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Chapter 1
Characterization Of Individual Particles
Cedric Briens April 16, 2010
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1. Introduction
1.The design of any operation involvingparticles requires precise information on
their properties2.The most important properties are density,
size and shape
3.This chapter defines these properties andreviews the techniques for theirmeasurement
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Outline
1 Introduction
2 Particle density
3 Particle size
4 Particle shape
5 Adhesion of particles6 Dustiness
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2. Particle density
Skeletal density
Apparent particle density
Bulk density
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What is the Skeletal density?
Density of the material from which particles
are formed: rsk
non-porouss
non-porouss
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What is the
apparent particle density?
non-porouss
p
mass of particle
volume of particle (including pores)r
non-porouss
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Relationship between rpand rsk
p
p sk
1 1
r rvolume of solid material volume of pores
solid mass
volume of solid material volume of pores
solid mass solid mass
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What is the bulk density?
Density of the bulk
powder: includes the voids in-
between the particles
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Relationship between rb= rp
b p 1r r
: voidage or volume fraction of bulk powder
occupied byvoids.
mass of solid mass of solid volume of bed volume of voids
volume of bed volume of particles volume of bed
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Example:
fluidized cracking catalyst
rsk= 2500 kg/m3
p= 0.50x10-3m3/kg
rp= 1100 kg/m3
rb= 500 kg/m
3
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Bulk density measurement
The bulk density depends on how the powder
is packed
Two extremes:
Loose or aerated bulk density
Compact or tapped bulk density
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Bulk density measurement
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Loose or aerated bulk density
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Compact or tapped bulk density
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Skeletal density measurement
Two pycnometry measurement techniques
may be used:
1) liquid pycnometry: inaccurate
2) gas pycnometry: elaborate but accurate
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Liquid pycnometry
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Liquid pycnometry
weighing mass of added water volume of added water
volume of flask volume of added water volume of solids material
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Liquid pycnometry
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Liquid pycnometry
Porous particles:
The liquid may
not fill allthe
pores
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Gas pycnometry
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Particle density measurement
1) Mercury pycnometry: assume that
mercury does not penetrate into the pores(Mercury is sometimes replaced bysilicone oil).Inaccurate
2) Caking detection: caking occurs whenthe pores are filled with liquid.Inaccurate
3) Gas adsorption isotherms
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Outline
1 Introduction
2 Particle density
3 Particle size
4 Particle shape
5 Adhesion of particles
6 Dustiness
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FCC
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FCC
tertiarycyclone
catch
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Talcumpowder
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Polymer C
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Polymer W
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Polymer E
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Characterizing the size of a
particle with a complex shape
Volume-equivalent particle diameter: diameter of
the sphere which has the same volume as the particle
Others:
Aerodynamic diameter: diameter of the sphere with a density of
1000 kg/m3
which falls at the same speed as the particle in ambientair
Sieve diameter
Diameters based on projected area
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Particle size cuts
Size cut i contains
the particles with a
diameter between
dpi- Ddpi/2
and
dpi+ Ddpi/2
particle diameter (dp), m
0 50 100 150 200 250 300 350 400 450 500 550 600
fraction
ofparticles
in
size
cut(x i)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
ximay be based on:weight
volume
area
number
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Mean diameters
pam i pi i
i i
plm i pi
i
i
i
i
psm pi
: d x d (note : x 1)
: ln d x ln d
For the arithmetic and log mean diameters, x may be any type of fracti
arithmetic mean
geometric or log mean
Sauter me
on
For the , x be the volume fracmu tist on :
1 x
an
d d
diameter
i
S di d
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Sauter-mean diameter and
specific area
p psm
p psm
mean specific surface (a):
particle surface in 1 kg of mixed size solids
6spherical particles: a
d
6non-spherical particles: a
d
r
r
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Median particle diameter
Diameter such that 50% of particles are
larger than this diameter and 50% aresmaller
The median diameter depends on the type of
fraction xi
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Comparison of various mean diameters for a typical size distribution
arithmetic mean diameter, m 221
from log-mean or geometric mean diameter, m 168
volume % harmonic or Sauter mean diameter, m 99
median diameter, m 192
arithmetic mean diameter, m 1.3
from log-mean or geometric mean diameter, m 1.0
number % harmonic mean diameter, m 0.9
median diameter, m 0.8
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Cumulative distribution
particle diameter (dp), m
0 100 200 300 400 500 600
weigh
t%
withadiametersmallerthandp
0
10
20
30
40
50
60
70
80
90
100
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Differential distribution
particle diameter (dp), m
0 100 200 300 400 500 600
derivative,wt%
/m
0.0
0.1
0.2
0.3
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Relationship between number and
weight distributions
Use Excel (or FBMODX)
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Combining two particle size
distributions of the same sample
For example, two measurement techniques
may provide the size distribution of asample for 2 different ranges of particle size
The easiest way is to use the cumulative
distribution
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Theoretical size distribution
functions
Useful for smoothing and interpolation
Do notuse for extrapolation
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Normal or gaussian distribution
p
2
pi pam2
d
p pi0
d dexp2
F(d ) d(d )
2
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Log-normal distribution
F d
d
d
d dd
p
pi
plm
g
g
pi
pi
dp( )
expln
ln
ln
( )
2
2
0
2
2
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Rosin-Rammler distribution
s
pp daexp1)d(F
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Weibul distribution
pm
minpp
d
ddX
Xexp1dF p
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Normal paper
If the distribution is gaussian, thecumulative distribution
will plot as a straight line
particle diameter (dp), m
0 100 200 300 400 500 600
weight%withadiametersmaller
thandp
0.001
0.01
0.1
1
10
30
50
70
90
99
99.9normal probability paper
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Log-normal paper
If the distribution is log-normal, thecumulative distribution
will plot as a straight line.
particle diameter (dp), m
1 10 100
weight%w
ithadiametersmalle
rthandp
0.001
0.01
0.1
1
10
30
50
70
90
99
99.9log-normal probability paper
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Particle size measurement
Accurate sampling is a crucial operation: moreerrors can be attributed to sampling than to theactual size analysis.
The two "golden rules of sampling" (Allen):
1) "a powder should be sampled while in motion" (toprevent segregation in non- moving powders)
2) "the whole of the stream should be taken for manyshort increments of time in preference to part of the
stream being taken for the whole of the time"(segregation).
With fine particles, sample dispersion is alsoimportant.
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Particle size measurement
i l i
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Particle size measurement
i l i
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Particle size measurement
Various methods:
1) Sieving: usually for dp> 50 m
2) Sedimentation or centrifugation in a liquid
3) Centrifugation in a gas
4) Elutriation
5) Impaction
6) Electrical conductivity7) Light scattering and blockage
8) Image analysis
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Sieving
Si i
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Sieving
Si i
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Sieving
time consuming shaking duration must be long enough to prevent
large errors
cannot be used with solids which attrit oragglomerate easily
if angular particles, does not give volume-equivalent diameter
Sieving results are often reported in terms of meshnumbers: a large mesh number means a small
particle size
Li h i
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Light scattering
The most popular technique
Measures the projected area of the particles and
thus provides the volume-equivalent diameterwhen the measurement cell is designed so as to
present the particles in a random orientation
Measures particle diameters from 0.5 to 3000 m
Both dry and wet measurements
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Dry methods: screening,elutriation,centrifugation in a gas, impaction, light
scattering
A frequent problem with these methods:
Particle-particle agglomeration due to Van der
Waals or electrostatic forces
Prevalent for small particles (high surface/volume)
Additives can help
h d
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Wet methods:sedimentation/centrifugation, electrical
conductivity, light scattering
Particle-particle agglomerates can be broken apartby a combination of surfactant additives and
ultrasonic vibrations
Surfactants may also promote agglomeration
Ultrasonic vibrations may promote agglomeration
or break particles
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Outline
1 Introduction
2 Particle density
3 Particle size
4 Particle shape
5 Adhesion of particles
6 Dustiness
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4. Particle shape
Introduction
Various shape factors
Shape factors from direct shape characterization
Shape factors from particle-fluid interactions
Shape factors from product quality tests
Measurement of particle shape
P ti l h l
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Particle shape: examples
- inks, paints, cosmetics: flaky particles cover morearea
- abrasives: better if highly angular
- fibers for plastics reinforcement: elongated forgood impact strength.
- rubber grains: must be round for good tensile
strength (otherwise, grains would align along onedirection and eventually tear)
- perfectly spherical particles have a smoother feelattractive for cosmetic applications
Shape factors from direct shape
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Shape factors from direct shape
characterization
Usually from image analysis
Example: for each particle, draw diameters
through its center of gravity, 30 degrees apart,and take the ratio of the smallest to the largestof these diameters
surface area of sphere with the same volume as the particle
actual surface area of the particle
Particle sphericity:
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Shape factors from particle-fluid
interactions
Many shape factors based on measured
particle-fluid interactions
See the chapter on Particulate-Fluid
interactions
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Shape factors from product
quality tests Flakiness index
round particles:
"flaky" particles:
Angularity index: based on Hausner ratio:
Angular particles are more cohesive
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Outline
1 Introduction
2 Particle density
3 Particle size
4 Particle shape
5 Adhesion of particles
6 Dustiness
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5. Adhesion of particles
Adhesion of particles on other particles or
on a flat surface may be very important forsome processes
There are very few techniques to
characterize such adhesion (e.g. theturntable)
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Outline
1 Introduction
2 Particle density
3 Particle size
4 Particle shape
5 Adhesion of particles
6 Dustiness
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6. Dustiness
filter
solidssample
suction
dust