Application Note RheolabQC
Suspension Rheology
Yield point and viscosity to describe the pumping and
transporting process of slurries
Example: Kaolin suspensions
measuring gap, independent of the measuring system
size and manufacturer.
Introduction
The processing and transport characteristics of slurries
are heavily dependent on their rheological properties.
Knowledge of the rheological parameters is therefore
essential, particularly when transporting a large amount
of slurry.
This report describes a measuring method for the
rheological assessment of slurries. The flow curve is
used to represent the pipe flow, the flow resistance and
pressure difference.
Keywords
Pressure difference, flow rate, yield point, flow curve,
Hagen-Poiseuille relation, Herschel-Bulkley model, ISO
3219 for cylinder measuring systems, slurries,
suspensions, viscosity, volumetric flow
Samples
Kaolin: Aluminum silicate hydrate Al4 (OH)8 [Si4O10]
Kaolin (china clay) is a potassium silicate of the mineral
kaolinite. It is created by the decomposition and
transformation of silicate rocks. Pure kaolin is snowwhite. When mixed with quartz or feldspath it is grayyellow (crude kaolin, kaolin sand). Kaolin which has been
created by the weathering of granite and feldspath can
be found in many locations around the world.
It is mined using wet-chemical flotation and subsequent
cleaning.
The main components of kaolin are SiO2 (35%) and
Al2O3 (46 % - 49 %). The pH value is approx. 5. The
particle size is between 2 µm and 20 µm. The particle
3
density is approx. 2.6 g/cm
The sample investigated for this report was a kaolin
suspension
with
a
volume
concentration
of
10 % solids in water.
Test procedure
All measurements were performed with an Anton Paar
RheolabQC rheometer with a sandblasted cylinder
measuring system CC27 according to ISO 3219. The
sandblasted surface reduces wall slipping effects. ISO
3219 describes the construction of the cylinder geometry
and defines the ratio of measuring cup diameter to
measuring bob diameter as 1.0847. This guarantees an
industrial standard for shearing the sample in the
Anton Paar Germany GmbH
Web: www.anton-paar.com
Fig.1: RheolabQC
When measuring slurries, the following points must be
taken into consideration:

The measuring system CC27 can be used for
particle sizes below 100 µm.

If the average particle size is considerably
higher than 100 µm, we recommend to use a
vane geometry with 4 vertical vanes
ST22/4V/40 in the CC27 measuring cup.
The measuring system is temperature controlled either in
a water bath or directly in the instrument by the
temperature-controlled measuring cell. The temperature
of the measuring system can be controlled using the
Rheoplus software. Using defined temperature profiles
enables further options to investigate the temperature
sensitivity of slurries. For example: setting a temperature
ramp from 5 °C to 40 °C with a heating rate of
-1
2 K/min (°C/min) and a constant shear rate of 100 s .
Tel.: +49 (0)711 720 91-0
E-mail: [email protected]
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AN_RLQC_Slurry_D.doc
Application Note RheolabQC
Suspension Rheology
Test conditions
2 s-1
1.3 l / min
1513 Pa / m
10 s-1
6.5 l / min
1663 Pa / m
50 s-1
33 l / min
2005 Pa / m
100 s-1
65 l / min
2137 Pa / m
200 s-1
130 l / min
2313 Pa / m
The measuring profile has one interval.
-1
Interval 1: Logarithmic shear rate ramp from 10 s to
-1
1000 s with 30 measuring points and a measuring point
duration of 10 s.
The test is controlled manually at the instrument or by the
Rheoplus software.
Results and discussion
The viscosity function describes the flow behavior at
different shear rates. If the flow is assumed to be laminar
and stationary, the shear rate on the pipe wall (b) and the
shear stress on the pipe wall (c) can be calculated using
the Hagen-Poiseuille relation:
(a) p

4Q
8  L  Q
; (b) w 
4
 R
  R3
; (c)  w

R  p
2 L
W = pipe wall; L = pipe length; Q = volumetric flow or flow rate;
R = pipe radius
Equation 1 a/b/c: Hagen-Poiseuille relations for
calculating the pressure difference (a), shear rate (b) and
shear stress (c) on the pipe wall.
Table 1: Shear rate, volumetric flow and pressure
difference per one meter of pipe length.
The relationship between volumetric flow and pressure
difference becomes clear if we observe the shear stress
more closely (Fig. 2). At low shear rates and low
volumetric flow, the shear stress and pressure difference
p in the pipe is already relatively high (p = 1663 Pa / m
-1
at 10 s ). Increasing the volumetric flow Q of slurry in the
pipe requires only a slight further increase of the
pressure difference. This is due to the shear-thinning
(pseudoplastic) behavior of the slurry, i.e. decreasing
viscosity with increasing shear rate.
The flow properties at „almost rest“, i.e. at the start of the
pumping process or during leveling, can be determined at
low shear rates. The yield point o,HB = 12 Pa was
calculated using the Herschel-Bulkley (H.B.) model. This
gives a pressure difference of p = 1000 Pa / m (table 2).
Yield point
p
calculated
Pipe diameter
D
per 1m pipe length
12 Pa
48 mm
1000 Pa / m
These formulas can be reduced to the following:
The pressure difference in the pipe is:

directly
stress:
Table 2: Yield point and initial pressure difference in one
meter of pipe, assuming horizontal and laminar flow.
Description of the flow process starting from a state
without any movement:
Until the yield point is reached, the resistance and
pressure in the pipe are increasing proportionally with no
significant resulting flow output.
p   W
proportional
to
the
shear
To pump or shear a slurry, the network forces in the
structure have to be exceeded (Hooke’s elasticity law). In
rheology, this initial ‚static friction’ is often called the ‚yield
point’  0 . A disproportionate amount of energy is
required to overcome the yield point. This is illustrated in
table 1:

A volumetric flow of 6.5 l / min of slurry in a one
meter pipe results in a pressure difference of p
= 1663 Pa / m.

Increasing the volumetric flow by ten times, i.e.
to 65 l / min slurry, results in p = 2137 Pa /m.
This means an increase of only 6 %.
Shear rate
Volumetric flow Q
Pressure difference
pipe with D = 48 mm
For 1m pipe length
Anton Paar Germany GmbH
Web: www.anton-paar.com
Better pump characteristics can be obtained by reducing
the yield point. Yield points which are too high make it
impossible to restart the pumping process. The slurry
comes to a standstill in the pipe.
Producing a shear-thinning slurry the pump output can be
increased without significantly increasing the energy
required. The viscosity of the sample should greatly
decrease with increasing volumetric flow.
The rheological properties can be influenced by varying
the slurry composition, e.g. the volume concentration
(amount of water), additives (solids, polymers, liquid),
particle size and pumping temperature.
Tel.: +49 (0)711 720 91-0
E-mail: [email protected]
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Application Note RheolabQC
Suspension Rheology
Summary
It was shown that the rheometer system RheolabQC with
the sandblasted cylinder measuring system CC27
according to ISO 3219 is very useful for the control of the
pumping process and for the characterization of slurries.
Besides measuring flow and viscosity curves, the yield
point can also be calculated, e.g. using the HerschelBulkley model. Measuring the yield point and the
viscosity function gives an important information for a
better understanding how slurries flow in pipes. It also
helps solve problems with slurries which are difficult to
pump.
40
10
Pa
35
Pa·s
30
  p
Kaolin 10% 1
CC 27 Sand; [d=0 mm]
1
25


20

Shear Stress

Viscosity
Kaolin 10% 1 [Yield Point Herschel-Bulkley]
tau0 = 12 Pa; b = 5.24; p = 0.2
15
0,1

Shear Stress

Viscosity
10
5
0
0
100
200
300
400
500
600
700
800
0,01
900 1/s 1 000
.
Shear Rate 
  Q
Fig. 2: Flow and viscosity curve with curve fitting and the calculation of the yield point using the HerschelBulkley model. The analysis routine and automated measuring profile are part of the RheolabQC instrument
and Rheoplus software package.
Text:
Klaus Wollny; 10.02.2005
Measurements:
Cape Tech., Cape Town, South Africa
Anton Paar Germany GmbH
Web: www.anton-paar.com
Tel.: +49 (0)711 720 91-0
E-mail: [email protected]
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