Particle technology tutorial

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Week # 1MR Chapter 1

Tutorial #1 MR #1.1, 1.4, 1.7.

To be discussed on Jan. 232013.

By either volunteer or class list.

MARTIN RHODES (2008) Introduction to Particle

Technology , 2nd Edition.Publisher John Wiley & Son,Chichester, West Sussex,England.


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Describing the size of asingle particle. Some

terminolgy aboutdiameters used inmicroscopy.

Equivalent circlediameter.

Martins diameter.

Ferets diameter.

Shear diameter.


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Describing the size of a single particle

Regular-shaped particles

The orientation of the particle on themicroscope slide will affect the

projected image and consequently themeasured equivalent sphere diameter.

Sieve measurement: Diameter of a

sphere passing through the same sieveaperture.

Sedimentation measurement:Diameter of a sphere having the samesedimentation velocity under thesame conditions.

Comparison of equivalent sphere diameters.


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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.


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Description of populations of particles

Typical differentialfrequency distribution

( )dF f xdx

=F: Cumulative distribution,integral of the frequency distribution.


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Typical cumulative frequency distribution


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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 oftendivide the size spectrum into sizeranges, and size distribution becomesa histogram.


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Conversion between distributions

Mass and number distributions for man-made objects orbiting the earth


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Total number of particles, N and total surface area Sare constant.Particle shape is

independent of size, s is constant.

V is the total volume of the particle population and v isthe factor relating the linear dimension of particle to its

volume.


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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 theconversions. 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 therequired distribution.


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Describing the population by a single number

Definitions of means


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Plot of cumulative frequency against weighting functiong(x). Shaded area is

Number-length mean: Arithmeticmean of the number distributionconserves the number and lengthof population.


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Comparison between measures of central tendency. Adapted fromRhodes (1990).

Surface-volume mean, Sauter mean: Arithmetic mean of surfacedistribution conserves the surfaceand volume of population.

The values of the differentexpressions of central tendencycan vary significantly.

Two quite different distributionscould have the same arithmeticmean or median.


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Equivalence of means

K s and K v do not vary with siz e

2

s s N dF x k dF =

Same Expression


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Common methods of displaying sizedistributions

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, z: standard deviation of log x


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Log-normal distribution plotted on linear coordinates

Log-normal distribution plotted on logarithmic coordinates


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Methods of particle size measurements:

Sieving Sieving: Dry sieving using woven wire sieves is

appropriate for particle size greater than 45 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 fourthroot of two (e.g. 45, 53, 63, 75, 90, 107 m).


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Methods of particle size measurements:

Microscopy The optical microscope may be used to measure particle

size down to 5 m. The electron microscope may be used for size analysis

below 5 m. Coupled with an image analysis system, the optical and

electron microscopy can give number distribution of sizeand shape.

For irregular-shaped particles, the projected area offered tothe viewer can vary significantly. Technique (e.g. applyingadhesive to the microscope slide) may be used to ensurerandom orientation .


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Methods of particle size measurement

Sedimentation

Size analysis by sedimentation

Re p


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Permeametry

Co: 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 willhave fallen below the sampling point.

C represents the suspension density for all particleswhich travel at a velocity


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Electrozone sensing

Schematic of electrozone sensing apparatus

As particle flow throughthe orifice,a voltage pulse is recorded.

The amplitude of the pulsecan be related to thevolume of particle theorifice.

Particle range:

0.3-1000 m.


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Particle technology tutorial