1

Challenges in particle design

Institute of Particle TechnologyUniversity of Erlangen- Nuremberg

*University of Paderborn

W. Peukert, V. Vassilev, H.- J. Schmid*

Outline

Particle Technology and particle propertiesNanoparticlesParticle formationCase study 1: Precipitation (liquid phase)Case study 2: Gas phase sintering (coagulation & sintering)Optimization of particle formationPerspectives

2

A universe of products

ca. 60% of theproducts in the chemical industry are solids

refined chemicals and consumer products (ca. 30000)

plastics, pharmaceuticals, dyes, solvents fertilizers, fibers, dispersions, cosmetics

intermediates (ca. 300)methanol, vinyl chloride, styrene, Urea,

formaldehyde, ethylene oxide, acetic acid, acrylonitrile, cyclohexane, acrylic acid

basic products (ca. 20)ethylene, propene, butadiene, benzene,

synthesis gas, acetylene, ammonia, sulfuric acid, sodium hydroxide, chlorine

raw materials (ca. 10)petroleum, natural gas, coal, biomass, rock salt, phosphate, sulfur, air, water 01_01.dsf

Product properties of dispersed systems… depend on particle size.

Property function (Rumpf 1967):Product property = f (dispersity, chemical composition)

Disperse property: - Particle size- Particle shape- Particle morphology- Particle surface… and their distributions.

3000 4 8 12 16 20

500

700

900

1100

1300

Particle Diameter x [nm]

Mel

ting

Poi

nt T

[K]

Au

Semiconductor (e.g. CdS)

0 20 40

50

100

Sugar residue on 20 μm sieve [%]

Test result equally „good“ = 100%

3

Multifunctional particle systems

Scratch resistant and transparent

UV-active, transparentFree flowing, no droplets

Source: Dupont

Nanoparticles: Size ratio …

10 nm relative to a „Gummibärchen“ …

… is similar to the Gummibärchen to the Mount Everest.

4

Size ratio for nanoparticles1 g carbon black has a surface of some 100 m2

A chain of these particlesreaches almost to

the sun.

A rough comparison

Aerosol reactors – „just firmlyattached to the ground“

Nanoparticles - Legos for researchers of today,

Building blocks of the future

Library of building blocks

Nanoparticulate wires

5

Ice creme in thepolarisation microscopeSource: BASF

Composites: Function follows structure

Processing Chain of Particle Technology

Feed Materials Crystallizing Filtering Drying Formulation

FinalProduct

Solution Suspension Filter Cake Powder Sugar cubes

Change of Product Properties

Change of Process Properties

Single-phasemulticomponentsystem

Single dispersedparticles

Wet agglomerates

Agglomeratedprimaryparticles

Agglomerates

Crystallizationability

Filterability Dryingproperties

Flow properties

Example: Crystallization of sugar

6

Surface,Molecule

Particles,Nanosystems

Processes &Applications

Lenght scale

Tim

e sc

ale

Microscale Mesoscale Macroscale

nm µm m

ComplexStructures

Multiscale and multiphysical approaches

fs

min

h

Hierarchical structure design

From molecules to functionsModelling and simulation

Key challengesStructure-property functionsProcess-structure functions

QM

MD, MCSD/BD, DEM

FEM, CFD, PBE

Systems integration in nanotechnology

Source: Yamaguchi et al., J. Nanoparticle Res. 2001

Property function: Property = f (dispersity, chemical composition)

Process function: Dispersity = f (process parameters, feed)

7

Process properties

process disperseproperties

applicationproperties

reactor geometryinlet / initial concentrationstemperature (distribution)residence time (distribution)…

T-Mixer

source: degussa

Dispersity

process disperseproperties

applicationproperties

particle size (distribution) primary particle size (distr.)surfacestructural properties

(e.g. fractal dimension)…

SiO2 BaSO4

TiO2 TiO2

8

Challenge: Inversion problems in particle size analysis

Particle size analysis, e.g. Fraunhofer diffraction, Ultrasound spectroscopy, Dynamic light scattering

laser

beam expander

particle ensemblelense detector

intensitydistribution

fSphericalparticle

Given measuring vector LUnknown PSD q(x)Fredholm Integral Equations

Inversion Fredholm‘scher Integrale: Problemstellung

Kleinste Messfehler / num. Genauigkeit extreme Fehler

( )LL

KKqq

Kcond

Δ⋅⋅≤

Δ −

43421

1Verstärkung von Ungenauigkeiten:

Typische Werte:

• Laserbeugung cond(K) = O(1012)• Oberflächen-Ladungsverteilung cond(K) = O(1013.. 1014)• Ultraschallextinktion cond(K) = O(1013.. 1015)

( )xqAL mxn ⋅= ( ) LAxq mxn ⋅= −1

9

Applications

process disperseproperties

applicationproperties

mobilityreactivitybio- availabilityoptical propertiessuspension rheology… analyzer

detector

laserpol.

θ

sample

++++

++++

+++

+++

length coordinate Lsupe

rsat

urat

ion

S

nuclei size xsize

dis

tribu

tion

q

mass, momentumand heat transfer,chemical reactions

phase transition transfer processesinterfacial process engineering

generation ofsupersaturation nucleation

growth

coagulation

stabilization

ripening, sintering

Principles of particle synthesis

Peukert et al., Adv. Powder Techn. 2003

10

Driving force of nucleation

Slnffln

aaln

TR *1

*1 ⋅ν=⋅ν=⋅ν=

⋅μΔ

Supersaturation as driving force:

SkTVx Mc

c ln4* γ

=

S < 1

S > 1

unstable

ΔGC

ΔG *CSurface tensiondominated

xCx *C

C2C

M

3c

C xSlnTkV

x6G γ⋅⋅π+⋅ν⋅⋅⋅

⋅π

−=Δ

C2C

M

3c

C xSlnTkV

x6G γ⋅⋅π+⋅ν⋅⋅⋅

⋅π

−=Δ

< 0 > 0

> 0 > 0

stable

( ) ( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅ν⋅⋅⋅

⋅γ⋅π⋅−⋅⋅⋅⋅

⋅γ

⋅⋅⋅⋅⋅⋅π⋅

= 23

2M

3c

Ac

M21

1

1

SlnTk3V16expNS*a

TkV2

Tkm2

pB

( )( ) ( ) ⎟

⎟⎠

⎞⎜⎜⎝

⎛

⋅ν⋅⋅⋅

⋅γ⋅π⋅−⋅

γ⋅⋅⋅⋅⋅⋅= 23

2M

3cc

MBA3

7A SlnTk3

V16expTk

VDNS*a23B

ZNdtdNB c ⋅⋅β== ∗

Nucleation rate and meta-stability

Gas phase (free molecular regime):

Liquid phase:

β: mass transfer to the surfaceNC*: equilibrium concentrationZ: Zeldovich factor

(accounts for non-equilibrium)

temperature ϑ

unstable area

meta-stable area

stable area

conc

entra

tion

c*, c

Classical nucleation theory

11

Constituing Equations

target quantity:particle density distribution

Population Balance Equation:

Nucleation:

Agglomeration:

Particle Growth:

realized for 2D cases (at the utmost)

with coupling only 1D distribution

systematic errors depend on discretization ↔computational effort

Solution Methods PBM

Moment models'sectional' modelsFEM- methodsMonte Carlo approaches

12

Simpliest Case: Method of Moments

Approach:PBM equationmultiply by xn Integration over x

ordinary DEQ's for moments ( )dxxqxM ii ∫

∞= 0 0[ ]

( ) ( )

)(')',(),'(),(

')',(),'(),(21

),()(),(

0

0

31'3331'33

xSdxxxtxntxn

dxxxxtxntxxn

xtxnxG

ttxn

+−

−−=

∂∂

+∂

∂

∫

∫

∞

∞

β

β

Experimental setupmixer geometry:feed tube Ø: 0.5 mmmain tube Ø: 1 mmmain tube length: 10 mm

experiment:BaCl2 + H2SO4 BaSO4+2HClcontinuous experimentspulsation-free flowstemperature controlled(25°C)

measurement:quasi-elastic light scattering,powder diffraction, TEM, BET

mixer capacity:80 kg/day BaSO4-nanoparticles

- Variation of feed composition- Re-number: 255 - 15000- Residence times: 0.7 - 40ms- Pressure drop: 0 - 15 bar- Mean specific power input εmean: 10 - 2·107 W/kg

13

Precipitation of Nanoparticles:A typical approach

Precipitation:mixing of eductsnucleationgrowthagglomeration

Target:product with well defined productssize distribution

∅ 1 mm

Feed 1Feed 2

mix

ing

zone

Overview to precipitation

feed

com

posi

tionnucleation

growth

agglomerationaggregation

disaggregation

particle sizedistribution,

product properties

super-saturation

micro-mixing

macro-mixing

specificpower inputm

ixer

geom

etry

&

oper

atin

gco

nditi

ons

collision rates &shear forces

inter-facial-energy

particle-particle-

interaction

flowin mixer

14

particle size in nm10 100 1000

volu

me

dens

ity d

istri

butio

n in

nm

-1

0.000

0.005

0.010

0.015

0.020

0.025

0.030Re = 6360Re = 1270Re = 636Re = 382Re = 255

Measured PSDs: Influence of mixing

size is reduced with increasing Re-number (mixing intensity)

0.5m BaCl2 +0.33m H2SO4

Re = 382

Re = 6360

particle size in nm10 100 1000 6000

cum

ulat

ive

volu

me

dist

ribut

ion

0.0

0.2

0.4

0.6

0.8

1.0R = 3.0 R = 2.0R = 1.5R = 1.2R = 1.1R = 1.0

Excess ofBa2+-ions out of

range

Effect of Ba2+ - excess on stabilization

BaCl2 + H2SO4 → BaSO4 + 2 HCl

Schwarzer et. al., Chem. Eng. Techn. (2002) 657-661

15

Population balance to simulate particle size distribution

Modeling of flow- field and mixing

Coupling via mass and component balances

plug-flow through mixer 1D resolution along mixer axismixing is completely micromixing-controlledMicromixing based on modified Engulfment model

mixing kinetics as function of specific power input ε (history through mixer)(Baldyga & Bourne, 1999; Schwarzer & Peukert, 2004)

Global precipitation model

homogeneous nucleationtransport-controlled particle growthdetailed model of interfacial energy (Gibbs adsorption isotherm)agglomeration due to Brownian motion and turbulence(only in presence of supersaturation)aggregation and electrostatic stabilizationtime scales in the range of hours and days sufficiently stableSimulation using Parsival by CiT GmbH, Galerkin h-p-method

precipitation time in s10-6 10-5 10-4 10-3 10-2 10-1

supe

rsat

urat

ion

0

200

400

600

800

1000

1200

mea

n (v

olum

e) p

artic

le s

ize

in n

m

0

20

40

60

80

100

120

no aggregation(W→∞)

no stabilization(W=1)

aggregation

particleformation

mixing &supersaturation

build-up

supersaturation

range

Time scales in precipitation

characteristic times in the order of µs to ms

0.5m BaCl2+

0.33m H2SO4ε = 1000 W/kg

16

mean specific power input εmean in W/kg

100 101 102 103 104 105 106 107

mea

n (n

umbe

r) pa

rticl

e si

ze in

nm

0

50

100

150

200

250constanttrianglestep 50%step 90%

perfect mixingmixing-

controlled

ε-profiles throughmixing zone:

Influence of ε-distribution through mixer

0.5m BaCl2+

0.33m H2SO4

importance of ε-distribution in mixerlimitation of model approach

ε-profilethrough mixer

evolution of mixing

particle sizedistribution

mixing rate coefficient

many different profiles

broaderdistribution

mean specific power input εmean in W/kg

100 101 102 103 104 105 106 107

mea

n (n

umbe

r) pa

rticl

e si

ze in

nm

0

50

100

150

200

250

300

perfect mixing

symbols: experiments lines: simulation

agglomeration?

mixing intensity

mixing-controlled

Comparison of results

good agreement between experiment and simulationmixing model capable of predicting mixing influence

0.5m BaCl2 +0.33m H2SO4

0.21m BaCl2 +0.14m H2SO4

0.15m BaCl2 +0.1m H2SO4

0.33m BaCl2 +0.22m H2SO4

supe

rsat

urat

ion

perfect stabilization

Schwarzer et al., AIChE J. 2004

17

particle size in nm20 40 60 80 100 120 140 160 180

norm

aliz

ed n

umbe

r den

sity

in n

m-1

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09Re = 6366Dasf = 0.094 Re = 382

Dasf = 6.4

simulation

experiment

Re = 738Dasf = 2.4

0.5m BaCl2 +0.33m H2SO4

Particle size distribution PSD (global model)

Efficient Coupling CFD ↔ PBM

Direct way:• grid from CFD• solve PBM for each volume element• transport by convection, dispersion

energy balance

Population balance

RANS

chem. reaction

( )444 3444 2144 344 2143421

source

2g

diffusion

kkconvection

k

kg NN21Inc

xND

xxNu

⎟⎠⎞

⎜⎝⎛ ρβ−+⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

=∂

ρ∂

convection diffusion source

18

Algorithms: Compartment-Models

Approach:much coarser grid for PBMassume total mixing in PBM cellstransport across PBM cells by convection (+ dispersion)Application: so far only stirred tank reactors

Advantage:• easily implemented• scalable (no. trajectories)

Disadvantage:

• no exchange between surrounding volume elementsonly for flows with strong main flow direction

Algorithms: Lagrange

Approach:trajectories for fluid volume elementsPBM along trajectory (no exchange with surrounding fluid)get resulting distribution from mixing individual distributions of volume elementsApplication: (so far) Precipitation in T- mixer

19

Coupled DNS - Population Balance approach

Computation of flow field with temporal and spatial resolution(3D) by Direct Numerical Simulation (DNS)(Cooperation with M. Manhart & F. Schwertfirm, Fluid Dynamics Group, Technische Universität München)

Lagrangian Particle Tracking to obtain histories of ε and macroscopic composition (passive scalar) along paths

Simulation of precipitation along a large number of pathsbased on presented global precipitation model, using ε-histories and the macroscopic composition as boundaryconditions

Composition of overall PSD by flow-rate-fraction weightedaveraging of individual PSDs

No back-coupling of particle formation on flow field

Direct Numerical Simulation and Particle Tracking

Instantaneous concentration field

Re = 1135• Grid: 5.5·106 cells (Cartesian)• pressure drop difference < 20%• 198 histories at 61 positions at

inletCalculated ε-histories

residence time in mixer in ms0.02 0.1 1 10

spec

ific

pow

er in

put ε

in W

/kg

10

100

1000

10000

100000path 1path 2path 3path 4step50

Re = 1135position 50

20

residence time in mixer in ms0.03 0.1 1 10 100

supe

rsat

urat

ion

S

0

200

400

600

800

1000

1200path 1path 2path 3path 4step50

Re = 1135position 50

Evolution of supersaturation along paths

Different levels (peak height) of supersaturations are reached

0.5m BaCl2 +0.33m H2SO4

particle size in nm20 40 60 80 100 120

num

ber d

ensi

ty d

istri

butio

n in

nm

-1

0.00

0.02

0.04

0.06

0.08

0.10

0.12path 1path 2path 3path 4step50

Re = 1135position 50

Computed individual PSDs along paths

Very different PSDs are obtained along the paths

0.5m BaCl2 +0.33m H2SO4

21

particle size nm0 50 100 150 200 250 300

mea

n nu

mbe

r den

sity

dis

tribu

tion

nm-1

0,000

0,005

0,010

0,015

0,020simulation experiment

Re = 500

0.5m BaCl2 + 0.33mH2SO4

particle size nm-10 50 100 150 200

mea

n nu

mbe

r den

sity

dis

tribu

tion

nm-1

0,00

0,01

0,02

0,03

0,04

0,05

SimulationExperiment

0.7m BaCl2 + 0.23mH2SO4

Re = 1100

Prediction of PSD

Spatial visualization of important subprocesses

• Evolution of subprocesses along their way through the mixer• Interpolating on a grid with 100 x 100 x 300 cells• Parameters:

• Specific power input• Concentration fields• Supersaturation• Nucleation rate• Mean particle size

22

3D-Visualization

Re = 500 Re = 1100

Nuc

leat

ion

rate

[1/m

3 s]

Part

icle

siz

e[m

]z/H = 0.5

++++

++++

+++

+++

length coordinate Lsupe

rsat

urat

ion

S

nuclei size xsize

dis

tribu

tion

q

mass, momentumand heat transfer,chemical reactions

phase transition transfer processesinterfacial process engineering

generation ofsupersaturation nucleation

growth

coagulation

stabilization

ripening, sintering

Principles of particle synthesis

Peukert et al., Adv. Powder Techn. 2003

23

Gas phase synthesis of nanoparticles

Typical process conditionsprimary particle size 2 - 300 nmtemperature 1200 - 2000 Kreaction time 1 µs - 10 msresidence time 1 - 10 msspecific area 10 – 1000 m²/glow apparent density 20 - 300 kg/m³

Methods:Flame hydrolysisHot wall reactorPlasmaLaser evaporationSprays……

Challenge: Optimal reactor geometry

Example: Carbon black, Source Degussa

Find the geometry, feed conditions and flow rate fora predefined time- temperature profile.

24

chem. reaction

precursor

sintering

growth

coagulation

product monomers

nuclei

monomers stable nuclei

nucleation

Relevant Mechanisms in Gas Phase Synthesis

Impaktor TEM-Grid

Membranfilter

Pumpe

Partikelsynthese

Prozessluft

Precursor

Quenchluft

sampling

Kurzzeit-Sinterreaktor

Pumpe

Quenchluft

Prozessluft

Excessluft

Impaktor TEM-Grid

Nanoparticles from the gas phase -Experimental set-up for sintering

Particle Synthesis

process air

precursor

quench air

Short-time Sintering Reactor

excess air

sampling

pumpquench air

process airsampling

b

x1x2

25

Multiscale modelling: viscous flow + van der Waals attraction

volume force in each grid cell

R r0

dimensionless time t·σ / η·a00.0 0.1 0.2 0.3 0.4 0.5

dim

ensi

onle

ss n

eck

size

R /

r 0

0.0

0.2

0.4

0.6

0.8

1.0experiments

Pokluda:viscous flow

CFD:viscous flow

CFD:viscous flow &van der Waals (r0 = 5 nm)

τf = tc / tf = 0.05τf = tc / tf = 0.0 τf = tc / tf = 0.05

Vagg = 2048·VP,0ttot = 11·tC

Coagulation & Sintering: 'Steady State'

τf = tc / tf = 0.1

26

τf = tc / tf = 0.1τf = tc / tf = 0.3

τf = tc / tf = 0.5

Vagg = 2048·VP,0ttot = 11·tC

Coag & Sinter: 'Steady State'

τf = tc / tf = 0.75

τf = tc / tf = 1.0 τf = tc / tf = ∞

τf = tc / tf = 4.0

Schmid et al., J. Nanoparticle Research 2005

Results (qualitatively)

Simulation (tc / tf = 0.2)Flame-made TiO2

27

Property function of aggregates:stationary mean drag force

number of particles, N0 20 40 60 80 100 120 140

0

5

10

15

20

drag

forc

e F d/F

d,pr

im [-

]

±15%

Df = 1.85

0.63N)(143

FF

primd,

d +=

Stokesian and Lattice-Boltzmann simulation

Binder et al., JICS 2006

Fractal aggregates as obtained from gas phase

Challenge: Derivation of properties of nanoscaled objects !

Aims of the project

process disperseproperties

applicationproperties

optimize • operation conditions

• reactor geometry

optimal control ofnon-linear hyperbolic-integro-partial differential equations

28

Product and Process Optimization

time & costs

expe

rimen

t1

proc

ess

mod

ifica

tion

expe

rimen

t2

expe

rimen

t3

proc

ess

mod

ifica

tion

expe

rimen

t4

• Typical optimization today:si

mul

atio

n1

sim

ulat

ion

2

expe

rimen

t1

• Aim:

Hierarchical Approach

Ø Applications with increasing complexity

Ø model reduction

grow

ing

com

plex

ity

optimal control ofnon-linear hyperbolic-integro-partial differential equations

Ø domain decomposition

Ø iterative de- coupling

Ø surrogate methods

Ø hierarchical .optimization .

(trust region)

29

Perspectives

process disperseproperties

applicationproperties

• materials

• processes

• applications

opens huge field

application of modern

methods to 'real problem'

Engineering

MathematicsPanel on Future Directions in Control, Dynamics and Systems. SIAM 2003