Introduction to Particle Technology
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Content
Preface to the Second Edition.
Preface to the First Edition.
Introduction..
1. Particle Size Analysis.
1.1 Introduction.
1.2 Describing The Size Of A Single Particle.
1.3 Description Of Populations Of Particles.
1.4 Conversion Between Distributions.
1.5 Describing The Population By A Single Number.
1.6 Equivalence Of Means.
1.7 Common Methods Of Displaying Size Distributions.
1.8 Methods Of Particle Size Measurement.
1.9 Sampling.
1.10 Worked Examples.
Test Yourself.
Exercises.
2. Single Particles in a Fluid.
2.1 Motion Of Solid Particles In A Fluid.
2.2 Particles Falling Under Gravity Through A Fluid.
2.3 Non-Spherical Particles.
2.4 Effect Of Boundaries On Terminal Velocity.
2.5 Further Reading.
2.6 Worked Examples.
Test Yourself.
Exercises.
3. Multiple Particle Systems.
3.1 Settling Of A Suspension Of Particles.
3.2 Batch Settling.
3.3 Continuous Settling.
3.4 Worked Examples.
Test Yourself.
Exercises.
4. Slurry Transport.
4.1 Introduction.
4.2 Flow Condition.
4.3 Rheological Models For Homogeneous Slurries.
4.4 Heterogeneous Slurries.
4.5 Components Of A Slurry Flow System.
4.6 Further Reading.
4.7 Worked Examples.
Exercises.
Test Yourself.
5. Colloids and Fine Particles.
5.1 Introduction.
5.2 Brownian Motion.
5.3 Surface Forces.
5.4 Result of Surface Forces on Behaviour in Air and Water.
5.5 Influences of Particle Size and Surface Forces on Solid/Liquid Separation by Sedimentation.
5.6 Suspension Rheology.
5.7 Influence of Surface Forces on Suspension Flow.
5.8 Nanoparticles.
5.9 Worked Examples.
Test Yourself.
Exercises.
6. Fluid Flow Through a Packed Bed of Particles.
6.1 Pressure Drop-Flow Relationship.
6.2 Filtration.
6.3 Further Reading.
6.4 Worked Examples.
Test Yourself.
Exercises.
7. Fluidization.
7.1 Fundamentals.
7.2 Relevant Powder And Particle Properties.
7.3 Bubbling And Non-Bubbling Fluidization.
7.4 Classification Of Powders.
7.5 Expansion Of A Fluidized Bed.
7.6 Entrainment.
7.7 Heat Transfer In Fluidized Beds.
7.8 Applications Of Fluidized Beds.
7.9 A Simple Model For The Bubbling Fluidized Bed Reactor.
7.10 Some Practical Considerations.
7.11 Worked Examples.
Test Yourself.
Exercises.
8. Pneumatic Transport and Standpipes.
8.1 Pneumatic Transport.
8.2 Standpipes.
8.3 Further Reading.
8.4 Worked Examples.
Test Yourself.
Exercises.
9. Separation of Particles From a Gas: Gas Cyclones.
9.1 Gas Cyclones - Description.
9.2 Flow Characteristics.
9.3 Efficiency Of Separation.
9.4 Scale-Up Of Cyclones.
9.5 Range Of Operation.
9.6 Some Practical Design And Operation Details.
9.7 Worked Examples.
Test Yourself.
Exercises.
10. Storage and Flow of Powders - Hopper Design.
10.1 Introduction.
10.2 Mass Flow And Core Flow.
10.3 The Design Philosophy.
10.4 Shear Cell Test.
10.5 Analysis Of Shear Cell Test Results.
10.6 Summary Of Design Procedure.
10.7 Discharge Aids.
10.8 Pressure On The Base Of A Tall Cylindrical Bin.
10.9 Mass Flow Rates.
10.10 Conclusions.
10.11 Worked Examples.
Test Yourself.
Exercises.
11. Mixing and Segregation.
11.1 Introduction.
11.2 Types Of Mixture.
11.3 Segregation.
11.4 Reduction Of Segregation.
11.5 Equipment For Particulate Mixing.
11.6 Assessing The Mixture.
11.7 Worked Examples.
Exercises.
12. Particle Size Reduction.
12.1 Introduction.
12.2 Particle Fracture Mechanisms.
12.3 Model Predicting Energy Requirement And Product Size Distribution.
12.4 Types Of Comminution Equipment.
12.5 Worked Examples.
Test Yourself.
Exercises.
13. Size Enlargement.
13.1 Introduction.
13.2 Interparticle Forces.
13.3 Granulation.
13.4 Worked Examples.
Exercises.
14. Health Effects of Fine Powders.
14.1 Introduction.
14.2 The Human Respiratory System.
14.3 Interaction of Fine Powders with the Respiratory System.
14.4 Pulmonary Delivery of Drugs.
14.5 Harmful Effects of Fine Powders.
Test Yourself.
Exercises.
15. Fire and Explosion Hazards of Fine Powders.
15.1 Introduction.
15.2 Combustion Fundamentals.
15.3 Combustion In Dust Clouds.
15.4 Control Of The Hazard.
15.5 Worked Examples.
Test Yourself.
Exercises.
16. Case Studies.
16.1 Case Study 1.
16.2 Case Study 2.
16.3 Case Study 3.
16.4 Case Study 4.
16.5 Case Study 5.
16.6 Case Study 6.
16.7 Case Study 7.
16.8 Case Study 8.
Notation.
References.
Index.
1
Particle Size Analysis
1.1 INTRODUCTION
In many powder handling and processing operations particle size and size distribution play a key role in determining the bulk properties of the powder. Describing the size distribution of the particles making up a powder is therefore central in characterizing the powder. In many industrial applications a single number will be required to characterize the particle size of the powder. This can only be done accurately and easily with a mono-sized distribution of spheres or cubes. Real particles with shapes that require more than one dimension to fully describe them and real powders with particles in a range of sizes, mean that in practice the identification of single number to adequately describe the size of the particles is far from straightforward. This chapter deals with how this is done.
1.2 DESCRIBING THE SIZE OF A SINGLE PARTICLE
Regular-shaped particles can be accurately described by giving the shape and a number of dimensions. Examples are given in Table 1.1.
The description of the shapes of irregular-shaped particles is a branch of science in itself and will not be covered in detail here. Readers wishing to know more on this topic are referred to Hawkins (1993). However, it will be clear to the reader that no single physical dimension can adequately describe the size of an irregularly shaped particle, just as a single dimension cannot describe the shape of a cylinder, a cuboid or a cone. Which dimension we do use will in practice depend on (a) what property or dimension of the particle we are able to measure and (b) the use to which the dimension is to be put.
If we are using a microscope, perhaps coupled with an image analyser, to view the particles and measure their size, we are looking at a projection of the shape of the particles. Some common diameters used in microscope analysis are statistical diameters such as 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) and shear diameter (particle width obtained using an image shearing device) and equivalent circle diameters such as the projected area diameter (area of circle with same area as the projected area of the particle resting in a stable position). Some of these diameters are described in Figure 1.1. We must remember that the orientation of the particle on the microscope slide will affect the projected image and consequently the measured equivalent sphere diameter.
Table 1.1 Regular-shaped particles
Figure 1.1 Some diameters used in microscopy
Figure 1.2 Comparison of equivalent sphere diameters
If we use a sieve to measure the particle size we come up with an equivalent sphere diameter, which is the diameter of a sphere passing through the same sieve aperture. If we use a sedimentation technique to measure particle size then it is expressed as the diameter of a sphere having the same sedimentation velocity under the same conditions. Other examples of the properties of particles measured and the resulting equivalent sphere diameters are given in Figure 1.2.
Table 1.2 compares values of these different equivalent sphere diameters used to describe a cuboid of side lengths 1, 3, 5 and a cylinder of diameter 3 and length 1.
The volume equivalent sphere diameter or equivalent volume sphere diameter is a commonly used equivalent sphere diameter. We will see later in the chapter that it is used in the Coulter counter size measurements technique. By definition, the equivalent volume sphere diameter is the diameter of a sphere having the same volume as the particle. The surface-volume diameter is the one measured when we use permeametry (see Section 1.8.4) to measure size. The surface-volume (equivalent sphere) diameter is the diameter of a sphere having the same surface to volume ratio as the particle. In practice it is important to use the method of size measurement which directly gives the particle size which is relevant to the situation or process of interest. (See Worked Example 1.1.)
Table 1.2 Comparison of equivalent sphere diameters
1.3 DESCRIPTION OF POPULATIONS OF PARTICLES
A population of particles is described by a particle size distribution. Particle size distributions may be expressed as frequency distribution curves or cumulative curves. These are illustrated in Figure 1.3. The two are related mathematically in that the cumulative distribution is the integral of the frequency distribution; i.e. if the cumulative distribution is denoted as F, then the frequency distribution dF/dx. For simplicity, dF/dx is often written as f(x). The distributions can be by number, surface, mass or volume (where particle density does not vary with size, the mass distribution is the same as the volume distribution). Incorporating this information into the notation, fN(x) is the frequency distribution by number, fS(x) is the frequency distribution by surface, FS is the cumulative distribution by surface and FM is the cumulative distribution by mass. In reality these distributions are smooth continuous curves. However, size measurement methods often divide the size spectrum into size ranges or classes and the size distribution becomes a histogram.
Figure 1.3 Typical differential and cumulative frequency distributions
Figure 1.4 Comparison between distributions
For a given population of particles, the distributions by mass, number and surface can differ dramatically, as can be seen in Figure 1.4.
A further example of difference between distributions for the same population is given in Table 1.3 showing size distributions of man-made objects orbiting the earth (New Scientist, 13 October 1991).
The number distribution tells us that only 0.2% of the objects are greater than 10 cm. However, these larger objects make up 99.96% of the mass of the population, and the 99.3% of the objects which are less than 1.0 cm in size make up only 0.01% of the mass distribution. Which distribution we would use is dependent on the end use of the information.
1.4 CONVERSION BETWEEN DISTRIBUTIONS
Many modern size analysis instruments actually measure a number distribution, which is rarely needed in practice. These instruments include software to convert the measured distribution into more practical distributions by mass, surface, etc.
Table 1.3 Mass and number distributions for man-made objects orbiting the earth
Relating the size distributions by number, fN(x), and by surface, fS(x) for a population of particles having the same geometric shape but different size:
Fraction of particles in the size range
Fraction of the total surface of particles in the size range
If N is the total number of particles in the population, the number of particles in the size range x to x + dx = NfN(x)dx and the surface area of these particles = (x2αS)NfN(x)dx, where αS is the factor relating the linear dimension of the particle to its surface area.
Therefore, the fraction of the total surface area contained on these particles [fS(x)dx] is:
where S is the total surface area of the population of particles.
For a given population of particles, the total number of particles, N, and the total surface area, S are constant. Also, assuming particle shape is independent of size, αS is constant, and so
where
Similarly, for the distribution by volume
where
where V is the total volume of the population of particles and αV is the factor relating the linear dimension of the particle to its volume.
And for the distribution by mass
where
assuming particle density ρp is independent of size.
The constants kS, kV and km may be found by using the fact that:
(1.4)
Thus, when we convert between distributions it is necessary to make assumptions about the constancy of shape and density with size. Since these assumptions may not be valid, the conversions are likely to be in error. Also, calculation errors are introduced into the conversions. For example, imagine that we used an electron microscope to produce a number distribution of size with a measurement error of ±2%. Converting the number distribution to a mass distribution we triple the error involved (i.e. the error becomes ±6%). For these reasons, conversions between distributions are to be avoided wherever possible. This can be done by choosing the measurement method which gives the required distribution directly.
1.5 DESCRIBING THE POPULATION BY A SINGLE NUMBER
In most practical applications, we require to describe the particle size of a population of particles (millions of them) by a single number. There are many options available; the mode, the median, and several different means including arithmetic, geometric, quadratic, harmonic, etc. Whichever expression of central tendency of the particle size of the population we use must reflect the property or properties of the population of importance to us. We are, in fact, modelling the real population with an artificial population of mono-sized particles. This section deals with...
