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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 colloids
1.2 Particle characterisation - Granulometry, 1.3 Particle size distributions, 1.4 Physical particle properties
Fig. 1.2
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 1.2
Size Scale 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
1
o
A 1 nm 1 µm 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 dispersed elements
molecules makromolecules, colloids
ultra-fines fines medium grain coarse
one-dimensional surface coatings, liquid films, membranes two-dimensional chains of macromolecules, needles, fibres, threads
Fig. 1.3
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 1.3
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
1 o
A 1 nm 1 µm 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 alloy
monodisperse = uniform-sized elements
Fig. 1.4
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 1.4
1 10 100 1000 nm
10–9 10–6 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 µm
Size Scale and Properties of Nanoparticles
Fig. 1.5
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 1.5
Expression of the Particle Size characte-ristic size
Eq./sketch measuring method, quantity r = 0...3
breadth: b length: l thickness: t 2/1
3/1
6lt2bt2lb2,lb,
b/1l/13
,tb,
3tlb,
21b
++
+
+++
(1) equivalent diameter d, for b ≈ l ≈ t (2) equivalent length l, for rods l >> b ≈ t (3) equivalent area lb ⋅ , for chips, plates b ≈ l >> t (4) equivalent mass tlbs ⋅⋅⋅ρ , for extreme
shaped clusters:
r = 0 number basis r = 1 length r = 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 aaoraa21
+
sieving, mass or volume basis d3
volume V equivalent diameter
equivalent volume diameter 3 /V6 π⋅
Coulter counter electrical method, number basis d0
area A equivalent diameter
equivalent projection area diameter π/A4
light extinction, number basis d0
surface area AS equiv. diameter
equivalent surface area diameter π/AS specific surface diameter SA/V
light extinction, number basis d0
physical feature equivalent diameter
Stokes diameter
( ) a18v
dfs
sSt ⋅ρ−ρ
η⋅⋅=
gravitational, centri-fugal sedimentation and impactor, mass basis d3
aerodynamic diameter a18v
d sa
η⋅⋅= sedimentation, mass
or volume basis d3 equivalent light-scattering diameter
low angle laser light-scattering method, number basis d0
b
t
a1 a2
vs
Fig. 1.6
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 1.6
Characterisation of particle size distributions
1. Particle size characteristics by 2. Particle size distribution function image analysis (cumulative distribution curve)
3. Frequency distribution of particle size (distribution density curve)
5. Particle size distribution function Q3(d) and frequency distribution of particle size q3(d) of the above example 4.
4. Example of measured particle size distribution
a) b)
dF FERET chord lengthdM MARTIN chord lengthdS maximum chord length
particle sizefractiondi-1 ... diin mm
mass
in kg
massfraction
Q3(di)-Q3(di-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
0.1800.6480.9191.9203.0211.0841.7480.7610.2320.054
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
ctio
n of
mea
sure
men
t
dFdMdS
0.20
0.15
0.1
0.05
00 4 8 12 16 20
particle size d in mm
dm,i =di-1 + di 2
qr(d) ≈ Qr(di) - Qr(di-1) di - di-1
q 3(d
) in
mm
-1
1
0,5
0 dmin d1 d2 dmaxd
∆Qr(d)Qr(d2)
Qr(d1)
Qr(d)
∆d
qr(d)
du di-1 di di+1 d0d
qr(d) = dQr(d)d(d) Mode dh
0 4 8 12 16 20Particle size d in mm
100 80
60
40
20
0
Q3(d
) in
%
Qr(d*<di)
Median d50
Characterisation of Granulometric Properties of Disperse Material Systems
Fig. 1.7
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 1.7
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, σln = 1
ln x50 = 3, σln = √3
ln x50 = 3, σln = 1
qr(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
dt2texp
21xQ
:normalizes
dtt21exp
21xQ
x21exp
21xq
168450
u 2
r
x 2
r
2
r
−=σ
σ−
=
−
π=
σµ−
⋅−π⋅σ
=
σµ−
⋅−π⋅⋅σ
=
∫
∫
∞−
∞−
( )
( )
( )
⋅=σ
σ−
=
≤≤⋅−
−=
σ−
−⋅π⋅σ
=
σ−
⋅−⋅π⋅⋅⋅σ
=
∫
16
84ln
ln
50
maxminmaxmax
min
x
0
2
ln
50
lnr
2
ln
50
lnr
xxln
219xlnxlnu
dddforddd
ddx
dtxlntln21exp
t1
21xQ
xlnxln21exp
2x1xq
( )
( )
−−
−−=
−−
−
−−
−=
∗
∗
−
∗∗
n
min
minr
n
min
min
1n
min
min
minr
xxxxexp1xQ
xxxxexp
xxxx
xxnxq
(1)
(2)
(3)
(5)
(6)
(7)
(8)
(10)
(11)
(12)
(13)for xmin = 0 and n = 1 follows theExponential Distribution if λ =
Q(x) = 1 - exp(-λ·x)
1x63
Typical frequency distributions and cumulative probability distributions
σ2 < σ1
σ1
qr(x)
0 x16 xh = x50 x84 x
Qr(x50) = 0,5
σ σ
Mode xh = x50 Median
Fig. 1.8
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 1.8
6. Three - parameter logarithmic normal distribution (L) with upper limit do and 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
99.9099.509790
50
1051
0.200.02
Qr(d
) L
d50 do
δ16 δ50 δ84d or δ
T
3 - parameterdistribution
transformeddistribution
8. RRSB - distribution in a double - logarithmic diagram
AS,V,K · d63 in m3/ m3
n 40
60 80 100 120 150 200 300 500 1000 2000 500010000
10-3 10-2 10-1 100 101 102
99.9999590
63.250
10
1
0.5
particle size d in mm
Pol
cum
ulat
ive
dist
ribut
ion
Q3(d
) in
% xx
xxx
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 µm
100 101 102 103 104
99.96040
20
6
0.5
10cu
mul
ativ
e di
strib
utio
n Q
(d) i
n %
50
5
full-
loga
rithm
ic n
et
RR
SB -
net
2
4
10
11
0.5
510
99.999.5
98969080604020
1 2 3 1 2 3 1 2 3
full-logarith-mic -net
RRSB-netlog - normalnet
99,995
10-1 100 101 102 103 10-2 10-1 100 101 102
Graphical characterisation of selected particle size distributions
Fig. 1.9
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 1.9
Statistical Moments of Particle Size Distributions
Complete k-th Moment of Particle Size Distribution Qr(d*<d) related to Quantity r:
( ) ( ) ( )d k rk
rd
dk
rd
d
m r i
k
r ii
N
M d d q d d d d d dQ d d du
o
u
o
* ,* *
, , ,( ) ( ) ( )= − ⋅ = − ⋅ ≈ − ⋅∫ ∫ ∑ ∗
=
µ1
(1)
First Initial Moment (k = 1, d* = 0) or Expected Value
M d d q d d d d dQ d dr m r rd
d
rd
d
m r i r ii
N
u
o
u
o
11
, , , , ,( ) ( ) ( )= = ⋅ = ⋅ ≈ ⋅∫ ∫ ∑=
µ (2)
Central Moment related to expectation (mean) dm,r
d k r k r m rk
rd
d
m r
u
o
M Z d d q d d d, , , ,( ) ( ) ( )= = −∫ (3)
Second Central Moment or Variance
Z d d q d d d d d dQ d d dr r m r r m r r m r i m ri
N
d
d
d
d
r iu
o
u
o
22 2 2 2
1, , , , , , ,( ) ( ) ( ) ( ) ( ) ( )= = − = − ≈ − ⋅
=∑∫∫σ µ (4)
Variance according to “Satz von Steiner”
σ µr r r r m r i r i m ri
N
Z M M d d22 2 1
2 2 2
1= = − ≈ ⋅ −
=∑, , ,, , , , , (5)
Incomplete k-th Initial Moment du...d, i...n and Complete Initial Moment du...do, i...n...N
d q d d d dk
u
m r ird
dk
i
n
r i( ) ( ), , ,∫ ∑≈ ⋅
= 1µ (6) d q d d d d
k
u
o
m r ird
dk
i
N
r i( ) ( ), , ,∫ ∑≈ ⋅
= 1µ (7)
Conversion from given quantity r to a searched quantity t of Frequency Distribution
q dd q d
Mt
t rr
t r r( )
( )
,=
⋅−
−
(8)
and Cumulative Distribution
Q dM
M
d q d d d
d q d d d
d
dt
t r r d
d
t r r d
d
t rr
d
d
t rr
d
d
m r it r
r ii
n
m r it r
r ii
Nu
u
o
u
u
o( )
( ) ( )
( ) ( )
,
,
, , ,
, , ,
= = ≈⋅
⋅
−
−
−
−
−
=
−
=
∫
∫
∑
∑
µ
µ
1
1
(9)
Conversion of cumulative distributions from number to mass basis or from mass to number basis
Q dd q d d d
d q d d d
d
d
d
d
d
d
m i ii
n
m i ii
Nu
u
o3
30
30
03
01
03
01
( )( ) ( )
( ) ( )
, , ,
, , ,
= ≈⋅
⋅
∫
∫
∑
∑=
=
µ
µ (10) Q d
d q d d d
d q d d d
d
d
d
d
d
d
m i ii
n
m i ii
Nu
u
o0
33
33
33
31
33
31
( )( ) ( )
( ) ( )
, , ,
, , ,
= ≈⋅
⋅
−
−
−
=
−
=
∫
∫
∑
∑
µ
µ (11)
Conversion of k-th complete initial moment of a known quantity r in a searched quantity t
MMMk t
k t r r
t r r,
,
,= + −
−
(12)
Fig. 1.10
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 1.10
Cumulative Particle Size Distribution, Mass and Number Basis
mass basis: ∫ ∑=
µ≈⋅=d
d
n
1ii,333
U
)d(d)d(q)d(Q
number basis: ∑
∑
∫
∫
=
=
−
−
µ
µ
≈
⋅⋅
⋅⋅
=N
1i3
i,m
i,3
n
1i3
i,m
i,3
d
d3
3
d
d3
3
0
d
d
)d(d)d(qd
)d(d)d(qd)d(Q
o
u
u
0
10
20
30
40
50
60
70
80
90
100
Verteilungsfunktion Q0(d) in %
0.5 1 5 10 50 100 500 1000
Partikelgröße in µm
Anzahlverteilung
0
10
20
30
40
50
60
70
80
90
100
Verteilungsfunktion Q3(d) in %
0.5 1 5 10 50 100 500 1000Partikelgröße in µm
Masseverteilung
Fig. 1.11
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 1.11
Multi-modal Frequency Distribution
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
particle size d in mm
freq
uenc
y di
stri
butio
n q*
(log
d)
subcollective 3
subcollective 2
subcollective 1
0.1 100.010.01.0
total frequency distribution:
[ ]q d t q d d dtot SC k k o k k kk
N
3 3 501
, , , , , ln,( , ) , , ,= ⋅∑=
µ σ
truncated log-normal distribution:
q dd d
d du
ko k
k o k3
2
2 2,,
ln, ,( ) exp=
−
⋅ ⋅ ⋅⋅ −
π σ
with
ud dd d
d dd dk
o k
o k
o k k
o k k=
⋅
−
−
⋅
−
1 50
50σ ln,
,
,
, ,
, ,ln ln
normalisation:
( )( )
( )q
dQ dd d
Q dd d
d
toti
i
i
33 3 3
1
,* ,log
loglog
loglog
= ≈ =
−
∆∆
µ
µSC,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
σln,k standard deviation of the
k-th subcollective
N total number of subcollectives
[ ] )t,d(Q)d(d2
uexp21,d,d,dQlim tot,3
u 2
1kkln,k,50k,ok,3k,SCN
=
−
π=σ⋅µ ∫∑
∞−
∞
=∞→
Fig. 1.12
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 1.12
Mass Fraction Related to the Number of Stressing Events
discrete mass balance model:
1,sc1,n1,sc S
nd
µ⋅−=µ
2,sc2,3,n1,sc1,3,n3,sc SS
nd
µ⋅+µ⋅=µ
1
N
1kk,sc =µ∑
=
n number of stressing events Sk,j kinetic constants for mass transfer from j to k subcollective
0 1 2 3 43
2
1
0,00,20,40,60,81,0
3
number of stressing events n
mass fraction µsc,k
k-th subcollective
measuredmodel
Fig. 1.13
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 1.13
Application of Image Analysis to Characterise Particle Size 1. 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: which pixel of original image is shown by 0 (black) or by 255 (white)
dequ
• min. and maximum Feret diameter • equivalent circle diameter
π/Ad ⋅= 2 ,
• shape factor 24UA
U ⋅⋅= πψ
U = circumference, A = projection area
Presentation of Particle Size Fractions in a Colour Code
direct-light
transmitted light
pixe
l num
ber
grey tone distribution0 255(black) (wite)
particle
direct-light
trans- mitted light
Fig. 1.14
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 1.14
Principle of Laser Light Diffraction large diffraction for particle size d ≈ λ wavelength, small diffraction for d >> λ
light diffraction pattern radial light intensity
distribution at detector
∫ ⋅⋅=max
min
d
di0tottot )d(d)d,r(I)d(qNI
particle size distribution
laser
lense systemsample cell Fourier
lensedetector
r
computer
ffocal distance
principle of laser light diffractometer
r
Fourier lense detector
prinziple of Fourier lense
Intensity I
r
100
50
0particle size
particle size distribution
cum
ulat
ive
dist
ribu
tion
Q3 i
n %
freq
uenc
y di
stri
butio
n q 3
in 1
/mm
Fig. 1.15
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 1.15
In-Line Particle Size Analysis (Sympatec)
isokinetic sampling device for a split particle stream: rotating sector moving pipe
D
α
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 laser light-scattering instrument (LALLS) d = 0.5 – 1750 µm
inductive sensor
on-line sampling
feed opening
Fig. 1.16
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 1.16
In-Line Particle Size Analysis (Malvern)
monitoring of size ranges: 0.5 - 200 µm 1.0 - 400 µm 2.25 - 850 µm
Injektion nozzle
laser
pressurized air
particlestream
isokinetic sampling
particle feed back
detector
Fig. 1.17
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 1.17
Principle of Photon – Correlation Spectrometer (PCS) in suspensions at rest: light scattering at dispersed particles, that oscillate by Brownian
molecular 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,
τ - retardation time)
τ⋅⋅⋅−
−∞→
=τ+⋅=τ ∫2
p KD2T
TTI,I edt)t(I)t(Ilim)(R
with p
B
D3Tkd⋅η⋅π⋅
⋅=
• EINSTEIN equation (d – particle size, kB – BOLTZMANN constant, T – absolute temperature, η - dynamic viscosity)
auto
corre
latio
n fu
nctio
n R
I,I( τ
)
retardation time τ
inte
nsity
of s
catte
red
light
time t
fine particle
coarse particle
Laser Optik Probenbehälter
Photomultiplier KorrelatorOptische Einheit
Fig. 1.18
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 1.18
Laser
Detectorsbackscatter
large angleforward angle
Fourier lens Sample chamber
Laser
Detectorsbackscatter
large angleforward angle
Fourier lens Sample chamber
Laser
Detectorsbackscatter
large angleforward angle
Fourier lens Sample chamber
Laser
Detectorsbackscatter
large angleforward angle
Fourier lens Sample chamber
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 dependenton 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 µm 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
Θ
Θ
page 1
Fig. 1.19
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 1.19
Fig. 1.20
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 1.20
Principle of Acoustic Attenuation Spectroscopy
during acoustic wave penetration, amplitude and intensity attenuation (damping) of
ultrasonic 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⋅π/λ suspension wave number, k fluid wave number, ϕs particle volume concentration, i = 1...n particle size fraction, ri particle radius, Ami reflected compression wave coefficient, ARe real contribution, m number of acoustic dispersion coefficient):
( ) miRe0m
n
1i3
i3
i,s2
AA1m2rk
i231
kK
⋅+⋅
ϕ⋅−=
∑∑
∞
==
Microwave and
DSP module
TransducerPositioning Table
Controlmodule
Discharge
Stopper motorand digitalencoder
Level sensor
Suspension
HF Receiver
LF Receiver
HF Transmitter
LF Transmitter
Stirrer
entrainmentx << λ
x >>scattering
λλ
RF generator RF detector
measuring zone
100
50
0particle size
particle size distribution
cum
ulat
ive
dist
ribu
tion
Q3 i
n %
freq
uenc
y di
stri
butio
n q 3
in 1
/mm
dam
ping
frequency
Fig. 1.21
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 1.21
Determination of Particle Size Distribution and Zeta-Potential usingElectroacoustic Effect - Electrokinetic Sonic Amplitude (ESA)
1. Physical PrincipleAlternating electric field (frequency range 1 to 20 MHz) generates particle oscillationsat velocities that depend on their size and zeta potential (O' Brien- Theory)
2. Measurement Setup
3. Data Analysis
adjusting q(d) and zeta-potential ζ fromthe measured mobility spectrum
Ep
s ZAESA µρ
ρϕω ⋅⋅∆
⋅⋅= )(
A(ω) calibration function ϕs volume fraction of particles ∆ρ suspension density difference ρp particle density Z acoustic impedance (complex resistance)
( )∫ ⋅= )()(,, dddqd sEm ϕζµµ
µm measured dynamic mobility ζ zeta-potential d particle diameter ϕs volume fraction of particles q(d) particle size frequency distribution
acoustic signal (ESA) as response
∆ρ ∼ ∆p
ηζεεµ ⋅⋅== rE E
v0
electrophoretic mobility (µE)
suspension
ESA-SignalProcessing
Particle motion in an electric field
Time
E;v
applied electric field particle velocity
ε0 permittivity of vacuum εr permittivity v particle velocity E electric field strength η viscosity
frequency
phas
e la
g
Mobility Spectrum
µm
dyn. mobility
phase lag
Fig. 1.22
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 1.22
Particle Density Measurement by HELIUM-Pycnometer Determination of pore–free 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: (VCell –VProbe) p1 • Pressure test in probe and expansion chamber: (VCell –VProbe) + VExp p2
• Calculation of probe volume and solid density, pre-measurement of particle mass ms by balance
1p/pV
VV21
ExpCellobePr −
−= and obePr
ss V
m=ρ
pressureprobe chamber
filterHelium
feed valve
overpressurevalve
prep./ test valve
discharge valve
VProbe
V Ex
p 5
V Ex
p 35
V Ex
p 15
0
VCell 5,
VCell 35,VCell 150
P
Fig. 1.23
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 1.23
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
TRHH
expC multimBET
+=
⋅∆−∆
=
∆H m free molar adsorption enthalpy of mono-layer
∆H multi molar bonding enthalpy of n multi-layers ≅ ∆Hcondensation
• Particle Surface:
l,mmono,gAg,MS V/VNAA ⋅⋅= AM,g cross-sectional area of adsorpt
molecule NA AVOGADRO-number Vm,l molar volume of condensed adsorpt
( ) 0BETmono,g
BET
BETmono,g0g
0 p/pCV
1CCV
1p/p1V
p/p⋅
⋅−
+⋅
=−
gas supplyP
PTdosingvalve
probe chamber
dewar vesselp0 - test chamber
liquid nitrogenN2 at T = 77 Kp0 = 101 kPa
T
vacuum
standard vessel
0 0.35 1
adso
rbed
gas
v ol
ume
Vg
desorption
adsorption
BET range sorption isotherms
relative partial pressure of gas p/p0
adsorbedgas molecules(adsorpt)
adsorptiv
particle surface(adsorbens)
( )0g
0
p/p1Vp/p
−
0p/p
BETmono,g CV1a⋅
=
( )BETmo n o,g
BET
CV1Cb
⋅−
=
relative gas pressure
Fig. 1.24
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 1.24
Regular Packing Structures
porosity ε, coordination number k
lattice type primitive basic face- face-centred space-centred centred
β α
γ
z c
by
x a
cubica = b = cα = β = γ = 90 °
monodispersesphere packingd = const.
hexagonala = b = cα = β = 90 ° γ = 120 °
sphere packing
a0 0,1nm k = 6 k = 12 k = 8≈
ε = 0,4764 ε = 0,3955
k = 12
ε = 0,2595
a0
d
octahedronvacancy
tetrahedronvacancy
Fig. 1.25
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 1.25
Fig. 1.26
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 1.26
Stressing and Flow of Wet Particle Dispersions
ad > 1 0 < < 0.2
ad
ad = 0
ϕss< 0.066 0.3 < ϕs <
π6
εs,0 =π6
pore saturation S = 1
ϕi = 0 ϕi ≥ 0ϕi = 0
particle in liquid dispersion (suspension) paste liquid in particle packingdiluted concentrated liquid saturated moist packing
suspensionand particleflow pattern
shear rate γ.
τ
γ.
ττ ≠ f (σ) τ
σ
γ.
τ
normal stress σ
.τ ≈ f ( )γflow function
cubical cellpackingmodel
ϕs
εs,0= (1+ )a
d-3
particleseparation
particle volumefraction
particlefriction
a
ad < 0-0.01 <
εsπ6>
S < 1
ϕi > 30°
τ
γ =. dux dy
yx
uxdy
τ
uxdy vx
ux
τσ
a
a
τ
τ
d
d
da
a
τ
τ
d
d
τ
τ
a
a
d
d
τ
τ
a
σ
τσ
vxdy
contactcontactdeformation
Fig. 1.27
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 1.27
Sampling
Fig. 1.28
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 1.28