P. Bowen, EPFL. 20/09/2019 1

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

Technologie des poudres

Des glissements de terrain au béton et des

avalanches au chocolat

Prof. P. Bowen, Dr. P. Derlet (PSI)

Week 2 – Lecture no. 3 - on website

PTG

•BOOKS

•The Colloidal Domain – D. F. Evans & H. Wennerström, Wiley, 1999,

• Principles of Ceramic Processing – J.S.Reed , Wiley, 1995. English

• T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic Press,1996

• Les Céramiques, J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Traité des Matériaux, Volume 16, PPUR, 2005

P. Bowen, EPFL. 20/09/2019 2

Course Contents - Plan

Réseau neurone – Neural network

- compaction

Laves Torrentielles–Debris Flow

Granular Dynamics –

DEM Modelling

Dr. Mark Sawley

1. Introduction – general introduction to course

– example transparent ceramics

2. Particle Packing and Powder Compaction

- Theoretical and empirical models (PB)

- Powder compaction (PD)

3 Particle-Particle Interactions (PB)

- Colloidal Dispersions

- DLVO –theory and limitations

- non-DLVO and steric forces

Exercises – particle interactions & rheology-HAMAKER & YODEL

4. Introduction to Atomistic Scale Simulations (PD)

- introduction to modeling of surfaces & interfaces at the atomic scale

- defects in metals – towards sintering

5. Sintering mechanisms (PD)

- metals, ceramics

- influence of microstructure

- simulation

Exercises – Atomistic modeling and DEM – LAMMPS

6. Advanced Powder Processing Technologies (PB)

- additive manufacturing – 3D printing

- laser sintering, Spark Plasma Sintering, Field assisted, cold sintering

P. Bowen, EPFL. 3

•Files of lectures to be found on PTG website : http://lmc.epfl.ch/PTG/Teaching

Week-day File # Powder Technology – Wednesday 10.15-13.00 – MXG 110

1- sept 18 1&2 PB PD General Course Introduction (1hr)– Example rheology – Yodel Intro (1hr)- Powder packing and

compaction – 1 (i) – (1hr)

2 – sept 25 2&3 PB/MS Powder packing and compaction – 1(ii), 2- Examples and DEM guest lecturer – (3hrs)

3 – oct 2 5&6 PB Particle – Particle Interactions 1 - 2hrs

Particle – Particle Interactions 2 (i) – 1hr

4 – oct 9 6&7 PB Particle – Particle Interactions 2 (ii)(1hr) &

Particle – Particle Interactions 3 (2hrs) - Download Hamaker & send YODEL-PB

5 – oct 16 PB Exercises – Intro to Hamaker & YODEL software & group projects (3hrs)

6 – oct 23 AM PB Exercises - Hamaker &Yodel Modelling – group projects (AM 2 hrs) presentation of interparticle

project results (1 hr)

7 – Oct 29 4 PD Powder packing and compaction -3 & 4(i) – (3hrs)

8 – nov 6 4&8 PD Powder packing and compaction - 4 (ii) – (1hr)

Introduction to atomistic scale simulations – (2hrs)

9 – nov -13 9& 11 PD Compaction, Sintering & Defects in metals at atomistic scale (2hrs)

Sintering Mechanisms – 1(i) (1 hr)

10 – nov 20 11 PD Sintering Mechanisms - 1 (ii) & 2 (3hrs)

11 -nov-27 10 PB New Technologies -1 Processing – Forming – Shaping (2hrs)

visit of Additive Manufacturing lab (1hr)

12 - dec 4 PD Excercises -Introduction to Molecular Dynamics Modelling using LAMMPS (3hrs) .

13 – dec 11 12 PB New Technologies-2 – Sintering Methods -

& Exam method

14 – dec 18 PD Excercises - MD- DEM modelling exercise using LAMMPS –particle packing - Effect of

parameters (3 hrs)

P. Bowen, EPFL. 20/09/2019 4

Particle Packing - Last week….started… today finish….

Literature Models

– Empirical Models

– Semi-empirical models - physics of particles

– Numerical and analytical (computer aided simulations)

Models evaluate packing or porosity in a packed powder as a function of 4

characteristics:

– Particle Shape - sphericity

– Modal Size differences in multimodal distributions

– Mean particle size

– Size distribution

Effect of agglomeration also plays an important role on particle packing

P. Bowen, EPFL. 20/09/2019 5

Aims of todays course

Two examples of powders in application or research where particle packing and rheological

behaviour linked to particle shape and dispersion (leading us to the next section of the

course colloidal dispersions)

Neural Network – applied to the particle packing of alumina particles in spray dried

granules - Thesis de Violaine Guerin – EPFL No. 3021 (2004)

Landslides or Alpine Debris Flow…..Eric Bardou (Thesis EPFL- 2479(2002))

Numerical simulation of Granular Dynamics using DEM - Dr. Mark Sawley (EPFL)

Typical Questions - Section Particle Packing

English Books for ceramic processing and powder dispersion

1. T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic

Press,1996

2. J.S. Reed - Principles of ceramic processing – J. Wiley & sons, 2nd Edition (1995)

P. Bowen, EPFL. 20/09/2019 6

Comparaison de la prédiction théorique et des résultats

expérimentaux la densité verte de poudres Bayer et l’alumine

de haute pureté en utilisant un réseau neurone

Thèse de Violaine Guerin – EPFL No. 3021 (2004)

Comparison of theoretical prediction and experimental

green density of high purity and Bayer alumina powders

using a neural network

P. Bowen, EPFL. 20/09/2019 7

Introduction

Goals :

Predicting green and sintered density using a neural network

Better understanding of the densification behavior

Design and predict microstructure

Powder characteristicsDensification behaviour

?

P. Bowen, EPFL. 20/09/2019 8

Particle packing and Neural Network approach

Ceramic Manufacturing - Generalities

- Packing of particles

- Mathematical models

- Neural network

Characteristics of powders and densities of Green Bodies

Using the results of the neural network as a predictive tool

Conclusions and future development

P. Bowen, EPFL. 20/09/2019 9

Ceramic Fabrication - Generalities

Different manufacturing processes-from powders- Compaction of granulated powders – uni-axial – CIP*- Suspension - casting (slip, tape, pressure)

Compaction of spray-dried granules$

Effects of parameters of the powder on the green densities

Compaction 3 steps

–Re-arrangement

–Deformation of granules

–Fracture of granules (rarely achieved)

Consider two families of powders

1. Bayer aluminas - low agglomeration factor

2. Non-Bayer finer more agglomerated

Pores inside the granules between the primary particles

and between the granules

Pore distribution - bimodal (inter-granular, intra-granular)

Particule primaire (0.1 -1µm)

Granulée pour la compression

(50-300µm)

* CIP – Cold isostatic pressing $ - see BAR05 p. 204-219

P. Bowen, EPFL. 20/09/2019 10

Alpha alumina – effect of agglomerates – week 1 Intro

• Particle size distribution shows small tail of agglomerates – leads to defects in

microstructure and low sintered densities (94%) – poor (hard) granules (50 mm)

and aggregates (2 mm)

0.1

1

.01 .1 1 5 10 2030 50 7080 9095 99 99.999.99

AKP50-non-broyéeAKP50-broyée

ES

Dia

mèt

re (

µm

)

% volume cumulés

P. Bowen, EPFL. 20/09/2019 11

Alpha alumina – effect of agglomerates

• Attrition milling 1 hr agglomerates removed

• Improved sintered density & microstructure

• Can we predict this from an analytical modelling approach?

Attrition milled 1hr – slip cast – 99%As received – slip cast – 94 %

F-S. Shiau, T-T. Fang, T-H Leu, Materials Chemistry and Physics, 57, 33-40 (1998).

P. Bowen, EPFL. 20/09/2019 12

Neural Network Approach

Neural network- compaction

P. Bowen, EPFL. 20/09/2019 13

Réseau neurone – Neural Network

• IW – weighted

hidden layer

- non-linear

function

• LW – weighted

output layer

- linear function

• b- bias

• Adjust until target

value achieved

P. Bowen, EPFL. 20/09/2019 15

Powder Characteristics & Treatment

31 a-alumina commercial powders from different producers (Prof. Hofmann,

Alusuisse)

2 families Bayer* (18) and Non-Bayer*(precipitated) (13)

Characterised by:

– Chemical Composition (Na, Si, Ti, Fe, Mg)

– Particle size distributions (laser diffraction)

– Powder X-ray diffraction (XRD)

– Specific Surface Area (SSA, BET model)

– Particle shape (SEM)

Spray dried (atomisation-spray drying)$ after wet milling

Addition of PVA as binder and PEG as plasticizer

Cold Isostatic Pressing (CIP)

– 200 MPa

– Cylinders, 2cm de diameter and 10 cm long

Spray dried granules

* Voir BAR05 – pages 111-113 $- BAR05 pages 196-203

P. Bowen, EPFL. 20/09/2019 16

Log-normal - Bayer Aluminas

Neuron network compared with

Kavanagh and Nolan log-normal model &

Experimental values for coarse powders

Median diameter (Dv50) and standard deviation (sv)

– verified experimentally

22 of the 32 followed reasonably well a log-normal

distribution (see BAR05 pages 64-65)1 µm

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

% F

req

uen

cy

Equivalent spherical diameter (µm}

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6

Fre

quen

cy

Diameter (µm)

Normal distribution Log Normal distribution

P. Bowen, EPFL. 20/09/2019 17

Neural Network (NN) - method

Program used NETS –

– Developed by NASA

Input Parameters – 5 neurons

– d10,d50 d90 volume based particle size

distribution

– Specific surface area

– Type of powder

- Bayer or Non-Bayer

NN – 10 intermediate neurons, 1 output

optimised with 28 powders then tested on 3

– Results predicted better than 5%

– Within the powder characteristics

« box » or set used to train the NN

Min (µm) Max (µm)

d90 0.60 20.0

d50 0.25 12.5

d10 0.15 4.0

• Can now use NN to predict behaviour

of powders within this range –

• Even if we do not have exact data for

particular Dv50 and s etc

• For clearer trends split Bayer and Non-

bayer into different Dv50 size ranges

P. Bowen, EPFL. 20/09/2019 18

Log-normal - Bayer Aluminas– fine particles (< 2mm)

For green (compact ) densities after CIP but before sintering

Predictions

RCP – Random Close

Packed

RLP - Random Loose

Packed

Particle packing model –

density of packing

increases with increasing

standard deviation(s)

Bayer Aluminas

corresponds to Random

Loose Packed when

s > 2.5

P. Bowen, EPFL. 20/09/2019 19

Log-normal - Bayer Aluminas

•Bayer aluminas (< 2mm) correspond

well to experimental data for the RLP

•after spray drying of granules

•Slight increase in the packing

fraction with the s of the original

PSD

•Compaction - 3 stages - re-

arrangement, deformation, fracture

•3rd stage rarely is reached with

typical technical conditions

•The packing fraction of the powder

within the granules dominates the

behavior

•Assuming that the binders* and

plasticizers* behave the same way for

all powders * See BAR05 – p.218-219

P. Bowen, EPFL. 20/09/2019 20

Log-normal - Bayer Aluminas

200 µm granule

Surface of

granule

1 µm

The density or packing in the granule depends on the following parameters

– Particle shape – non-spherical negative →lower packing fraction

– Broad size distribution – positive improves packing fraction

– Need good dispersion and colloidal stability with low degree or no aggregates or agglomerates

– The dispersion also influences the rheology – important for spraying

– We need a minimum viscosity but with a maximum of solids loading to create dense granules via spray drying – optimum with respect to above parameters

P. Bowen, EPFL. 20/09/2019 21

Influence of PSD width and particle size dv50

Precipitated powders

Non-Bayer

Bayer Powder

sg rv

1 2 3 4 50.3

0.4

0.5

0.6

0.7

0.8

De

nsi

té r

ela

tive

Déviation standard géométrique sg

RCP S&M

RLP N&K

RCP N&K

RLP D&T

d50

=0,75mm

d50

=1,6mm

d50

=3,75mm

sg et/ou dv50 rv

1 2 3 4 50.3

0.4

0.5

0.6

0.7

0.8

De

nsité

re

lative

Déviation standard géométrique sg

d50

=0.75mm

d50

=1.6mm

d50

=3mm

RCP N&K

RLP N&K

Application of Neural Network

P. Bowen, EPFL. 20/09/2019 22

Spray Dried Alumina Powders

* ' 1*0.6 0.6granules particules facteur d empilementr r= = =

30mm

Primary Particles Bayer

Theoretical Density

(relative density =1)

Granules

Density RLP

(relative density =0.6)

BAYER

* ' 0.6*0.6 0.36granules agglomérats facteur d empilementr r= = =

PrimaryAgglomerates

Density RLP

(relative density =0.6

)

Granules

DensityRLP

(relative density =0.6)

PRECIPITATED

Non-BAYER

Packing factor

Packing factor

= 𝜌𝑎𝑔𝑔𝑙𝑜𝑚é𝑟𝑎𝑡𝑠

P. Bowen, EPFL. 20/09/2019 23

Conclusions

Neural Networks

Useful tool for prediction of ceramic green body densities (and sintered see thesis (Violaine Guerin – EPFL No. 3021 (2004))

Allows insight into behaviour of powder during compaction and sintering from standard powder characteristics

Useful for optimisation in industry – evaluation of new powder lots

Should also be applicable to metallic powders

Can in fact use the programme in reverse – machine learning approach – i.ewe have optimised an algorithm for a given range of powder characteristics –now we can create virtual powder needed to create certain green or sintered density or microstructure – or find which powder needed for desired sintered density

Modelling

Modelling of materials processing and microstructures – numerical modelling methods

e.g. Finite Element Methods (FEM)– Discrete Element Methods (DEM) –

P. Bowen, EPFL. 20/09/2019 24

Les laves torrentielles en milieu alpin

Eric Bardou

eric.bardou@unil.ch

EPFL Thesis No. 2479 (2002)

Effect of the Clay Type on the Rheology of an Heterogeneous Dense

Granular Material.

Implication for the Study of Alpine Debris Flow

Eric Bardou, Paul Bowen, Pascal Boivin (EPFL), Phil Banfill (HWU, UK)

Powder Page – Landslide simulation - http://www.granular.com/

Earth Surface Processes and Landforms

Earth Surf. Process. Landforms 32, 698–710 (2007)

P. Bowen, EPFL. 20/09/2019 25

Scope of working length scale!!!

Du bassin versant – Alpine Watershed…..

Aux feuillets argileux

- Clay platelets

-Diameter Microns

--thickness 20-100nm

P. Bowen, EPFL. 20/09/2019 26

Exemple

P. Bowen, EPFL. 20/09/2019 27

Description du phénomène – Description of the phenomenon

Transport of bed load (charge de fond)

Debris (mud) flow

The transfer of sediment a problem

between geology and hydraulics

Bed load – saltation (hopping), rolling, sliding

P. Bowen, EPFL. 20/09/2019 28

Definition

front

tailbody

Lateral section

• Grains >400

microns

• Fluid – matrix

• < 400microns

• Model system for

sizes < 20mm

The debris or mudflows are granular flows - lubricated kinematically –

they are of a transient nature - simple model - two-phases

- grains and fluid

P. Bowen, EPFL. 20/09/2019 29

Particle sizes – (grains & matrix < 20mm)

ar g

il es silts

sabl e

sfi n

s

sabl e

sm

oye

ns

sabl e

sgr o

ssi e

r s

graviers

0.001 0.01 0.1 1 100

20

40

60

80

100

[mm]20

fracti

on

cu

mu

lée [

%]

viscoplastic

collisional-frictional

frictional-viscous

Bed load

Argiles

• Fluid – matrix < 400microns • Grains >400 microns

Clays Fine Medium CoarseSands

Gravels

P. Bowen, EPFL. 20/09/2019 30

Rheological Models➢ Different types of fluid behaviour – Newtonian and non-Newtonian

➢Various models used to extract information e.g. yield stress – all give very similar results

M. Palacios. -Química del Cemento – Enero 2010

(Ferraris, C. F. , 1999)

• Yield Stress – t0 Minimum stress to make liquid or suspension flow

• Typical of systems with attractive network

• Yoghurt – Cement - Ceramic slurries – (see BAR05)

30

P. Bowen, EPFL. 20/09/2019 31

Influence of clays

Size

range

(mm)

Particle class Solids

weight

(%)

Solids

volume

(%)

0.0 - 0.02 clay size 4.1 11.4

0.02 - 0.05 silt size 13.0 12.0

0.05 - 0.1 fine sand 5.7 5.4

0.1 - 0.5 medium sand 26.4 24.4

0.5 - 1.0 coarse sand 13.1 12.1

1.0 - 2.0 very coarse sand 3.5 3.2

2.0-20.0 gravel 34.2 31.6

• Grains >400 microns

• Fluid – matrix

• < 400 microns

With clays

Without clays

P. Bowen, EPFL. 20/09/2019 32

Model system PSD – (grains & matrix < 20mm)

Argiles

Model PSD

P. Bowen, EPFL. 20/09/2019 33

2,8 mm

Why – plate –plate?

• easy to use

• No jamming of particles

• Roughened surfaces to

avoid wall-slip

• Low cost….

150 tests

Rheometer plate-plate

Rheology – Matrix (<400mm)

P. Bowen, EPFL. 20/09/2019 34

Rheology with model PSD up to 20 mm

Herriot Watt University (UK) – ciment expert – Prof. Phil Banfill

Sample wieghts for each test

30 kg !!! dry!!!

Measure torque – off-centre to

avoid moving through same area

of sample – effective viscosity

P. Bowen, EPFL. 20/09/2019 35

Clays – main industrial use – porcelain ceramics!

Kaolin

(50-55%)

Feldspath

(25%)

Quartz

(20-25%)

Porcelaine

(dure)

P. Bowen, EPFL. 20/09/2019 36

Structure of clays 1:1 & 2:1

Konan eta l J.Coll.Interf.Sci

307(1) 2007, 101–108

(a) Structure of 1:1 clay mineral e.g. kaolin

(b) Structure of 2:1 clay mineral, e.g montmorillonite

P. Bowen, EPFL. 20/09/2019 37

Argile (2:1) – swelling – Na Montmorillonite

Atomistic model of the one-layer

hydrate of sodium montmorillonite

O: red,

H: white,

Si: yellow,

Na: blue,

Al: purple,and

Mg: green

This simulation super cell consists of

two interlayer regions made up by 8

unit cells

Exchange of Na+ with Li+ - extra

water of hydration interlayer spacing

increased – pillared clays – catalysis

Mg2+ substitutes Al3+ ….Na+ in

interlayer charge compensation

Si

Si

Si

Si

Al(Mg)

Na

P. Bowen, EPFL. 20/09/2019 38

Variation of clay - Evolution of effective-viscosity

Sample SCR [g/g] Swelling clay proportion in

the bulk [g/g]

Md 1 0 0 ( only kaolinite)

Md 2 0.27 0.005

Md 3 0.54 0.01

Md 4 0.8 0.02

Relation between water content (%wt) (W) and

effective viscosity(K) for 4 mixtures

1:1 clay - Kaolinite China Clay™ (commercial)

2:1 clay - Smectite - extracted from watershed

soils (SCR swelling clay ratio = 2:1 / 1:1)

K

w

P. Bowen, EPFL. 20/09/2019 39

Comparaison with Natural Debris Flows

swelling

Non

-swelling

MD1

Model

Mixture

MD4

Model

Mixture

P. Bowen, EPFL. 20/09/2019 40

Future …….

• Theory : harmonise the classification (fluid-grains) and flow regimes….

• Lab : better understand the effects of the different clays and particles (size

and disitribution)

• Observations in-situ : modes of release – the trigger….

• Modelling : try and relate to regional parameters – clay content, soluble

ions, degree of aggregation, interparticle forces….

Submitted project failed maybe another project… some day….

P. Bowen, EPFL. 20/09/2019 41

Can you answer these questions? (1)

Give a field of application or an everyday example of Powder Technology

How is particle packing important for rheology?

How do aggregates influence the microstructure of a ceramic?

How can this effect the optical properties of polycrystalline alumina ceramics?

What are the different types of models used to describe the packing of particles?

Describe an example of a model in detail.

What is the difference between Random loose packed (RLP) and Random close packed (RCP) ?

For monodispersed spherical particles what is the maximum packing fraction for random close packing RCP? For an ordered array of monodispersed spheres ?

How is the packing of particle modified

- when the particle size has a log-normal distribution?

- if the particles are not spherical ?

- for dry powder as a function of size e.g when the size is reduced?

P. Bowen, EPFL. 20/09/2019 42

Can you answer these questions? (2)

What are the different forces that can act on particles and influence their packing .

-which forces dominate for particles < 1 micron

- which force dominates for particles > 100 microns

What is the effect of agglomeration on the particle packing – how can one describe quantitatively the degree of agglomeration ?

For a bimodal distribution of two monodispersed powders what is the maximum packing fraction that can be attained?

For a multimodal distribution of powders what is the maximum packing fraction that can be attained – give an example of where this is used in practice.

What are the limitations of using a multimodal packing method for ceramic fabrication?

What type of packing is found for ultrafine alumina powders produced by precipitation and how could this be improved ? What is its significance for the dry pressing of ceramic pieces?

Describe DEM modeling and give an example of its application to Particle Technology

P. Bowen, EPFL. 20/09/2019 43

BIBLIOGRAPHIE

BAR05 J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Céramiques, Les Traité des Matériaux, Volume 16, PPUR, 2005

BRO50 G. BROWN, Flow of fluids through porous media 1 - Single Fluid phase,1950, pp. 210-216

DEX72 A.R. DEXTER, D.W. TANNER, Packing densities of mixtures of spheres withlog-normal size distributions, Nature physical science, 1972, vol. 238, pp. 31-32

DIN00 D.R. DINGER, One-dimensional packing of spheres, Part I, American ceramic society bulletin, 2000, pp. 71-76

*FLA04aR.J. Flatt, ‘Towards a prediction of superplasticized concrete rheology’, Materials and structures 27 (269) (2004) 289-300

FLA04b R.J. Flatt, N. Martys, L.Bergström The Rheology of Cementitious Materials, MRS Bulletin, may 2004, pp. 314-318

GER89A R.M. GERMAN, Packing of monosized nonspherical particles, Book “Powder packing characteristics”, 1989, pp. 122-133

GER89B R.M. GERMAN, Introduction to particle packing, Book “Powder packing characteristics”, 1989, pp. 1-20

MIL78 J.V. MILEVSKI, Handbook of fillers and reinforcement plastics, Eds Van Nostrand, 1978

NAR85 M. NARDIN, E. PAPIRER, J. SCHULTZ, Powder Technology, 1985, 44, pp.131-140

NAV99 P. Navi, C. Pignat, Three - dimensional characterization of the pore structure of a simulated cement paste, Cement and Concrete Research 29 (1999) 507-514

*NOL93 G.T. NOLAN, P.E. KAVANAGH, Computer simulation of random packings of spheres with log-normal distributions, Powder technology, 1993, vol. 76, pp.

309-316

*NOL94 G.T. NOLAN, P.E. KAVANAGH, The size distribution of interstices in random packings of spheres, Powder technology, 1994, vol. 78, pp. 231-238

NOL95 G.T. NOLAN, P.E. KAVANAGH, Random packing of nonspherical particles, Powder technology, 1995, vol. 84, pp. 199-205

PHI96 A.P. PHILIPSE, The random contact equation and its implications for(colloidal) rods in packings, suspensions, and anisotropic powders, American chemical society, 1996, 12, n°5, pp. 1127-33

PHI97 A.P. PHILIPSE, A. VERBERKMOES, Statistical geometry of caging effects in random thin-rod structures, Physica A, 1997, 235, pp. 186-193

SOH68 H.Y. SOHN, C. MORELAND, The effect of particle size distribution on packing density, Canadian journal of chemical engineering, 1968, vol. 46, pp.162-167

P. Bowen, EPFL. 20/09/2019 44

BIBLIOGRAPHIE

SUZ01 M. SUZUKI, H. SATO, M. HASEGAWA, M. HIROTA, Effect of size distribution on taping properties of fine powders, Powder technology, 2001,118, pp. 53-57

SUZ83 M. SUZUKI, T. OSHIMA, Estimation of the coordination number in a multicomponent mixture of spheres, Powder technology, 1983, 35, pp. 159-166

SUZ85 M. SUZUKI, T. OSHIMA, Coordination number of a multicomponent randomly packed bed of spheres with size distribution, Powder technlogy,1985, 44, pp. 213-8

WAK75 R.J. WAKEMAN, Packing densities of particles with log-normal sizedistributions, Powder technology, 1975, 11, pp. 297-299

*YU93 A.B. YU, N. STANDISH, Characterisation of non-spherical particles from theirpacking behaviour, Powder technology, 1993, vol. 74, pp. 205-213

YU97 A.B. YU, J. BRIDGWATER, A. BURBIDGE, On the modelling of the packingof fine particles, Powder technology, 1997, 92, pp. 185-194

ZOK91 F. ZOK , F.F. LANGE , Packing density of composite powder mixtures,journal of American ceramic society , 1991, 74

n°8, pp. 1880-85

Mark L. Sawley

Maître d’enseignement et de recherche (MER)

SGM – STI – EPFL

Numerical simulation of granular dynamics

using the Discrete Element Method

SMX course - Powder Technology

Autumn semester 2018

2

General aspects

§ Motivation

§ Industrial applications

§ Numerical simulation

Implementation

§ DEM technology

§ DEM implementation

§ Basic examples

Applications

§ Particulate flows

§ Materials processing

§ Multiphase flows

General aspects Presentation overview

3

Why study granular dynamics?

• granular materials are omnipresent

• granular materials exhibit a wide range of interesting fundamental behaviour

• granular dynamics are important for numerous industrial processes

General aspects Motivation

Why use the Discrete Element Method?

• conceptually simple technique

• can be applied to a wide range of different cases

• provides very detailed information regarding granular processes

• can provide results in agreement with experimental observation

4

Physical characteristics

& behaviour

• shape

• microstructure

• dilatancy

• cohesion

• segregation

• clustering

• self-organization

• …

General aspects Motivation

5

Industrial applications

• food & agriculture

• mineral processing

• steel making

• chemical

• pharmaceutical

• plastic

• metal

• ceramic

• geophysical

• …

General aspects Motivation

Dry granulation of pharmaceutical tablets

milling active ingredientsblending with excipients

granulation

screening

blending with lubricant

tabletting

final product

General aspects Industrial applications

6

multiphase processes

Manufacturing of breakfast cereals

grain storage conveying

drying

flaking

extrudingfinal products

mixing

General aspects Industrial applications

7

8

Numerical simulation of granular dynamics

-0.1

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

number

verti

cal p

ositi

on, z

[m

]

10 - 80 mm

10 - 20 mm

20 - 40 mm

40 - 80 mm

vsi_4000

table ejecteurs

cylindre

Provides valuable information :

• both qualitative and quantitative

• increase basic understanding of process

• virtual prototyping tool

• reduce significantly production costs

• improve product performance

• minimize time-to-market for new products

• complementary to experimentation

General aspects Numerical simulation

9

Types of particulate materials to be simulated

• Free-flowing granular materials

- dry (inter-particle collisional forces, e.g. dry sand)

- moist (inter-particle attractive forces, e.g. wet sand, powder)

• Powders

- large cohesive assemblies

• Rheologically-complex flowing materials

- polymers, paste, sludge …

• Wet particulate materials

- suspensions, blood …

• Agglomerate solid materials

- natural materials (e.g. rocks)

- man-made materials (e.g. concrete)

General aspects Numerical simulation

10

Coupled multi-method applications for multiphase flows

solidsprocessing

fluidprocessing

dry

granular

moist

granular

wet

granular

particle-laden

fluid fluid

coupled DEM/CFDDEM CFD

• Complementary simulation technologies can be coupled

- Computational Fluid Dynamics (CFD)

- Discrete Element Method (DEM)

[ coupled DEM / Finite Element Method (FEM) is also employed ]

General aspects Numerical simulation

11

Discrete Element Method (DEM)

• Basic aspects

- particle-based (Lagrangian) method

- based on solving Newton equations for an ensemble of

particles and their neighbouring boundary objects

- track the position, velocity and spin of all the individual

particles

- detect all contacts between particles and with the

boundary objects

- model the contact forces & torques acting on the particles

(and boundary objects)

Implementation DEM technology

12

General approach

• “Soft particle” approach

- continuous interaction between “deformable” particles (particles can slightly overlap)

- calculate time-dependent collisional process

- “time driven” methodology

- most commonly employed approach

Implementation DEM technology

• Improved computational performance using a two-step contact detection process :

- spatial sorting (find near neighbours)

- individual contact testing

Goal is to reduce operation count from O(N2) to O(N) or O(N logN)

13

Implementation DEM technology

define geometry (boundary objects)

set initial positions and velocities

find near neighbours

calculate forces & torques on particles

calculate physical quantities of interest

move particles and objects due to forces

t2 >> t

1

t1

test for particle contacts

Basic DEM algorithm

• Soft particle approach

14

Modelling of inter-particle forces & torques

• “Physics” is incorporated in the inter-particle interaction model

• Different physical phenomena can be modelled :

- contact forces

- body forces (e.g. gravity)

- rolling resistance

- cohesion (due to moisture, electrostatics, van der Waals …)

- interstitial fluid

- breakage / agglomeration

- …

Implementation DEM technology

15

Implementation DEM technology

Modelling of inter-particle forces & torques

• Contact (collision)

• repulsive force between particles

• Cohesion

• attractive force between particles

• Cluster

• particles in cluster “glued” together

16

Implementation DEM technology

Modelling of inter-particle forces & torques (cont.)

• Bond

• force inhibits relative motion of particles

• Torsional beam

• repulsive force between particles

• Sintering

• overlapping particles “glued” together

17

Modelling of inter-particle contact : relationship between force and overlap

• Example : Cundall model

- based on a combination of linear springs & dashpots

Implementation DEM technology

18

Implementation DEM technology

• The normal contact force Fn (aligned with particle centres) is :

Fn = kn dn + Cnnn ,

where dn is the overlap between particles in the normal direction

nn is the relative velocity of the particles in the normal direction

kn is the normal spring constant (spring stiffness)

Cn is the normal damping coefficient

The damping constant Cn is related to the coefficient of restitution e :

Cn = 2 g [ mred kn ]½

; g = - ln(e) / [ p2+ ln

2(e) ] ½

where mred is the reduced mass = m1

m2

/ ( m1

+ m2

)

Modelling of inter-particle contact : Cundall model

19

Modelling of inter-particle contact : Cundall model

Implementation DEM technology

• The tangential contact force Ft (aligned normal to the particle centres) is :

Ft = kt dt + Ctnt ,

where dt is the overlap between particles in the tangential direction

nt is the relative velocity of the particles in the tangential direction

kt is the tangential spring constant (spring stiffness)

Ct is the tangential damping coefficient

The tangential contact force is limited by the Coulomb frictional limit

Þ particles slide over each other (surface contact shears)

Ft = min ( µ Ft , ò kt nt dt + Ct nt )

where µ is the coefficient of friction

20

Implementation DEM technology

Moving particles due to forces & torques

• Solve Newton equations of motion for particles (and boundary objects)

where

Fij is the total force on particle i due to contact with particle j

Mi j is the total torque on particle i due to contact with particle j

position xi = ui

velocity ui = S Fij / mi

orientation qi = wi

spin wi = S Mij / Iij

j

.

.

.

.

Time-dependent differential equations are solved using a explicit integration method

21

Schematic diagram of DEM implementation

Implementation DEM implementation

geometry design &

surface meshing

Newton

solver

visualization

quantitative

analysis

Pre-processing Computation Post-processing

particle

initializationmodelling

improvement

22

Influence of model choice

• Rectangular hourglass containing 400 identical particles

standard cohesive particles agglomerate material

Implementation Basic examples

23

Influence of particle shape

• Different basic approaches :

• composite particles

(e.g. form cluster by joining spheres)

• non-spherical primitives

- ellipsoids

- spherocylinders

- superquadrics

…

• polygonal assemblies

Implementation Basic examples

non-spherical particles

(5-particle cluster)

24

Influence of interstitial fluid

• Three basic approaches :

• solve Navier-Stokes equations for

interstitial region (coupled DEM/CFD)

• solve Navier-Stokes equations for

porous medium (coupled DEM/CFD)

• add empirical drag force to each particle

(DEM only)

Implementation Basic examples

spherical particles

(empirical drag force)

25

Different types of simulations involving particulate flows and

materials processing of industrial interest have been computed

• industrial flow processing (e.g. mixing, transport)

• geological flows (e.g. avalanches, landslides)

• industrial materials processing (e.g. drilling)

Applications Overview

26

Pétanque

Applications Particulate flows

DEM simulationexperimentation

A candidate for the 2024 Olympic Games

. . . and a physical model for granular damping

27

Blast furnace filling – granular damping in a rotating chute

Results Particulate flows

without support plates with support plates

in collaboration with ArcelorMittal

28

Ball millfor crushing and grinding

of mineral ore

courtesy Magotteaux SA

Comparison of computed and

experimental power draw

800 mm x 400 mm cylindrical mill

rotational speed : 70% critical

19,116 spherical balls

particle diameter : 15 mm

Applications Particulate flows

29

Landslides, rockfalls & debris flow

courtesy of CSIRO, Australia

2.5 x 4 km2

rectangular section

165,000 spherical particles

particle diameter : 2 - 10 m

total mass : 10 million tonnes (2.5 million m3)

S. Wiederseiner – EPFL semester project

Applications Particulate flows

30

Ribbon blender

Applications Particulate flows

high cohesionlow cohesion

500 mm x 300 mm container

dual ribbons rotating at 30 rpm

100,000 spherical particles

particle diameter : 6 mm

particles coloured according

to initial position

influence of inter-particle cohesion on mixing

31

Ribbon blender

Applications Particulate flows

computed mixing in lateral direction :

GMMI(x,y,z) =

0.0

0.5

1.0

1.5

2.0

2.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0time [s]

Mix

ing

(GM

MI x

)

no cohesion

low inter-particle cohesion

high inter-particle cohesion

fully mixed

v = 30 rpmd = 6 mm

e = 0.3µ = 0.75

Δ t = 5 ms

Mixing rates

g no = -0.300

g low = -0.143

g high = -0.044

centre of mass of one colour particle

centre of mass of all particles

32

Applications Particulate flows

in collaboration with Sika

33

Applications Particulate flows

34

Applications Particulate flows

35

Agglomerate solid materials

• Three basic steps :

• creation of agglomerate material sample

• creation of inter-particle bonds

• testing of material structural properties

Applications Materials processing

36

Agglomerate solid materials

• Growing particle technique for constructing material :

Applications Materials processing

3D rectangular slab (160 mm x 40 mm x 20 mm)

11,009 spherical particles

particle diameter - initial : 0.8 - 2.0 mm

final : 1.1 - 3.4 mm

37

Agglomerate solid materials

• Flexion testing :

Applications Materials processing

2D rectangular slab (160 mm x 40 mm)

21,243 circular particles

particle diameter : 0.3 - 1.0 mm

inter-particle cohesion

38

Applications Materials processing

Particle comminution

• complex mechanisms involving breakage (normal forces) and attrition (tangential forces)

• particles coloured by normal force

• breakage depends on cumulative

energy loss and/or maximum force

• appropriate material breakage

properties required

39

Applications Materials processing

40

Applications Materials processing

40

41

Sprouted bed

S. Wiederseiner – SGM Master project

Applications Multiphase flows

forced air flow

vertical silo containing

glass beads

Coupled DEM-CFD simulation

for advanced drying of

granular material

42

Coupled fluid-particle simulation

• Pouring beer - “the ultimate multiphase flow”

- liquid (simulated by CFD - Smoothed Particle Hydrodynamics)

- bubbles (simulated by DEM)

Applications Multiphase flows

courtesy of CSIRO, Australia

43

General aspects Further information

Basic DEM textbooks are not common

• A. Munjiza “The combined finite discrete element method” (Wiley 2004)

• Book chapters / review articles (e.g. by P.A. Cundall, J.R. Williams or P.W. Cleary)

• CSE Master course “Particle-based methods” at EPFL-SMA (Spring semester)

Conference proceedings

• e.g. International conference on discrete element methods,

Powder & Grains, ECCOMAS Particles conference

• General engineering conferences

Rapidly growing number of scientific papers

• e.g. Granular Materials, Powder Technology

• Many other engineering journals

2018