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

Chapter 5 Discussion Page 5.4
Whatever <strong>the</strong> point is at which <strong>the</strong> viscous sub-layer breaks down <strong>the</strong> fact still remains that
<strong>the</strong> viscous sub-layer <strong>of</strong> a homogeneous slurry cannot exist if it is smaller than <strong>the</strong> <strong>particle</strong>s
which comprise <strong>the</strong> slurry. As can be seen from Figure 4.18 (mixture 2) <strong>the</strong> viscous sub­
layer thickness is smaller than <strong>the</strong> <strong>particle</strong>s which comprise <strong>the</strong> slurry at higher waIl shear
stresses. The thickness <strong>of</strong> <strong>the</strong> viscous sub-layer for kaolin clay (Figure 4.16) is smaller than
<strong>the</strong> <strong>particle</strong>s which comprise <strong>the</strong> slurry at higher shear stresses but a much smaller fraction
than mixture 2. At <strong>the</strong>se higher wall shear stress values <strong>the</strong> Slatter model best models <strong>the</strong>
test data for <strong>the</strong> kaolin clay and mixture 2 test sets. This could be ascribed to <strong>the</strong> fact that
Slatter's model accounts for <strong>the</strong> <strong>particle</strong>s affecting <strong>the</strong> viscous sub-layer.
To confirm that <strong>the</strong> <strong>particle</strong>s will affect <strong>the</strong> viscous sub-layer and are relevant for turbulent
flow analysis <strong>the</strong> number concentration <strong>of</strong> large <strong>particle</strong>s in <strong>the</strong> viscous sub-layer was
calculated. In order to calculate <strong>the</strong> number concentration a few assumptions had to made.
The assumptions were as follows:
• <strong>the</strong> <strong>particle</strong>s comprising <strong>the</strong> slurry are spherical in shape;
• <strong>the</strong> large <strong>particle</strong>s were taken to be greater than one half <strong>of</strong> <strong>the</strong> thickness <strong>of</strong> <strong>the</strong>
viscous sub-layer in turbulent flow;
• one metre <strong>of</strong> pipe tubing was considered for calculations;
• an average radius is assumed for <strong>the</strong>" large <strong>particle</strong>s.
From Figure 4.16 to Figure 4.18 we can determine <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> viscous sub-layer in
turbulent flow. The thickness <strong>of</strong><strong>the</strong> viscous sub-layer for kaolin clay, mixture 1 and mixture
2 is approximately 40JLm, 300JLm and 55JLm respectively. The percentage <strong>of</strong> large <strong>particle</strong>s
present in <strong>the</strong> viscous sub-layer can <strong>the</strong>refore be determined from <strong>the</strong> PSD (ie. percentage
<strong>of</strong> Particles greater than one half <strong>the</strong> viscous sub-layer thickness). From <strong>the</strong> diameter and
Viscous SUb-layer thickness <strong>the</strong> volume <strong>of</strong> <strong>the</strong> viscous sub-layer can be determined and
knOWing <strong>the</strong> percentage <strong>of</strong> large <strong>particle</strong>s <strong>the</strong> volume taken up by <strong>the</strong> <strong>particle</strong>s in <strong>the</strong> viscous
Sub-layer can be calculated. The mass <strong>of</strong> <strong>particle</strong>s can be obtained from <strong>the</strong> volume and
jensityand similarly by considering one <strong>particle</strong> present in <strong>the</strong> viscous sub-layer, it's mass
:an be calculated and hence <strong>the</strong> number <strong>of</strong> <strong>particle</strong>s. The results obtained are shown in