Particle size analysis

advertisement
UEMK3223
Introduction to Particle Technology
DR. SIM LAN CHING
Email: [email protected]
Office: KB 804
Assessment System and Breakdown of Marks
• Course Work Assignments : 20%
• Tests, Mid-term : 20%
• Final Examination 60%
Important Date
• Teaching: Week 1,4 &5 (Dr Sim)
Week 2,3,6 & 7 (Dr Lim)
• Tutorial 1 to be covered by Prof. Tee on week 2.
Tutorial 2 to be covered by Dr. Lim on week 3.
Tutorial 3 to be covered by Dr. Steven on week 4
Tutorial 4 to be covered by Dr. Lee Tin Sin on week 5
Tutorial 5 to be covered by Prof. Tee on Week 6.
Tutorial 6 to be covered by Dr. Lee on Week 7.
• Assignments : TBA by Dr Lim
• Mid-term : Week 5 (13/11 – Tues)
References
Main References:
•McCabe, W. L., Smith, J. C. & Harriott, P. (2005). Unit operations of
chemical engineering. (7th ed.). Mc-Graw Hill. (ISBN : 0-07-118173-3)
•Rhodes, M. (2008). Introduction to particle technology. (2nd ed.).
Wiley (ISBN : 978-0-470-01428-8)
Additional References:
• Perry, R. H. & Green, D.W. (1998). Perry’s chemical engineers’ handbook.
(7th ed.). McGraw-Hill International Editions. (ISBN: 0-07-115982-7)
• Geankoplis, C. (2003). Transport processes and separation process
principles. (4th ed.). Prentice Hall PTR. (ISBN : 0-13-101367-X)
• Online Journals and documents
Objective of Unit:
Acquire knowledge related to particle technology including
• Particle characterisation, and
• Particle interactions in different types of fluids
• in order to identify and solve problems arising when handling particular
material.
Learning Outcome of Unit:
By the end of this unit, students should be able to:
1. Determine the properties of solids.
2. Analyse storage, conveying, transport and mixing of solids in fluid
systems.
3. Assess particle size reduction and enlargement systems.
4. Evaluate separation systems for solid from gases and liquids using
screening, filtration and sedimentation methods.
5. Design solid handling equipments.
What is Particle?
•
Nobody knows!!!
• "Everything is a particle!" - Wallace H. Coulter
What is Particle?
• Simple Definition of PARTICLE
• a very small piece of something
• a very small amount of something
• Physics : any one of the very small parts of matter (such as a
molecule, atom, or electron)
Particle
Why do we study Particles?
•The first is the interfacial properties of particulate systems.
•Applied in paints, coatings, catalysts, taste and texture, dessicants,
adsorbents, rapid dissolution, abrasives, cutting tools, composite
materials, ceramics and powder metallurgy.
•The second quality is that materials in particulate form:
Example: powders, slurries, droplets, emulsions can often be handled,
transported and processed with greater ease and economy than the
same materials in bulk forms.
•The third quality arises, as particles get so small that their size
approaches molecular dimensions
http://perc.ufl.edu/particle.asp
What is Particle Technology?
• Techniques for processing and handling particulate solids
Why we need to learn Particle Technology?
• Most chemical engineers will find themselves working with particles
at some point in their professional life
Subjects of particle technology
• Chemical engineers meet particulate solids in carrying out many unit
operations
•
•
•
•
•
•
Bulk storage,
Crushing and grinding,
Filtration.
Crystallization
Solid Fluid Reaction
Particle size separation, such as
• sieving, tabling, flotation,
• Qualitative separation such as
• Magnetic separation, and/or electrostatic recipitation,
• Fluidization, flocculation, Centrifugal separation, Liquid filtration, particle size
analysis, powder metallurgy,
• Nanotechnology, particle characterization by shape, and others.
Describing the size of a single particle
Regular-shaped particles
Shape
Sphere
Cube
Cylinder
Cuboid
Cone
Dimensions
Radius
Side length
Radius and
height
Three side
lengths
Radius and
height
Irregular-shaped particles
• No single physical dimension can adequately describe the
particle
• Describing the size of a single particle. Some terminology
about diameters used in microscopy to be used
Laboratory method for particle size
measurement
Method
Approximate Size
(μm)
Gravity Sedimentation 2-100
Type of Size
Distribution
By Mass
Microscopy
• Optical
• Electron
0.8-150
0.001-5
By Number
Sieving
37-4000
By Mass
Size Terminology
µm
µm
µm
µm
Unit
• Coarse particles: inches or
millimeters
• Fine particles: screen size
• Very fine particles: micrometers
or nanometers
• Ultra fine particles: surface area
per unit mass, m2/g
Characterization of Solid Particles
Which Size can be measured?
• Individual solid particles are characterized by their size, shape, and
density
oDiameter of a sphere which has the same property as the particle itself –
that is the same volume, same settling velocity, etc.
oDiameter of a circle which has the same property and the projected outline
of the particle – that is the same projected area or same perimeter.
oLinear dimension measured parallel to a particular direction.
• Equivalent circle diameter.
(projected area diameter (area of
circle with same area as the
projected area ))
•
Martin’s diameter
(length of the line which bisects the
particle image)
• Feret’s diameter.
(distance between two tangents on
opposite sides of the particle)
• Shear diameter.
(particle width obtained using an
image shearing device)
Equivalent Diameters
1) The sphere of the same volume as the particle
1
3
6 
Volume-equivalent sphere diameter, xv   Vp 
π 
where Vp is the volume of the particle
2) The sphere of the same surface area as the particle1
2
 6  1/2
Surface-equivalent sphere
diameter,
xS  =Sp 
Surface-equivalent
sphere
diameter,
 π 
where Sp is the surface of the particle
3) The sphere of the same surface area per unit volume as
the particle
     ℎ
6
=
=
  
  ℎ

Example 1
Particle Distribution
Description of populations of particles
Description of populations of particles
Description of populations of particles
Description of populations of particles
Typical differential frequency distribution
Typical cumulative frequency distribution
• Frequency distribution and cumulative are related
mathematically
• Cumulative distribution denoted by F, frequency distribution
dF
is written as
 f ( x)
dx
• Distributions can be by number, surface, mass or volume.
Description of populations of particles
D[1,0] =
D[2,0] =
1
 0 (  )
2
 0 (  )
If you are catalyst engineer and want
to compare these spheres on the basis
of surface area because higher surface
area, higher activity of catalyst. Thus,
2

mean diameter =
No. particles is
inherent in
formulae.
Give rise the
need to count
large numbers
of particles
Thus can use,
If you want to compare these spheres
4
on the basis of weight (  3 ). Thus,
D[3,0] =
3
 0 (  )
3
mean diameter =
3
3

D [4,3] – usually
used in laser
diffraction
D [3,2]
Description of populations of particles
Distributions can be by number, surface, mass or volume.
1+4+9
Test Your Understanding, use D[1,0]……..or
D[4,3] ??
• If we have a process stream we are not interested that there are 3.5
million particles in it, we are more interested that there is 1 kg or 2 kg
of gold.
• If you are in clean room making wafers of silicon or gallium arsenide.
Here if one particle lands on our wafer it will tend to produce a
defect.
Description of populations of particles
Description of populations of particles
v
v
Assume  
   3
100
40
80
Volume (%)
Number (%)
30
20
10
60
40
20
0
0
1
2
Size (nm)
3
1
2
Size (nm)
3
Description of populations of particles
 It’s important to select suitable method of measurement which
directly gives particle size which is relevant to situation
 Consequences of interconversion between number, length and
volume/mass means
Imagine that our electron measurement technique is subject to an error of
± 3%  ℎ  .
When we convert the number mean size to a mass mean size then as the mass
mean is a cubic function of the diameter then our errors will be cubed or
± 27%   ℎ  
Description of populations of particles
• Cumulative distribution denoted by F, frequency distribution is written as
dF
 f ( x)
dx
Typical cumulative frequency distribution




fN(x) is the frequency distribution by number
fS(x) is the frequency distribution by surface
FS is the cumulative distribution by surface
FM is the cumulative distribution by mass
Comparison between distributions
Fraction of number
Fraction of volume
Conversion between distributions
Fraction of particles in the size range
x to x+dx = f N ( x)dx
• Cumulative distribution
denoted by F, frequency
distribution is written as
dF
 f ( x)
dx
Fraction of the total surface of particles in the size range
x to x+dx = fS ( x)dx
Assume N is the total number of particles in the population,
The number of particles in the size range
Typical cumulative frequency
distribution
x to x+dx = N f N ( x)dx
Surface area of these particles =  2    
where S is the factor relating linear dimension of particle to its surface area.
The fraction of the total surface area contained on these particles [ f S ( x)dx] is
 2    

where S is the total surface area of the population of particles.
For a given population of particles :
1)
2)
Total number of particles, N and total surface area S are constant.
Assume particle shape is independent of size, so s is constant.
where V is the total volume of the
population of particles and  is the
factor relating the linear dimension
of the particle to its volume.
Example 2
Describing the population by a single number
• Definitions of means
where x is the mean and g is the weighting function.
weighting function is different for each mean definition.
Plot of cumulative frequency against weighting function g(x).
Shaded area is
Comparison between measures of central tendency.
Adapted from Rhodes (1990).
Comparison of the valuea of
different means and mode
and median for a given
particle size distribution
highlights :
1) The values of the different
expressions of central
tendency can vary
significantly.
2) Two quite different
distributions could have
the same arithmetic mean
or median.
Equivalence of Means
Means of different distributions can be equivalent
Arithmetic mean of a surface distribution,
_
The harmonic mean xhV of a volume
distribution is defined as
Same
Expression
Relationship between surface and volume
Surface-volume
mean can be
calculated as
then,
Recalling,
dFs  x2ksdFN
then,
Note : Ks and Kv do not vary with size
1)
2)
the arithmetic mean of the surface distribution, or
the harmonic mean of the volume distribution
Common methods of displaying size distributions
Arithmetic-normal Distribution
Log-normal Distribution
z  log x
z: Arithmetic mean of z,
sz: standard deviation of log x
Arithmetic-normal distribution
with an arithmetic mean of 45
and standard deviation of 12.
Log-normal distribution plotted on
linear coordinates
Log-normal distribution plotted
on logarithmic coordinates
Methods of particle size measurements
Sieving
• Dry sieving using woven wire sieves is a simple, cheap method of size analysis
• Suitable for particle sizes greater than 45 μm. Sieving gives a mass distribution and a size known as the sieve
diameter.
• Since the length of the particle does not hinder its passage through the sieve apertures (unless the particle is
extremely elongated), the sieve diameter is dependent on the maximum width and maximum thickness of
the particle.
• The most common modern sieves are in sizes such that the ratio of adjacent sieve sizes is the fourth root of
two (eg. 45, 53, 63, 75, 90, 107 μm).
• Air jet sieving, in which the powder on the sieve is fluidized by a jet or air, can achieve analysis down to 20
μm.
• Analysis down to 5 μm can be achieved by wet sieving, in which the powder sample is suspended in a liquid.
Microscopy
• The optical microscope may be used to measure particle size
down to 5 mm.
• The electron microscope may be used for size analysis below 5
mm.
• Coupled with an image analysis system, the optical and electron
microscopy can give number distribution of size and shape.
• Such systems calculate various diameters from the projected
image of the particles (e.g. Martin’s, Feret’s, shear, projected
area diameters, etc.).
• For irregular-shaped particles, the projected area offered to the
viewer can vary significantly. Technique (e.g. applying adhesive
to the microscope slide) may be used to ensure “random
orientation”.
Laser Diffraction
How Laser Diffraction Works?
• When light passing through a suspension, the diffraction angle is inversely
proportional to the particle size.
• An instrument consist of a laser as a source of coherent light of known fixed
wavelength (typically 0.63 μm), a suitable detector (usually a slice of
photosensitive silicon with a number of discrete detectors, and some means of
passing the sample of particles through the laser light beam (techniques are
available for suspending particles in both liquids and gases are drawing them
through the beam).
• This method gives a volume distribution and measures a diameter known as the
laser diameter.
• Particle size analysis by laser diffraction is very common in industry today. The
associated software permits display of a variety of size distributions and means
derived from the original measured distribution.
Permeametry
1) Size analysis method based on fluid flow through
a packed bed.
2) Carmen-Kozeny equation for laminar flow through
packed bed of uniformly sized spheres of
diameter x
where  -p is the pressure drop across the bed
  is the porosity
 U is the superficial fluid velocity.
where:
• is the total height of the bed;
• is the superficial or "empty-tower" velocity;
• is the viscosity of the fluid;
• is the porosity of the bed;
• x is the sphericity of the particles in the packed bed;
• D is the diameter of the related spherical particle U = v/D2
Example 3
1.28 g of a powder of particle density 2500 kg/m3 are charged into the
cell of an apparatus for measurement of particle size and specific
surface area by permeametry. The cylindrical cell has a diameter of 1.14
cm and the powder forms a bed of depth 1 cm. Dry air of density 1.2
kg/m3 and viscosity 18.4 x 10-6 Pa s flows at a rate of 36 cm3/min
through the powder (in a direction parallel to the axis of the cylindrical
cell) and producing a pressure difference of 100 mm of water across the
bed. Determine
(i) the surface-volume mean diameter [20.08 mm]
(ii) the specific surface of the powder sample [119.5 m2/kg]
Electrozone sensing
As particle flow through the orifice, a voltage pulse is
recorded.
The amplitude of the pulse can be related to the
volume of particle the passing orifice.
By electronically counting and classifying the pulses
according to amplitude this technique can give a
number distribution of the equivalent volume sphere
diameter.
Particle range: 0.3-1000 mm.
Errors if more than 1 particle passes through the
orifice at a time.
Sedimentation
Sedimentation
Assumptions:
1. The suspension is sufficiently dilute for the
particles to settle as individuals (i.e. not hindered
settling).
2. Motion of the particles in the liquid obeys Stokes’
law (true for particles typically smaller than 50 μm).
3. Particles are assumed to accelerate rapidly to their
terminal free fall velocity UT so that the time for
acceleration is negligible.
All particles travel at terminal velocity
defined by Stokes’ law
UT = h/t,
thus
Download
Related flashcards
Create Flashcards