Powder flowability at low stresses: ball indentation...Flowability measurement ØMore commonly...
Transcript of Powder flowability at low stresses: ball indentation...Flowability measurement ØMore commonly...
Powder flowability at low stresses: ball indentation
Colin Hare
Department of Chemical and Process Engineering, University of Surrey
Ø Uniaxial compression test
Powder flowability
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σ1 σc σ1 : pre-consolidation stress σc : unconfined yield stress = flow function, ffc
[1} Schulze, D., 2007 “Powders and bulk solids: behaviour, characterization, storage and flow”, Springer
Flowability measurement
Ø More commonly measured with shear cells
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σn
τ
σ1
σ
τ
σ1 σc
[1} Schulze, D., 2007 “Powders and bulk solids: behaviour, characterization, storage and flow”, Springer
Ø Ball indentation2
Ø Elastically deforming region provides additional constraint:
Proposed method
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Fmax
cσ.CH =
( )2maxmax
hRh2πF
AFH
-==
[2] Hassanpour, A., Ghadiri, M., 2007 “Characterisation of flow of loosely compacted cohesive powders by ball indentation”, Particle & Particle Systems Characterization 24, 117-123
Ball indentation
Ø Routinely used for characterising hardness of continuum solids Ø C is known for metals (~3)3
Ø C can be calculated from material properties for organics & polymers4
Ø Indentation procedure has been established5: Ø Indenter size to be used for a given particle size
Ø Minimum amount of powder needed Ø Bed diameter
Ø Bed height
Ø To what depth the indent should be made
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[3] Tabor, D., 1951 “The hardness of metals”, Clarendon Press [4] Johnson, K.L., 1985 “Contact mechanics”, Cambridge University Press [5] Zafar, U., Hare, C., Hassanpour, A., Ghadiri, M., 2017 “Ball indentation on powder beds for assessing
flowability: Analysis of operation window”, Powder Technology 310, 300-306.
Indenter size
Minimum:
6
00.5
11.5
22.5
33.5
44.5
5
0 5 10 15 20 25 30 35
Hard
ness
(kPa
)
Di/Dp
[5] Zafar, U., Hare, C., Hassanpour, A., Ghadiri, M., 2017 “Ball indentation on powder beds for assessing flowability: Analysis of operation window”, Powder Technology 310, 300-306.
Bed height
Minimum amount of powder
Bed diameter
7
01234567
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Hard
ness
(kPa
)
Di/Dd
02468
101214
0 25 50 75 100 125 150 175
Hard
ness
(kPa
)
Bed height/Particle diameter
[5] Zafar, U., Hare, C., Hassanpour, A., Ghadiri, M., 2017 “Ball indentation on powder beds for assessing flowability: Analysis of operation window”, Powder Technology 310, 300-306.
Indentation depth
8
0
5
10
15
20
25
30
35
0 0.2 0.4 0.6 0.8 1
h/Ri
Hard
ness
(kPa
)
[5] Zafar, U., Hare, C., Hassanpour, A., Ghadiri, M., 2017 “Ball indentation on powder beds for assessing flowability: Analysis of operation window”, Powder Technology 310, 300-306.
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Ø Indenter diameter ≥ 17 dp Ø Bed diameter ≥ 1.5 DInd Ø Bed height ≥ 40 dp
Ø Dimensionless penetration depth (h/Ri) ≥ 0.4
Indentation procedure
Size d50 (μm)
Diameter (mm) Bed height (mm)
Bed Volume (mm3) Indenter Bed
50 0.85 1.7 2 5 100 1.7 3.4 4 40 200 3.4 6.8 8 300 500 8.5 17 20 4500
[5] Zafar, U., Hare, C., Hassanpour, A., Ghadiri, M., 2017 “Ball indentation on powder beds for assessing flowability: Analysis of operation window”, Powder Technology 310, 300-306.
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Ø Generally we want to know the unconfined yield stress Ø Need to know constraint factor
Ø How does constraint factor vary with particle properties? Ø Can shear cell data be reliably extrapolated to low stress?
Materials Ø Indentation tested for wide range of powders Ø Silanised glass beads (varying size distributions) Ø Food powders – sweetener, maize starch, pea protein Ø Inorganic powders – limestone, titania, talc, copper
Methods Ø FT4 shear cell Ø Ball indentation
Determining constraint factor
0
0.5
1
1.5
2
2.5
3
3.5
0 2 4 6 8 10 12
Unco
nfin
ed y
ield
stre
ngth
(kPa
)
Major principal stress (kPa)
45-53 μm 53-63 μm 63-75 μm 75-90 μm 90-106 μm
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Unconfined Yield Strength ffc=1 ffc=2
ffc=4
ffc=10
0
1
2
3
4
5
6
7
0 2 4 6 8 10 12
Hard
ness
(kPa
)
Major principal stress (kPa)
45-53 μm 53-63 μm 63-75 μm 75-90 μm 90-106 μm
12
Hardness
13
Constraint factor
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
Con
stra
int f
acto
r
Major principal stress (kPa)
63-75 μm 53-90 μm 45-106 μm 63-75 μm + 10% <25 μm
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Size distribution effect
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Adhesion to the piston
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Low stress behaviour
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Comparison of techniques
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Shearing at low stresses
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Food powders – shear cell ffc=1 ffc=2
ffc=4
ffc=10
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Constraint factor
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Slip-stick behaviour: pea protein
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Slip-stick behaviour: pea protein
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Slip-stick: strain rate effect
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12 14
Unco
nfin
ed y
ield
stre
ngth
(kPa
)
Major principal stress (kPa)
maize starch indmaize starch
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 0.5 1 1.5 2
Unco
nfin
ed y
ield
stre
ngth
(kPa
)
Major Principal Stress (kPa)
shear cellball indentation
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Comparison of techniques - maize
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Shearing at low stresses
0
5
10
15
20
25
30
35
0 5 10 15 20 25
Hard
ness
(kPa
)
Major principal stress (kPa)
titaniatalclimestonecopper
26
Inorganic powders
27
Inorganic powders
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Ø Flowability cannot be easily measured at low stresses using shear cells Ø Target stresses often not obtained Ø Determined yield locus may be inconsistent
Ø Ball indentation can provide reproducible measurements of flowability at
low stresses Ø Requires constraint factor to be known (or determined)
Ø Constraint factor found to be independent of applied stress Ø Though varies (~ 2 – 6) for different materials Ø Reduces slightly with d50, though increases with fines addition
Ø Several powders exhibit sharp reduction in shear stress at lower stresses Ø Behaviour at higher stresses cannot be reliably extrapolated
Conclusions
Future work
Ø DEM will be used to analyse C at low stresses
Ø And influence of particle shape on C
Ø Experimentally assess dependency of C on surface energy
Ø A range of coatings applied to different batches
Ø Investigate indentation at high-strain rates
Ø Optimisation of shear cell procedure at low stresses Ø Number of pre-shear steps applied
Ø Defined end point – i.e acceptable deviation to define steady state
Ø Required agreement between consecutive pre-shears
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Acknowledgements
Collaborators
Ø Dr Umair Zafar
Ø Dr Massih Pasha
Ø Mr Alex Stavrou
Ø Prof. Mojtaba Ghadiri
Ø Dr Ali Hassanpour
Ø Mr Tim Freeman
Ø Dr Marty Murtagh