.

The forces which act at long range, the body forces, are experienced by all fluid elements; the two most common examples are gravitational and electromagnetic in origin. The electromagnetic force on an element depends on quantities like its electrical charge, but the gravitational force, i.e. the weight of the element, depends only on its mass; this is the only example of body force to be considered from now on. If a fluid element P which occupies the point x at a certain time t has volume V and if the fluid in the neighbourhood of x at that time has density ρ, then the gravitational force on the element is ρVg.

Stress

Short-range forces are exerted on the element P by those other elements with which it is in contact, and by no other. They consist of all the intermolecular forces exerted by molecules just outside the surface of P on the molecules just inside.

The pulmonary circulation conveys the entire output of the right ventricle via the pulmonary arteries to the alveolar capillaries and returns the blood, via the pulmonary veins, to the left atrium. The lung has a second, though far smaller, circulation, the bronchial circulation. This arises from the thoracic aorta, supplies systemic arterial blood to the lung, has some interconnections (anastomoses) with the pulmonary microcirculation and drains into the systemic venous system.

The pulmonary circulation differs from the systemic circulation in several important respects. For example, it is a low-pressure, low-resistance system; the time-average excess pressure in the pulmonary arteries is only about 2 × 103 Nm−2 (15mm Hg or 20cm H2O), or approximately one-sixth of that in the systemic arteries, while the total blood flow rate through the lungs is the same as that through the systemic circulation. Further differences are that the pulmonary arteries have much thinner walls than the systemic arteries, and the pulmonary vascular bed is apparently not regionally specialized. In addition, vasomotor control in the pulmonary vessels is believed to be relatively unimportant under normal conditions; unlike the systemic arteries and veins, the vessels do not undergo large active changes in their dimensions.

The main function of the lungs is the exchange of oxygen and carbon dioxide between the air and the blood. However, any gas for which there is a difference in partial pressure between pulmonary capillary blood and alveolar gas will diffuse across the alveolar capillary membrane.

The term ‘mass transfer’ or ‘mass transport’ encompasses a vast range of processes involving the movement of matter within a system. It is not possible to provide a simple definition of its scope, except to state that we are concerned with the movement of particular molecular species within a system and with the factors which affect the movement. We can introduce the subject by means of two simple examples, although these in no way describe its full breadth.

A puddle of water on the road surface slowly evaporates, the liquid water progressively being transferred as vapour to the air above it. The rate of evaporation depends upon such factors as humidity, the ambient air temperature relative to the ground and the speed of the wind over the surface of the puddle.

If a crystal of copper sulphate is dropped into a beaker of water it slowly dissolves in the water and produces a concentrated solution around the crystal surface. In time this dissolved material diffuses further and further into the surrounding water. The speed with which the crystal dissolves and the rate of transfer of dissolved copper sulphate to the bulk of the water phase can be modified by a number of factors. For example, the process would occur more quickly in hot water than cold, or if the beaker were stirred.

The walls of blood vessels are elastic and can change their size or shape when different forces are applied to them. These forces include both the pressures and shear stresses exerted by the blood, and the constraints imposed by surrounding tissue. In this chapter, therefore, we both outline the basic principles governing the mechanics of deformable solids and show to what extent they are applicable to blood vessel walls, rather than leaving the application to a later chapter. The essentials of solid mechanics are of course contained in Newton's laws of particle motion; a solid material, like a fluid, can be thought of as split up into a large number of small elements, to each of which the laws can be applied. Again, the forces on the elements consist of long-range body forces and short-range stress forces; it is in the relationship between the stresses and the deformations of the material that solid and fluid mechanics differ.

Definitions of elastic properties

We should begin with a few definitions. An elastic material is one which deforms when a force is applied to it, but returns to its original configuration, without any dissipation of energy, when the force is removed. This means that all the elements return to their original positions. The first understanding of elasticity was obtained by Robert Hooke (the English astronomer and physicist) in 1678, from experiments with metal wires.

This chapter is concerned with the mechanical properties of the blood and its constituents. We shall examine in Chapters 12 to 15 the flow of blood in blood vessels and its contact with their walls. The mechanics of fluids, discussed in Chapters 4 and 5, provide a background to the material that follows.

Blood is a suspension of the formed elements (the various blood cells) and some liquid particles (the chylomicrons) in the plasma. Plasma itself is an aqueous solution containing numerous low molecular weight organic and inorganic materials in low concentration, and about 7% by weight of protein (Table 10.1). The mechanical property of blood which is of principal interest to us is its viscosity. In order to understand what determines the viscosity of whole blood we must first consider what governs the viscosity of simple fluids and suspensions, then the mechanical properties of the plasma (p. 155) and the suspended elements (p. 157), and finally whole blood (p. 169).

Viscosity of fluids and suspensions

It was noted in Chapter 1 that the physical features of liquids, gases and solids are directly related to their molecular structure and that both liquids and gases are classed as fluids, because they flow when a shear stress is applied. The property which relates the rate of shearing to the shear stress is the viscosity (p. 37) and we must now consider the factors that determine the viscosity of a fluid.

It helps in understanding the physics of a liquid if at the same time we consider a gas. Gases are much less dense than liquids; therefore, the molecules of a gas are farther apart than those of a liquid.

The science of mechanics comprises the study of motion (or equilibrium) and the forces which cause it. The blood moves in the blood vessels, driven by the pumping action of the heart; the vessel walls, being elastic, also move; the blood and the walls exert forces on each other, which influence their respective motions. Thus, in order to study the mechanics of the circulation, we must first understand the basic principles of the mechanics of fluids (e.g. blood), and of elastic solids (e.g. vessel walls), and the nature of the forces exerted between two moving substances (e.g. blood and vessel walls) in contact.

As well as studying the relatively large-scale behaviour of blood and vessel walls as a whole, we can apply the laws of mechanics to motions right down to the molecular level. Thus, ‘mechanics’ is taken here to include all factors affecting the transport of material, including both diffusion and bulk motion.

The study of mechanics began in the time of the ancient Greeks, with the formulation of ‘laws’ governing the motion of isolated solid bodies. The Greeks believed that, for a body to be in motion, a force of some sort had to be acting upon it all the time; the physical nature of this force, exerted for example on an arrow in flight, was mysterious. The need for such a force was related to one of the paradoxes of the Greek philosopher Zeno: that the arrow occupies a given position during one instant, yet is simultaneously moving to occupy a different position at a subsequent instant.

When I arrived at the Physiological Flow Studies Unit, Imperial College, in 1971, the writing of The Mechanics of the Circulation was already underway. The book had been commissioned by Oxford University Press to be delivered in 1972 and the Tuesday afternoon book meeting was a regular event. From the outset, the purpose of the book was seen as presenting cardiovascular mechanics in a rigorous but accessible way. It was not meant to be a textbook, but an introduction to the subject that would be useful to a wide range of readers from medical students to experts in either mechanics or cardiovascular physiology.

The Mechanics of the Circulation was finally published in 1978 and it was obvious that the authors had succeeded in their purpose. It was a truly interdisciplinary book, its authors having trained in medicine, mathematics and engineering, but there was a continuity of style and content that remains unusual in multidisciplinary, multi-author books. Individual authors wrote the first drafts of the different sections of the book closest to their expertise, but they all had an equal say in the final product which, as evidenced by the time it took to write the book and the heat that was generated in those weekly meetings, was no easy task. The book had an enormous impact on the emerging field of cardiovascular mechanics and, by extension, on the development of the discipline of bioengineering as an essentially multidisciplinary field of study. It was reprinted and published as a paperback.

The book had an enormous impact on the emerging field of cardiovascular mechanics and, by extension, on the development of the discipline of bioengineering as an essentially multidisciplinary field of study. It was reprinted and published as a paperback.