fig_mpe_1

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Fig. 1.1

Prof. Dr. J. Tomas, chair of Mechanical Process Engineering

Fig_MPE_1 Mechanical Process Engineering - Particle Technology Disperse Systems Prof. Dr. J. Tomas 31.03.2014 Figure 1.1

1. Dispersity of particulate systems,1.1 About rocks, gravel, lumps, nuggets, corn, particles, nanoparticles and

colloids1.2 Particle characterisation - Granulometry,1.3 Particle size distributions,1.4 Physical particle properties

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Fig. 1.2



Size Scale of Polydisperse (Material) Particle Systems

10-10

10-9

10-8

10-7

10-

10-5

10-4

10-3

10-2

10-1

1

1o

A 1 nm 1 m 1 mm 1 cm 1 m

wave length of visible light:

visual ability of human eye

X-rays and electron interferences

ultra-microscope light microscope

electron microscope

capacitive und inductive sensors

dispersity molecular-disperse colloid-disperse

high-disperse,

ultra-fine

fine-disperse coarse-disperse

pore dispersity microporous mesoporous macroporous

dispersedelements

molecules makromolecules,

colloids

ultra-fines fines medium grain coarse

one-dimensional surface coatings, liquid films, membranes

two-dimensional chains of macromolecules, needles, fibres, threads

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Fig. 1.3



Blatt 2

Mixtures of Polydisperse (Material) Particle Systems

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

disper-

sant

disperse

phase 1o

A 1 nm 1 m 1 mm 1 cm 1 m

gas gas gas mixture

liquid aerosol, fog

solid aerosol, smoke

transition l-g foam

liquid gas solution, lyosol,

hydrosol

bubble system

liquid micro-emulsion emulsion

solid suspension

solid gas xerogel, porous membrane rigid-foam insulation

liquid gel liquid filled, porous solid material

solid mixed crystal, solid solution, s-s alloymonodisperse = uniform-sized elements

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Fig. 1.4



1 10 100 1000 nm

10

10

m

Quantum effects

Strongly developed

surface effects

Polymers

Ceramic powders

Tobacco smoke

Nanoparticles for

life sciences

Bioavailability

Proteins

Virus, DNS

Atmospheric

aerosols

Metal powders

0,001 0,01 0,1 1 m

Size Scale and Properties of Nanoparticles

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Fig. 1.5



Expression of theParticle Size

characte-

ristic size

Eq./sketch measuring method,

quantity r = 0...3

breadth: b

length: lthickness: t 2/1

3/1

6

lt2bt2lb2,lb,

b/1l/1

3

,t

b,

3

tlb,

2

1b

+++

+++

(1) equivalent diameterd, for b l t(2) equivalent lengthl, for rodsl >> b t(3) equivalent area lb , for chips, plates

b l >> t(4) equivalent mass tlbs , for extreme

shaped clusters:

r = 0 number basis

r = 1 lengthr = 2 area

r = 3 volume basis

image analysis d0

geometric anal. d0

geometric anal. d0

mass balancing d3

Feret

diameter

image analysis,

number basis d0

Martin

diameter 21 AAA += image analysis,

number basis d0

sieve

diameter( ) 2121 aaoraa

2

1+ sieving, mass or

volume basis d3

volume V

equivalent

diameter

equivalent volume diameter3 /V6

Coulter counter

electrical method,

number basis d0

area A

equivalent

diameter

equivalent projection area

diameter /A4

light extinction,

number basis d0

surface area

ASequiv.diameter

equivalent surface area diameter /AS

specific surface diameter SA/V

light extinction,

number basis d0

physical

feature

equivalent

diameter

Stokes diameter

( ) a18v

dfs

sSt

=

gravitational, centri-

fugal sedimentation

and impactor, mass

basisd3

aerodynamic diametera

18vd sa

=

sedimentation, mass

or volume basis d3

equivalentlight-scattering

diameter

low angle laser light-scattering method,

number basis d0

b

t

a1 a2

vs

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Fig. 1.6



Characterisation of particle size distributions

1. Particle size characteristics by 2. Partic le size distribut ion funct ion image analysis (cumulative distr ibution curve)

3. Frequency dis tribution of particle size (distribution density curve)

5. Particle size distribution function Q3(d) and frequency dist ribution of particle size q3(d) of the above example 4.

4. Example of measured particle size distribution

a) b)

dF FERET chord lengthdMMARTIN chord lengthdS maximum chord length

particle sizefractiond i-1... d iin mm

mass

in kg

massfraction

Q3(d i)-Q3(d i-1)in %

cumulativefraction

Q3(d) in%

- 0.16 0.16 ... 0.63

0.63 ... 1.25 1.25 ... 2.5 2.5 ... 5.0 5.0 ... 6.3 6.3 ... 1010 ... 1616 ... 20 + 20

0.1800.648

0.9191.9203.0211.0841.7480.7610.2320.054

1.7 6.1

8.718.128.610.316.6 7.2 2.2 0.5

1.7 7.8

16.5 34.6 63.2 73.5 90.1 97.3 99.5100.0

10.567 100.0

dire

ctionofmeasurement

dFdMdS

0.20

0.15

0.1

0.05

00 4 8 12 16 20

particle size d in mm

dm,i=d i-1+ d i 2

qr(d) Qr(d i) - Qr(d i-1) di- d i-1

q3

(d)inmm-1

1

0,5

0dmin d1 d2 dmax

d

Qr(d)Qr(d2)

Qr(d1)

Qr(d)

d

qr(d)

du d i-1 d i di+1 d0d

qr(d) =dQ r(d)d(d) Mode dh

0 4 8 12 16 20

Particle size d in mm

100

80

60

40

20

0

Q3

(d)in%

Qr(d*

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Fig. 1.7



Normal Distribution (GAUSSIAN Distribution):

Four - Parameter Log - Normal Distribution:

WEIBULL Distribution:

0 5 10 15 x

qr(x)

0.3

0.2

0.1

ln x50= 1, ln= 1

ln x50= 3, ln= 3

ln x50= 3, ln= 1

q r(x)

2.0

1.0

n = 0.5 n = 5.5

n = 3

n = 2

n = 1

for xmin= 0 and x* = x63= 1

0 1 2 x

( )

( )

( )

( )2

xx4xxu

with

dt2

texp

2

1xQ

:normalizes

dtt

2

1exp

2

1xQ

x

2

1exp

2

1xq

168450

u 2

r

x 2

r

2

r

=

=

=

=

=

( )

( )

( )

=

=

=

=

=

16

84ln

ln

50

maxminmax

max

min

x

0

2

ln

50

ln

r

2

ln

50

ln

r

x

xln

2

19

xlnxlnu

dddforddd

ddx

dtxlntln21exp

t1

21xQ

xlnxln

2

1exp

2x

1xq

( )

( )

=

=

n

min

minr

n

min

min

1n

min

min

min

r

xx

xxexp1xQ

xx

xxexp

xx

xx

xx

nxq

(1)

(2)

(3)

(5)

(6)

(7)

(8)

(10)

(11)

(12)

(13)

for xmin= 0 and n = 1 follows the

Exponential Distribution if =

Q(x) = 1 - exp(-x)

1x63

Typical frequency distributions and cumulative probability distributions

2<

1

1

q r(x)

0 x16 xh = x50 x84 x

Qr(x50) = 0,5

Mode xh = x50 Median

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Fig. 1.8



6. Three - parameter logarithmic normal distribution (L) with upper limit doand transformation (T)

7. Comparison of particle size distribution functions in a full -logarithmic , RRSB and log - normal diagram (net)

1 5 10 5 10 5

99.90

99.50

97

90

50

105

1

0.20

0.02

Qr(

d)

L

d50 do

16 50

d or

T

3 - parameterdistribution

transformeddistribution

8. RRSB - dist ribution in a doub le - logarithmic di agram

AS,V,K d63in m3/ m3

n

40

60

80 100 120 150 200 300 500

1000 2000 500010000

10-3 10-2 10-1 100 101 102

99.9

999590

63.250

10

1

0.5


Pol

cumulativedistribution

Q3

(d)in%

xx

x

x

x

x

x

x

x

0

0.1

0.3

0.2

0.4

0.5

0.6

0.7

0.8

0.9

1.01.11.21.31.41.61.82.02.54.0 3.03.5

10 15 20 25 30987.57.0

1 Log-Normal distribution2 RRSB-distribution3 GGS-distribution

particle size d in m

100 101 102 103 104

99.9

6040

20

6

0.5

10

cumulativedistributionQ(d)in%

50

5

full-logarithmicnet

RRSB-net

2

4

10

11

0.5

5

10

99.999.5

989690

80

60

40

20

1 2 3 1 2 3 1 2 3

full-logarith-mic -net

RRSB-net

log - normalnet

99,9

95

10-1 100 101 102 103

10-2 10-1 100 101 102

Graphical characterisation of selectedparticle size distributions

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Fig. 1.9



Statistical Moments of Particle Size Distributions

Complete k-th Momentof Particle Size Distribution Qr(d*

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Fig. 1.10



Cumulative Particle Size Distribution, Mass and Number Basis

mass basis:

=

d

d

n

1i

i,333

U

)d(d)d(q)d(Q

number basis:

=

=

=

N

1i3

i,m

i,3

n

1i3

i,m

i,3

d

d

3

3

d

d

3

3

0

d

d

)d(d)d(qd

)d(d)d(qd

)d(Qo

u

u

0

10

20

30

40

50

60

70

80

90

100

Vert

eilungsfunktion

Q0(d)

in

%

0. 5 1 5 10 50 100 500 1000

Partikelgre in m

Anzahlverteilung

0

10

20

30

40

50

60

70

80

90

100

Verteilungsfunktion

Q3(d)

in

%

0.5 1 5 10 50 100 500 1000

Partikelgre in m

Masseverteilung

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Fig. 1.11



Multi-modal Frequency Distribution

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8


frequen

cydistributionq*(logd)

subcollective 3

subcollective 2

subcollective 1

0.1 100.010.01.0

total frequency distribution:

[ ]q d t q d d d

tot SC k k o k k kk

N

3 3 501, , , , , ln,

( , ) , , ,= =

truncated log-normal distribution:

q dd d

d d

uk

o k

k o k

3

2

2 2,

,

ln, ,

( ) exp=

with

ud d

d d

d d

d dk

o k

o k

o k k

o k k

=

1 50

50 ln,

,

,

, ,

, ,

ln ln

normalisation:

( )( )

( )q

dQ d

d d

Q d

d d

d

tot

i

i

i

33 3 3

1

,* ,

log

log

log

loglog

= =

SC,k(t) mass fraction of the k-th

subcollective (subpopulation)

q3,k frequency distribution

of the k-th subcollective

do,k upper limit of the particle size

of the k-th subcollective

d50,k median particle size of the

distribution function

ln,k standard deviation of the

k-th subcollective

N total number of subcollectives

[ ] )t,d(Q)d(d2

uexp

2

1,d,d,dQlim tot,3

u 2

1k

kln,k,50k,ok,3k,SCN

=

=

=

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Fig. 1.12



Mass Fraction Related to the Number of Stressing Events

discrete mass balance model:

1,sc1,n

1,scS

n

d=

2,sc2,3,n1,sc1,3,n

3,sc

SSn

d

+=

1

N

1kk,sc ==

n number of stressing events

Sk,j kinetic constants for mass transfer from j to k subcollective

0 12 3

43

2

1

0,0

0,20,4

0,6

0,8

1,0

3

number of stressing events n

mass fraction sc,k

k-th subcollective

measured

model

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Fig. 1.13



Application of Image Analysis to Characterise Particle Size1. Image of Microscope by CCD-camera

2. Definition of Threshold Value

3. Conversion of Grey Tone Image in a

Binary Image (Binarisation)

4. Classification of Particles

dF,mi

dF,ma

Definition of grey tone limits

for particle detection in a 8-bit

grey tone image

Binary image means: whichpixel of original image is shown

b 0 black or b 255 white

dequ

min. and maximum Feret diameter equivalent circle diameter

/Ad 2 ,

shape factor2

4U

AU

U= circumference, A= projectionarea

Presentation of Particle Size Fractions

in a ColourCode

direct-light

transmitted

light

pixelnu

mber

grey tone distribution0 255(black) (wite)

particle

direct-

lighttrans-

mitted

light

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Fig. 1.14



Principle of Laser Light Diffraction

large diffraction for particle size d wavelength, small diffraction for d >>

light diffraction pattern

radial light intensitydistribution at detector

=max

min

d

d

i0tottot )d(d)d,r(I)d(qNI

particle size distribution

laser

lense system

sample cellFourier

lense

detector

r

computer

f

focal distance

principle of laser light diffractometer

r

Fourier lensedetector

rinzi le of Fourier lense

Intensity I

r

100

50

0

particle size


cumulativedistributionQ

3in%

frequencydistributionq3in

1/mm

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Fig. 1.15



In-Line Particle Size Analysis (Sympatec)

isokinetic sampling device for a split particle stream:

rotating sector moving pipe

D

D

d

particle loaded air stream

drive for rotating

sampling device

dispersion air

laser beam

detector with

sensor array

nozzle and

sample cell

low-angle laserlight-scattering

instrument

(LALLS)

d = 0.5 1750

m

inductive sensor

on-line sampling

feed opening

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Fig. 1.16



In-Line Particle Size Analysis (Malvern)

monitoring of size ranges: 0.5 - 200 m

1.0 - 400 m

2.25 - 850 m

Injektion nozzle

laser

pressurized air

particle

stream

isokinetic sampling

particle

feed back

detector

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Fig. 1.17



Principle of Photon Correlation Spectrometer (PCS)

in suspensions at rest: light scattering at dispersed particles, that oscillate by Brownianmolecular motion

Determination of intensity time function of scattered light (reasons: interferences,change of particle number concentration within the charac-teristic volume element)

and calculation of autocorrelation function:

Autocorrelation function (Dp particle diffusion coefficient, K scattered light vector,- retardation time)

=+=

2p KD2

T

TT

I,I edt)t(I)t(Ilim)(R withp

B

D3

Tkd

=

EINSTEIN equation (d particle size, kB BOLTZMANN constant, T absolutetemperature, - dynamic viscosity)

autocor

relationfunctionR

I,I(

)

retardation time

in

tensityofscatteredlight

time t

fine particle

coarse particle

Laser Optik Probenbehlter

Photomultiplier Korrelator

Optische Einheit

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Fig. 1.18



Laser

Detectors

backscatter

large angle

forward angle

Fourier lens Sample chamber

Laser

Detectors

backscatter

large angle

forward angle


Laser

Detectors

backscatter

large angle

forward angle


Laser

Detectors

backscatter

large angle

forward angle


1. Physical Principle

Laser diffraction technique is based on the phenominon that particles scatter lightin all directions (backscattering and diffraction) with an intensity that is dependent

on particle size

- the angle of the deflected laser beam is inverse proportional to the particle size

2. Measurement setup

Using two laser beams with different wavelength (red and blue light) additional

information to particles smaller 0,2 m is obtained

red light setup

- scattering light hits only forward angle detectors

blue light setup

- blue light (wavelength 466 nm) leads to a scattering signal for small particles

(isotropic scattering pattern) which can be detected from large angle- and

backscatter- detectors

page 1

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Fig. 1.19



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Fig. 1.20



Principle of Acoustic Attenuation Spectroscopy

during acoustic wave penetration, amplitude and intensity attenuation (damping) ofultrasonic frequency spectrum (1 to 100 MHz) in high concentrated particle

suspensions with sizes d = 10 nm 1 mm

detection of attenuation (damping) spectrum

correlation between attenuation characteristics

and particle size distribution (K = 2/

suspension wave number, k fluid wave number,

sparticle volume concentration, i = 1...n

particle size fraction, riparticle radius, Ami

reflected compression wave coefficient, ARereal

contribution, m number of acoustic dispersion

coefficient):

( ) miRe0m

n

1i3

i

3

i,s

2

AA1m2rk

i231

kK +

=

==

Microwave

and

DSP module

Transducer

Positioning Table

Control

module

Discharge

Stopper motor

and digital

encoder

Level sensor

Suspension

HF Receiver

LF Receiver

HF Transmitter

LF Transmitter

Stirrer

entrainmentx >scattering

RF generator RF detector

measuring zone

100

50

0

particle size


cumulativedistributionQ3in%

frequencydistributionq3in1/mm

damping

fre uenc

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Fig. 1.21



Determination of Particle Size Distribution and Zeta-Potential using

Electroacoustic Effect - Electrokinetic Sonic Amplitude (ESA)

1. Physical Principle

Alternating electric field (frequency range 1 to 20 MHz) generates particle oscillations

at velocities that depend on their size and zeta potential (O' Brien- Theory)

2. Measurement Setup

3. Data Analysis

adjusting q(d)and zeta-potential from

the measured mobility spectrum

E

p

s ZAESA

)(

A(

) calibration function

s volume fraction of particles

suspension density difference

p particle density

Z acoustic impedance (complex resistance)

)()(,, dddqd sEm

m measured dynamic mobility

zeta-potentiald particle diameter

s volume fraction of particles

q(d) particle size frequency distribution

acoustic signal (ESA) as response

p

rEE

v0

electrophoretic mobility (E)

suspension

ESA-Signal

Processing

Particle motion in an electric field

Time

E;v

applied e lectric field particle velocity

0 permittivity of vacuumr permittivity

v particle velocity

E electric field strength

viscosity

frequency

phasela

g

Mobility Spectrum

mdyn. mobility

phaselag

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Fig. 1.22



Particle Density Measurement by HELIUM-Pycnometer

Determination of porefree particle volume by gas pressure measurement in a double-chamber system by HELIUM gas (migration access of internal pores dPore> 0,1 nm)

Pressure measurement in probe chamber: (VCellVProbe) p1

Pressure test in probe and expansion chamber: (VCellVProbe) + VExp p2

Calculation of probe volume and solid density, pre-measurement of particle mass msby balance

1p/p

VVV

21

Exp

CellobePr =

and obePr

ss

V

m=

pressureprobe chamber

filter

Helium

feed valve

overpressurevalve

prep./ test valve

discharge valve

VProbe

VExp

5

VExp

35

VExp

150

VCell 5,

VCell 35,VCell 150

P

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Fig. 1.23



Measurement of Particle Surface by Gas Adsorption according to

BRUNAUER, EMMET and TELLER Physical adsorption of gas molecules at particle surfaces in multi-layers due to VAN

DER WAALS interaction

BET- line, valid for: 0.05 < p/p0< 0.3

Adsorpt mono-layer coverage:

ba

1V mono,g +

=

BET- constant:

aba

TRHHexpC multimBET +=

=

Hm free molar adsorption enthalpy ofmono-layer

Hmulti molar bonding enthalpy of nmulti-layers Hcondensation

Particle Surface:

l,mmono,gAg,MS

V/VNAA = AM,g cross-sectional area of adsorpt

moleculeNA AVOGADRO-number

Vm,l molar volume of condensed adsorpt

( ) 0BETmono,gBET

BETmono,g0g

0 p/pCV

1C

CV

1

p/p1V

p/p

+

=

gas supplyP

PTdosingvalve

probe chamber

dewar vessel

p0- test chamber

liquid nitrogenN2 at T = 77 K

p0= 101 kPa

T

vacuum

standard vessel

0 0.35 1

ads

orbedgasvolumeV

g

desorption

adsorption

BET range sorption isotherms

relative partial pressure of gas p/p0

adsorbedgas molecules(adsorpt)

adsorptiv

particle surface(adsorbens)

( )0g0

p/p1V

p/p

0p/p

BETmono,g CV

1a

=

( )

BETmono,g

BET

CV

1Cb

=

relative gas pressure

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Fig. 1.24



Regular Packing Structures

porosity

, coordination number k

lattice type primitive basic face- face-centred space-centred

centred

z c

b

y

x

a

cubic

a = b = c

= = = 90

monodisperse

sphere

packing

d = const.

hexagonal

a = b = c

= = 90

= 120

sphere

packing

a0 0,1nm k = 6 k = 12 k = 8

= 0,4764 = 0,3955

k = 12

= 0,2595

a0

d

octahedron

vacancy

tetrahedron

vacancy

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Fig. 1.25



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Fig. 1.26



Stressing and Flow of Wet Particle Dispersions

ad

> 1 0 < < 0.2a

dad

= 0

ss

< 0.066 0.3

S < 1

i>30

=duxdy

y

x

ux

dy

uxdy

vxux

a

a

d

d

da

a

d

d

a

a

d

d

a

vxdy

contactcontactdeformation

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Fig. 1.27



Sampling

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Fig. 1.28


fig_mpe_1

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