Simulation of the Packing of Cohesive Particles

1
Simulation of the Packing of Cohesive Particles

• AB Yu, RY Yang, RP Zou, KJ Dong and XZ An
• Centre for Simulation and Modelling of
  Particulate Systems
• School of Material Science and Engineering
• University of New South Wales
• Sydney, NSW 2502
• Australia
• 31 August 2006

2
Contents

• Introduction
• Simulation Method
• Results and Discussion
• Packing of fine particles
• Settling of particles in liquids
• Compaction of fine particles
• Packing of wet particles
• Conclusions

3
Introduction

• What is particle packing ?

Packing is an assembly of particles
4
Packing of particles in nature
5
Introduction

• Industrial perspective

6
Introduction

• Industrial perspective

7
Introduction
Compacted Particulate products

• Manufacture near-net-shaped components with
  sufficient strength
• Automotive Parts
• Ceramic Greens
• Food Industry
• Pharmaceutical Tablets
• Civil Engineering (Soil evaluation)

8
Introduction

• Variables involved

Particle Properties Mass Particle shape
Dimensionless size distribution Absolute
particle size Elasticity Resilience Surface
properties Container Properties Shape Size Elas
ticity Surface properties Packing
Method Intensive of deposition Velocity of
depositing Treatment after packing
9
An example effect of moisture content

• Cohesive particles
• Cohesive inter-particle forces larger than
  gravity force
• fine and/or wet particles
• Behave differently
• agglomerate/aggregate/cluster
• more like a solid instead of individuals

What keeps sand-castle up Nature, 387 (1997)
10
Research aims

• To develop numerical models that can simulate the
  packing of cohesive particles
• To characterise the packing structure using
  various techniques
• To quantify the packing and force structures in
  relation to particle characteristics and
  materials properties
• To establish the relationship between packing
  structure and cohesive forces.

11
Simulation Method

• Numerical models
• Limitation of previous numerical models
• sequential addition and collective rearrangement
• no force considered
• assumed packing growth and stability criteria
• Dynamic simulation
• Discrete element method (DEM)

12
Simulation Method (Cont.)

• Experiment vs. numerical simulation
• Experiment
• bulk and surface measurements
• little force information
• expensive and erroneous
• Numerical simulation
• detailed packing and force information
• cost-effective
• validation required

13
Simulation Method (Cont.)

• Translational motion
• Rotational motion

Schematic illustration of the forces acting on
particle i .
14
Simulation Method (Cont.)

• Normal contact force
• Tangential contact force
• Capillary force
• van der Waals force

15
Simulation Method (Cont.)

• Particles settling in a liquid
• Tangential contact force
• Normal contact force
• van der Waals force
• Gravity force
• Buoyancy force
• Magnus lift force
• Viscous drag force

16
Simulation Method (Cont.)

• Liquid flow is one dimensional flow with a
  constant mass flow rate across the packing bed.
• The local porosity ei is assumed only to be a
  function of its height. That is, the simulated
  box has been sliced into pieces along the
  sediment direction as the computational cell for
  fluid phase. The particles in the same slice have
  the same local porosity.

17
Plastic Deformation (Elastic/plastic Force)
18
Simulation Method (Cont.)

• Particle Packing
• Packing of fine particles
• Self-agglomeration of fine particles
• Sedimentation/filtration
• Transport Properties
• Permeability
• Effective thermal conductivity
• Particulate rheology
• Particle Flow
• Hopper BF flow
• Heaping/piling process
• Mixing granulation
• Particle-fluid Flow
• Fluidization
• BF raceway flow
• Cyclones

19
I. Packing of Fine Particles
Course
Fine
20
Packing of Fine Particles (Cont.)

• Simulation conditions
• Packing in a rectangle box of 15d ? 15d ? 100d
  with periodical boundary condition implemented in
  X and Y directions.
• 3500 particles are generated with no overlap, and
  initial packing porosity 0.94.
• Settling under gravity, where all the considered
  forces effective.

21
Packing of Fine Particles (Cont.)
t0.0s t0.06s t0.08s t0.1s
Snapshots showing the formation of a packing at
different times (animation)
22
Packing of Fine Particles (Cont.)
23
Packing of Fine Particles (Cont.)
2 4 6 8 10
24
Packing of Fine Particles (Cont.)

Coordination number
25
Packing of Fine Particles (Cont.)
26
Packing of Fine Particles (Cont.)
Radial distribution function
Radial distribution function, g(r) (-)

• Particle size decreases
• First peak higher and narrower
• Second peak no split
• Third and beyond not present

2 1 0
27
Packing of Fine Particles (Cont.)
Voronoi Tessellation

• Split the total volume into the Voronoi
  Polyhedron (VP) owned by each particle
• Useful for the study of transport properties,
  e.g. thermal conductivity

28
Packing of Fine Particles (Cont.)

• Topological properites
• edge number of each face
• face number of each VP
• Metric properties
• perimeter and area of VP face
• surface area and volume of VP
• Effect of packing density or particle size

29
Packing of Fine Particles (Cont.)
Edge and Face Numbers
The distribution of the number of edges (left)
and faces (right) per polyhedron as a function of
packing density
30
Packing of Fine Particles (Cont.)
ltf gt vs. packing density

• result is comparable with others (experiment or
  simulation)
• difference is attributed to the algorithm used in
  the simulation
• Oger random sequential adsorption particles in
  the packing are not in contact packing is not
  stable under gravity

31
Packing of Fine Particles (Cont.)
Face perimeter
Face area
VT area
VT volume
32
Packing of Fine Particles (Cont.)
Lewis and Desch Law
33
Packing of Fine Particles (Cont.)
Force structure and distribution
34
Packing of Fine Particles (Cont.)
Force structure and distribution

Probability density function of the van der Waals
force (left) and contact force (right) relative
to gravity for different sized particles
35
Packing of Fine Particles (Cont.)

Macro vs micro properties
Porosity, the most typical macroscopic packing
property, can be related to microscopic force,
i.e. the van der Waals force on individual
particles.
36
II. Settling of Particles in Liquids
Model validation
Figure 2. Liquid viscosity and Hamaker constant
as a function of the volume ratio of toluene in
the mixtures of the diiodomethane and toluene.
Figure 1. Packing fraction of different sized
glass beads as a function of the effective
gravitational acceleration ?g ((1-?f/?p)g .
Points are the measured results ?,d500 µm ?,
d250 µm ?, d110 µm and , results of Onoda
and Liniger (Onoda et al. 1990). Lines are the
simulated results.
37
Settling of Particles in Liquids (Cont.)
Effects of material properties
Figure 3. Packing fraction as a function of (a),
Hamaker constant when ?f2200 kg /m3 (?) and
?f2400 kg /m3 (?) (b), particle size when ?f0
(?), ?f1000 kg /m3 (?), and Ha 0 J, ?f1000 kg
/m3 (?) (c), liquid density when Ha0 J and
d250 µm (), d1000 µm (?), d250 µm () (d),
liquid viscosity when Ha 0, d250 µm (),
d1000 µm (?), d250 µm (?). Default values
listed in Table 1 are used for unspecified
parameters.
38
Settling of Particles in Liquids (Cont.)
Effects of material properties
(a)
(b)
(c)
Figure 4. Radial distribution function for
different material properties (a) particle size,
(b) liquid density, and (c) liquid viscosity.
39
Settling of Particles in Liquids (Cont.)
Dynamic evolution of a particle
(a)
(b)
Figure 9. Evolution of (a) position (solid line)
and velocity (dashed line) and (b) forces of a
particle with time in a settling process, d 100
µm.
40
Settling of Particles in Liquids (Cont.)
Dynamic evolution of a particle
Figure 10. Packing fraction as a function of the
force ratio ?, ? and ?, ?. lines are the
correlation as
41
III. Compaction of Fine Particles
Packing Structures (10mm Particles)
42
Force Structures (10mm Particles)
Compaction of Fine Particles (Cont.)

• Force chains form the backbones of a packing
  which support most of the external load.
• A quantitative definition of the large backbone
  force is difficult
• the forces are distributed continuously.
• Golden ratio 1.618 is used
• if Fi gt 1.618ltFgt then Fi is regarded as the large
  backbone force.

43
Force Orientation
Compaction of Fine Particles (Cont.)
Large backbone forces
All forces
44
Compaction of Fine Particles (Cont.)
Jamming States

• Jamming states can be identified and explained
  from the evolution of force structures
  Geometrical (bond) jamming state (C 0.55) and
  mechanical (rigidity) jamming State (C 0.64)

45
IV. Packing of Wet Coarse Particles

• The capillary force associated with wet particles
  plays a similar role to the van der Waals
  associated with fine particles.
• There is a need to understand the effect of
  liquid content on the packing and force
  structures.
• The inter-relationships between porosity,
  moisture content and the capillary force are not
  clear.

Dry vs wet
46
Packing of Wet Particles (Cont.)
47
Packing of Wet Particles (Cont.)

Porosity as a function of liquid content (water)
for the packing of 1mm and 0.25 mm particles
48
Packing of Wet Particles (Cont.)

• Radial distribution for 1 mm (left) and 0.25 mm
  (right) glass beads.

49
Packing of Wet Particles (Cont.)
M 0.0 M 4 M 20

• Variation of force structure with moisture
  content for 0.25 mm glass beads.

50
Packing of Wet Particles (Cont.)

• Inter-relationship between porosity, moisture
  content and capillary force

51
Conclusions

• DEM simulation is a cost-effective way to study
  the packing of cohesive (fine or wet) particles
• The packing structures has been characterised,
  showing a strong dependence on particle size,
  materials properties, and liquid content
• Force structure has been analysed, and its
  relationship with packing structure has been
  established.

52
Acknowledgment
Contributed by Dr. R. P. Zou, Dr. C. L. Feng, Dr.
Z. P. Zhang, Dr. D. Pinson, Dr. M. L. Gan, Dr. R.
Y. Yang, Dr. J. Q. Xu, Dr. X. Z. An, Mr. X. Y.
Lin, Mr. K. J. Dong, Mr. X. Lu
Financial support from KCC, ARC, BHP (Bluescope
Steel BHP-Billiton), UNSW, ERDC, Alcoa, CSIRO