21
Particle Size Measurement
Particle Size Measurement
Powder Technology Series Edited by B. Scarlett
Department of Chemical Engineering University of Technology Loughborough
~Cill[(~D©D® ®D~® ~®Cill~llil [(®mru®[fi)~
TERENCE ALLEN Ph.D.
Senior Lecturer in Powder Technology University of Bradford
THIRD EDITION
Springer-Science+Business Media, B.V.
ISBN 978-0-412-15410-2 ISBN 978-1-4899-3063-7 (eBook) DOI 10.1007/978-1-4899-3063-7
© 1968, 1975, 1981 T. Allen Originally published by Chapman & Hall in 1981 Softcover reprint of the hardcover 3rd edition 1981
All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from the Publisher.
British Library Cataloguing in Publication Data
Allen, Terence Particle size measurement.-3rd ed.-{Powder technology series). 1. Particle size determination I. Title 620'.43
II. Series TA418.8
ISBN 978-0-412-15410-2
80-49866
Contents
Editor's foreword to the first edition xvii
Preface to the first edition xix
Preface to the third edition xxi
Acknowledgements xxii
1 Sampling of powders 1 1.1 In troducti on 1 1.2 Theory 1 1.3 Golden rules of sampling 5 1.4 Bulk sampling 5
1.4.1 Sampling from a moving stream of powder 6 1.4.2 Sampling from a conveyor belt or chute 12 1.4.3 Sampling from a bucket conveyor 13 1.4.4 Bag sampling 13 1.4.5 Sampling spears 13 1.4.6 Sampling from wagons and con tainers 15 1.4.7 Sampling from heaps 15
1.5 Slurry sampling 17 1.6 Sample dividing 20
1.6.1 Scoop sampling 22 1.6.2 Coning and quartering 24 1.6.3 Table sampling 24 1.6.4 Chute splitting 24 1.6.5 The spinning riffler 26
1.7 Miscellaneous devices 28 1.8 Reduction from laboratory sample to analysis sample 30 1.9 Reduction from analysis sample to measurement sample 32 1.10 Experimental tests of sample-splitting techniques 33
2 Sampling of dusty gases in gas streams 36 2.1 In troduction 36
vi Contents
2.2 Basic procedures 39 2.2.1 Sampling positions 39 2.2.2 Temperature and velocity surveys 40 2.2.3 Sampling points 41
2.3 Sampling equipment 41 2.3.1 Nozzles 44 2.3.2 Dust-sampling collector 46 2.3.3 Ancillary apparatus 51 2.3.4 OIWine dust extraction 51 2.3.5 The Andersen stack sampler 52
2.4 Corrections for anisokinetic sampling 54 2.5 Probe orientation 59 2.6 Radiation methods 60
3 Sampling and sizing from the atmosphere 64 3.1 Introduction 64 3.2 Inertial techniques 68 3.3 Filtration 77 3.4 Electrostatic precipitation 79 3.5 Electrical charging and mobility 81 3.6 Thermal precipitation 82 3.7 The quartz microbalance 86 3.8 Light scattering 86
3.8.1 Discussion 94 3.9 Miscellaneous techniques 95
4 Particle size, shape and distribution 103 4.1 Particle size 103 4.2 Particle shape 107
4.2.1 Shape coefficients 107 4.2.2 Shape factors 110 4.2.3 Applications of shape factors and shape coefficients 113 4.2.4 Shape indices 118 4.2.5 Shape regeneration by Fourier analysis 119 4.2.6 Fractal dimension characterization of textured surfaces 119
4.3 Determination of specific surface from size distribution data 121 4.3.1 Number distribution 121 4.3.2 Surface distribution 121 4.3.3 Volume distribution 122
4.4 Particle size distribution transformation between number, surface and mass 122 4.5 Average diameters 124 4.6 Particle dispersion 129 4.7 Methods of presenting size analysis data 130
Contents vii
4.8 Devices for representing the cumulative distribution as a straight line 133 4.8.1 Arithmetic normal distributions 133 4.8.2 The log-normal distribution 135 4.8.3 The Rosin-Rammler distribution 139 4.8.4 Mean particle sizes and specific surface evaluation for
Rosin-Rammler distributions 140 4.8.5 Other particle size distribution equations 140 4.8.6 Simplification of two-parameter equations 140 4.8.7 Evaluation of non-linear distributions on log-normal paper 141 4.8.8 Derivation of shape factors from parallel log-normal curves 145
4.9 The law of compensating errors 146 4.10 Alternative notation for frequency distribution 149
4.10.1 Notation 149 4.10.2 Moment of a distribution 150 4.10.3 Transformation from qt(x) toqr(x) 150 4.10.4 Relation between moments 151 4.10.5 Means of distributions 151 4.10.6 Standard deviations 152 4.10.7 Coefficient of variance 152 4.10.8 Applications 153
(a) Calculation of volume-specific surface 153 (b) Calculation of the surface area of a size increment 153
4.10.9 Transformation of abscissa 154 4.11 Phi-notation 156 4.12 Manipulation of the log-probability equation 157
4.12.1 Average sizes 158 4.12.2 Derived average sizes 159 4.12.3 Transformation of the log-normal distribution by count
into one by weight 160 4.13 Relationship between median and mode of a log-normal distribution 161 4.14 An improved equation and graph paper for log-normal evaluations 161
4.14.1 Applications 162
5 Sieving 165 5.1 Introduction 165 5.2 Woven-wire and punched plate sieves 166 5.3 Electroformed rnicromesh sieves 167 5.4 British Standard specification sieves 169 5.5 Methods for the use of frne sieves 171
5.5.1 Machine sieving 171 5.5.2 Wet sieving 172 5.5.3 Hand sieving 173 5.5.4 Air-jet sieving 174 5.5.5 The sonic sifter 175
viii Contents
5.5.6 Felvation 176 5.5.7 Self-organized sieve (SORSI) 177
5.6 Sieving errors 178 5.7 Mathematical analysis of the sieving process 180 5.8 Calibration of sieves 183
6 Microscopy 187 6.1 Introduction 187 6.2 Optical microscopy 187
6.2.1 Sample preparation 188 6.2.2 Particle size distributions from measurements on plane sections
through packed beds 190 6.3 Particle size 191 6.4 Transmission electron microscopy (TEM) 192
6.4.1 Specimen preparation 193 6.4.2 Replica and shadowing techniques 195 6.4.3 Chemical analysis 196
6.5 Scanning electron microscopy (SEM) 196 6.6 Manual methods of sizing particles 197
6.6.1 Graticules 198 6.6.2 Training of operators 201
6.7 Semi-automatic aids to microscopy 201 6.8 Automatic counting and sizing 207 6.9 Quantitative image analysers 208 6.10 Specimen improvement techniques 209 6.11 Statistical considerations governing the determination of size distributions
by microscope count 210 6.11.1 Frequency distribution determination 210 6.11.2 Weight distribution determination 211
6.12 Conclusion 211
7 Interaction between particles and fluids in a gravitational field 215 7.1 Introduction 215 7.2 Relationship between drag coefficient and Reynolds number for a sphere
settling in a liquid 216 7.3 The laminar flow region 217 7.4 Critical diameter for laminar flow settling 218 7.5 Particle acceleration 219 7.6 Errors due to the fmite extent of the fluid 220 7.7 Errors due to discontinuity of the fluid 222 7.8 Brownian motion 223 7.9 Viscosity of a suspension 225 7.10 Calculation of terminal velocities in the transition region 225 7.11 The turbulent flow region 229
Contents ix
7.12 Non-rigid spheres 230 7.13 Non-spherical particles 231
7.13.1 Stokes' region 231 7.13.2 The transition region 234
7.14 Concentration effects 235 7.15 Hindered settling 240
7.15.1 Low-concentration effects 241 7.15.2 High-concentration effects 242
7.16 Electro-viscosity 243
8 Dispersion of powders 246 8.1 Discussion 246 8.2 The use of glidants to improve flowability of dry powders 252 8.3 Density determination 252 8.4 Viscosity 256 8.5 Sedimentation systems 256 8.6 Densities and viscosities of some aqueous solutions 261 8.7 Standard powders 262
9 Incremental methods of sedimentation size analysis 267 9.1 Basic theory 267
9.1.1 Variation in concentration within a settling suspension 267 9.1.2 Relationship between density gradient and concentration 268
9.2 Resolution for incremental methods 269 9.3 The pipette method 270
9.3.1 Experimental errors 274 9.4 The photosedimentation technique 276
9.4.1 Introduction 276 9.4.2 Theory 277 9.4.3 The extinction coefficient 279 9.4.4 Photosedimentometers 280 9.4.5 Discussion 283
9.5 X-ray sedimentation 283 9.6 Hydrometers 287 9.7 Divers 289 9.8 The specific gravity balance 291 9.9 Appendix: worked examples 291
9.9.1 Wide-angle scanning photosedimentometer: analysis of silica 291 9.9.2 Conversion from surface distribution to weight distribution 293 9.9.3 The LADAL X-ray sedimentometer: analysis of tungstic oxide 295
10 Cumulative methods of sedimentation size analysis 10.1 Introduction 10.2 Line-start methods
298 298 298
x Contents
10.3 Homogeneous suspensions 10.4 Sedimentation balances
10.4.1 The Gallenkamp balance 10.4.2 The Sartorius balance 10.4.3 The Shimadzu balance 10.4.4 Other balances
299 301 303 305 306 308
10.5 The granumeter 308 10.6 The micromerograph 308 10.7 Sedimentation columns 310 10.8 Manometric methods 314 10.9 Pressure on the walls of the sedimentation tube 315 10.10 Decanting 315 10.11 The {3-back-scattering method 317 10.12 Discussion 318 10.13 Appendix: An approximate method of calculating size distribution from
cumulative sedimentation results 319
11 Fluid classification 325 11.1 Introduction 325 11.2 Assessment of classifier efficiency 325 11.3 Systems 331 11.4 Counterflow equilibrium classifiers in the gravitational field-elutriators 331
11.4.1 Water elutriators 334 11.4.2 Air elutriators 11.4.3 Zig-zag classifiers
11.5 Cross-flow gravity classifiers 11.5.1 The Warmain cyclosizer
11.6 Counterflow equilibrium classifiers in the centrifugal field 11.6.1 The Bahco classifier 11.6.2 The BCURA centrifugal e1utriator 11.6.3 Centrifugal e1utriation in a liquid suspension
11.7 Cross-flow equilibrium classifiers in the centrifugal field 11. 7.1 Analysette 9 11. 7.2 The Donaldson classifier 11.7.3 The Micromeritics classifier
11.8 Other commercially available classifiers 11.9 Hydrodynamic chromatography
337 341 341 341 343 343 344 344 344 344 345 347 347 347
12 Centrifugal methods 350 12.1 Introduction 350 12.2 Stokes' diameter determination 351 12.3 Line-start technique 352
12.3.1 Theory 352 12.3.2 Line-start technique using a photometric method of analysis 352
Contents xi
12.3.3 Early instruments: the Marshall centrifuge and the MSA particle size analyser 354
12.3.4 The photocentrifuge 356 12.3.5 The Joyce-Loeb1 disc centrifuge 357
12.4 Homogeneous suspension 359 12.4.1 Sedimentation height small compared with distance from
centrifuge axis 359 12.5 Cumulative sedimentation theory for a homogeneous suspension 360 12.6 Variable-time method (variation of P with t) 361 12.7 Variable inner radius (variation of Pwith S) 362 12.8 Shape of centrifuge tubes 363 12.9 Alternative theory (variation of P with S) 364 12.10 Variable outer radius (variation of PwithR) 365 12.11 Incremental analysis with a homogeneous suspension 365
12.11.1 The Simcar centrifuge 365 12.11.2 General theory 366
12.12 The LADALX-ray centrifuge 372 12.13 The LADAL pipette withdrawal centrifuge 377
12.13.1 Theory for the LADAL pipette withdrawal technique 377 (a) Calculation of particle size 377 (b) Calculation of frequency undersize 379
12.14 The supercentrifuge 382 12.15 The ultracentrifuge 384 12.16 Conclusion 384 12.17 Appendix: Worked examples 386
12.17.1 Simcar centrifuge 386 (a) Determination of F factors 386 (b) Experimental results 387
12.17.2 X-ray centrifuge 388 (a) Determination of F factors 388 (b) Experimental results 388
12.17.3 LADAL pipette centrifuge 389
13 The electrical sensing zone method of particle size distribution determination (the Coulter principle)
13.1 Introduction 13.2 Operation 13.3 Calibration 13.4 Evaluation of results 13.5 Theory 13.6 Effect of particle shape and orientation 13.7 Coincidence correction 13.8 Pulse shape 13.9 End-point determination
392 392 392 393 396 397 400 401 404 407
xii Con ten ts
13.10 Upper size limit 13.11 Commercial equipment 13.12 Conclusions
14 Radiation scattering methods of particle size detennination 14.1 Introduction 14.2 Scattered radiation
14.2.1 The Rayleigh region (D ~ X) 14.2.2 The Rayleigh-Gans region (D ~ X)
14.3 State of polarization of the scattered radiation 14.4 Turbidity measurement 14.5 High-order Tyndall spectra (HOTS) 14.6 Particle size analysis by light diffraction 14.7 Light-scattering equipment 14.8 Holography 14.9 Miscellaneous
408 408 411
414 414 418 418 419 420 421 423 424 425 426 428
15 Penneametry and gas diffusion 43f 15.1 Flow of a viscous fluid through a packed bed of powder 432 15.2 Alternative derivation of Kozeny's equation using equivalent capillaries 434 15.3 The aspect factor k 435 15.4 Other flow equations 436 15.5 Experimental applications 440 15.6 Preparation of powder bed 441 15.7 Constant-pressure permeameters 441 15.8 Constant-volume permeameters 445 15.9 Fine particles 448 15.10 Types of flow 449 15.11 Transitional region between viscous and molecular flow 449 15.12 Experimental techniques for deterrniningZ 450 15.13 Calculation of permeability surface 451 15.14 Diffusional flow for surface area measurement 453 15.15 The relationship between diffusion constant and specific surface 454 15.16 Non-steady-state diffusional flow 455 15.17 Steady-state diffusional flow 457 15.18 The liquid phase permeameter 460 15.19 Application to hindered settling 462
16 Gas adsorption 16.1 Introduction 16.2 Theories of adsorption
16.2.1 Langmuir's isotherm for ideal localized monolayers 16.2.2 BET isotherm for multilayer adsorption 16.2.3 The n-layer BET equation
465 465 466 466 468 472
Contents xiii
16.2.4 Discussion of BET theory 473 16.2.5 Mathematical nature of the BET equation 474 16.2.6 Shapes of isotherms 476 16.2.7 Modifications of the BET equation 478 16.2.8 The Huttig equation 479 16.2.9 The relative method of Harkins and Jura (HJr) 479 16.2.10 Comparison between BET and HJr methods 481 16.2.11 The Frenkel-Halsey-Hill equation (FHH) 481 16.2.12 The Dubinin-Radushkevich equation (D-R) 481 16.2.13 The VA-tmethod 484 16.2.14 Kiselev's equation 487
16.3 Experimental techniques - factors affecting adsorption 488 16.3.1 Degassing 488 16.3.2 Pressure 488 16.3.3 Temperature and time 489 16.3.4 Adsorbate 489 16.3.5 Interlaboratory tests 490
16.4 Experimental techniques - volumetric methods 490 16.4.1 Principle 490 16.4.2 Volumetric apparatus for high surface area 491 16.4.3 Volumetric apparatus for low surface area 493
16.5 Experimental techniques - gravimetric methods 494 16.5.1 Principle 494 16.5.2 Single-spring balances 494 16.5.3 Multiple-spring balances 495 16.5.4 Beam balances 495
16.6 Continuous-flow gas chromatographic methods 496 16.6.1 Commercially available continuous-flow apparatus 501
16.7 Standard volumetric gas-adsorption apparatus 502 16.7.1 Worked example 503
16.8 Commercially available volumetric- and gravimetric-type apparatus 505
17 Other methods for determining surface area 514 17.1 In troduction 514 17.2 Calculation from size distribution data 515 17.3 Adsorption from solution 516
17.3.1 Orientation of molecules at the solid-liquid interface 516 17.3.2 Polarity of organic liquids and adsorbents 517 17.3.3 Drying of organic liquids and adsorbents 519
17.4 Methods of analysis of amount of solute adsorbed on to solid surfaces 519 17.4.1 Langmuir trough 520 17.4.2 Gravimetric method 520 17.4.3 Volumetric method 520
xiv Contents
17.4.4 The Rayleigh interferometer 17.4.5 The precolumn method
17.5 Theory for adsorption from solution 17.6 Quantitative methods for adsorption from a solution
17.6.1 Adsorption of non-electrolytes 17.6.2 Fatty acid adsorption 17.6.3 Adsorption of polymers 17.6.4 Adsorption of dyes 17.6.5 Adsorption of electrolytes 17.6.6 Deposition of silver 17.6.7 Adsorption of p-nitrophenol 17.6.8 Other systems
17.7 Theory for heat of adsorption from a liquid phase 17.7.1 Surface free energy of a fluid 17.7.2 Surface entropy and energy 17.7.3 Heat of immersion
17.8 Static calorimetry 17.9 Flow microcalorimetry
17.9.1 Experimental procedures - liquids (a) Pulse adsorption (b) Equilibrium adsorption (c) Successive adsorption
17.9.2 Calibration 17.9.3 Determination of the amount of solute adsorbed:
the precolurnn method 17.9.4 Gases 17.9.5 Application to the determination of surface area
17.1 0 Density me thod
520 521 521 522 522 522 523 523 524 524 525 525 526 526 527 527 529 530 530 531 531 532 532
533 533 534 534
18 Determination of pore size distribution by gas adsorption 538 18.1 Miscellaneous techniques 538 18.2 The Kelvin equation 538 18.3 The hysteresis loop 541 18.4 Relationship between the thickness of the adsorbed layer and the
relative pressure 544 18.5 Classification of pores 546 18.6 The Cis method 546 18.7 Pore size distribution determination of mesopores 547
18.7.1 Modelless method 547 18.7.2 Cylindrical core model 550 18.7.3 Cylindrical pore model 551 18.7.4 Parallel plate model 555
18.8 Analysis of micropores: the MP method 558 18.9 Miscellaneous 560
19 Mercury porosimetry 19 .1 Introduction 19.2 Literature survey 19.3 Con tact angle and surface tension for mercury 19.4 Principle 19.5 Theory for volume distribution determination 19.6 Theory for surface distribution determination
19.6.1 Cylindrical pore model 19.6.2 Modelless method
19.7 Theory for length distribution determination 19.8 Worked example 19.9 Comparison with other techniques 19.1 0 Correction factors
20 On-line particle size analysis 20.1 Introduction 20.2 Stream-scanning
20.2.1 The HIAC particle counter 20.2.2 The Climet particle counting systems 20.2.3 The Royco liquid-borne particle monitors 20.2.4 The Nuclepore Spectrex Prototron particle counter 20.2.5 The Procedyne particle size analyser 20.2.6 Optical-electronic method 20.2.7 Miscellaneous optical methods 20.2.8 Echo measurements 20.2.9 The Langer acoustical CoUll ter (Erdco) 20.2.10 The Coulter on-line monitor 20.2.11 On-line automatic microscopy 20.2.12 Comparison between stream-scanning techniques
20.3 Field-scanning
Contents
20.3.1 Some properties of the size distributions of milled products 20.3.2 Static noise measurement 20.3.3 Ultrasonic attenuation measurements: the Autometrics PSM
systems 100 and 200 20.3 .4 fj-ray attenuation: the Mintex/Royal School of Mines
slurry sizer 20.3.5 X-ray attenuation and fluorescence 20.3.6 Laser diffraction
(a) The Cilas Granulometer 226 (b) The Leeds and Northrup Microtrac (c) The Malvern Particle and Droplet Sizer
20.3.7 Classification devices (a) Counter-flow classifiers (b) Cross-flow air classifier; the Humboldt PSA-type TDS
xv
564 564 566 568 569 571 574 574 575 576 576 578 579
583 583 583 585 587 587 588 588 589 590 592 592 593 595 596 596 596 598
598
602 604 606 606 606 607 607 607 609
xvi Contents
20.3.8 Hydrocyclones 20.3.9 Screening: The Cyclosensor 20.3.10 Automatic sieving machines 20.3.11 Gas flow permeametry 20.3.12 Pressure drop in nozzles 20.3.13 Non-Newtonian rheological properties 20.3.14 Correlation techniques
Problems
Appendix 1 Equipment and suppliers
Appendix 2 Manufacturers' and suppliers' addresses
Author Index
Subject Index
610 611 612 615 616 616 617
621
639
647
655
674
Editor's foreword to the first edition
The study of the properties and behaviour of systems made up of particulate solids has in the past received much less attention than the study of fluids. It is, however, becoming increasingly necessary to understand industrial processes involving the production, handling and processing of solid particles, in order to increase the efficiency of such systems and to permit their control. During the past few years this has led to an increase in the amount of study and research into the properties of solid particle systems. The results of this effort are widely dispersed in the literature and at the moment much of the information is not available in a form in which it is likely to influence the education of students, particularly in chemical engineering, who may later be employed in industrial organizations where they will be faced with the problems of solids' handling. It is also difficult for the engineer responsible for the design or selection of solids' handling equipment to make use of existing knowledge, with the result that industrial practice is not always the best that is achievable. It is hoped that the publication of a series of monographs on Powder Technology, of which this is the first, will help by providing accounts of existing knowledge of various aspects of the subject in a readily available form.
It is appropriate that the first monograph in this series should deal with the measurement of the size of small particles since this is the basic technique underlying all other work in powder technology. The reliability of research results, for example, on the size reduction of solid particles, cannot be better than the reliability of the particle size measurement techniques employed. Too often the difficulties and limitations of size measurement are ignored in such work, so that any conclusions become suspect. The importance of a thorough understanding of the problems involved in measuring the size of small particles for anyone working in any aspect of powder technology is therefore difficult to overestimate. It is hoped that this monograph, written by an experienced size analyst who has studied critically most of the methods described, will be of value in encouraging an informed and critical approach to the subject and that it will help in the selection of equipment and in realistic assessment of the value of particle size measurements.
Preface to the first edition
Although man's environment, from the interstellar dust to the earth beneath his feet, is composed to a large extent of finely divided material, his knowledge of the properties of such materials is surprisingly slight. For many years the scientist has accepted that matter may exist as solids, liquids or gases although the dividing line between the states may often be rather blurred; this classification has been upset by powders, which at rest are solids, when aerated may behave as liquids, and when suspended in gases take on some of the properties of gases.
It is now widely recognized that powder technology is a field of study in its own right. The industrial applications of this new science are far reaching. The size of fine particles affects the properties of a powder in many important ways. For example, it determines the setting time of cement, the hiding power of pigments and the activity of chemical catalysts; the taste of food, the potency of drugs and the sintering shrinkage of metallurgical powders are also strongly affected by the size of the particles of which the powder is made up. Particle size measurement is to powder technology as thermometry is to the study of heat and is in the same state of flux as thermometry was in its early days.
Only in the case of a sphere can the size of a particle be completely described by one number. Unfortunately, the particles that the analyst has to measure are rarely spherical and the size range of the particles in anyone system may be too wide to be measured with anyone measuring device. V.T. Morgan tells us of the Martians who have the task of determining the size of human abodes. Martian homes are spherical and so the Martian who landed in the Arctic had no difficulty in classifying the igloos as hemispherical with measurable diameters. The Martian who landed in North America classified the wigwams as conical with measurable heights and base diameters. The Martian who landed in New York classi fied the buildings as cuboid with three dimensions mutually perpendicular. The one who landed in London gazed about him despairingly before committing suicide. One of the purposes of this book is to reduce the possibility of further similar tragedies. The above story illustrates the problems involved in attempting to defme the size of particles by one dimension. The only method of measuring more than one dimension is microscopy. However, the mean ratio of significant dimensions for a particulate system may be determined by using two methods of analysis and fmding the ratio of the two mean sizes. The proliferation of measuring techniques is due to the wide range of sizes and size dependent properties
xx Preface to the first edition
that have to be measured; a twelve-inch ruler is not a satisfactory tool for measuring mileage or thousandths of an inch and is of limited use for measuring particle volume or surface area. In making a decision on which technique to use, the analyst must first consider the purpose of the analysis. What is generally required is not the size of the particles, but the value of some property of the particles that is size dependent. In such circumstances it is important whenever possible to measure the desired property, rather than to measure the 'size' by some other method and then deduce the required property. For example, in determining the 'size' of boiler ash with a view to predicting atmospheric pollution, the terminal velocity of the particle should be measured; in measuring the 'size' of catalyst particles, the surface area should be determined, since this is the property that determines its reactivity. The cost of the apparatus as well as the ease and the speed with which the analysis can be carried out have then to be considered. The final criteria are that the method shall measure the appropriate property of the particles, with an accuracy sufficient for the particular application at an acceptable cost, in a time that will allow the result to be used.
It is hoped that this book will help the reader to make the best choice of methods. The author aims to present an account of the present state of the methods of measuring particle size; it must be emphasized that there is a considerable amount of research and development in progress and the subject needs to be kept in constant review. The interest in this field in this country is evidenced by the growth of committees set up to examine particle size measurement techniques. The author is Chairman of the Particle Size Analysis Group of the Society for Analytical Chemistry. Other committees have been set up by The Pharmaceutical Society and by the British Standards Institution and particle size analysis is within the terms of reference of many other bodies. International Symposia were set up at London, Loughborough and Bradford Universities and it is with the last-named that the author is connected. The book grew from the need for a standard text-book for the Postgraduate School of Powder Technology and is published in the belief that it will be of interest to a far wider audience.
Terence Allen
Postgraduate School of Powder Technology University of Bradford
Preface to the third edition
The response to this book has been most encouraging and as a result a third edition has been written. The five years since the advent of the second edition have been full of technological changes and in order to be comprehensive it has become necessary to enlarge the edition.
With regard to the first three chapters on sampling, it is with some regret that I note that the 'golden rules of sampling' are observed more in the breach than in the commission. On the positive side it is good to see that man is becoming more aware of the need to monitor and control his environment. Chapter 4 has been greatly enlarged and a statement on the German approach to mathematical handling of size data has been presented. The chapter on centrifugal methods has been expanded to present a full statement on the disc centrifuges, and Chapter 13 has also been expanded to give a fuller statement of the Coulter principle. The chapters on surface area determination have also been enlarged due, in no small part, to the enormous interest in this parameter which has produced a considerable number of important advances. Pore size determination has been expanded to two chapters and, finally, a new chapter has been added on 'On-line particle size analysis'. My thanks go to my colleague Dr N. G. Stanley-Wood for permission to borrow extensively from his lecture notes in writing this new chapter.
It is my sincere hope that you find in this book a full statement on this particular field of analysis. Omissions and errors do have a tendency to creep in despite one's best endeavours and I would like to thank those who have drawn these to my attention in the past and hope they will continue to do so.
Terence Allen
Postgraduate School of Powder Technology University of Bradford
Acknowledgments
I would like to express my grateful thanks to Dr Brian H. Kaye for introducing me to the fascinating study of particle size analysis. My thanks are also due to numerous workers in this field for the helpful discussions we have had. Bradford University has provided me with a well-equipped laboratory in which, in teaching others, I have learnt some of the secrets of this science. One of my students was Mr T.S. Krishnamoorthy and the chapter on gas adsorption is taken from his M.Sc. thesis. At Bradford, Mr. John C. Williams has always had the time to offer helpful advice and criticism. I make no apology for taking up so much of his time since his advice was invariably good and whatever virtue this book possesses is due, in part, to him.
My thanks are also due to holders of copyright for permission to publish and to many manufacturers who have given me full details of their products.
Finally, I would like to thank my wife for her forbearance while the writing of this book has been in progress.
Terence Allen
