the effect of the particle size distribution on non-newtonian turbulent ...

Chapter 2 Literature Review Page 2.6
However, even though <strong>the</strong> above statements can be taken to be true for Newtonian fluids
<strong>the</strong>re are times when certain fluids deviate from <strong>the</strong> Newtonian behaviour. From <strong>the</strong>oretical
considerations as presented by Grunberg & Nissan (1945) it can be concluded that at high
rates <strong>of</strong> shear <strong>the</strong> viscosity <strong>of</strong> <strong>the</strong>se fluids (eg. n-pentane) may become a function <strong>of</strong><strong>the</strong> shear
rate. O<strong>the</strong>r fluids which behave as Newtonian at lower shear stresses also exhibit non­
Newtonian behaviour above certain shear stresses. In experiments conducted by We1tmann
(1948) it was shown that several oils have a non-Newtonian behaviour above a limiting shear
stress <strong>of</strong> approximately 958 Pa. This seems to contradict <strong>the</strong> fact that normally at high
Reynolds numbers non-Newtonian behaviour decreases (see section 2.5.3.d).
i Examples <strong>of</strong> Newtonian behaviour include:
• all gases,'
• all liquids or solutions <strong>of</strong> low molecular weight (Metzner, 1956).
2.5.2 Non-Newtonian fluids
Unlike Newtonian fluids, <strong>the</strong> term viscosity has no meaning for a non-Newtonian fluid unless
it is related to a particular shear rate (Holland, 1973). However, an apparent viscosity can
be defiiled as (Holland 1973, Wilson 1986):
Non-Newtonian fluids are normally divided into one <strong>of</strong> two categories (Metzner, 1956):
(a) Fluids with properties independent <strong>of</strong> tome or <strong>the</strong> duration <strong>of</strong> shear.
(2.5)
(b) More complex fluids where <strong>the</strong> relationship between shear stress and shear
rate depends on <strong>the</strong> duration <strong>of</strong> shear.
A graphical representation <strong>of</strong> several possible relationships between shear stress and shear
rate for non-Newtonian fluids, called a rheogram, is showlLin Figure 2.2.