2. Introduction
Industrial Relevance & Key issues
• Selection of appropriate mills is conducted by trial
and error – particularly true for organic solids for
which our fundamental understanding is limited.
• Costly and time consuming
3. Milling Issues
Process Engineering:
• Scaling of power consumption, energy utilisation and capacity
• Milling aids
• Method of application of stresses, i.e. point loading,
distributed loading or loading accompanied by frictional
traction, etc.
Material-Related Issues:
• Feed and product characteristics
• Smallest possible particle size which could be comminuted.
• Size distribution of comminuted materials for feed materials larger
than this limit.
• Level of stresses required for comminution to a certain size
range.
• Mechanical activation and mechanochemical processing
4. Energy Laws
ΔS
Energy utilization: EA
Kick
Walker et al. (1937): Bond
dx
dE = −k n Rittinger
x
Rittinger (1867): n = 2
Kick (1885): n = 1
Bond (1952): n = 1.5
EA
5. Coupled Effects of Process Engineering –
Product Characteristics
Product Quality Polymorphic form
Product size range - Phase change -
- Amorphous content and stability -
6. Methods of Stressing Particles
1. Impact
2. Compression
3. Shear
4. Attrition
Milling is an art at present. The science of size
reduction is at its infancy and cannot yet satisfy the
demands of industry. As a simple example, we
cannot even predict the size distribution of a given
material impacting on a single rigid target!
Empiricism is still the order of the day.
7. Scope of Lectures
• Equipment: Iain Crosley
• Product characteristics affected by the
process and feed: John Sherwood
• Fundamentals: Mojtaba Ghadiri
8. School of something
FACULTY OF OTHER
Putting Science into the Art of Milling
Mojtaba Ghadiri
Procter & Gamble Grinding Day
24th February 2010
9. Objectives & Methodology
To establish a functional relationship amongst evolved
product characteristics, feed material properties and
mill dynamics for milling of organic materials
Characterise single Indirect measurement Analysis of milling based
particle breakage of mechanical properties on dynamics and
under high strain rate at under chosen conditions single particle properties
ambient conditions
10. Deformation Modes
(a) rigid-perfectly plastic,
(b) elastic-perfectly plastic,
(c) rigid-plastic with work-hardening, and
(d) elastic-plastic with work-hardening.
(a) (b) (c) (d)
10
11. Breakage Modes
Brittle Failure Mode Semi-Brittle Failure Mode
• Pre-existing internal and surface flaws • Cracks are initiated by plastic flow.
affect the strength. • Indentation fracture analysis can be
• High compliance: surface flaws used to describe the breakage.
• Low compliance: internal flaws • Lateral cracks are responsible for
• Stress field is independent of strain chipping and wear.
rate. • Radial and median cracks are
• Predictive analysis is difficult. responsible for fragmentation.
• Predictive models are available.
• Statistical analysis, e.g. Weibull
distribution is used to describe the
data.
12. Material Properties Accounting
for Breakage
Resistance against elastic deformation
- Young’s modulus, E
Resistance against plastic deformation
- Yield stress and hardness, Y & H
Resistance against crack propagation
- Fracture toughness, Kc
Temperature and strain rate affect these parameters
14. Analysis of Breakage for Semi-Brittle
Failure Mode: CHIPPING
The volume of chips is estimated based on the propagation of
lateral cracks. The calculation of the ratio of volume of chips
to the volume of original particle gives rise to a dimensionless
group which describes the breakage propensity for this mode
(Ghadiri and Zhang, 2002).
2
ρv l H
ξ = αη = α 2
Kc
15. Various Materials
α-Lactose Sucrose Sorbitol Aspirin
H= 640MPa H=645MPa H=645MPa+ H=140MPa+
Kc=0.16MPa.m0.5 Kc=0.08MPa.m0.5 Kc=0.08MPa.m0.5 Kc=0.16MPa.m0.5
Material H/K c 2 Tm , oC Tc , oC
Sucrose 100781 186 60-75
α-LM 23795 201 118
Aspirin 3570 139 -30
MCC 293 265 160
MCC Starch Starch (☼) 250 170*
H=168MPa H= 78MPa
Kc=0.76MPa.m0.5 Kc not yet available H – Hardness; Kc – Fracture toughness
☼ Not yet available
* Decrease with increasing moisture content
+ Measured using nano-indentation on single crystals
16. Project Sqeeze used this approach
X-ExtMailInfo: <tantawy.h@pg.com> bdc-notes003.na.pg.com
[155.125.116.11]
Subject: Squeeze Mechnical properties
To: Mojtaba Ghadiri <m.ghadiri@leeds.ac.uk>
Cc: mcgoff.mg@pg.com, howard.p.2@pg.com
From: tantawy.h@pg.com
Date: Thu, 15 Mar 2001 13:41:37 +0000
X-MIMETrack: Serialize by Router on BDC-NOTES003.NA.PG.COM/PGI(Release 5.0.3 (Intl)|21
March 2000) at 03/15/2001 08:43:21 AM
Dear Mojtaba,
Attached is a write-up of the mechanical properties of Squeeze that we feel is
the reasons behind the particle low propensity for fracture under plant
conditions of compressive, shear & impact conditions. I thought there may be
time for you reveiw before meeting tomorrowing morning.
Look forward to seeing you tomorrow,
(See attached file: Squeeze Mechanical Property Definitions.doc)
Kind Regards sam
Squeeze Mechanical Property Definitions.doc
17. Project Sqeeze used this approach
1. A water-soluble and/or a water-dispersible particle having a mean particle
diameter of less than 20mm, preferably less than 2mm, and having a Hardness
(H) of 500 MPa or less, when measured at a temperature of 20oC, a relative
humidity of 20%; and a Fracture Toughness (Kc) of 0.04 MPa.m1/2 or greater,
when measured at a temperature of 20oC, a relative humidity of 20% and a
strain rate of 30 s-1; said particle comprises an active ingredient, said particle is
obtained by a non-freeze dry process.
2. A particle according to any preceding claim, wherein said particle has a
Fracture toughness of 2 MPa.m1/2 or greater and/or a Hardness of 200 MPa
or less, when measured at a temperature of 20oC and a relative humidity
of 20%.
3. A particle according to any preceding claim, wherein said particle has a ratio of
H/Kc2 of 312500 Pa-1.m-1/4 or less, preferably from 50 Pa-1.m-1/4 or less.
18. Analysis of Breakage for Semi-Brittle
Failure Mode: FRAGMENTATION
Extension of radial and median cracks causes fragmentation. Based
on crack extension proposed by Ghadiri and Zhang (2002), the
fragmentation force is given by:
4 3 4 3 1 3
Ffr ∝K c l H
2 3 4 5 6
20. Transition Velocities
Chipping – Fragmentation Transition
Hutchings (1992) specified a critical load for fragmentation
based on the indentation fracture model of Hagan (1981):
4
K c
Fcf ∝ 3
For velocity: H
4
Kc 1 2 -1 2 -2
V fr ∝ [ ] H ρ l
H
Transition Velocities
21. Particle Shear & Impact
Prototype Design
Porous ring (1mm thickness) Bracket
Etching
Rotameter Cabinet Seal Roller abrasion
Orifice
22. Single Particle Impact Testing
Feeding funnel Manual feeding
Glass tube
Photodiodes Glass Photodiodes
Target
tube
Target
Collection
Filter chamber Collection
PI
chamber
Vacuum line Filter
connection
Vacuum line
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23. Single Particle impact testing
Experimental procedure
• 2 g of sample used in each test for statistical
reliability
• Product sieved using 2 sieves below original
* M de
• Extent of breakage
R = × 100%
M m + M de
on the assumption that handling losses are due to a
combination of losses from mother, debris and feed
particles
* 2
• Extent of breakage R* related to R = c1 v
where
α ρH l
c1 = 2
KC
24. Single Particle impact tests -
Results
Aspirin - ambient temperature and humidity
Size range μm C1 C1/l R2
• Breakage propensity increases with particle
size and impact velocity
425 - 500 0.0483 104.4 0.996
355 - 425 0.0415 106.4 0.981 • C1/l remains relatively constant with
300 - 355 0.0319 97.4 0.989
particle size
250 - 300 0.0231 84.0 0.988 • Well described by Ghadiri & Zhang model
(2002)
26. Results of single particle impact Tests
Mechanical properties from impact test (ambient temperature)
0.16 Material (C1/ρ d)ave
Aspirin Sucrose Sorbitol Aspirin 0.0700
0.12 Sucrose 0.0244
MCC Starch Lactose
Sorbitol 0.0356
α-LM 0.0058
0.08
MCC 0.0028
C1/(ρ d)
Starch 0.0018
0.04
0
-0.04
0 200 400 600 800
Particle size, micron
H C1 H
C1 = α ρd 2 ,
K = α 2
K
c ρd c
27. Single Particle impact tests -
Results
Effect of temperature on breakage of
Aspirin
• Breakage propensity increases with
temperature
• Value of C1 increases with temperature
• Ratio of H/Kc2 increases with
temperature
• Similar results obtained from two
separate studies
Temperature C1 R2
* 2 α ρH l
(-) 20 °C 0.0281 0.986 R = c 1v c1 =
25 °C 0.0410 0.994 K C2
70 °C 0.0561 0.989
28. Single Particle impact tests -
Results
Effect of temperature on breakage of Aspirin
Arrhenius relationship
E 1
ln k = ln A + − a
R T
Temperature C1 R2
(-) 20 °C 0.0281 0.986
25 °C 0.0410 0.994
70 °C 0.0561 0.989
• Effect of temperature fits well to Arrhenius plot
• Activation energy – May be described as the energy required to move
dislocations and initiate fracture
30. Agglomerate Breakage
Breakage energy is related linearly to the incident
energy (Moreno, 2003):
1 4 3 2
N C ΓA ∝ Nρ πR V
2 3
The damage ratio is given by:
N C ρR 3V 2
∝
N ΓA
N C ρD 5 / 3 E 2 / 3V 2
∝
N Γ5 / 3
2/ 3
N C ρDV ED 2
∝ ×
N Γ Γ
31. Now from LEFM: K = EΓ
2
c
is gives the damage ratio as:
2/3
NC ρDV H E ED
2
∝ × ×
H Γ
2
N Kc
32. Analysis of Breakage
for Brittle Mode
Weibull Analysis (1951): Probability of fracture, S, when a brittle
material is subjected to stress:
σ m
S = 1 − exp − z
σ
s
33. Impact Breakage
in Brittle Mode
Vogel and Peukert (2002):
S = 1 − exp[ − f mat x (Wk − Wk ,min ) ]
where fmat is a material parameter, x is particle size,
Wk is kinetic energy and Wk,min is the minimum kinetic
energy which causes breakage.
34. Bulk Tests
Methods: Features:
• Compression • Reflect particle interactions
• Close to industrial case
• Shear
• Difficult to interpret
• Fluid bed • Only useful for relative
comparison
• Ball mill
• Hydrodynamic interactions
• Tumbler depend on scale
• Misleading
• Vibration
35. Analysis of Bulk Milling
Can common conceptual models be analysed with
recourse to single particle breakage characteristics?
First Order Rate Process:
d Mi
=- K i M i
dt
Population Balance model:
d Mj n
= - S j M j + ∑ B j ,i S i M i
dt i = j +1
36. First Order Milling Rate
Dt - D l
= exp ( - K p t )
D0 - D l
Dt = d50 of the mill sample at time t Dl = d50 of the sample at milling limit
D0 = d50 of the feed material, d50 = median of the sample
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37. Example: Analysis of Single Ball Milling
Detachable
Stainless steel 50 mm (11 ml)
jar holder milling jar
12 mm
y z
x
Jar movement
Counter Detachable
weight
cooling jacket
38. Approach
Single Particle 3D-DEM
Impact Testing Simulation
?
Determine the Analyse the
material properties mill performance
Develop a predictive
model for milling
Single Ball Milling
39. Samples
Microcrystalline Cellulose (MCC) <250 mm (BS410
Sieve)
100 µm Ranges selected for
testing:
• 212 – 250 mm
• 180 – 212 mm
• 150 – 180 mm
• 90 – 106 mm
• 63 – 75 mm
• MCC is widely used as excipient or inert in the pharmaceuticals
industry.
40. Milling of MCC at 18 Hz
1.0 Original MCC
2 212-250 µm
Kp = 0.0038, R = 0.9864 180-212 µm
0.8
150-180 µm
2
Kp = 0.0057, R = 0.9965 90-106 µm
(Dt-Dl)/(D0-Dl)
0.6 63-75 µm
2
Kp = 0.0047, R = 0.9943
0.4 2
Kp = 0.0041, R = 0.9947
2
0.2 Kp = 0.0024, R = 0.9978
2
Kp = 0.0016, R = 0.9946
0.0
0 1000 2000 3000 4000 5000 6000
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41. Milling of MCC at 25 Hz
1.0 Original MCC
2
Kp = 0.0073, R = 0.8837 212-250 µm
0.8 180-212 µm
150-180 µm
(Dt - Dl) / (D0- Dl)
2
Kp = 0.0144, R = 0.9689 90-106 µm
0.6
2
Kp = 0.0129, R = 0.9793
0.4
2
Kp = 0.0108, R = 0.9823
0.2
2
Kp = 0.0045, R = 0.9735
0.0
0 1000 2000 3000 4000 5000 6000
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42. Milling Rate Constant
at 18 & 25 Hz
0.016
0.014 18 Hz
0.012 25 Hz
K p = 6.262E-05 d
0.01
R 2 = 0.9410
Kp (s-1)
0.008
0.006
0.004 K p = 2.463E-05 d
0.002 R 2 = 0.9982
0
50 100 150 200 250 300
Mean Sieved Feed Size, d (µm)
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43. Single Particle Impact Testing
The extent of breakage
Manual feeding
(R*) is determined by
gravimetric analysis.
M de
R =*
Glass Photodiodes
M m + M de tube
Target
Mde = mass of debris
Mm = mass of mother particles PI Collection
chamber
Filter
44. Extent of Impact Breakage
8
2
R* (212-250 µm) Fitting Equation: R* = C v
7 R* (180-212 µm)
ρH d 2
Extent of Breakage (%)
6 R* (150-180 µm) R =α
*
2
v
R* (90-106 µm) Kc
5
C = 0.0009 C = 0.0007
4 2
3
R = 0.9915 R2 = 0.9877
C = 0.0008
2
R2 = 0.9924 C = 0.0003
1
R2 = 0.9671
0
0 20 40 60 80 100
-1
Impact Velocity, v (m s )
45. Dependence of Milling Rate
on Particle Properties
0.016
0.014 MCC-18 Hz
0.012 MCC-25 Hz
0.01
Kp (s-1)
0.008 K p = 16.237 C
0.006
R 2= 0.9965
0.004 K p = 6.3714 C
0.002
R 2= 0.9357
0
0 0.0002 0.0004 0.0006 0.0008 0.001
C (s2 m-2)
46. DEM Simulations
to estimate input energy
y z
x
wn φ
Dashpot Spring
Ks Slider
ηn Kn
µf
ηs ws
Compressive force Shear force
∆w n Fs = K s ( ∆w s + r1∆φ1 + r2 ∆φ2 )
Fn = K n ∆w n + ηn ( ∆w s + r1∆φ1 + r2 ∆φ2 )
∆t + ηs
∆t
47. DEM Simulations
DEM simulation at 25 Hz of milling frequency in the
single ball mill
48. Milling Power
• Milling energy (En ) is deduced from the relative
velocity (v ) and reduced mass (m) of the two objects in
contact by: n
1
E n = ∑ mv j
2
j =1 2
• Each simulation is run for up to 3 s of real time (t ) with
a time step of 0.2 ms.
• Milling power (Pn ) is deduced from:
En
Pn =
t
49. Simulation Results of MCC
250
Milling Power, Pn (J s-1)
At 18Hz P n = 0.1954 d
200 At 25Hz R 2 = 0.9677
150
100
P n = 0.0853 d
50
R 2 = 0.9584
0
0 250 500 750 1000 1250 1500
Particle Size, d (µm)
50. Dependence of Milling Rate
on Power
0.016
0.014 MCC-18 Hz
0.012 MCC-25 Hz
0.01
Kp (s-1)
0.008
K p = 0.0003 E n
0.006
0.004 R 2 = 0.9713
0.002
0
0 10 20 30 40 50
Power, P n (J s-1)
51. Unification of Results
0.016
0.014 MCC-25 Hz
0.012
MCC-18 Hz
0.01
Kp (s-1)
0.008
K p = 0.1386 P n α H / K c 2
0.006
R 2 = 0.9902
0.004
0.002
0
0 0.02 0.04 0.06 0.08 0.1 0.12
P n α H / K c 2 (m2 s-1)
53. Unification of Results
Milling Rate Constant, Kp (s )
0.09 MCC-18 Hz
-1
0.08 MCC-25 Hz
0.07 αLM-25 Hz
0.06 Starch-25 Hz
0.05 Sucrose-12 Hz
0.04 Sucrose+Aerosil-25 Hz
0.03 K p = 0.1218 P n α H / K c 2
0.02 R 2 = 0.9826
0.01
0
0 0.1 0.2 0.3 0.4 0.5 0.6
2 2 -1
P n α H / K c (m s )
54. Conclusions
The results presented provide evidence that
the milling behaviour of a material can be
quantified from the knowledge of mechanical
properties and the mill dynamics as
follows:
Pn H
Kp ∝ :
Kc
Kp = milling rate constant Pn = milling energy
H = hardness Kc = fracture toughness
55. What to do next?
On Milling:
•Short term: Consultancy
•Medium term: Four months MSc projects
•Long term: PhD, KTP and PDRA
On continuing training:
•Powder Flow
•Mixing and Segregation
•Sizing, etc
56. Analysis of Segregation of Mixtures
Vibrated heap experiment
Experimental Set-Up
Heaps of binary mixtures of
glass beads
High Speed Video at 1000 fps
57. Analysis of Segregation of Mixtures
Vibrated heap experiment
(a) CASE 1 (b) CASE 2 (c) CASE 3
58. Analysis of Segregation of Mixtures
Vibrated heap experiment:
different size, density and cohesion
•First test - CASE 1:
• For case where both types of beads are free flowing, system segregates (a)
•Second test – CASE 2:
• Light fine beads cohesive to different levels, solid coarse beads free-flowing
• At higher cohesion level light fine beads formed clusters that accumulated at the
bottom and the top of the heap (b)
•Third test – CASE 3:
• Solid coarse beads cohesive to different levels, light fine beads free-flowing
• At an increased cohesion no segregation was observed (c)
(a) CASE 1 (b) CASE 2 (c) CASE 3
Segregates Highly segregates Does not segregate
