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Basic concepts

1

VISCOSITY
Shear stress, t F v h Blood (h) Viscosity (h) Shear rate, v/h HOW VISCOSITY IS DEFINED. A fluid is located between two parallel plates. The shear force, F, divided by the contact area between the liquid and the plate gives the shear stress, t . The shear rate is the difference in velocity between the different layers and can here be calculated as the velocity ofthe top plate (the bottom plate does not move) and the distance between the plates, i.e., shear rate is g = v/h. The ratio of shear stress and shear rate is the viscosity. If we change the plate velocity or change the distance between the plates, shear stress and shear rate will change. The slope of the relation between shear stress-shear rate gives the viscosity (h ). If a straight line isobtained, as for plasma, we call the fluid Newtonian. Plasma

Description

v

Consider the experiment shown in the figure above. The top plate is moved with Shear rate (g) constant velocity (v) by the action of a shearing force F, and the bottom plate is kept in place (velocity is zero). The result is that the different layers of the blood move with different velocities. The difference in VELOCITYand shear rate velocity in the different blood layers causes a shearing action (friction) between them. The rate of shear (g) is the relative displacement of one fluid layer with respect to the next. In general, the shear rate is the slope of the velocity profile as shown in the figure on the right. In our particular example where the velocity profile is linear, going from zero at the bottom to vat the top plate. Therefore, the slope of the velocity profile, and thus the rate of shear, is equal to v/h, h being the distance between the plates. The units of shear rate are 1/s. The force needed to obtain a certain velocity depends on the contact area (A) between fluid and plates. Instead of force, the term shear stress is used, defined as the force 2 2 per area t = F/A with units Pa orNewton/m (N/m ). We may think of the following experiment: we pull the top plate at different velocities v and we measure the shear force F. When we plot the shear stress,, t, against the shear rate, g. We obtain a relation, the slope of which is the viscosity (figure in box):

2

Viscosity

h = shear stress/shear rate =t / g
The units of viscosity are Pa.s = Ns/m , or Poise (dynes.s/cm ).Fluids with a straight relationship between shear stress and shear rate are called Newtonian fluids, i.e., viscosity does not depend on shear stress or shear rate. Viscosity is sometimes called dynamic viscosity in contract to the kinematic viscosity, which is defined as viscositydivided by density h/r. Viscosity of blood Blood consists of plasma and particles, such as the red blood cells. Theviscosity of blood thus depends on the viscosity of the plasma, in combination with the hematocrit (Ht). Higher hematocrit implies higher viscosity. The relation between hematocrit and viscosity is complex and many formulas exist. One of the simplest is the one by Einstein:
4 2 0 Einstein’s model Human blood
2 2

0

0.2 0.4 Hematocrit

0.6

VISCOSITY as function of hematocrit

h = hplasma (1+ 2.5 Ht)
The viscosity of plasma is about 0.015 Poise (1.5 cP) and the viscosity of whole blood -3 at a physiological hematocrit of 45 is about 3.2 centipoise (cP) , or 3.2 10 Pa.s. Anomalous viscosity or non-Newtonian behavior of blood The viscosity of blood depends on its velocity of the blood. More exactly formulated, when velocity (shear rate) increases viscosity decreases. At highervelocity the disc-shaped Red Blood cells (RBC’s, erythrocytes) orient in the direction of the flow and viscosity is lower. For extremely low shear rates formation of RBC aggregates may occur, thereby increasing viscosity to very high values. It has even been suggested that a certain minimum shear stress is required before the blood will start to
6 4 2 0 0.2 5 0.5 1 2 Shear rate (1/s) 10 20 50 100...