Abstract
Blood rheology is a challenging subject owing to the fact that blood is a mixture of a fluid (plasma) and of cells, among which red blood cells make about 50% of the total volume. It is precisely this circumstance that originates the peculiar behavior of blood flow in small vessels (i.e., roughly speaking, vessel with a diameter less than half a millimeter). In this class we find arterioles, venules, and capillaries. The phenomena taking place in microcirculation are very important in supporting life. Everybody knows the importance of blood filtration in kidneys, but other phenomena, of not less importance, are known only to a small class of physicians. Overviewing such subjects reveals the fascinating complexity of microcirculation.
Highlights
It is well known that blood is a mixture of plasma and of a variety of cell populations: red blood cells (RBCS), white blood cells (WBCS), platelets
We review some recent results in modeling blood flow in such small vessels, considering three areas: (i) Flow in capillaries, i.e., vessels whose size is even smaller than RBCs diameter, taking into account that capillaries allow some plasma to seep through the walls, owing to the presence of fenestration
We have reviewed a model for blood flow in fenestrated capillaries based on an approach outside the standard fluid dynamical context
Summary
It is well known that blood is a mixture of plasma (a liquid slightly denser than water carrying a large number of molecular species performing a huge amount of tasks) and of a variety of cell populations: red blood cells (RBCS), white blood cells (WBCS), platelets. Cells of the other families, though extremely important, contribute only 1% to blood volume, so they do not play any significant role in blood rheology Such a composite nature is a source of considerable difficulties in modeling blood rheology. Geometrical symmetries play an important role, since all flows considered are axisymmetric, and this is largely exploited throughout the paper in connection with the smallness of the vessel’s aspect ratio. We review some recent results in modeling blood flow in such small vessels, considering three areas:. (iii) The amazing phenomenon of the progressive reduction of blood apparent viscosity when the vessel diameter is reduced (roughly in the range 30 μm to 300 μm) This phenomenon, discovered about ninety years ago, known as the Fårhæus–Lindquist effect, has received a satisfactory explanation and a correct interpretation only very recently. We will take this opportunity to present further elaborations of the various models
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