Flow in blood vessels

Fluid does not flow as one uniform mass through a tube, and neither does blood flowing through the circulation. Blood flow varies according to the size of the vessel. In the arteries, arterioles, venules, and veins flow is laminar. Flow through the capillaries is single file. In the ventricles there is turbulent flow which allows mixing of saturated and unsaturated blood.

Laminar flow

Laminar flow occurs in cylindrical tubes. The fluid behaves as if it were a set of concentric shells or laminas moving at slightly different speeds. The lamina against the side of the tube is actually fixed to it by molecular cohesive forces and has zero velocity. The lamina next to it slides slowly past this non-slip lamina. Subsequent laminas all slip past each other and so gradually appear to flow faster than each other. At the entrance of a cylinder the laminas present a plug-like profile. Once flow is established the profile becomes parabolic (Fig 3), with the central lamina experiencing the greatest velocity.

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Fig. 3 Laminar flow in a cylinder illustrating the change from a plug-like flow profile to a parabolic flow profile.

The situation is complicated in the case of blood as the fluid is actually a mixture of two phases: plasma and red cells. The velocity profile is blunted compared with that of water.

The movement of one lamina against another results in shearing. One effect of this is that red cells are displaced towards the centre of the column of fluid, resulting in 'axial flow', leaving a marginal layer of cell-deficient plasma along the vessel wall. This layer is only 2 to 4 pm thick, but in arterioles, which have a diameter of only 30 to 40 pm, it reduces the relative viscosity of blood. Lower viscosity means that less pressure is needed to perfuse the microvasculature and blood flow improves.

Single-file flow in capillaries

As the width of a red cell (8 pm) exceeds that of a capillary (5-6 pm), flow can only occur in single file with the cells slightly deformed. There is no possibility of laminar flow, and the cells and plasma move by 'bolus flow'. Red cell deformability is an essential prerequisite for bolus flow of this type. Thus the friction seen when lamina flows against lamina is eliminated, but there is still friction between the cells and the capillary wall. This is minimized by a thin film of plasma.

Polymorphonuclear leukocytes, which are larger, rounder, and stiffer than red cells, move more slowly through capillaries and so impair flow. In inflammation, adhesion of these cells to the endothelium can result in a very detrimental impairment of microvascular blood flow.

Turbulent flow

Darcy's law suggests that there is a linear relationship between flow and effective perfusion pressure. In practice this is not the case; above a certain critical pressure difference flow increases as the square root of pressure. This is because there has been a transition from laminar flow to turbulent flow in which swirling cross-currents dissipate some of the pressure energy of a fluid as heat. A number of variables promote turbulence: a high fluid velocity V; a large diameter D; a high fluid density r. However, an increase in viscosity h reduces turbulence. The relationship between these variables defines the Reynolds number (Re):

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