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

Chapter 2 Literature Review Page 2.38
(2.77)
Tests conducted by Slatter (1994) confirmed <strong>the</strong> model to be more accurate than <strong>the</strong> Torrance
(1963) model and Wilson & Thomas (1985, 1987) model against which experimental data
was compared. This model was also supported by <strong>the</strong> experimental data <strong>of</strong>Park et al (1989)
and Xu et al (1993).
2.11.6 Maude & Whitmore Correlation
Maude & Whitmore (1956, 1958) are two <strong>of</strong> <strong>the</strong> few researchers, if not <strong>the</strong> only two before
Slatter (1994), to take any account <strong>of</strong> <strong>the</strong> <strong>effect</strong> <strong>particle</strong>s play in turbulent flow.
Tests ·were conducted in thin vertical 2,2mm, 3,5mm and 5mm diameter tubes using emery
slurries at six different concentrations. The <strong>particle</strong> <strong>size</strong> <strong>distribution</strong> <strong>of</strong> <strong>the</strong> emery slurries
fell within <strong>the</strong> range 20 to 40JLm. Data was presented in <strong>the</strong> form <strong>of</strong>curves <strong>of</strong> friction factors
against Reynolds numbers.
The main observation <strong>of</strong> Maude & Whitmore (1958) was that <strong>the</strong> turbulent friction factor
(based on <strong>the</strong> wall viscosity) was initially higher than <strong>the</strong> Newtonian friction factor but fell
below at increased Reynolds numbers. This observation is contradictory to <strong>the</strong> more widely
publicised finding that <strong>the</strong> non-Newtonian friction factor is always less than <strong>the</strong> Newtonian
friction factor (eg Wilson, 1986).
The phenomena encountered by Maude & Whitmore (1958) were explained in <strong>the</strong> following
<strong>the</strong>oretical terms. The mixing length, as developed by Prandtl, is defined as <strong>the</strong> mean
distance which fluid elements move at right angles to <strong>the</strong> direction <strong>of</strong> flow before <strong>the</strong>y
acquire <strong>the</strong> velocity <strong>of</strong> <strong>the</strong> layer <strong>the</strong>y have entered. Hence, <strong>the</strong> fluid element would pursue
an oscillating passage down <strong>the</strong> tube. However, inertial forces would prevent any high
denSity <strong>particle</strong>s from following exactly <strong>the</strong> velocity changes <strong>of</strong> <strong>the</strong> fluid. The <strong>particle</strong>s
Would instead oscillate with a smaller amplitude and <strong>the</strong> mean mixing length <strong>of</strong> <strong>the</strong>
suspension would decrease with an increase in solids concentration as compared to that <strong>of</strong>
<strong>the</strong> raw fluid. They postulated that <strong>the</strong> <strong>effect</strong>ive mixing length is reduced by a <strong>the</strong>oretical