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Particle Size Measurement
Powder Technology Series
EDITED BY BRIAN SCARLETT
Delft University of Technology The Netherlands
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 and Hall were one of the first 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 hope 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.
Particle Size Measurement T. Allen 4th edn, hardback (041235070 X), 832 pages
Powder Porosity and Surface Area S. Lowell and Joan E. Shields
2nd edn, hardback (0412252406), 248 pages
Pneumatic Conveying of Solids R.D. Marcus, L.S. Leung, G.E. Klinzing and F. Rizk
Hardback (0412214903), 592 pages
Particle Technology Hans Rumpf Translated by F.A. Bull
Hardback (0 412 35230 3), 216 pages
Particle Size Measurement
TERENCE ALLEN
Senior Consultant E.I. Dupont de Nemour and Company
Wilmington, Delaware USA
FOURTH EDITION
CHAPMAN AND HALL LONDON. NEW YORK. TOKYO. MELBOURNE. MADRAS
UK
USA
JAPAN
Chapman and Hall, 11 New Fetter Lane, London EC4P 4EE
Chapman and Hall, 29 West 35th Street, New York NY10001
Chapman and Hall Japan, Thomson Publishing Japan, Hirakawacho Nemoto Building, 7F, 1-7-11 Hirakawa-cho, Chiyoda-ku, Tokyo 102
AUSTRALIA Chapman and Hall Australia, Thomas Nelson Australia, 480 La Trobe Street, PO Box 4725, Melbourne 3000
INDIA Chapman and Hall India, R. Sheshadri, 32 Second Main Road, CIT East, Madras 600 035
First edition 1968 Second edition 1975 Third edition 1981 Fourth edition 1990
© 1968, 1975, 1981, 1990 T. Allen
Softcover reprint of the hardcover 4th edition 1990
Typeset in 10/12pt Times by Best-set Typesetter Ltd, Hong Kong
T.J. Press Ltd, Padstow, Cornwall
ISBN-13: 978-94-010-6673-0 DOl: 10.1007/978-94-009-0417-0
e-ISBN-13: 978-94-009-0417-0
All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, or stored in any retrieval system of any nature, without the written permission of the copyright holder and the publisher, application for which shall be made to the publisher.
British Library Cataloguing in Publication data Allen, Terence
Particle size measurement. - 4th ed. 1. Particles. Size. Measurement I. Title II. Series 620.43
Library of Congress Cataloging-in-Publication Data Available
Contents
Acknowledgements
Preface to the fourth edition
Preface to the first edition
Editor's foreword to the first edition
Editor's foreword to the fourth edition
xv 111
XIX
XX
XXll
XX111
1 Sampling of powders 1 1.1 Introduction 1 1.2 Theory 2 1.3 Weight of sample required 5 1.4 Statistical considerations 7 1.5 Golden rules of sampling 8 1.6 Bulk sampling 9
1.6.1 Stored non-flowing material 9 1.6.2 Stored free-flowing material 9 1.6.3 Moving powders 10 1.6.4 Sampling from a moving stream of powder 10 1.6.5 Sampling from a conveyor belt or chute 13 1.6.6 Sampling from a bucket conveyor 16 1.6.7 Bag sampling 16 1.6.8 Sampling spears 16 1.6.9 Sampling from wagons and containers 19 1.6.10 Sampling from heaps 21
1.7 Slurry sampling 23 1.8 Sample dividing 23
1.8.1 Scoop sampling 25 1.8.2 Coning and quartering 29 1.8.3 Table sampling 29 1.8.4 Chute splitting 29 1.8.5 The spinning riffler 31
1.9 Miscellaneous devices 33 1.10 Reduction from laboratory sample to analysis sample 34 1.11 Reduction from analysis sample to measurement sample 37 1.12 Experimental tests of sample-splitting techniques 38
vi Contents
2 Sampling of dusty gases in gas streams 41 2.1 Introduction 41 2.2 Basic procedures 44
2.2.1 Sampling positions 44 2.2.2 Temperature and velocity surveys 45 2.2.3 Sampling points 46
2.3 Sampling equipment 47 2.3.1 Nozzles 47 2.3.2 Dust-sampling collector 50 2.3.3 Ancillary apparatus 57 2.3.4 On-line dust extraction 57 2.3.5 The Andersen stack sampler 58
2.4 Corrections for anisokinetic sampling 60 2.5 Probe orientation 66 2.6 Radiation methods 67
3 Sampling and sizing from the atmosphere 72 3.1 Introduction 72 3.2 Inertial techniques 76 3.3 Filtration 87 3.4 Electrostatic precipitation 88 3.5 Electrostatic charging and mobility 90 3.6 Thermal precipitation 92 3.7 The quartz microbalance 95 3.8 Optical sensing zone methods 97
3.8.1 Air Technology 102 3.8.2 Atcor Net 2000 102 3.8.3 Bausch and Lomb 102 3.8.4 Beckman 103 3.8.5 Centre for Air Environmental Studies 103 3.8.6 Climet Series 7000 103 3.8.7 Coulter Model 550 contamination monitor 103 3.8.8 Dynac 104 3.8.9 Gardner 104 3.8.10 G.C.A. Miniram 104 3.8.11 Insitec PCSV-P 104 3.8.12 Kratel Partoscope 105 3.8.13 Leitz Tyndalloscope 105 3.8.14 Met One particle counters 105 3.8.15 Pacific Scientific Hiac/Royco particle counting systems 106 3.8.16 Particle Measuring Systems 106 3.8.17 RAC particle monitors 107 3.8.18 Rotheroe and Mitchell digital dust indicator 108 3.8.19 Saab photometer 108
Contents vii
3.8.20 Sartorius 108 3.8.21 Sinclair 108 3.8.22 Techecology 109 3.8.23 TSI particle counters 109 3.8.24 The particulate volume monitor 109
3.9 Condensation nucleus counters 110 3.10 Diffusion battery 110 3.11 The aerodynamic particle size analyser 112 3.12 Miscellaneous techniques 114
4 Particle size, shape and distribution 124 4.1 Particle size 124 4.2 Particle shape 128
4.2.1 Shape coefficients 129 4.2.2 Shape factors 132 4.2.3 Applications of shape factors and shape coefficients 135 4.2.4 Shape indices 140 4.2.5 Shape regeneration by Fourier analysis 141 4.2.6 Fractal dimension characterization of textured surfaces 142
4.3 Determination of specific surface from size distribution data 144 4.3.1 Number distribution 144 4.3.2 Surface distribution 144 4.3.3 Volume distribution 145
4.4 Particle size distribution transformation between number. surface and mass 145
4.5 A verage diameters 147 4.6 Particle dispersion 153 4.7 Methods of presenting size analysis data 153 4.8 Devices for representing the cumulative distribution curve as a
straight line 156 4.8.1 Arithmetic normal distributions 156 4.8.2 The log-normal distribution 159 4.8.3 The Rosin-Rammler distribution 163 4.8.4 Mean particle sizes and specific surface evaluation for
Rosin - Rammler distributions 164 4.8.5 Other particle size distribution equations 164 4.8.6 Simplification of two-parameter equations 165 4.8.7 Evaluation of non-linear distributions on
log-normal paper 166 4.8.8 Derivation of shape factors from parallel
log-normal curves 169 4.9 The law of compensating errors 170 4.10 Alternative notation for frequency distribution 173
4.10.1 Notation 174
vi i i Contents
4.10.2 Moment of a distribution 174 4.10.3 Transformation from qt(x) to qlx) 174 4.10.4 Relation between moments 175 4.10.5 Means of distributions 176 4.10.6 Standard deviations 177 4.10.7 Coefficient of variation 177 4.10.8 Applications 177 4.10.9 Transformation of abscissa 179
4.11 Phi-notation 181 4.12 Manipulation of the log-probability equation 182
4.12.1 Average sizes 183 4.12.2 Derived average sizes 185 4.12.3 Transformation of the log-normal distribution by
count into one by weight 186 4.13 Relationship between median and mode of a log-normal
distribution 187 4.14 An improved equation and graph paper for log-normal
evaluations 187 4.14.1 Applications 189
5 Sieving 192 5.1 Introduction 192 5.2 Woven-wire and punched plate sieves 193 5.3 Electroformed micro mesh sieves 194 5.4 British Standard specification sieves 197 5.5 Methods for the use of fine sieves 198
5.5.1 Machine sieving 199 5.5.2 Wet sieving 200 5.5.3 Hand sieving 202 5.5.4 Air-jet sieving 203 5.5.5 The sonic sifter 204 5.5.6 Felvation 206 5.5.7 Self-organized sieve (SORSI) 207
5.6 Sieving errors 208 5.7 Mathematical analysis of the sieving process 210 5.8 Calibration of sieves 213
6 Microscopy 217 6.1 Introduction 217 6.2 Optical microscopy 217
6.2.1 Sample preparation 219 6.2.2 Particle size distributions from measurements on
plane sections through packed beds 221 6.3 Particle size 221
Contents ix
6.4 Transmission electron microscopy (TEM) 223 6.4.1 Specimen preparation 224 6.4.2 Replica and shadowing techniques 226 6.4.3 Chemical analysis 227
6.5 Scanning electron microscopy (SEM) 227 6.6 Manual methods of sizing particles 228
6.6.1 Graticules 229 6.6.2 Training of operators 232
6.7 Semi-automatic aids to microscopy 233 6.8 Automatic counting and sizing 240 6.9 Automatic image analysis 241 6.10 Specimen improvement techniques 243 6.11 Statistical considerations governing the determination of size
distributions by microscope count 243 6.11.1 Frequency distribution determination 243 6.11.2 Weight distribution determination 244
6.12 Conclusion 245
7 Interaction between particles and fluids in a gravitational field 249 7.1 Introduction 249 7.2 Relationship between drag coefficient and Reynolds number
for a sphere settling in a liquid 251 7.3 The laminar flow region 252 7.4 Critical diameter for laminar flow settling 253 7.5 Particle acceleration 254 7.6 Errors due to the finite extent of the fluid 255 7.7 Errors due to discontinuity of the fluid 257 7.8 Brownian motion 258 7.9 Viscosity of a suspension 261 7.10 Calculation of terminal velocities in the transition region 261 7.11 The turbulent flow region 266 7.12 Non-rigid spheres 266 7.13 N on-spherical particles 267
7.13.1 Stokes' region 267 7.13.2 The transition region 270
7.14 Concentration effects 272 7.15 Hindered settling 278
7.15.1 Low-concentration effects 278 7.15.2 High-concentration effects 279
7.16 Electro-viscosity 280
8 Dispersion of powders 285 8.1 Discussion 285 8.2 Theory of wetting 286
x Contents
8.3 The use of glidants to improve flowability of dry powders 293 8.4 Density determination 293 8.5 Viscosity 297 8.6 Sedimentation systems 298 8.7 Densities and viscosities of some aqueous solutions 303 8.8 Standard powders 304
9 Incremental methods of particle size determination 310 9.1 Basic theory 310
9.1.1 Variation in concentration within a settling suspension 310
9.1.2 Relationship between density gradient and concentration 311
9.2 Resolution for incremental methods 312 9.3 The pipette method 313
9.3.1 Experimental errors 317 9.4 The photosedimentation technique 320
9.4.1 Introduction 320 9.4.2 Theory 321 9.4.3 The extinction coefficient 323 9.4.4 Photosedimentometers 325 9.4.5 Discussion 327
9.5 X-ray sedimentation 328 9.6 Hydrometers 332 9.7 Divers 335 9.8 The specific gravity balance 336 9.9 Appendix: Worked examples 337
9.9.1 Wide-angle scanning photosedimentometer: analysis of silica 337
9.9.2 Conversion from surface distribution to weight distribution 338
9.9.3 The LADAL X-ray sedimentometer: analysis of tungstic oxide 339
10 Cumulative methods of sedimentation size analysis 344 10.1 Introduction 344 10.2 Line-start methods 344 10.3 Homogeneous suspensions 345 10.4 Sedimentation balances 346
10.4.1 The Gallenkamp balance 349 10.4.2 The Sartorius balance 351 10.4.3 The Shimadzu balance 353 10.4.4 Other balances 353
10.5 The granumeter 355
10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13
11 11.1 11.2 11.3 11.4
11.5
11.6
11.7
11.8 11.9 11.10
12 12.1 12.2 12.3
Contents xi
The micromerograph Sedimentation columns Manometric methods Pressure on the walls of the sedimentation tube Decanting The ~-back-scattering method Discussion Appendix: An approximate method of calculating size distribution from cumulative sedimentation results
Fluid classification Introduction Assessment of classifier efficiency Systems Counterflow equilibrium classifiers in the gravitational field -elutriators 11.4.1 Water elutriators 11.4.2 Air elutriators 11.4.3 Zig-zag classifiers Cross-flow gravity classifiers 11.5.1 The Warmain cyclosizer 11.5.2 The Humboldt particle size analyser TDS 11.5.3 The cross-flow elbow classifier Counterflow equilibrium classifiers in the centrifugal field 11.6.1 The Bahco classifier 11.6.2 The BCURA centrifugal elutriator 11.6.3 Centrifugal elutriation in a liquid suspension 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 Other commercially available classifiers Hydrodynamic chromatography Sedimentation field flow fractionation (SFFF)
Centrifugal methods Introduction Stokes' diameter determination Line-start technique 12.3.1 Theory 12.3.2 Line-start technique using a photometric method of
analysis 12.3.3 Early instruments: the Marshall centrifuge and the
MSA particle size analyser
356 356 361 362 362 364 365
366
373 373 373 379
380 382 386 389 390 390 391 392 392 392 394 394 394 394 395 397 397 398 399
405 405 406 407 407
407
410
XII Contents
12.3.4 The photocentrifuge 411 12.3.5 Disc photocentrifuges 413 12.3.6 The cuvette photocentrifuge 415
12.4 Homogeneous suspension 416 12.4.1 Sedimentation height small compared with distance
from centrifuge axis 416 12.4.2 The Alpine sedimentation centrifuge 417 12.4.3 The Mikropul Sedimentputer 417
12.5 Cumulative sedimentation theory for a homogeneous suspension 417
12.6 Variable-time method (variation of P with t) 419 12.7 Variable inner radius (variation of P with S) 420 12.8 Shape of centrifuge tubes 421 12.9 Alternative theory (variation of P with S) 422 12.10 Variable outer radius (variation of P with R) 423 12.11 Incremental analysis with a homogeneous suspension 424
12.11.1 The Simcar centrifuge 424 12.11.2 General theory 425
12.12 The LADAL X-ray centrifuge 432 12.13 The LADAL pipette withdrawal centrifuge 435
12.13.1 Theory for the LADAL pipette withdrawal technique 437
12.14 The supercentrifuge 442 12.15 The ultracentrifuge 445 12.16 Conclusion 445 12.17 Appendix: Worked examples 447
12.17.1 Simcar centrifuge 447 12.17.2 X-ray centrifuge 449 12.17.3 LADAL pipette centrifuge 450
13 The electrical sensing zone method of particle size distribution determination (the Coulter principle) 455
13.1 Introduction 455 13.2 Operation 456 13.3 Calibration 457 13.4 Evaluation of results 460 13.5 Theory 461 13.6 Effect of particle shape and orientation 465 13.7 Coincidence correction 466 13.8 Pulse shape 470 13.9 Multiple aperture method for powders having a wide size
distribution 474 13.9.1 General 474 13.9.2 Sieving technique 474
Contents xiii
13.9.3 Sedimentation technique 474 13.10 Carrying out a mass balance 475 13.11 End-point determination 476 13.12 Upper size limit 477 13.13 Commercial equipment 477 13.14 Conclusions 479
14 Radiation scattering methods of particle size determination 483 14.1 Introduction 483 14.2 Scattered radiation 487
14.2.1 The Rayleigh region (D ~ A) 487 14.2.2 The Rayleigh-Gans region (D < A) 488
14.3 State of polarization of the scattered radiation 490 14.4 Turbidity measurement 491 14.5 High-order Tyndall spectra (HOTS) 494 14.6 Particle size analysis by light diffraction 495 14.7 Light-scattering equipment 496 14.8 Holography 498 14.9 Miscellaneous 499
15 Permeametry and gas diffusion 503 15.1 Flow of a viscous fluid through a packed bed of powder 503 15.2 Alternative derivation of Kozeny's equation using equivalent
capillaries 505 15.3 The aspect factor k 506 15.4 Other flow equations 508 15.5 Experimental applications 512 15.6 Preparation of powder bed 513 15.7 Constant -pressure permeameters 514 15.8 Constant -volume permeameters 519 15.9 Fine particles 521 15.10 Types of flow 522 15.11 Transitional region between viscous and molecular flow 522 15.12 Experimental techniques for determining Z 524 15.13 Calculation of permeability surface 525 15.14 Diffusional flow for surface area measurement 526 15.15 The relationship between diffusion constant and specific
surface 528 15.16 Non-steady-state diffusional flow 530 15.17 Steady-state diffusional flow 532 15.18 The liquid phase permeameter 535 15.19 Application to hindered settling 537
xiv Contents
16 Gas adsorption 540 16.1 Introduction 540 16.2 Theories of adsorption 541
16.2.1 Langmuir's isotherm for ideal localized monolayers 541 16.2.2 BET isotherm for multilayer adsorption 544 16.2.3 The n-layer BET equation 548 16.2.4 Discussion of BET theory 549 16.2.5 Mathematical nature of the BET equation 551 16.2.6 Shapes of isotherms 553 16.2.7 Modifications of the BET equation 555 16.2.8 The Huttig equation 556 16.2.9 The relative method of Harkins and Jura (HJr) 556 16.2.10 Comparison between BET and HJr methods 558 16.2.11 The Frenkel- Halsey-Hill equation (FHH) 559 16.2.12 The Dubinin-Radushkevich equation (D-R) 559 16.2.13 The V A - t method 562 16.2.14 Kiselev's equation 565
16.3 Experimental techniques - factors affecting adsorption 566 16.3.1 Degassing 566 16.3.2 Pressure 567 16.3.3 Temperature and time 567 16.3.4 Adsorbate 567 16.3.5 Interlaboratory tests 568
16.4 Experimental techniques - volumetric methods 569 16.4.1 Principle 569 16.4.2 Volumetric apparatus for high surface area 569 16.4.3 Volumetric apparatus for low surface area 571
16.5 Experimental techniques - gravimetric methods 573 16.5.1 Principle 573 16.5.2 Single-spring balances 573 16.5.3 Multiple-spring balances 574 16.5.4 Beam balances 574
16.6 Continuous-flow gas chromatographic methods 575 16.6.1 Commercially available continuous-flow apparatus 580
16.7 Standard volumetric gas-adsorption apparatus 581 16.7.1 Worked example using BS4359 standard apparatus 583
16.8 Commercially available volumetric- and gravimetric-type apparatus 587
17 Other methods for determining surface area 597 17.1 Introduction 597 17.2 Calculation from size distribution data 598 17.3 Adsorption from solution 599
17.3.1 Orientation of molecules at the solid-liquid interface 599
Contents xv
17.3.2 Polarity of organic liquids and adsorbents 601 17.3.3 Drying of organic liquids and adsorbents 602
17.4 Methods of analysis of amount of solute adsorbed on to solid surfaces 603 17.4.1 Langmuir trough 603 17.4.2 Gravimetric method 604 17.4.3 Volumetric method 604 17.4.4 The Rayleigh interferometer 604 17.4.5 The precolumn method 605
17.5 Theory for adsorption from a solution 605 17.6 Quantitative methods for adsorption from a solution 606
17.6.1 Adsorption of non-electrolytes 606 17.6.2 Fatty acid adsorption 606 17.6.3 Adsorption of polymers 607 17.6.4 Adsorption of dyes 607 17.6.5 Adsorption of electrolytes 609 17.6.6 Deposition of silver 609 17.6.7 Adsorption of p-nitrophenol 609 17.6.8 Other systems 610
17.7 Theory for heat of adsorption from a liquid phase 611 17.7.1 Surface free energy of a fluid 611 17.7.2 Surface entropy and energy 612 17.7.3 Heatofimmersion 612
17.8 Static calorimetry 614 17.9 Flow microcalorimetry 615
17.9.1 Experimental procedures -liquids 616 17.9.2 Calibration 618 17.9.3 Determination of the amount of solute adsorbed: the
precolumn method 618 17.9.4 Gases 619 17.9.5 Application to the determination of surface area 620
17.10 Density method 620
18 Determination of pore size distribution by gas adsorption 624 18.1 Miscellaneous techniques 624 18.2 The Kelvin equation 624 18.3 The hysteresis loop 627 18.4 Relationship between the thickness of the adsorbed layer and
the relative pressure 631 18.5 Classification of pores 633 18.6 The as method 634 18.7 Pore size distribution determination of mesopores 634
18.7.1 Modelless method 635 18.7.2 Cylindrical core model 638
xvi Contents
18.7.3 Cylindrical pore model 639 18.7.4 Parallel plate model 643
18.8 Analysis of micropores: the MP method 645 18.9 Miscellaneous 649
19 Mercury porosimetry 653 19.1 Introduction 653 19.2 Literature survey 655 19.3 Contact angle and surface tension for mercury 658 19.4 Commercial equipment 658 19.5 Theory for volume distribution determination 663 19.6 Theory for surface distribution determination 665
19.6.1 Cylindrical pore model 665 19.6.2 Modelless method 667
19.7 Theory for length distribution determination 668 19.8 Worked example 668 19.9 Hysteresis 670 19.10 Delayed intrusion 672 19.11 Anglometers 672 19.12 Assessment of mercury porosimetry 674
19.12.1 Effect of experimental errors 674 19.12.2 Effect of interconnecting pores 674 19.12.3 Effect of contact angle 676 19.12.4 Other errors 677
19.13 Comparison with other techniques 677 19.14 Correction factors 678
20 On-line particle size analysis 682 20.1 Introduction 682 20.2 Stream-scanning techniques 683
20.2.1 Brinkmann analyser 685 20.2.2 Climet particle counting systems 685 20.2.3 Flowvision 686 20.2.4 Hiac/Royco (Pacific Scientific) particle counters 686 20.2.5 Horiba particle size analysers 691 20.2.6 The Insitec particle counter 691 20.2.7 Kane May particle size analysers 691 20.2.8 Kratel Partascope 691 20.2.9 Lasentec 692 20.2.10 Met One liquid particle counter 693 20.2.11 Particle Measuring Systems 693 20.2.12 Polytec 694 20.2.13 Procedyne particle size analyser 695 20.2.14 Spectrex Prototron particle counter 696
Contents xvii
20.2.15 Talbot optical-electronic method 698 20.2.16 Miscellaneous optical methods 698 20.2.17 Echo measurement 699 20.2.18 The Erdco acoustical counter 700 20.2.19 The Coulter on-line monitor 701 20.2.20 On-line automatic microscopy 703 20.2.21 Comparison between stream-scanning techniques 704
20.3 Field-scanning techniques 704 20.3.1 Some properties of size distributions of milled
products 704 20.3.2 Static noise measurement 705 20.3.3 Ultrasonic attenuation measurements 706 20.3.4 ~-ray attenuation 711 20.3.5 X-ray attenuation and fluorescence 713 20.3.6 Low-angle laser light scattering 715 20.3.7 Classification devices 719 20.3.8 Hydrocyclones 721 20.3.9 Screening: the Cyclosensor 723 20.3.10 Automatic sieving machines 723 20.3.11 Gas-flow permeametry 727 20.3.12 Pressure drop in nozzles 727 20.3.13 Non-Newtonian rheological properties 728 20.3.14 Correlation techniques 728 20.3.15 Photon correlation spectroscopy 729
Problems
Appendix 1 Equipment and suppliers
Appendix 2 Manufacturers' and suppliers' addresses
Author index
Subject index
738
759
767
775
799
Acknowledgements
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
Preface to the fourth edition
Powder technology is a subject in its own right, and powder characterization is central to an understanding of this discipline.
In the eight years since the printing of the third edition of Particle Size Measurement there have been two big changes in my life. After thirty years of academia I have returned to industry, and after a lifetime in Great Britain I have emigrated to the United States.
In industry the initial demand is to relate powder properties to product performance and then to maintain powder consistency. This requires on-line or rapid off-line analysis which, in turn, has led to the demand for a whole range of new instruments whose primary function is process monitoring.
Historically, chemical engineering courses have concentrated on the behaviour of fluids, and engineers enter industry relatively unschooled in the subject of powder behaviour . Yet, when my colleagues Reg Davies and John Boughton surveyed three thousand Dupont products, they discovered that 80% involved powder at some stage of their manufacture. The results of this survey illustrate the need for more training in this key subject.
This edition reflects the changing image of powder characterization towards in-process size analysis. Hence the chapter covering on-line analysis has been largely re-written. Apart from this, I have expanded certain sections and describe the new instruments that have been introduced since the last edition.
The emphasis here is on commercial equipment and for an up-date on research and development in this area I recommend the reviews Particle Size Analysis by Barth, H.G. and Sun, S.T., Anal. Chern., 57, 151R, 1985 and 142R, 1987, and Critical Reviews in Analytical Chemistry by Miller, B.Y. and Lines, R., 20(2), 75-116,1988.
Terence Allen
Senior Consultant £,1. Dupont de Nemours
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 classified 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 define 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 par-
Preface to the first edition xxi
ticulate system may be determined by using two methods of analysis and finding the ratio of the two mean sizes. The proliferation of measuring techniques is due to the wide range of sizes and size dependent properties 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
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 1T"'ch of the information is not available in a form in which it is likely to influenL ~ the education of students, particularly in chemical engineering, who may later ''': employed in industrial organizations where they will be faced with the prob, ~ms 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 witl' the measurement of the size of small particles since this is the basic technique underlying all other work in powder technology. The reliability of researcl, results, for example, on the size reduction of solid particles, cannot be bette. 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.
J.e. Williams
Editor's foreword to the fourth edition
This book has now reached its fourth edition and is undoubtedly the standard reference book on particle size measuring techniques. The book started life as a short course text and, in its successive editions, it has Lcen polished and extended to become a balanced and comprehensive text. full of information and reflecting great experience. This book is the flaPJp of the series and I hope that many other books will follow it to the S()' .,e level of maturity.
Brian Scarlett
January 1990