Week # 1
MR Chapter 1
•
Tutorial #1
•
MR #1.1, 1.4, 1.7.
•
To be discussed on Jan. 22
2014.
•
By either volunteer or
class list.
MARTIN RHODES (2008)
Introduction to Particle
Technology
, 2nd Edition.
Publisher John Wiley & Son,
Chichester, West Sussex,
England.
•
Describing the size of a
single particle. Some
terminolgy about
diameters used in
microscopy.
•
Equivalent circle
diameter.
•
Martin’s diameter.
•
Feret’s diameter.
•
Shear diameter.
Describing the size of a single particle
•
Regular

shaped particles
•
The orientation of the particle on the
microscope slide will affect the
projected image and consequently the
measured equivalent sphere diameter.
•
Sieve measurement: Diameter of a
sphere passing through the same sieve
aperture.
•
Sedimentation measurement:
Diameter of a sphere having the same
sedimentation velocity under the
same conditions.
Comparison of equivalent sphere diameters.
Comparison of equivalent diameters
•
The volume equivalent sphere diameter is a commonly used equivalent
sphere diameter.
•
Example: Coulter counter size measurement. The diameter of a sphere
having the same volume as the particle.
•
Surface

volume diameter is the diameter of a sphere having the same
surface to volume ratio as the particle.
Shape
Cuboid
Cylinder
(Example)
Cuboid: side lengths of 1, 3, 5.
Cylinder: diameter 3 and length 1.
Description of populations of particles
•
Typical differential
frequency distribution
( )
dF
f x
dx
F: Cumulative distribution,
integral of the frequency distribution.
•
Typical cumulative frequency distribution
•
Comparison between distributions
•
For a given population of particles,
the distributions by mass, number
and surface can differ dramatically.
•
All are smooth continuous curves.
•
Size measurement methods often
divide the size spectrum into size
ranges, and size distribution becomes
a histogram.
Conversion between distributions
•
Mass and number distributions for man

made objects orbiting the earth
•
Total number of particles, N and total surface area S
are constant.
•
Particle shape is
independent of size,
a
s
is constant.
V is the total volume of the
particle population and
a
v
is
the factor relating the linear
dimension of particle to its
volume.
dx
f
s
V
dx
x
Nf
x
dx
f
N
v
v
)
(
)
(
3
a
Assumptions for conversions among
different distribution functions
•
It is necessary to make assumptions about the
constancy of shape and density with size.
•
Calculation errors are introduced into the
conversions.
•
Example: 2% error in FN results in 6% error in
FM. (Recalling the relationship between mass and
diameter).
•
If possible, direct measurements be made with the
required distribution.
Describing the population by a single number
•
Definitions of means
•
Plot of cumulative frequency against weighting function
g(x). Shaded area is
Number

length mean: Arithmetic
mean of the number distribution
conserves the number and length
of population.
•
Comparison between measures of
central tendency. Adapted from
Rhodes (1990).
•
Surface

volume mean, Sauter
mean: Arithmetic mean of surface
distribution conserves the surface
and volume of population.
•
The values of the different
expressions of central tendency
can vary significantly.
•
Two quite different distributions
could have the same arithmetic
mean or median.
Equivalence of means
K
s
and K
v
do not vary with size
2
s s N
dF x k dF
Same Expression
Common methods of displaying size
distributions
Arithmetic

normal Distribution
Log

normal Distribution
log
z x
Arithmetic

normal distribution with an arithmetic mean of 45 and standard deviation of 12.
z: Arithmetic mean of z,
s
z
: standard deviation of log x
•
Log

normal distribution plotted on linear coordinates
•
Log

normal distribution plotted on logarithmic coordinates
Methods of particle size measurements:
Sieving
•
Sieving: Dry sieving using woven wire sieves is
appropriate for particle size greater than 45
m
m.
The length of the particle does not hinder it
passage through the sieve aperture.
•
Most common modern sieves are in sizes such that
the
ratio of adjacent sieve sizes is the fourth
root of two
(e.g. 45, 53, 63, 75, 90, 107
m
m).
Methods of particle size measurements:
Microscopy
•
The optical microscope may be used to measure particle
size down to 5
m
m.
•
The electron microscope may be used for size analysis
below 5
m
m.
•
Coupled with an image analysis system, the optical and
electron microscopy can give
number
distribution of size
and shape.
•
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
”.
Methods of particle size measurement
•
Sedimentation
•
Size analysis by sedimentation
•
Re
p
<0.3. Motion of the
particle obeys Stoke’s law.
•
The suspension is
sufficiently dilute (No
hindered settling).
•
Particles are assumed to
accelerate rapidly to their
terminal free fall velocity,
time for acceleration is
negligible.
•
Permeametry
C
o
: original uniform suspension density
.
Sampling point: C at time t after the start of settling.
At time t all particles traveling faster than h/t will
have fallen below the sampling point.
C represents the suspension density for all particles
which travel at a velocity <= h/t.
See Example 1.3
The diameter calculated from the Carman

Kozeny equation is the
arithmetic mean of the surface distribution.
•
Electrozone sensing
•
Schematic of electrozone sensing apparatus
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
orifice.
Particle range:
0.3

1000
m
m.
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