Contents
Acknowledgements
xvii
Preface
xix
Editor’s foreword
xxi
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
Powder sampling
Introduction
Sample selection
Sampling stored material
1.3.1
Sampling stored non-flowing material
1.3.2
Sampling from heaps
1.3.3
Sampling stored bulk free-flowing powders
1.3.4
Sampling from sacks and drums
1.3.5
Sampling from trucks and railcars
Sampling flowing streams
1.4.1
Sampling from a conveyor belt
1.4.2
Point samplers
1.4.3
Sampling from falling streams
1.4.4
Stream sampling ladles
1.4.5
Traversing cutters
1.4.6
Sampling dusty material
1.4.7
In-line sampling
Sample reduction
1.5.1
Scoop sampling
1.5.2
Cone and quartering
1.5.3
Table sampling
1.5.4
Chute splitting
1.5.5
Spinning rifflers
1.5.6
Commercial rotary sample dividers
1.5.7
Miscellaneous sampling devices
Slurry sampling
Reduction of laboratory sample to measurement sample
Number of samples required
Theoretical statistical errors on a number basis
Practical statistical errors on a number basis
Theoretical statistical errors on a weight basis
Practical statistical errors on a weight basis
Experimental tests of sampling techniques
1
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7
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Contents
1.14
Weight of sample required
1.14.1 Gross sample
1.14.2 Sampling by increments
2
2.1
2.2
2.3
2.4
2.5
Data presentation and interpretation
Introduction
Particle size
Average diameters
Particle dispersion
Particle shape
2.5.1
Shape coefficients
2.5.2
Shape factors
2.5.3
Applications of shape factors and shape coefficients
2.5.4
Shape indices
2.5.5
Shape regeneration
2.5.6
Fractal dimensions characterization of textured surfaces
2.5.7
Other methods of shape analysis
2.5.8
Sorting by shape
Determination of specific surface from size distribution data
2.6.1
Determination of specific surface from a number count
2.6.2
Determination of specific surface from a surface count
Tabular presentation of particle size distribution
Graphical presentation of size distribution data
2.8.1
Presentation on linear graph paper
Standard forms of distribution functions
Arithmetic normal distribution
2.10.1
Manipulation of the normal equation
The log-normal distribution
2.11.1
Relationship between number mean sizes for a lognormal distribution
2.11.2
Derived mean sizes
2.11.3
Transformation between log-normal distributions
2.11.4
Relationship between median and mode of a lognormal
equation
2.11.5
An improved equation and graph paper for log-normal
evaluations
2.11.6
Application
Johnson's SB distribution
Rosin-Rammler-Bennet-Sperling formula
Other distribution laws
2.14.1 Simplification of two parameter equations.
2.14.2 Comments
The law of compensating errors
Evaluation of nonlinear distributions on log-normal paper
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
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Contents vii
2.17
2.18
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
2.16.1
Bimodal intersecting distributions.
2.16.2
Bimodal non- intersecting distributions.
2.16.3
Other distributions
2.16.4
Applications of log-normal plots
2.16.5
Curve fitting
2.16.6
Data interpretation
Alternative notations for frequency distribution
2.17.1
Notation
2.17.2
Moment of a distribution
2.17.3
Transformation from qt(x) to qr(x)
2.17.4
Relation between moments
2.17.5
Means of distributions
2.17.6
Standard deviations
2.17.7
Coefficient of variation
2.17.8
Applications
2.17.9
Transformation of abscissae
Phi-notation
Particle size analysis by image analysis
Introduction
Standards
Optical microscopy
3.3.1
Upper size limit for optical microscopy
3.3.2
Lower size limit for optical microscopy
Sample preparation
Measurement of plane sections through packed beds
Particle size
Calibration
3.7.1
Linear eyepiece graticules
3.7.2
Globe and circle graticules
Training of operators
Experimental techniques
Determination of particle size distribution by number
Conditions governing a weight size determination
3.11.1
Illustrative example of the calculation of a size
distribution by weight
Semi-automatic aids to microscopy
Automatic aids to microscopy
3.13.1
Beckman Coulter RapidVUE
3.13.2
Micromeretics OptiSizer PSDA™ 5400
3.13.3
Oxford VisiSizer
3.13.4
Retsch Camsizer
3.13.5
Malvern Sysmex Flow Particle Image Analyzer
FPIA-2100 automated particle shape and size analyzer
3.13.6
Sci-Tec PartAn - video Image Analyser
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3.14
3.15
3.16
3.17
3.18
3.19
3.20
Quantitative image analysis
3.14 1
Calibration of image analyzers
3.14.2
Experimental procedures
3.14.3
Commercial quantitative image analysis systems
3.14.4
Confocal laser-scanning microscopy
3.14.5
On-line microscopy
3.14.6
Flatbed scanners
3.14.7
Dark field microscopy
3.14.8
Phase contrast microscopy
3.14.9
Polarized light microscopy (PLM)
3.14.10 Dipix 1440F power scope imaging microscope
3.14.11 Transmission wide field phase contrast microscopy
Electron microscopy
Transmission electron microscopy (TEM)
3.16.1
Specimen preparation for TEM
3.16.2
Replica and shadowing techniques
3.16.3
Chemical analysis
Scanning electron microscopy
Other scanning electron microscopy techniques
Errors involved in converting a number to a volume count
Evaluation of procedures
4
Particle size analysis by sieving
4.1
Introduction
4.2
Standard sieves
4.3
Tolerances for standard sieves
4.4
Woven-wire and punched plate sieves
4.5
Electroformed micromesh sieves
4.6
Mathematical analysis of the sieving process
4.7
Calibration of sieves
4.8
Sieving errors
4.9
Methods of sieving
4.10 Amount of sample required
4.11 Hand sieving
4.12 Machine sieving
4.13 Wet sieving
4.13.1
Manual
4.13.2
Wet sieving by machine
4.14 Air-jet sieving
4.15 The Sonic Sifter
4.16 The Seishin Robot Sifter
4.17 Automatic systems
4.17.1
The Rotex Gradex 2000 particle size analyzer
4.17.2
Labcon automatic sieve system
4.17.3
Gilson Compu-Sieve« analysis system
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Contents ix
4.18
4.19
4.20
4.21
4.22
4.23
4.24
Ultrasonic sieving
The sieve cascadograph
Felvation
Self organized sieves (SORSI)
Shape separation
Correlation with light scattering data
Conclusions
5
5.1
5.2
5.3
5.4
Fluid classification
Introduction
Assessment of classifier efficiency
Systems
Counter-flow equilibrium classifiers in a gravitational field
elutriators
Theory for elutriators
Water elutriators
Air elutriators
Counter-flow centrifugal classifiers;
Zig-zag gravitational classifiers
Zig-zag centrifugal classifiers
The Warmain Cyclosizer
Cross-flow gravitational classification
5.12.1
The Humboldt particle size analyzer TDS
Cross-flow centrifugal classifiers
5.13.1
Analysette 9
5.13.2
The Donaldson Acucut classifier
Cross-flow elbow classifier
Micromeretics classifier;
Fractionation methods for particle size measurement
Hydrodynamic chromatography
Capillary hydrodynamic fractionation ;
Capillary zone electrophoresis
Size exclusion chromatography
Field flow fractionation
5.21.1
Sedimentation field flow fractionation (SFFF)
5.21.2
Centrifugal field flow fractionation
5.21.3
Time-delayed exponential SFFF
5.21.4
Thermal field flow fractionation
5.21.5
Magnetic field flow fractionation
5.21.6
Flow field flow fractionation
5.21.7
Steric field flow fractionation
5.21.8
Multi-angle light scattering (MALS)
The Matec electro-acoustic system EAS-8000
Continuous split fractionation
Classification by decantation;
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
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Contents
Interaction between particles and fluids
6.1
Introduction
6.2
Settling of a single homogeneous sphere under a gravitational
force
6.2.1
Relationship between settling velocity and particle size
6.2.2.
Calculation of particle size from settling velocity in the
laminar flow region
6.3
Size limits for gravity sedimentation
6.3.1 Upper size limit
6.3.2 Lower size limit
6.4
Time for terminal velocity to be attained
6.5
Errors due to the finite extent of the fluid (wall effects)
6.6
Errors due todiscontinuity of the fluid
6.7
Viscosity of a suspension
6.8
Non-rigid spheres
6.9
Non-spherical particles
6.9.1 Stokes' region
6.9.2 Relationship between fiber diameter and Stokes diameter
6.9.3 Transition region
6.10 Relationship between drag coefficient and Reynolds number in the
transition region
6.11 The turbulent flow region
6.12 Concentration effects
6.13 Hindered settling
6.13.1
Low concentration effects
6.13.2
High concentration effects
6.14 Electro-viscosity
6.15 Dispersion of powders
6.15.1
Dry powder dispersion
6.15.2
The use of glidants to improve flowability of dry
powders
6.15.3
Wet powder dispersion
6.15.4
Role of dispersing agents
6.15.5
Wetting a powder
6.15.6
Determination of contact angle ()
6.15.7
Deagglomerating wetted clumps
6.15.8
Suspension stability
6.15.9
Tests of dispersion quality
6.16 Powder density
6.17 Liquid viscosity
6.18 Standard powders
6.19 National Standards
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Contents xi
7
Gravitational sedimentation methods of particle size
determination
7.1
Introduction
7.2
Resolution of sedimenting suspensions
7.3
Concentration changes in a suspension settling under gravity
7.4
Homogeneous incremental gravitational sedimentation
7.4.1
The pipette method of Andreasen
7.5
Theory for the gravity photosedimentation technique
7.5.1
The Beer Lambert law
7.5.2
The extinction coefficient
7.5.3
Turbidity measurements (Turbidimetry)
7.5.4
The photosedimentation technique
7.5.5
Commercial photosedimentometers
7.5.6
Sedimentation image analysis
7.5.7
Transmission fluctuation spectrometry
7.6
Theory for concentration determination with the x-ray
gravitational sedimentation technique
7.6.1
X-ray sedimentation
7.7
Relationship between density gradient and concentration
7.8
Hydrometers and divers
7.8.1
Introduction
7.8.2
Theory
7.8.3
Depth of immersion
7.8.4
Experimental procedure
7.8.5
Divers
7.9
Homogeneous cumulative gravitational sedimentation
7.9.1
Introduction
7.9.2
Theory
7.9.3
Sedimentation balances
7.9.4
Sedimentation columns
7.10 Line-start incremental gravitational sedimentation
7.10.1
Photosedimentation
7.11 Line-start cumulative gravitational sedimentation
7.11.1
Introduction
7.11.2
Methods
8
8.1
8.2
8.3
8.4
Centrifugal sedimentation methods of particle size
determination
Introduction
Stokes' equation for centrifugal sedimentation
8.2.1
General theory
Homogeneous, incremental, centrifugal sedimentation
8.3.1
General theory
Variable time method (r and S constant, t variable)
8.4.1
General theory
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xii Contents
8.4.2
8.16
8.17
8.18
8.19
The Simcar pipette disc centrifuge (r constant, S
assumed constant, t variable)
8.4.3
Worked example
8.4.4
The Ladal x-ray disc centrifuge(r constant, S constant, t
variable)
8.4.5
Discussion of the Kamack equation
Variable time and height method (S constant, both r and t vary)
8.5.1
Stokes diameter determination
8.5.2
Mass frequency undersize determination
8.5.3
DuPont/Brookhaven scanning x-ray disc centrifugal
sedimentometer
8.5.4
Worked example
Variable inner radius (Both S and t vary, r remains constant)
8.6.1
Stokes diameter determination
8.6.2
Ladal pipette disc centrifuge
8.6.3
Worked example
8.6.4
Mass frequency undersize determination
Photocentrifuges
8.7.1
Introduction
8.7.2
Disc photocentrifuges.
8.7.3
Homogeneous mode
Line-start incremental centrifugal sedimentation
8.8.1
Line-start, incremental centrifugal technique
8.8.2
Discussion of line-start theory
8.8.3
BI-DCP disc (photo)centrifuge particle size analyzer
Cuvette photocentrifuges
Homogeneous, cumulative, centrifugal sedimentation
8.10.1
General theory
Variable time method (variation of P with t)
Sedimentation distance small compared with distance from
centrifuge axis
8.12.1
Hosokawa Mikropul Sedimentputer
8.12.2
Alpine long-arm centrifuge
Variable inner radius (variation of P with S)
8.13.1
Alternative theory (variation of P with S)
Variable outer radius (variation of P with R)
Line-start cumulative centrifugal sedimentation
8.15.1
MSA analyzer
Particle size analysis using non-invasive dielectric sensors
Supercentrifuge
Ultracentrifuge
Conclusions
9
9.1
Stream scanning methods of particle size measurement
Introduction
8.5
8.6.
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
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406
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417
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Contents xiii
9.2
9.3
9.4
9.5
9.6
The electrical sensing zone method (the Coulter principle)
9.2.1
Introduction
9.2.2
Operating principle
9.2.3
Theory for the electrical sensing zone method
9.2.4
Effect of particle shape and orientation
9.2.5
Pulse shape
9.2.6
Effect of coincidence
9.2.7
Multiple aperture method for powders having a wide
size range
9.2.8
Calibration
9.2.9
Carrying out a mass balance
9.2.10
Oversize counts on a mass basis using the Coulter
Counter
9.2.11
Apparatus
9.2.12
Limitations of the method
Fiber length analysis
Optical particle counters
9.4.1
Light blockage
9.4.2
Optical disdrometer
9.4.3
Light scattering
Commercial instruments
9.5.1
Aerometrics
9.5.2
Canty Vision
9.5.3
Climet
9.5.4
Contamination Control Systems
9.5.5
Danfoss VisionSensor
9.5.6
Faley Status
9.5.7
Flowvision
9.5.8
Galai
9.5.9
Kane May
9.5.10
Kowa
9.5.11
Kratel
9.5.12
Malvern
9.5.13
Pacific Scientific Hiac/Royco, Met One
9.5.14
Particle Measuring Systems
9.5.15
Partikel Messetechnik
9.5.16
Particle Sizing Systems
9.5.17
Polytec
9.5.18
Rion
9.5.19
Spectrex
Dwell time
9.6.1.
Brinkmann 201 analyzer
9.6.2
Focused Beam Reflectance Measurement (FBRM)
Lasentec
9.6.3
Messetechnik Optical Reflectance Method (ORM)
449
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452
455
457
459
460
461
463
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466
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468
469
470
470
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474
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xiv Contents
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
9.19
9.20
10
10.1
10.2
10.3
9.6.4
Procedyne
Aerodynamic time-of-flight measurement
9.7.1
Thermo Systems Incorporated
9.7.2
Ancillary equipment
Laser Doppler velocimetry (LDV)
Laser phase Doppler principle
9.9.1
TSI Aerometrics phase Doppler particle analyzer
9.9.2
Discusion
9.9.3
Differential phase-Doppler anemometry
9.9.4
Bristol Industrial Research Association
9.9.5
Dantec Particle Dynamic Analyzer
Hosokawa Mikropul E-Spart Analyzer
Shadow Doppler velocimetry
Other light scattering methods
Interferometers
9.13.1
Mach Zehnder type interferometer
9.13.2
The TSI Liquitrak™ interferometer
Flow ultramicroscope.
9.14.1
ISPA image analysis system
Measurement of the size distribution of drops in dispersions
Dupont electrolytic grain size analyzer
Light pressure drift velocity
Impact size monitor
Monitek acoustic particle monitors
Erdco Acoustical Counter
497
497
497
500
501
501
502
502
503
504
504
505
506
507
508
508
509
510
510
510
512
512
513
513
514
Field scanning methods of particle size measurement
Introduction
Single point analyzers
10.2.1
Static noise measurement
10.2.2
Ultrasonic attenuation
10.2.3
-ray attenuation
10.2.4
X-ray attenuation and fluorescence
12.2.5
Counter-flow classifiers
10.2.6
Hydrocyclones
10.2.7
The Cyclosensor
10.2.8
Automatic sieving machines
10.2.9
Gas flow permeametry
10.2.10 Correlation techniques
Light scattering and attenuation
10.3.1
Introduction
10.3.2
Effect of extinction coefficient on turbidity
10.3.3
Transient turbidity
10.3.4
Holography
10.3.5
State of.polarization of the scattered radiation
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527
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528
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530
531
531
531
532
535
536
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Contents xv
10. 4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.14
10.3.6
Forward/backward intensity ratio (FBR)
10.3.7
Optical back-scattering
10.3.8 Transmission fluctuation spectroscopy
Light scattering theory
10.4.1
The Rayleigh region (d)
10.4.2
The Rayleigh-Gans region (D < )
10.4.3
High order Tyndall spectra (HOTS)
10.4.4
Light diffraction
10.4.5
Early commercial light scattering equipment
Multi angle laser light scattering; (MALLS)
10.5.1
Theoretical basis for MALLS instruments
10.5.2
Commercial instruments
10.5.3.
Discussion
Malvern (Insitec) Ensemble Particle Concentration Size (EPCS)
Systems
Optical incoherent space frequency analysis
10.7.1 Retsch Crystalsizer
Pulse displacement technique (PDT)
Small angle x-ray scattering (SAXS)
Near infra-red spectroscopy (NIR)
Ultrasonic attenuation
10.11.1 Introduction
10.11.2 Theoretical basis for ultrasonic instruments
10. 11.3 Discussion
Matec Acoustosizer (ACS)
Ultrasonic attenuation and velocity spectrometry
Photon correlation spectroscopy (PCS)
10.14.1 Introduction
10.14.2 Principles
10.14.3 Through dynamic light scattering
10.14.4 Particle size
10.14.5 Concentration effects
10.14.6 Particle interaction
10.14.7 Particle size effects
10.14.8 Polydispersity
10.14.9 The controlled reference method
10.14.10 Multi-angle measurements
10.14.11 Commercial equipment
10.14.12 Discussion
10.14.13 Spectral turbidity
10.14.14 Diffusion wave spectroscopy (DWS)
10.14.15 Photon migration
10.15 Turbo-Power Model TPO-400 in-line grain size analyzer
10.16 Concentration monitors
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596
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602
603
603
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xvi Contents
10.17 Shape discrimination
10.18 Miscellaneous
10.18.1 Back-scatter intensity
10.18.2
Spectroscopy; photo-acoustic (PAS) and photo-thermal
(PTS)
10.18.3 Transient electric birefringence
10.18.4 Crossed lasers
10.18.5 Frequency domain photon migration
10.18.6 Laser induced incandescence (LII)
10.18.7 Spectral transmission and extinction
10.18.8 Turbiscan multiple light scattering measurements
604
604
604
Appendix
623
Manufacturers and suppliers
605
605
606
606
607
607
608
Author index
628
Subject index
651