Particle Size Measurement

512 Pages·1996·23.098 MB·English

by  Terence Allen

Particle Size
Measurement
Volume 1
Powder sampling and particle size
measurement
Fifth edition
TERENCE ALLEN
Formerly Senior Consultant
E.I. Dupont de Nemur and Company
Wilmington, Delaware, USA
CHAPMAN & HALL
London . Weinheim . New York . Tokyo . Melbourne . Madras
Publlrhed by Chapman & Ball, 2-6 Boundary Row, London SEl 8HN, UK
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Chapman & Hall. 2-6 Boundary Row, London SEI 8HN. UK
Chapman & Hall GmbH. Pappelallee 3.69469 Weinheim, Gerrnany
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Australia
Chapman & Hall India. R. Seshadri. 32 Second Main Road. CiT East. M a b6 00 035.
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Fist edition 1968
Second edition 1975
Third edition 1981
Fourth edition 1990
Fifth edition 1997
6 1968. 1975, 1981. 1990. 1997 T. Allen
Printed in Great Britain at TJ. Ress (Padstow) Lrd., Padstow. Cornwall
ISBN 0 412 72950 4
0 412 75350 2 (2 volume sd)
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Powder Technology Series
EDITED BY
BRIAN SCARLETT and GENJI JMBO
De@ University of Technology Chubu Powtech Plaza Lab
The Netherlands Japan
Many materials exist in the form of a disperse system, for example powders. pastes,
slurries, emulsions and aerosols. The study of such systems necessarily arises in
many technologies but may alternatively be regarded as a separate subject which is
concerned with the manufacture, characterization and manipulation of such systems.
Chapman & Hall were one of the fust publishers to recognize the basic importance of
the subject, going on to instigate this series of books. The series does not aspire to
define and confine the subject without duplication, but rather to provide a good home
for any book which has a contribution to make to the record of both the theory and
the application of the subject. We bope that all engineers and scientists who concern
themselves with disperse systems will use these books and that those who become
expert will contribute further to the series.
Chemistry of Powder Production
Yasuo Arai
Hardback (0 412 39540 I), 292 pages
Partide Size Analysis
Claus Bemhardt
Translated by H. Finken
Hardback (0 412 55880 7). 428 pages
Particle Classification
K. Heiskanen
Hardback (0 412 49300 4). 330 pages
Powder Surface Area md Porosity
S. Lowell and Joan E. Shields
3rd edn, hardback (0 412 39690 4). 256 pages
Pneumatic Conveying dSdids
R.D.M arcus, L.S. Leung. G.E.K linzing and F. Rizk
Hardback (0 412 21490 3). 592 pages
Principles of Flow in Disperse Systems
0.M olerus
Hardback (0 412 40630 6). 314 pages
Padele Technology
Hans Rumpf
Translated by F.A. Bull
Hardback (0 412 35230 3). 216 pages
Processing of Particulate Solids
J.P.K. Seville, U. Tiizan and R. Clift
Hardback (0 751 40376 8). 384 pages
Contents
Acknowledgements xv
Preface to the the fifth edition xvii
Preface to the the first edition xix
Editor's foreword xx i
Powder sampling 1
Introduction 1
Sample selection 2
Sampling stored material 4
1.3.1 Sampling stored non-flowing material 5
1.3.2 Sampling stored free-flowing material 7
Sampling flowing streams 8
1.4.1 Sampling from a conveyor belt 9
1.4.2 Point samplers 10
1.4.3 Sampling from falling streams 12
1.4.4 Stream sampling ladles 13
1.4.5 Traversing cutters 14
1.4.6 Sampling dusty material 16
1.4.7 Moving flap sampler 17
Sample reduction 19
1.5.1 Scoop sampling 19
1.5.2 Cone and quartering 20
1.5.3 Table sampling 2 0
1. 5.4 Chute splitting 22
1.5.5 The rotary sample divider 23
1. 5.6 Miscellaneous sampling devices 2 3
Sluny sampling 2 4
Reduction of laboratory sample to measurement sample 27
Number of samples required 2 8
Theoretical statistical emrs on a number basis 3 1
Practical statistical errors on a number basis 3 3
Theoretical statistical errors on a weight basis 35
Practical statistical errors on a weight basis 3 6
Experimental tests of sampling techniques 37
Weight of smple requircd 3 8
1.14.1 Gross sample 3 8
1.14.2 Sampling by incrcmcnts 4 0
vi Contents
Data presentation and interpretation 44
Introduction 44
Particle size 4 5
Average diameters 5 0
Particle dispersion 54
Particle shape 5 4
2.5.1 Shape coefficients 5 5
2.5.2 Shapefactors 56
2.5.3 Shape regeneration by Fourier analysis 58
2.5.4 Fractal dimensions characterization of textured
surfaces 59
2.5.5 Other methods of shape analysis 62
2.5.6 Sorting by shape 6 2
Determination of specific surface from size distribution
data 6 2
2.6.1 from a number count 63
2.6.2 from a surface count 6 3
2.6.3 from a volume (mass) count 6 4
Tabular presentation of particle size distribution 6 5
Graphical presentation of size distribution data 68
2.8.1 Presentation on linear graph paper 68
Standard forms of distribution functions 6 9
Arithmetic normal distribution 69
2.10.1 Manipulation of the normal equation 7 1
The log-normal distribution 7 2
2.1 1.1 Relationship between number mean sizes
for a log-normal distribution 74
2.1 1.2 Derived mean sizes 77
2.1 1.3 Transformation between log-normal distributions 7 8
2.1 1.4 Relationship between median and mode
of a log-normal equation 7 9
2.1 1.5 An hpmved equation and graph paper for
log-normal evaluations 8 0
2.1 1.6 Application 80
Johnson's SB distribution 8 1
Rosin-Rarnmler, Bemet-Sperling formula 83
Other distribution laws 8 4
2.14.1 Simplification of two-parameter equations 8 5
2.14.2 Comments 8 6
The law of compensating errors 8 6
Evaluation of non linear distributions on log-normal paper 88
2.16.1 Bimodal intersecting distributions 93
2.16.2 Bimodal non-intersecting distributions 9 3
2.16.3 Other distributions 94
2.16.4 Applications of log-normal plots 94
2.16.5 Curve fitting 94
Contents vii
Alternative notations for frequency distribution
2.17.1 Notation
2.17.2 Moment of a distribution
2.17.3 Transformation from qt(x) to qdx).
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
2.1 7.9 Transformation of abscissae
Phi-notation
Particle size by image analysis 112
Introduction 112
Optical microscopy 113
3.2.1 Upper size limit 114
3.2.2 Lower size limit 114
Sample preparation 115
Measurement of plane sections through packed beds 117
Particle size 117
Calibration 118
3.6.1 Linear eyepiece graticules 118
3.6.2 Globe and circle graticules 120
Training of operators 120
Experimental techniques 12 1
Determination of particle size distribution by number 122
Conditions governing a weight size determination 124
3.10.1 Illustrative example of the calculation of
a size distribution by weight 125
Quantitative image analysis 128
3.1 1 .I Calibration of image analyzers 128
3.1 1.2 Experimental procedures 128
3.1 1.3 Commercial quantitative image analysis systems. 13 7
3.1 1.4 On-line microscopy 140
Electron microscopy 140
Transmission electron microscopy 14 1
3.1 3.1 Specimen preparation for TEM 142
3.13.2 Replica and shadowing techniques 145
3.1 3.3 Chemical analysis 145
Scanning electron microscopy 146
Other scanning electron microscopy techniques 148
Errors involved in converting a number to a volume count 148
Particle size analysis by sieving
Introduction
Woven-wire and punched plate sieves
Electroforrned micromesh sieves
viii Contents
Woven-wire and punched plate sieves
Electroformed micromesh sieves
Standard sieves
Mathematical analysis of the sieving process
Calibration of sieves
Sieving emrs
Methods of sieving
Amount of sample
Hand sieving
Machine sieving
Wet sieving
4.12.1 Manual
4.12.2 Wet sieving by machine
Air-Jet sieving
The Sonic Sifter
The Seishin Robot Sifter
Automatic systems
4.16.1 The Gradex particle size analyzer
4.1 6.2 Labcon automatic sieve system
Ultrasonic sieving
The sieve cascadograph
Felvation
Self organized sieves (SORSI)
Shape separation
Correlation with light scattering data
Conclusions
Fluid classification
Introduction
Assessment of classifier efficiency
Systems
Counter-flow equilibrium classifiers in a
gravitational field-elutriators
Cross-flow gravitational classification
5.5.1 The Warmain Cyclosizer
5.5.2 The Humboldt particle size analyzer TDS
Counter-flow centrifugal classifiers
Cross-flow centrifugal classifiers
Zig-zag classifiers
Cross-flow elbow classifier
Fractionation methods for particle size measurement
Hydrodynamic chromatography
Capillary hydrodynamic fractionation
Capillary zone electrophoresis
Size exclusion chromatography
Ficld flow fractionation
5.15.1 Sedimentation field flow fractionation
Contents ix
5.15.2 Time-delayed-exponential SF3
5.15.3 Thermal field flow fractionation
5.15.4 Magnetic field flow fractionation
5.15.5 Flow field flow fractionation
5.15.6 Steric field flow fractionation
The Matec electro-acoustic system EAS-8000
Continuous SPLIT fractionation
Classification by decantation
Interaction between fluids and particles
Introduction
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 in the
laminar flow region
Size limits for gravity sedimentation
6.3.1 Upper size limit
6.3.2 Lower size limit
Time for terminal velocity to be attained
Wall effects
Errors due to discontinuity of the fluid
Viscosity of a suspension
Non-rigid spheres
Non-spherical particles
6.9.1 Stokes region
6.9.2 Transition region
Relationship between drag coefficient and Reynolds
number in the transition region
The turbulent flow region
Concentration effects
Hindered settling
6.13.1 Low concentration effects
6.13.2 High concentration effects
Electro-viscosity
Dispersion of powders
6.15.1 Dry powder dispersion
6.15.2 The use of glidants to improve flowability of
dry powdels
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)
6.15.7 Deagglornerating wetted clumps
6.15.8 Suspension stability
6.15.9 Tests of dispersion quality
x Contents
Sedimentation theory
Powder density
Liauid viscositv
~egolutiono f &dimenring suspensions
Concentration changes in a suspension settling
under gravity
Relationship between density gradient and concentration
7.5.1 Hydrometers
Theory for the gravity photosedimentation technique
7.6.1 The Beer-Lamben law
7.6.2 The extinction coefficient
Theory for concentration determination with
the x-ray gravitational sedimentation technique
Theory for mass oversize distribution determination for
cumulative, homogeneous, gravitational sedimentation
Stokes equation for centrifugal sedimentation
7.9.1 General theory
Stokes diameter determination for cumulative
and incremental line-start techniques
7.10.1 Incremental, line-start, centrifugal technique
7.10.2 Homogeneous, cumulative, centrifugal
technique
7.10.3 Sedimentation distance small compared
with distance from centrifuge axis
Line-start technique using a photocentrifuge
7.1 1.1 Introduction
7.1 1.2 Homogeneous mode
7.1 1.3 Line-start mode
Theory for mass oversize distribution determination for
cumulative, homogeneous, centrifugal sedimentation
Theory for mass oversize distribution determination for
incremental, homogeneous, centrifugal sedimentation
7.13.1 General theory
7.13.2 Variable time method
7.13.3 Variable inner radius (pipette withdrawal)
7.1 3.4 Variable measurement radius (scanning x-ray
centrifuge)
Sedimentation methods of particle size measurement
Introduction
Homogeneous incremental gravitational sedimentation
8.2.1 The pipette method of Andreasen
8.2.2 The photosedimentation technique
8.2.3 X-ray sedimentation
8.2.4 Hydrometers and divers
Homogeneous cumulative gravitational sedimentation
Contents xi
8.3.1 Introduction
8.3.2 Balances
8.3.3 Sedimentation columns
Line-start incremental gravitational sedimentation
8.4.1 Photosedimentation
Line-start cumulative gravitational sedimentation
8.5.1 Introduction
8.5.2 Methods
Homogeneous incremental centrifugal sedimentation
8.6.1 Introduction
8.6.2 The Simcar pipette disc centrifuge
8.6.3 The Ladal pipette disc centrifuge
8.6.4 The Ladal x-ray disc centrifuge
8.6.5 The Du Pont/Brookhaven scanning x-ray disc
centrifugal sedimentometer (BI-XDC)
8.6.6 The BI-DCP disc @hoto)centrifuge
Cuvet photocentrifuges
Homogeneous cumulative centrifugal sedimentation
8.8.1 Methods
Line-start incremental centrifugal sedimentation
8.9.1 Disc photocentrifuges
Line-start cumulative centrifugal sedimentation
8.10.1 MSA analyzer
Particle size analysis using non-invasive dielectric sensors
Conclusions
Stream scanning methods of particle size measurement
Introduction
The electrical sensing zone method
(The Coulter hinciple)
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
9.2.1 1 Apparatus
9.2.12 Limitations of the method
9.2.1 3 Coulter Multisizer mass balance calculation
for BCR 70 standard quartz powder
Fiber length analysis