Yielding of Coarse-Fine Particle Mixtures in Mineral Slurries
Shane P. UsherParticulate Fluids Processing Centre
Dept. Chemical & Biomolecular Engineering The University of Melbourne, Australia
P ti l Mi tIndustries
Particle Mixtures • Water/Wastewater• Algae for Biofuels• Desalination• Minerals Processing• Ceramics• Pulp and Paper• Blood and many more
Theory & MethodsShear Rheology
Processes• Flow • Shear Rheology
• Compressional Rheology
• FlowPumping and Mixing
• Dewatering • Compressional Rheology DewateringThickeners, Filters, Centrifuges
Material PropertiesMaterial Properties
Gel Point, gg Minimum solids volume fraction
at which the suspension forms a continuously networked structure th t t it it i ht t ththat transmits its weight to the suspension below.
Can make an approximate measure from a batch settling experimentexperiment.
Material PropertiesMaterial Properties
Compressive Yield Stress, Py()y Minimum compressive force
required for a suspension to yield and compress.
Shear Yield Stress, y() Minimum shear force required
for a suspension to yield and flflow.
Material PropertiesMaterial Properties
Yi ld St M tYield Stress Measurement
Vane technique Developed by Nguyen and Boger
0.2 rpm
p y g y g1983
measurement of shear yield stress via Haake Rheometer
slurryvane
slurry
Nguyen QD, Boger DV, Journal of Rheology, 29 (1985) 335-347 Pashias N, Boger DV, Summers J, Glenister DJ, Journal of
Rheology, 40 (1996) 1179-1189
Poly-disperse mixturesy p
• Bi-disperse mixtures• Poly-disperse mixturesParticle Size DistributionParticle Size Distribution
• Measurements• Equilibrium Batch Settling• Yield stress measurement• Shear rheology measurements
Determination of bi-disperse mixtureDetermination of bi-disperse mixture Shear rheology measurements
• Model developmentdisperse mixture propertiesdisperse mixture properties
• What is the minimum required information?
Development of an industrial tool for
di ti f ti
Development of an industrial tool for
di ti f tiprediction of propertiesprediction of properties
Materials - Solids
Alumina AKP-50 (4000 kg m-3, d50 0.14 m, IEP 9.2)
Calcium Carbonate Omyacarb-2 (2700 kg m-3, d50 3.5 m, IEP 8)y ( g , 50 , ) Omyacarb-40 (2700 kg m-3, d50 32.5 m, IEP 8)
Sand AKP-50 (2600 kg m-3 d50 1083 m) AKP 50 (2600 kg m , d50 1083 m)
Materials - Electrolyte Potassium Nitrate Solution
0.01 M KNO3 (aq) at pH 9.2
Materials Electrolyte
Gel Point (Bi-disperse mixtures)
Measured
( p )
1.2
Vane technique
Predicted
1
, (-
)
Predicted Mixture solids volume fraction
(mixture) ( fine) (coarse) 0.6
0.8
me
Frac
tion
Coarse fraction( ) ( )
( ) ( ) ( )
coarse coarse
mixture fine coarse
S
0.4
olid
s Vol
um
Predictions0
0.2
0 0 2 0 4 0 6 0 8 1So
)( 0 SSfineg
0 64 f d( ) 1cp coarse S S
0 0.2 0.4 0.6 0.8 1
Sand Fraction, S (v/v)(max)
)(
)()(
0,1
SSSS fineg
fmixtureg
g = cp = 0.64 for coarse sand( )
( ) (max), 1pg mixture S S
S
1.2
1
, (-
)0.8
e Fr
actio
n,
0.6
lids V
olum
0.4
Sol
0.2
00 0.2 0.4 0.6 0.8 10 0.2 0.4 0.6 0.8 1
Sand Fraction, S (v/v)
Yield Stress Constitutive Equation
Yield stress data is fitted to a
q
2000
constitutive equation:
1500
Pa)
cp is the close packing fractiona b and k are empirical fitting parameters
1000
ess, y
() (
Gel point and close packing fraction predicted as described.
a, b and k are empirical fitting parameters
500
Yie
ld S
tr
b is assumed 0.002, while a and kparameter variation is determined as a function of sand fraction
00 0.2 0.4 0.6 0.8 1
Solids Volume Fraction, (v/v)
Yield Stress Constitutive Equation56
Yield stress data is fitted to a
q
a u1S u23
4
aconstitutive equation:
1
2
a
cp is the close packing fractiona b and k are empirical fitting parameters
00 0.2 0.4 0.6 0.8 1
Sand Fraction, S (v/v)8
Gel point and close packing fraction predicted as described.
a, b and k are empirical fitting parameters
6
8
b is assumed 0.002, while a and kparameter variation is determined as a function of sand fraction
4k2
00 0.2 0.4 0.6 0.8 1
Sand Fraction, S (v/v)
Herschel Bulkley model
Sh t h
y
10000 Shear stress versus shear
rate data also determined using the vane
Pure AKP-50
Data is fitted to Herschel Bulkley equation 1000
) (P
a)
.
Yield stress determined using prediction method 100tr
ess,
g p k and m fitted to data
Again, can determine variation of parameters Sh
ear S
t
variation of parameters with coarse fraction. 10
0.1 1 10 100 1000 10000 100000
h ( 1).Shear rate, (s-1).
Sedimentation and Segregationg g
Particles settle due to gravity, even when the solids concentration is greater that the
10000the solids concentration is greater that the gel point.Larger particles can settle faster.
1000Pa)
Stokes Law For isolated particles. Gives maximum potential rate of 100tre
ss,
) (P
.
Gives maximum potential rate of segregation
2coarsed gV
100
Shea
r St
Invalid region
18coarse
coarsegV
, (1 )fine suspension fine fine fine medium
100.1 1 10 100 1000 10000 100000
Shear rate, (s-1).
where Vcoarse = the velocity of coarse particledcoarse = the diameter of coarse particle∆ th d it diff b t ti l d fi ti l i
,fine suspension fine fine fine medium
∆ρ = the density difference between coarse particle and fine particle suspension g = the acceleration due to gravityη = the viscosity of fine particle suspension at a given shear rate
ConclusionsConclusions
Rheology of bi-disperse mixtures can be predicted: g and cp variations can be predicted for bi-disperse mixtures
based on pure component properties based on pure component properties, requires significant particle size difference.
y and Py variations can be predicted uses a constitutive equation.
versus variations can be predicted using Herschel Bulkley parameters that vary with mixture
composition. Sedimentation and segregation can compromise measurements
Timescale of segregation must be longer than that of measurement.
Further WorkFurther Work
Polydisperse mixtures: g and cp can be accurately predicted for mixtures of 3 or more
components provided that particle size differences arecomponents, provided that particle size differences are significant.
The challenge is to quantify the impact of particle size distribution overlapoverlap.
Dewatering: Compressive yield stress, Py() variations can be similarly be y
predicted for mixtures. Settling rate predictions…
A k l d tAcknowledgements
PFPC (Particulate Fluids Processing Centre) a Special Research PFPC (Particulate Fluids Processing Centre), a Special Research Centre of the Australian Research Council (ARC).
Rio Tinto – Mark Coghill and Nikk Vagias Seoul National University - Sanghyuk Lim Melbourne University - Peter Scales, Ashish Kumar, Nicky Duan, Cecilia
Aurellia Xiaodun SunAurellia, Xiaodun Sun
