CHAPTER 8 



The rheology of blood 



L. E. B A Y L I S S | Department of Physiology, University College, London 



CHAPTER CONTENTS 



Some Fundamental Definitions 

 Flow in Tubes 



The Kinetic Energy Conection 

 Turbulence 



Turbulence in blood 

 Viscosity of Suspensions 



Effect of Temperature on the Viscosity of Blood 

 The Non-Newtonian Flow of Blood 

 Orientation of the Red Cells 

 Coherence Resistance and Friction 

 Flow of Blood in Very Small Tubes 

 The Finite Summation Correction 

 The Wall Effect 



Effect of the Marginal Sheath on the Pressure-to-Flow Ratio 

 Transit Times of Cells and Plasma and the Dynamic Hema- 

 tocrit 

 Origin of the Anomalous Flow Properties of Blood 

 Motion of Red Cells Toward the Axis of the Tube 

 Direct observation of blood flowing in a tube 

 Deduction from the variation of apparent viscosity with 

 radius of the tube 

 General Conclusions 



RHEOLOGY IS THE STUDY of the properties of a material 

 — or of a system of materials — which aflfect the way in 

 which it flows. Suppose that a force acts on a system 

 in such a way as to produce a deformation or change 

 of shape; if the system is solid, the deformation is 

 limited, and tlie original shape is regained when the 

 force is removed; if it is liquid, the deformation in- 

 creases continuously so long as the force is acting, 

 and remains when the force is removed. There are, 

 however, many kinds of apparently solid materials 

 in which the shape is regained incompletely, so that 

 there is some permanent deformation; and there are 

 many kinds of apparently liquid systems — particu- 

 larly colloidal systems — in which a small force, for 



example, will produce only a limited deformation, 

 which may or may not be reversed when the force is 

 removed, while a larger force will produce a pro- 

 gressively increasing deformation or flow. In the 

 process of clotting or coagulation blood clearly be- 

 haves as a system which has the properties both of a 

 liquid and of a solid, and the study of these properties 

 may properly be regarded as part of the rheology of 

 blood. But when circulating in the vessels of an 

 animal or, indeed, in any conditions in which the 

 phenomenon of clotting is excluded, blood would 

 appear to be an obvious liquid. It has, nevertheless, 

 certain peculiar properties, and it is not to be re- 

 garded as an "ordinary" liquid. It is with these 

 properties that we are now mainlv concerned. 



SOME FUNDAMENT.-^L DEFINITIONS 



Suppose that a liquid is flowing from one place to 

 another. We imagine two parallel plane surfaces 

 within it, such that one is in motion with respect to 

 the other while remaining parallel to it. The velocity 

 of one plane relative to that of the other, divided by 

 the distance between them (i.e., the "velocity gra- 

 dient") is the "rate of shear" of the liquid; it is meas- 

 ured in centimeters per second, per centimeter dis- 

 tance, or in (seconds)"^. (It is usually necessary to 

 suppose that the planes are very close together, since 

 the velocity gradient may vary in different parts of 

 the liquid.) In order to create a given rate of shear, 

 a force must be exerted, the magnitude of which 

 will depend on the area of the planes considered; 

 for each unit area, the magnitude of the force is the 

 "shearing stress," which is measured in dynes per 

 square centimeter. The ratio of the shearing stress to 

 the rate of shear is, in ideal conditions, a quantity 



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