particle size analysis-2011
TRANSCRIPT
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Dr Ali Nokhodchi
PARTICLE SIZEANALYSIS
-Particle shape
-Particle size distribution
-Particle size measurements
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Particle size Analysis
Primary characteristics, relating tobasic material properties, particulate size,shape and surface area
Secondary characteristics, behaviouralproperties such as flow, bulk and tappeddensity, compactibility, lubricity
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The ideal particle and reality
Sol id Sphere
One dimension (radius) describessize, shape, surface area, volume
Sol id Geometr ical Part ic les
Two-three dimensions required todescribe size, shape, surface area,
volume
r
r
hh
h
wl r
Solid Irregu lar Partic lesSize and shape can only be
approximated, surface area and
volume can be measured
Porou s Irregular Part ic lesSize, shape, surface area and
volume can only be approximated
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Particle Shape TerminologyAcicular: needle-shaped
Angular : sharp edged; having a roughly polyhedral shape
Dendritic: having a branched crystalline shape
Fibrous: thread-likeFlaky : plate-like
Granular : irregular but of approximately spherical overall form
Irregular : lacking any symmetry
Modular : having a rounded, irregular shape
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Particle shape
The thickness is the height of the particlewhen it is resting in its position of maximumstability.
The breadth is the minimum distance betweentwo tangential planes which are perpendicular
to those defining the thickness and breadth.
The length is the distance between two planeswhich are perpendicular to those defining thethickness and breadth.
x
yz
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Shape factors
Elongation ratio = length/breadth
Flakiness ratio = breadth/thickness
Bulkiness factor= projected area/(length xbreadth)
The ratio of two equivalent diameters obtained by differentmethods is termed a shape factor.
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Circularity
Circumscribed circle (dc)
Inscribed circle (di)
dc=10 mmdi= 1 mm
Circularity=0.1
dc=10 mmdi= 5 mmCircularity=0.5
P i l i i fl di l i
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Particle size influences dissolution
DissolutionSmall particles dissolves more rapidly than larger ones.
Drug in Solid
Dosage Form
Drug Crystals
Exposed to GI Fluids
Drug Dissolved
In GI Fluids
Drug in
Blood
Dissolution Absorption
Release from
Dosage Form
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Particle size effect on bioavailability of a poorly
soluble drug
Particle sizedissolution rate ?Bioavailability ?
Other examples:
Tetracycline
Aspirin
Sulphonamides
Digoxin
Dicoumarol
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1 g
1 cm
1 cm
1 cmSurface area = area/face 6 faces = 6 cm2
Weight-specific surface area = Sw = [surface area/weight]
Therefore , Sw = 6 cm2 /g
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The total surface area in 1 g is now: [1012 cubes][6 x 10-8 cm2/cube]
Sw = 6 104 cm2 = 60000 cm2
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Range of particle size and units
Pharmaceutical system usually are confined to anarrower size range
Most pharmaceutical systems lie in the range 1mm to 10 mm
Colloidal range is considered less than 1 mm 1 mm forms useful boundary since the properties
of colloidal materials are often very different tothose of coarser systems, and the techniquesused to study them are quite distinct from thoseused for larger particulates
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Individual particle characteristics
The way that we characterise the particles largely
depends on the technique used to measurethem.
The way that we measure a particle size is as
important as the value of the measured size. Forexample, how would you quantify yourself ifmeasured by
1) Circumference around your waist?
2) Diameter of a sphere of the same displacement
volume as your body? 3) Length of your longest chord (height)?
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As you can deduce, the measured values have different
meanings and wil l be important relative to those meanings. I f
you are sizing a li fe jacket belt you would be interested in the
f irst size (circumference around your waist). I f you are
buying a sleeping bag I suggest the last one (length of your
longest chord) .We have already been using a length to describeparticle size, with the intention that it indicatesthe distance from one side of the particle to itsopposite side.The description is unambiguous in the case of aspherical particle, example: emulsion droplet or
microsphere.
Measures of Particle size
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The ideal particle and reality
Sol id Sphere
One dimension (radius) describessize, shape, surface area, volume
Sol id Geometr ical Part ic les
Two-three dimensions required todescribe size, shape, surface area,
volume
r
r
hh
h
wl r
Solid Irregu lar Partic lesSize and shape can only be
approximated, surface area and
volume can be measured
Porou s Irregular Part ic lesSize, shape, surface area and
volume can only be approximated
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Particle sizing of powders
1 cm
1 cm
1 cm
Large, geometric objects:Size is described in three
dimensions (minimum)
Small, irregular particles:Three dimensional size
description is impractical,
only one dimension
(average diameter) is used.
1 m
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What is the diameter of this particle?
1
23
4
What should we do if the particle is irregular?
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Measures of Particle size
The problem can be solved by quoting theparticle size of a non-spherical particle asthe diameter of a sphere which is in some
way equivalent to the particle; such asphere is termed an equivalent sphereand the diameter is an equivalentdiameter.
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Measures of Particle size Example:
Weigh a particle
measure its density
Find the particle volume
The volume equivalent sphere is the spherewhich has the same volume as the irregularparticle, and is characterised by the volumeequivalent diameter.
Mass= 1gDensity=2 g/cm3
Volume= 0.5 cm3
V=(4/3)r3
0.5= (4/3) 3.14r3
R3= (0.5/4.19)=0.119r=0.49 cmDiameter = 0.98 cm
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r
h
r
h
r
h
Size of cylinder Aspect
ratio
Equivalent
spherical
diameter
(m)
Height
(m)
Diameter
(m)
20 20 1:1 22.9
40 20 2:1 28.8
100 20 5:1 39.1
For cylinder:
Radius= 10 m, h= 100 m
Volume of cylinder
Volume of cylinder = 3.14 (10)2x100
Volume of cylinder = 3.14 x 10000
Volume of sphere =
Volume of sphere =(4/3) 3.14 x r3
In equivalent assumption both volume
should be the same
(4/3) x 3.14 x r3 =3.14 x 10000
4r3 = 3x10000
r3= 30000/4
r3= 7500 r=19.5 diameter= 2 x r
diameter = 39.1 m
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Selected ESDs
da (the projected area diameter): the diameterof a sphere having the same projected area asthe particle in question
dv (the volume diameter) the diameter of a
sphere having the same volume as the particle ds (the surface diameter) the diameter of a
sphere having the same surface area as theparticle
dst (the stokes diameter) the diameter of a
sphere having the same density and free-fallvelocity in given fluid as the particle
dsieve (the sieve diameter) the diameter of asphere that is just able to pass through thesame square aperture as the particle
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Illustrations of equivalent diameters
dp da dv dsa dmass ds
xm/s2dst
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Selected EDSs (continued)
dF (Ferets diameter) the (mean) value betweenpairs of parallel tangents to the projected outlineof the particle
dM (Martins diameter) the (mean) chord lengthof the projected outline of the particle
dd (aerodynamic diameter) the diameter of asphere with the same viscous drag as a particlein a fluid at the same viscosity
dM1
dF1
dM2
dF2
dM3
dF3
* Ferets and Martins diameters are
taken from a statistical mean of
diameters measured from different
particle orientations.
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There are many different ways of defining equivalent
diameters. All of these diameters will generally be
different-unless the particle really is a sphere:
Projected area diameter da Projected perimeter diameter dp
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ESDs for a simple shape
Bear in mind that all equivalent diameters available to us will be differentfor a given irregular particle.
Select an equivalent diameter (and associated measurement technique)which is relevant to the property of the particle that we are interested in.
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To obtain a good description of the particle system, we must selectan equivalent diameter (and associated measurement technique)
which is relevant to the property of the particle in which we are
interested.
e.g. Paint pigment particles: Projected area diameter
measured by microscopy.
Aerosol deposition in the lungs: Aerodynamic diameter
measured by inertial impaction methods.
Sedimentation properties of the material: Stokesdiameter
Which equivalent diameter do you
use?
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Arithmetic mean
The mean value is the center of gravity of thedistribution. It is calculated using thefollowing equation:
1
21 2 3 4 5 6 7 8 9 10 11
6 6 6 6 6 6 6 6 6 6 6
Calculate the arithmetic mean for the particle populations 1 & 2.
Arithmetic Mean (d = ESD)
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Arithmetic Mean (d = ESD)
Number-length mean diameter which is
arithmetic mean of a number distribution
of length; D [1, 0]
1 m 3 m 5 m 8 m 10 m
Calculate the arithmetic mean for the above particle populations.
3x1 + 1x3 + 5x5 + 2x8 + 2x10 = 67Dav = [67/13] = 5.15 m
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Assume a simple situation of 10particles having the following length
(i.e., ESDs) in m :
1, 3, 3, 4, 5, 2, 2, 6.5, 6, 5
What are the arithmetic and geometric means?
Arithmetic
mean
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Geometric mean
Thegeometric mean is calculated using thefollowing equation:
Calculate the geometric mean for the particle populations 1 & 2.
1
21 2 3 4 5 6 7 8 9 10 11
6 6 6 6 6 6 6 6 6 6 6
Geometric Mean (d =ESD)
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Geometric Mean (d =ESD)
1 um 3 um 5 um 8 um 10 um
Calculate the geometric mean for the particle populations 1 & 2.
log dg = 1/12 x [3xlog1 + 1xlog3 + 4xlog5 + 2xlog8 + 2xlog10]log dg = 1/12 x [0 + 0.48 +2.80 + 1.81 + 2 ]log dg = 0.59
dg = 3.89 m
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Geometric mean
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Number Surface area mean diameter
D [2, 0]
Thesurface mean diameter (SMD) isthe calculated using the followingequation:
Calculate the SMD for the particle populations 1 & 2.
SMD = n1d12 + n2d22 + n3d32 + = nd
2
n n
where n1, n2, = number of particles in size
groups d1, d2 , and n is the total number
of particles (i.e., n1 + n2 + )
N b V l /M di
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Number-Volume/Mass mean diameter
D [3, 0]
The volume-number mean diameter is the diameter of a particle having
average weight (i.e. weight = volume density)
therefore, dnv is uniquely related to Nw, the specific particle number
VMD =n1d13 + n2d23 + n3d33 +
=nd3
n n
where n1, n2, = number of particles in size
groups d1, d2 , and n is the total number of
particles (i.e., n1 + n2 + )
3 3
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Volume-surface mean diameter; D [3, 2]
Surface area moment mean (Sauter mean diameter)
The volume surface mean diameter(VSMD) is calculated using the followingequation:
Calculate the VMD for the particle populations 1 & 2.
VSMD =n1d13 + n2d23 + n3d33 +
=nd3
where n1, n2, = number of particles in size
groups d1, d2
n1d12 + n2d22 + n3d32 + nd2
It is defined as the diameter of a sphere that has the samevolume/surface area ratio as a particle of interest
Typical statistics (d= ESD)
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Typical statistics (d= ESD)
d=(0.5 + 1)/2 = 0.75 m
nd = 2 x 0.75 = 1.5
nd2 = 2 x (0.75)2 = 1.13
nd3
= 2 x (0.75)3
= 0.85
dnl=265.5/118 = 2.25 m D[1, 0]
dns =(640.89/118)1/2 = 2.33 m D[2, 0]
dnv = (1645.25/118)1/3 = 2.41 m D[3, 0
dvs = 1645.25/640.89 = 2.57 m D[3, 2]
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Particle size distribution
A particle population which consists of spheres or equivalent
spheres with uniform dimensions is monosized and its
characteristics can be described by a single diameter or equivalent
diameter.
Unusual for the particles to be completely monosized in a batch:
most powders contain particles with a large number of different
equivalent diameters.
What do we do to compare the characteristics of two or more
powders consisting of particles with many different diameters?
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Particle size distribution
No. ofparticles
Particlesize (m)
No. ofparticles
Particle size(m)
50
50
Mean
5
15
10
10
10
10
mean
5
10
15
10
1
2
1 2 3 4 5 6 7 8 9 10 11
6 6 6 6 6 6 6 6 6 6 6
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Particle size distribution
We would not only want to know aboutthe characteristics of the average'particle, but have some idea of the
variation between the particles. Divide the data into size classes
Draw a histogram of the number of particles ineach size class.
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Particle size distributionsFrequency Distribution Data
ESD(m)
Number ofparticles
(frequency)
Per centparticles
(% frequency)
0-1 0 0
1-2 4 0.92-3 25 5.4
3-4 50 10.7
4-5 86 18.5
5-6 93 20.0
6-7 88 18.9
7-8 67 14.4
8-9 39 8.4
9-10 14 3.0
0
4
25
50
86
93
88
67
39
14
0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10 Frequency histogram
466
F(%) = (4/466) x100 = 0.9%
S h hi t
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Such a histogram:
- reflect the distribution of particle sizes.
- presents an interpretation of the particle size distribution.
- enables the percentage of particles having equivalent.
diameter to be determined.- allows different particle size distribution to be compared.
Normal: symmetrical about mean (+) skewed Bimodal
Commonly encountered distributions
% per mm
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Particle size [mm]
% per mm
% per mm
Particle size [mm]
Distributions may have apointed or rounded shape,
this is quantified as the kurtosis of the distribution.
A distribution which ispointedis termed leptokurtic.
A distribution which isflattenedis termedplatykurtic.
l b
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Particlesize[mm]
Numberofparticles
In band
Percentagein range
d
Percentageunder size
Percentageover size
1-2 4 0.86 99.14
2-3 25 5.36 93.78
3-4 50 10.73 16.95 83.05
4-5 86 18.45 35.40 64.6
5-6 93 19.96 55.36 44.646-7 88 18.89 74.24 25.76
7-8 67 14.38 88.62 11.38
8-9 39 8.37 96.99 3.01
9-10 14 3.00 100 0
%in range= (4/466)*100= %undersize=(0.86+5.36)=6.220.86
0.86
6.22
Total particles= 466
Less than 2 m
Larger than 2 m
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The graph shows, at any
size, what fraction of the
particles are smaller than
that size, and so is termed
apercentage undersize graph.
The two curves are
mirror images aroun
a horizontal axis.The graphs shows, at any
size, what fraction of theparticles are larger than
that size, and so termed
apercentage oversize graph.
Typical statistics (d = ESD)
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Typical statistics (d = ESD)
%n=(2/118)x100= 1.69
Cumulative undersize = 1.69+8.47=10.69=10.69+18.64=28.80
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Particle
size
(m)number of
particles
10 1
20 2
30 3
40 450 3
60 2
70 1
Plot Cumulative % undersize and oversize (number and massdistributions) against particle size. Determine the median ofeach distribution.
Question?
T th d f l tti di t ib ti
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Two methods of plotting distributions:
Incremental & cumulative
0
25
50
75
100
1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10
No. of particles
in band
Particle size [micrometers]
0
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10
Cumulative % undersize
Cumulative % oversize
Micrometers
The histogram is termed
an incrementaldistribution
because it shows how many
particles fall within a given
size increment.
A cumulat ivedistribution
shows how much material
lies above or below a
particular size.
Cumulative(%)
Incremental? C m lati e?
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Incremental? Cumulative?
Which to use?
Both are widely used, since various particle sizeanalysis methods lead to one or the other.
Examples:
Sieving: sorts out the material which issufficiently small to fall through one sieve, but toolarge to fall through a finer one, and so sorts theparticles into increments. Plotting this dataleads to an incremental distribution.
Sedimentation: where all the material largerthan a certain size has sedimented at a particulartime, naturally leads to a cumulativedistribution.
Representing the size distribution:
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Representing the size distribution:
Number, Area & Mass distributions
It is important to realise that, for aparticular sample of material, the curvesdescribing the distribution of particle
number, area, and mass will not beidentical in SHAPE.
One million 1 micrometer sphericalparticles will occupy the same volume as
one 100 micrometer (the number/volumerelationship)
V= 4/3r3
30
(1/10)x100 = 10%
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0
10
20
1 2 3 4 5 6 7 8 9 10
Particle s ize [micrometer]
%
Number distribution
Area distribution
Volume distribution
It is evident from this example that we need to specify which type of
distribution we are using.
The particular type of distribution obtained depends on thesizing method used.
- Sievingandsedimentation: provide the mass of material in a
given size band.
- Coulter counter: measure the number of particles in a given
band.
2 m
(1/10)x100 = 10%
Area = [(2)2/385]x100=1%
Total surface area for 10particles
Number of Particle size Surface Mass dist.
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Number ofparticles
Particle size(mm)
Surfacearea (mm2)
Mass dist.(mm3)
1
11
1
1
11
1
1
1
1
23
4
5
67
8
9
10
1
49
16
25
3649
64
81
100
?
?27
?
?
??
512
?
?
53
Total 10 particlesF(%) = (no. particles/total)x 100F (%) = (1/10)x 100 = 10%
Total surface area is 385F(%) = (surface area of 1st Particle/total)x 100F (%) = (1/385)x 100 = 0.26%
Total 10 particlesF(%) = (no. particles/total)x 100
F (%) = (1/10)x 100 = 10%
Total surface area is 385F(%) = (surface area of 1st Particle/total)x 100
F (%) = (100/385)x 100 = 26%
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Difference between number distribution and mass
distribution
Dr Ali Nokhodchi 54
% by number %by massSize (cm) Number of
objects
10-1000 7000 0.2 99.961-10 17500 0.5 0.03
0.1-1 3500000 99.3 0.01
Total 3524500 100 100
Number mean diameter =1.6 cm
Mass mean diameter = 500 cm
So, which one is correct or important?
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Characterization of particle size
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Characterization of particle size
distributions
Histograms contain a great amount of
data, which may be summarized by
statistics to yield a measure of:
Central tendency Dispersion
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Measures of central tendency
Central tendency = the tendency of the particle sizeto cluster around a particular value. Such values areevident as a peak in the particle size distribution.These values are normally known as averages ormeans of set of data.
Three different quantities are in common use:
1. Mode
2. Median
3. Mean
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Median
The median value is the size which splits thedistribution into two halves, with 50% of the mass orparticle number larger, and 50% of the mass or particlenumber smaller. It is always given the symbol D50.
The easiest way to find the D50 is to construct a
cumulative graph, from which the 50% point can beread off directly.
0
25
50
75
100
0 5 10 15 20 25 30 35 40 45 50 55
Cumulative
(%)
Particle size (um)
0
25
50
75
100
0 20 40 60
16 um
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Median
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Mode
The value of the peak of the distribution ( Themode of the distribution is the most commonvalue occurring in distribution). If the distributionhas two or more peaks, it is said to be bimodal
or multimodal.
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60
Particle size
Percentage/micron
Mode
Unimodal distribution
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Number of
Particles
particle size
(um) Frequency
(%)
Cumulative
under size(%)
Mean
diameter
3 50
5 100
10 150
20 200
25 250
20 300
10 350
5 400
2 450
1. Arithmetic mean?
2. Determine mode and median?
3. Plot Cumulative undersize against particle size?
4. Plot Frequency against particle size?
Span = D -D /D
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Span = D90% -D10%/D50%
Span for A= (340-20)/100Span A= 3.2
Span for B= (340-30)/150Span B = 2.1
2
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Model Distributions
Particle size distributions may take many forms,but there are small number of model distributionswhich are of particular interest.
may allow us to infer something about the
material or the processes through which it haspassed
Normal distribution
lognormal distribution
0 2CumulativeIncremental
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0
184%
50%
16%
3 5 7
Mean - Mean Mean +
Normal distribution with X=5 and s = 2.
0
0.2
The standard deviation is the difference between
the 16% and 50%, or the 50% and 84% points.
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Positively skewed
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Positively skewed
distribution
Normal
a: lognormal distribution with
Mode =5 and =2.
lognormal distribution of fig. a. plotted on a
logarithmic x axis.
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The lognormal distribution
Examples:
Particles reduced by grinding follow lognormal
distribution.-Emulsion made by valve homogenizer
Particles grown by crystallisation often show alognormal distribution of size.
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Normal and lognormal distributions on linear probability
paper.
Normal and lognormal distributions on log- probability
paper.
Number Cumulative
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Number
of Particle %frequency particle size
Cumulative
(%)
3 3 50 3
5 5 100 8
10 10 150 18
20 20 200 38
25 25 250 63
20 20 300 83
10 10 350 93
5 5 400 97
2 2 450 100
Total 100 100
Question? Determine the type of distribution.
99.99
Probability graph
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Particle size diameter (um)
99.9
99.8
99
98
95
90
80
70
60
50
4030
20
10
5
2
1
0.5
0.2
0.1
0.05
0.01
Cumulative
(%)
100 200 300 400 500 600 700 800 900 1000 1100
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Particle size diameter (um)
10 20 30 40 50 60 70 80 90 200 300 400 500 600 800 1000
100 700 900
99.99
99.9
99.8
9998
95
90
80
70
60
5040
30
20
10
5
2
1
0.5
0.2
0.1
0.05
0.01
Cumulative
(%)
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Techniques
Technique ESD Sizerange
Wet /dry
Manual /automatic
Speed
Sieving ds > 45
m
Dry /
wet
Manual Slow
Microscopy dp > 1nm
Dry /wet
Manual Slow
Sedimentation dst > 0.5
m
Wet Manual Medium
Coulter
counter
dv >0.1
m
Wet Automatic Fast
Laser light
scattering
dv,
da
> 1
nm
Wet Automatic Fast
Dry sieving
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y g
The results are expressed in the form of a cumulat ive und ersize
percentage distr ibu t ion.
Fill seal agitate weighStacking the sieves in order of ascending aperture size and placing thepowder on the top sieve and agitating, the powder is classified intofractions.A closed pan, a receiver, is placed at the bottom of the stack to collectthe fines and a lid is placed on top to prevent loss of powder.Agitation may be manual or mechanical.
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What does sieving measure?The sieve equivalent diameter(d
s) is defined as the size
of a sphere that will just pass through the aperture of a
particular sieve. This is a two-dimensional value.
ds ds
ds ds
Types of dry sieves
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Types of dry sieves
Punched sieves:
Usually circular, 1 mm to 10 cm apertures
Woven sieves:
Apertures are square, > ~50 m
This type of sieve was originally specified in terms of themesh number, which is the number of wires to the inchof mesh cloth; e.g. a 120 mesh sieve has 120 wires perinch.
Etched sieves:
Circular, finer sieves ( ~5 mm).
Remember!It i i t t t if th h f th i
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It is important to specify the shape of the sieve
mesh, i.e. square-meshed or round-hole.
Example:A 100 mm sphere will just pass through the hole of 100 mm
square or round-hole sieve, but an irregular particle may
pass through one sieve and not the other.
The part ic le wou ld have dif ferent sieve diameters (ds ) in
round o r square hole sieves!
In practice dry sieving is predominant
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p y g p
Sieving times:It is recommended that sieving be continued until less than 0.2%
of material passes a given sieve aperture in any 5-minute interval.
The material separated in the sieves is measured on a weight basis
providing a mass (or volume distribution). The results are usually
presented as a percentage mass against sieve equivalent diameter.
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Sieving time
90%
10 20
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Wet sieving
When?
Fine powder (
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When to use sieving
Sieving is a basic technique and is employed wheneverany of the following conditions, or combination ofthem, hold:
Separates fractions
Excellent method for powders with agood flowability
(coarse powders) Excellent method for powders that exhibit a range of
different densities (causes difficulties for sedimentationtechniques)
Excellent method for powders that exhibit different
refractive indices (causes difficulties for light scatteringtechniques)
Excellent method for water-soluble or conductivepowders (causes difficulties for Coulter countermeasurements).
Sieving is best avoided when:
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Sieving is best avoided when:
Cannot be used when powder is too fine Cannot be used when particles are fragile
and may break during sieving
Not an appropriate method for particles in
the form ofelongated needles Cannot be used when powder adheres to
the sieve
Cannot be used when powder forms
clumps Cannot be used when powder easily
acquires an electrostatic charge
Powder must be relatively robust
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Sieving errors may arise fromFactors influencing the probability that a particle will
correctly present itself at an aperture include:
Theparticle size distribution of the powder The number of particles on the sieve (load):A good
starting point is 50-100g for 100 mm sieves and 200g for200 mm sieves.
Thephysical properties of the particles (e.g., surface) The method of shaking the sieve The dimension and shape of the particles
Obtaining a correct size distribution during a sievingoperation also depends on the following variables:
Durat ionof sieving
Variation of sieve aperture