THE RHEOLOGY OF BLOOD 



149 



cm-, for example, the viscosity of Kiimin's ox blood 

 (31) was 1.5 times the asymptotic value; whereas in 

 some samples of dog blood, the same proportionate 

 increase in viscosity occurred at r = 25 dynes per 

 cm', and at f = 1 dyne per cm-, the viscosity was 

 3 to 4 times the asymptotic value. 



We may imagine that when a sample of blood is at 

 rest, a large fraction of the cells — and perhaps all of 

 them — are attached to one another by coherence 

 forces. If a gradually increasing shearing stress is 

 applied, the cells will be dragged apart as soon as its 

 value exceeds the "friction" introduced by the 

 coherence force. According to the Buckingham- 

 Reiner conception, this force is the same between 

 any two pairs of cells, and the "plug" will break up 

 into separate cells. But as Maude & Whitmore (34) 

 have suggested, it may be that at first the plug breaks 

 up into aggregates or "clumps" of cells, and that these 

 break up into separate cells when the shearing stress 

 is increased still further. This implies that the co- 

 herence force between any one pair of cells is not the 

 same as that between any other pair: as the shearing 

 stress is increased, those with the smallest coherence 

 are dragged apart first, and those with the largest 

 coherence last. Thus the value of the "friction pres- 

 sure" to be inserted in the Buckingham-Reiner equa- 

 tion will be small when the shearing stress is small, 

 and will increase to a maximum value when the last 

 pair of cells breaks apart; the pressure-flow line will 

 thus rise gradually, as observed, and will not "take 

 off" abruptly from the axis of pressure. We may 

 consider, alternatively, that the clumps of cells will 



enclose and immobilize a certain volume of the 

 suspending plasma; the viscosity of the blood will 

 then be large, and will fall gradually as the clumps 

 break up. 



On this view, when the shearing stress applied to a 

 tube is small, the apparent viscosity of the blood will 

 depend largely on the magnitude and variation of the 

 coherence forces between the red cells, about which 

 little is known. Unless the shearing stress is very small, 

 the axial core of blood, within the marginal sheath, 

 will have a thin outer layer of fully separated and 

 more or less orientated cells; within these, there will be 

 aggregates of cells, progressively increasing in average 

 size towards the axis of the tube; in the immediate 

 neighborhood of the axis, these may join up into a 

 solid plug. In the asymptotic conditions, the whole of 

 the core will contain separated and perhaps orientated 

 cells. In so far as the apparent viscosity of the blood is 

 determined by the coherence forces, it should be the 

 same in tubes of different dimensions, provided the 

 average shearing stress is the same. But if orientation 

 or axial accumulation of the red cells plays a signifi- 

 cant part, the viscosity of the blood at any point in 

 the tube may be determined partly by the rate of 

 shear at this point. This will introduce an element of 

 instability, since, if increase in the rate of shear lowers 

 the viscosity, the rate of shear will be still further 

 increased, and so on; the consequences are difficult to 

 predict. The unexplained dififerences between the 

 flow properties of different samples of blood, appa- 

 rently similar in composition, may perhaps result 

 from some such complicating effects. 



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2. Barr, G. a Monograph of Viscomelry. London : Oxford 

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4. Bayliss, L. E. The axial drift of the red cells when blood 

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