The new sub-title of Volume 2, Particle Technology and Separation Processes, reflects both the emphasis of the new edition and the current importance of these two topics in Chemical Engi
Trang 2CHEMICAL ENGINEERING
VOLUME 2 FIFTH EDITION
Particle Technology and
Separation Processes
Trang 3J M COULSON & J F RICHARDSON
Chemical Engineering, Volume 1, Sixth edition
Fluid Flow, Heat Transfer and Mass Transfer
(with J R Backhurst and J H Harker)
Chemical Engineering, Volume 3, Third edition
Chemical and Biochemical Reaction Engineering, and Control
(edited by J F Richardson and D G Peacock)
Chemical Engineering, Volume 6, Third edition
Chemical Engineering Design
(R K Sinnott)
Chemical Engineering, Solutions to Problems in Volume 1
(J R Backhurst, J H Harker and J F Richardson)
Chemical Engineering, Solutions to Problems in Volume 2
(J R Backhurst, J H Harker and J F Richardson)
Trang 4CHEMICAL ENGINEERING
VOLUME 2 FIFTH EDITION
Particle Technology and
University of Newcastle upon Tyne
OXFORD AMSTERDAM BOSTON LONDON NEW YORK PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Trang 5An imprint of Elsevier Science
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
Third edition (SI units) 1978
Reprinted (with revisions) 1980, 1983, 1985, 1987, 1989
Fourth edition 1991
Reprinted (with revisions) 1993, 1996, 1997, 1998, 1999, 2001
Fifth edition 2002
Copyright 1991, 2002, J F Richardson and J H Harker All rights reserved
The right of J F Richardson and J H Harker to be identified as the authors of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988
All rights reserved No part of this publication may be reproduced in
any material form (including photocopying or storing in any medium by
electronic means and whether or not transiently or incidentally to some
other use of this publication) without the written permission of the
copyright holder except in accordance with the provisions of the Copyright,
Designs and Patents Act 1988 or under the terms of a licence issued by the
Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London,
England W1P 0LP Applications for the copyright holder’s written
permission to reproduce any part of this publication should be addressed
to the publishers
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN 0 7506 4445 1
Typeset by Laserwords Private Limited, Chennai, India
Printed and bounded in Great Britain by the Bath Press, Bath
Trang 6Preface to the Fourth Edition xix
Preface to the 1983 Reprint of the Third Edition xxi
Preface to Third Edition xxiii
Preface to Second Edition xxv
Preface to First Edition xxvii
Acknowledgements xxix
INTRODUCTION xxxi
1 Particulate Solids 1
1.1 INTRODUCTION 1
1.2 PARTICLE CHARACTERISATION 2
1.3 PARTICULATE SOLIDS IN BULK 22
1.4 BLENDING OF SOLID PARTICLES 30
1.5 CLASSIFICATION OF SOLID PARTICLES 37
1.6 SEPARATION OF SUSPENDED SOLID PARTICLES FROM FLUIDS 67
1.7 FURTHER READING 91
1.8 REFERENCES 92
1.9 NOMENCLATURE 93
2 Particle Size Reduction and Enlargement 95
2.1 INTRODUCTION 95
2.2 SIZE REDUCTION OF SOLIDS 95
2.3 TYPES OF CRUSHING EQUIPMENT 106
2.4 SIZE ENLARGEMENT OF PARTICLES 137
2.5 FURTHER READING 143
2.6 REFERENCES 143
2.7 NOMENCLATURE 144
3 Motion of Particles in a Fluid 146
Trang 73.2 FLOW PAST A CYLINDER AND A SPHERE 146
3.3 THE DRAG FORCE ON A SPHERICAL PARTICLE 149
3.4 NON-SPHERICAL PARTICLES 164
3.5 MOTION OF BUBBLES AND DROPS 168
3.6 DRAG FORCES AND SETTLING VELOCITIES FOR PARTICLES IN NON- NEWTONIAN FLUIDS 169
3.7 ACCELERATING MOTION OF A PARTICLE IN THE GRAVITATIONAL FIELD 173
3.8 MOTION OF PARTICLES IN A CENTRIFUGAL FIELD 185
3.9 FURTHER READING 187
3.10 REFERENCES 188
3.11 NOMENCLATURE 189
4 Flow of Fluids through Granular Beds and Packed Columns 191
4.1 INTRODUCTION 191
4.2 FLOW OF A SINGLE FLUID THROUGH A GRANULAR BED 191
4.3 DISPERSION 205
4.4 HEAT TRANSFER IN PACKED BEDS 211
4.5 PACKED COLUMNS 212
4.6 FURTHER READING 232
4.7 REFERENCES 232
4.8 NOMENCLATURE 234
5 Sedimentation 237
5.1 INTRODUCTION 237
5.2 SEDIMENTATION OF FINE PARTICLES 237
5.3 SEDIMENTATION OF COARSE PARTICLES 267
5.4 FURTHER READING 286
5.5 REFERENCES 286
5.6 NOMENCLATURE 288
Trang 86.1 CHARACTERISTICS OF FLUIDISED
SYSTEMS 291
6.2 LIQUID-SOLIDS SYSTEMS 302
6.3 GAS-SOLIDS SYSTEMS 315
6.4 GAS-LIQUID SOLIDS FLUIDISED BEDS 333
6.5 HEAT TRANSFER TO A BOUNDARY SURFACE 334
6.6 MASS AND HEAT TRANSFER BETWEEN FLUID AND PARTICLES 343
6.7 SUMMARY OF THE PROPERTIES OF FLUIDISED BEDS 357
6.8 APPLICATIONS OF THE FLUIDISED SOLIDS TECHNIQUE 358
6.9 FURTHER READING 364
6.10 REFERENCES 364
6.11 NOMENCLATURE 369
7 Liquid Filtration 372
7.1 INTRODUCTION 372
7.2 FILTRATION THEORY 374
7.3 FILTRATION PRACTICE 382
7.4 FILTRATION EQUIPMENT 387
7.5 FURTHER READING 434
7.6 REFERENCES 435
7.7 NOMENCLATURE 435
8 Membrane Separation Processes 437
8.1 INTRODUCTION 437
8.2 CLASSIFICATION OF MEMBRANE PROCESSES 437
8.3 THE NATURE OF SYNTHETIC MEMBRANES 438
8.4 GENERAL MEMBRANE EQUATION 442
8.5 CROSS-FLOW MICROFILTRATION 442
8.6 ULTRAFILTRATION 446
Trang 98.8 MEMBRANE MODULES AND PLANT
CONFIGURATION 455
8.9 MEMBRANE FOULING 464
8.10 ELECTRODIALYSIS 465
8.11 REVERSE OSMOSIS WATER TREATMENT PLANT 467
8.12 PERVAPORATION 469
8.13 LIQUID MEMBRANES 471
8.14 GAS SEPARATIONS 472
8.15 FURTHER READING 472
8.16 REFERENCES 473
8.17 NOMENCLATURE 474
9 Centrifugal Separations 475
9.1 INTRODUCTION 475
9.2 SHAPE OF THE FREE SURFACE OF THE LIQUID 476
9.3 CENTRIFUGAL PRESSURE 477
9.4 SEPARATION OF IMMISCIBLE LIQUIDS OF DIFFERENT DENSITIES 478
9.5 SEDIMENTATION IN A CENTRIFUGAL FIELD 480
9.6 FILTRATION IN A CENTRIFUGE 485
9.7 MECHANICAL DESIGN 489
9.8 CENTRIFUGAL EQUIPMENT 489
9.9 FURTHER READING 500
9.10 REFERENCES 500
9.11 NOMENCLATURE 501
10 Leaching 502
10.1 INTRODUCTION 502
10.2 MASS TRANSFER IN LEACHING OPERATIONS 503
10.3 EQUIPMENT FOR LEACHING 506
10.4 COUNTERCURRENT WASHING OF SOLIDS 515
Trang 10STAGES 519
10.6 NUMBER OF STAGES FOR COUNTERCURRENT WASHING BY GRAPHICAL METHODS 526
10.7 FURTHER READING 540
10.8 REFERENCES 540
10.9 NOMENCLATURE 540
11 Distillation 542
11.1 INTRODUCTION 542
11.2 VAPOUR LIQUID EQUILIBRIUM 542
11.3 METHODS OF DISTILLATION TWO COMPONENT MIXTURES 555
11.4 THE FRACTIONATING COLUMN 559
11.5 CONDITIONS FOR VARYING OVERFLOW IN NON-IDEAL BINARY SYSTEMS 581
11.6 BATCH DISTILLATION 592
11.7 MULTICOMPONENT MIXTURES 599
11.8 AZEOTROPIC AND EXTRACTIVE DISTILLATION 616
11.9 STEAM DISTILLATION 621
11.10 PLATE COLUMNS 625
11.11 PACKED COLUMNS FOR DISTILLATION 638
11.12 FURTHER READING 649
11.13 REFERENCES 649
11.14 NOMENCLATURE 652
12 Absorption of Gases 656
12.1 INTRODUCTION 656
12.2 CONDITIONS OF EQUILIBRIUM BETWEEN LIQUID AND GAS 657
12.3 THE MECHANISM OF ABSORPTION 658
12.4 DETERMINATION OF TRANSFER COEFFICIENTS 666
Trang 11CHEMICAL REACTION 675
12.6 ABSORPTION ACCOMPANIED BY THE LIBERATION OF HEAT 681
12.7 PACKED TOWERS FOR GAS ABSORPTION 682
12.8 PLATE TOWERS FOR GAS ABSORPTION 702
12.9 OTHER EQUIPMENT FOR GAS ABSORPTION 709
12.10 FURTHER READING 714
12.11 REFERENCES 715
12.12 NOMENCLATURE 717
13 Liquid Liquid Extraction 721
13.1 INTRODUCTION 721
13.2 EXTRACTION PROCESSES 722
13.3 EQUILIBRIUM DATA 725
13.4 CALCULATION OF THE NUMBER OF THEORETICAL STAGES 728
13.5 CLASSIFICATION OF EXTRACTION EQUIPMENT 742
13.6 STAGE-WISE EQUIPMENT FOR EXTRACTION 744
13.7 DIFFERENTIAL CONTACT EQUIPMENT FOR EXTRACTION 750
13.8 USE OF SPECIALISED FLUIDS 763
13.9 FURTHER READING 766
13.10 REFERENCES 767
13.11 NOMENCLATURE 769
14 Evaporation 771
14.1 INTRODUCTION 771
14.2 HEAT TRANSFER IN EVAPORATORS 771
14.3 SINGLE-EFFECT EVAPORATORS 778
14.4 MULTIPLE-EFFECT EVAPORATORS 780
14.5 IMPROVED EFFICIENCY IN EVAPORATION 791
14.6 EVAPORATOR OPERATION 802
Trang 1214.8 FURTHER READING 823
14.9 REFERENCES 823
14.10 NOMENCLATURE 825
15 Crystallisation 827
15.1 INTRODUCTION 827
15.2 CRYSTALLISATION FUNDAMENTALS 828
15.3 CRYSTALLISATION FROM SOLUTIONS 853
15.4 CRYSTALLISATION FROM MELTS 868
15.5 CRYSTALLISATION FROM VAPOURS 875
15.6 FRACTIONAL CRYSTALLISATION 885
15.7 FREEZE CRYSTALLISATION 888
15.8 HIGH PRESSURE CRYSTALLISATION 890
15.9 FURTHER READING 893
15.10 REFERENCES 894
15.11 NOMENCLATURE 897
16 Drying 901
16.1 INTRODUCTION 901
16.2 GENERAL PRINCIPLES 901
16.3 RATE OF DRYING 904
16.4 THE MECHANISM OF MOISTURE MOVEMENT DURING DRYING 912
16.5 DRYING EQUIPMENT 918
16.6 SPECIALISED DRYING METHODS 957
16.7 THE DRYING OF GASES 963
16.8 FURTHER READING 964
16.9 REFERENCES 965
16.10 NOMENCLATURE 967
17 Adsorption 970
17.1 INTRODUCTION 970
17.2 THE NATURE OF ADSORBENTS 974
Trang 1317.4 MULTICOMPONENT ADSORPTION 993
17.5 ADSORPTION FROM LIQUIDS 994
17.6 STRUCTURE OF ADSORBENTS 994
17.7 KINETIC EFFECTS 1002
17.8 ADSORPTION EQUIPMENT 1008
17.9 REGENERATION OF SPENT ADSORBENT 1026
17.10 FURTHER READING 1047
17.11 REFERENCES 1047
17.12 NOMENCLATURE 1049
18 Ion Exchange 1053
18.1 INTRODUCTION 1053
18.2 ION EXCHANGE RESINS 1054
18.3 RESIN CAPACITY 1054
18.4 EQUILIBRIUM 1056
18.5 EXCHANGE KINETICS 1060
18.6 ION EXCHANGE EQUIPMENT 1066
18.7 FURTHER READING 1073
18.8 REFERENCES 1073
18.9 NOMENCLATURE 1074
19 Chromatographic Separations 1076
19.1 INTRODUCTION 1076
19.2 ELUTION CHROMATOGRAPHY 1077
19.3 BAND BROADENING AND SEPARATION EFFICIENCY 1080
19.4 TYPES OF CHROMATOGRAPHY 1083
19.5 LARGE SCALE ELUTION (CYCLIC BATCH) CHROMATOGRAPHY 1088
19.6 SELECTIVE ADSORPTION OF PROTEINS 1093
19.7 SIMULATED COUNTERCURRENT TECHNIQUES 1096
19.8 COMBINED REACTION AND SEPARATION 1098
Trang 14METHODS 1099
19.10 FURTHER READING 1100
19.11 REFERENCES 1100
19.12 NOMENCLATURE 1103
20 Product Design and Process Intensification 1104
20.1 PRODUCT DESIGN 1104
20.2 PROCESS INTENSIFICATION 1110
20.3 FURTHER READING 1134
20.4 REFERENCES 1134
Appendix 1137
A1 STEAM TABLES 1138
A2 CONVERSION FACTORS FOR SOME COMMON SI UNITS 1147
Problems 1149
Trang 15Preface to the Fifth Edition
It is now 47 years since Volume 2 was first published in 1955, and during the vening time the profession of chemical engineering has grown to maturity in the UK, andworldwide; the Institution of Chemical Engineers, for instance, has moved on from its 33rd
inter-to its 80th year of existence No longer are the heavy chemical and petroleum-based tries the main fields of industrial applications of the discipline, but chemical engineeringhas now penetrated into areas, such as pharmaceuticals, health care, foodstuffs, andbiotechnology, where the general level of sophistication of the products is much greater,and the scale of production often much smaller, though the unit value of the products isgenerally much higher This change has led to a move away from large-scale continuousplants to smaller-scale batch processing, often in multipurpose plants Furthermore, there
indus-is an increased emphasindus-is on product purity, and the need for more refined separationtechnology, especially in the pharmaceutical industry where it is often necessary to carryout the difficult separation of stereo-isomers, one of which may have the desired thera-peutic properties while the other is extremely malignant Many of these large moleculesare fragile and are liable to be broken down by the harsh solvents commonly used inthe manufacture of bulk chemicals The general principles involved in processing thesemore specialised materials are essentially the same as in bulk chemical manufacture, butspecial care must often be taken to ensure that processing conditions are mild
One big change over the years in the chemical and processing industries is the emphasis
on designing products with properties that are specified, often in precise detail, by thecustomer Chemical composition is often of relatively little importance provided that the
product has the desired attributes Hence product design, a multidisciplinary activity, has become a necessary precursor to process design.
Although undergraduate courses now generally take into account these new ments, the basic principles of chemical engineering remain largely unchanged and this
require-is particularly the case with the two main topics of Volume 2, Particle Mechanics and
Separation Processes In preparing this new edition, the authors have faced a typical
engineering situation where a compromise has to be reached on size The base has increased to such an extent that many of the individual chapters appear to meritexpansion into separate books At the same time, as far as students and those from otherdisciplines are concerned, there is still a need for a an integrated concise treatment inwhich there is a consistency of approach across the board and, most importantly, a degree
knowledge-of uniformity in the use knowledge-of symbols It has to be remembered that the learning capacity
of students is certainly no greater than it was in the past, and a book of manageableproportions is still needed
The advice that academic staffs worldwide have given in relation to revising the book
has been that the layout should be retained substantially unchanged — better the devil
we know, with all his faults! With this in mind the basic structure has been maintained.
However, the old Chapter 8 on Gas Cleaning, which probably did not merit a chapter
xvii
Trang 16on its own, has been incorporated into Chapter 1, where it sits comfortably beside othertopics involving the separation of solid particles from fluids This has left Chapter 8 free
to accommodate Membrane Separations (formerly Chapter 20) which then follows on logically from Filtration in Chapter 7 The new Chapter 20 then provides an opportunity
to look to the future, and to introduce the topics of Product Design and the Use of
Intensified Fields (particularly centrifugal in place of gravitational) and miniaturisation,
with all the advantages of reduced hold-up, leading to a reduction in the amount ofout-of-specification material produced during the changeover between products in thecase multipurpose plants, and in improved safety where the materials have potentiallyhazardous properties
Other significant changes are the replacement of the existing chapter on Crystallisation
by an entirely new chapter written with expert guidance from Professor J W Mullin, theauthor of the standard textbook on that topic The other chapters have all been updated andadditional Examples and Solutions incorporated in the text Several additional Problemshave been added at the end, and solutions are available in the Solutions Manual, and now
on the Butterworth-Heinemann website
We are, as usual, indebted to both reviewers and readers for their suggestions and forpointing out errors in earlier editions These have all been taken into account Please keep
it up in future! We aim to be error-free but are not always as successful as we would like
to be! Unfortunately, the new edition is somewhat longer than the previous one, almostinevitably so with the great expansion in the amount of information available Whenever
in the past we have cut out material which we have regarded as being out-of-date, there isinevitably somebody who writes to say that he now has to keep both the old and the neweditions because he finds that something which he had always found particularly useful
in the past no longer appears in the revised edition It seems that you cannot win, but wekeep trying!
J F RICHARDSON
J H HARKER
Trang 17Preface to the Fourth Edition
Details of the current restructuring of this Chemical Engineering Series, coinciding withthe publication of the Fourth Edition of Volumes 1 and 2 and to be followed by neweditions of the other volumes, have been set out in the Preface to the Fourth Edition ofVolume 1 The revision involves the inclusion in Volume 1 of material on non-Newtonianflow (previously in Volume 3) and the transference from Volume 2 to Volume 1 of
Pneumatic and Hydraulic Conveying and Liquid Mixing In addition, Volume 6, written by
Mr R K Sinnott, which first appeared in 1983, nearly thirty years after the first volumes,acquires some of the design-orientated material from Volume 2, particularly that related
to the hydraulics of packed and plate columns
The new sub-title of Volume 2, Particle Technology and Separation Processes, reflects
both the emphasis of the new edition and the current importance of these two topics
in Chemical Engineering Particle Technology covers the basic properties of systems of
particles and their preparation by comminution (Chapters 1 and 2) Subsequent chaptersdeal with the interaction between fluids and particles, under conditions ranging from thoseapplicable to single isolated particles, to systems of particles freely suspended in fluids,
as in sedimentation and fluidisation; and to packed beds and columns where particlesare held in a fixed configuration relative to one another The behaviour of particles in
both gravitational and centrifugal fields is also covered It will be noted that Centrifugal
Separations are now brought together again in a single chapter, as in the original scheme
of the first two editions, because the dispersal of the material between other chapters inthe Third Edition was considered to be not entirely satisfactory
Fluid– solids Separation Processes are discussed in the earlier chapters under theheadings of Sedimentation, Filtration, Gas Cleaning and Centrifugal Separations Theremaining separations involve applications of mass-transfer processes, in the presence
of solid particles in Leaching (solid– liquid extraction), Drying and Crystallisation InDistillation, Gas Absorption and Liquid– Liquid Extraction, interactions occur betweentwo fluid streams with mass transfer taking place across a phase boundary Usually theseoperations are carried out as continuous countercurrent flow processes, either stagewise (as
in a plate-column) or with differential contacting (as in a packed-column) There is a casetherefore for a generalised treatment of countercurrent contacting processes with each
of the individual operations, such as Distillation, treated as particular cases Althoughthis approach has considerable merit, both conceptually and in terms of economy ofspace, it has not been adopted here, because the authors’ experience of teaching suggeststhat the student more readily grasps the principles involved, by considering each topic
in turn, provided of course that the teacher makes a serious attempt to emphasise thecommon features
The new edition concludes with four chapters which are newcomers to Volume 2, eachwritten by a specialist author from the Chemical Engineering Department at Swansea —
xix
Trang 18Adsorption and Ion Exchange (Chapters 17 and 18)(topics previously covered in Volume 3)
by J H Bowen
Chromatographic Separations (Chapter 19)
by J R Conder
andMembrane Separations (Chapter 20)
by W R Bowen.
These techniques are of particular interest in that they provide a means of separatingmolecular species which are difficult to separate by other techniques and which may bepresent in very low concentrations Such species include large molecules, sub-micrometresize particles, stereo-isomers and the products from bioreactors (Volume 3) The separa-
tions can be highly specific and may depend on molecular size and shape, and the
configuration of the constituent chemical groups of the molecules
Again I would express our deep sense of loss on the death of our colleague, ProfessorJohn Coulson, in January 1990 His two former colleagues at Newcastle, Dr John Back-hurst and the Reverend Dr John Harker, have played a substantial part in the preparation
of this new edition both by updating the sections originally attributable to him, and byobtaining new illustrations and descriptions of industrial equipment
Finally, may I again thank our readers who, in the past, have made such helpful tions and have drawn to our attention errors, many of which would never have been spotted
sugges-by the authors Would they please continue their good work!
July 1990
Note to Fourth Edition — Revised Impression 1993
In this reprint corrections and minor revisions have been incorporated The principalchanges are as follows:
(1) Addition of an account of the construction and operation of the Szego GrindingMill (Chapter 2)
(2) Inclusion of the Yoshioka method for the design of thickeners (Chapter 5).(3) Incorporation of Geldart’s classification of powders in relation to fluidisation charac-teristics (Chapter 6)
(4) The substitution of a more logical approach to filtration of slurries yieldingcompressible cakes and redefinition of the specific resistance (Chapter 7)
(5) Revision of the nomenclature for the underflow streams of washing thickeners tobring it into line with that used for other stagewise processes, including distillationand absorption (Chapter 10)
(6) A small addition to the selection of dryers and the inclusion of Examples(Chapter 16)
JFR
Trang 19Preface to the 1983 Reprint of the
Third Edition
In this volume, there is an account of the basic theory underlying the various Unit tions, and typical items of equipment are described The equipment items are the essentialcomponents of a complete chemical plant, and the way in which such a plant is designed
Opera-is the subject of Volume 6 of the series which has just appeared The new volume includesmaterial on flowsheeting, heat and material balances, piping, mechanical construction andcosting It completes the Series and forms an introduction to the very broad subject ofChemical Engineering Design
xxi
Trang 20Preface to Third Edition
In producing a third edition, we have taken the opportunity, not only of updating thematerial but also of expressing the values of all the physical properties and characteristics
of the systems in the SI System of units, as has already been done in Volumes 1 and 3 The
SI system, which is described in detail in Volume 1, is widely adopted in Europe and isnow gaining support elsewhere in the world However, because some readers will still bemore familiar with the British system, based on the foot, pound and second, the old unitshave been retained as alternatives wherever this can be done without causing confusion.The material has, to some extent, been re-arranged and the first chapter now relates
to the characteristics of particles and their behaviour in bulk, the blending of solids,and classification according to size or composition of material The following chaptersdescribe the behaviour of particles moving in a fluid and the effects of both gravitationaland centrifugal forces and of the interactions between neighbouring particles The oldchapter on centrifuges has now been eliminated and the material dispersed into the appro-priate parts of other chapters Important applications which are considered include flow ingranular beds and packed columns, fluidisation, transport of suspended particles, filtrationand gas cleaning An example of the updating which has been carried out is the addition of
a short section on fluidised bed combustion, potentially the most important commercialapplication of the technique of fluidisation In addition, we have included an entirelynew section on flocculation, which has been prepared for us by Dr D J A Williams ofUniversity College, Swansea, to whom we are much indebted
Mass transfer operations play a dominant role in chemical processing and this isreflected in the continued attention given to the operations of solid– liquid extraction,distillation, gas absorption and liquid– liquid extraction The last of these subjects, togetherwith material on liquid– liquid mixing, is now dealt within a single chapter on liquid– liquidsystems, the remainder of the material which appeared in the former chapter on mixinghaving been included earlier under the heading of solids blending The volume concludeswith chapters on evaporation, crystallisation and drying
Volumes 1, 2 and 3 form an integrated series with the fundamentals of fluid flow,heat transfer and mass transfer in the first volume, the physical operations of chemicalengineering in this, the second volume, and in the third volume, the basis of chemicaland biochemical reactor design, some of the physical operations which are now gaining
in importance and the underlying theory of both process control and computation Thesolutions to the problems listed in Volumes 1 and 2 are now available as Volumes 4 and
5 respectively Furthermore, an additional volume in the series is in course of preparationand will provide an introduction to chemical engineering design and indicate how theprinciples enunciated in the earlier volumes can be translated into chemical plant
We welcome the collaboration of J R Backhurst and J H Harker as co-authors in thepreparation of this edition, following their assistance in the editing of the latest edition
of Volume 1 and their authorship of Volumes 4 and 5 We also look forward to theappearance of R K Sinnott’s volume on chemical engineering design
xxiii
Trang 21Preface to Second Edition
This text deals with the physical operations used in the chemical and allied industries.These operations are conveniently designated “unit operations” to indicate that each singleoperation, such as filtration, is used in a wide range of industries, and frequently undervarying conditions of temperature and pressure
Since the publication of the first edition in 1955 there has been a substantial increase inthe relevant technical literature but the majority of developments have originated inresearch work in government and university laboratories rather than in industrial compa-nies As a result, correlations based on laboratory data have not always been adequatelyconfirmed on the industrial scale However, the section on absorption towers containsdata obtained on industrial equipment and most of the expressions used in the chapters
on distillation and evaporation are based on results from industrial practice
In carrying out this revision we have made substantial alteration to Chapters 1, 5,
6, 7, 12, 13 and 15∗ and have taken the opportunity of presenting the volume pagedseparately from Volume 1 The revision has been possible only as the result of the kind co-operation and help of Professor J D Thornton (Chapter 12), Mr J Porter (Chapter 13),
Mr K E Peet (Chapter 10) and Dr B Waldie (Chapter 1), all of the University atNewcastle, and Dr N Dombrowski of the University of Leeds (Chapter 15) We want inparticular to express our appreciation of the considerable amount of work carried out by
Mr D G Peacock of the School of Pharmacy, University of London He has not onlychecked through the entire revision but has made numerous additions to many chaptersand has overhauled the index
We should like to thank the companies who have kindly provided illustrations of theirequipment and also the many readers of the previous edition who have made usefulcomments and helpful suggestions
Chemical engineering is no longer confined to purely physical processes and the unitoperations, and a number of important new topics, including reactor design, automaticcontrol of plants, biochemical engineering, and the use of computers for both processdesign and control of chemical plant will be covered in a forthcoming Volume 3 which
Trang 22Preface to First Edition
In presenting Volume 2 of Chemical Engineering, it has been our intention to cover what
we believe to be the more important unit operations used in the chemical and processindustries These unit operations, which are mainly physical in nature, have been classified,
as far as possible, according to the underlying mechanism of the transfer operation Inonly a few cases is it possible to give design procedures when a chemical reaction takesplace in addition to a physical process This difficulty arises from the fact that, when wetry to design such units as absorption towers in which there is a chemical reaction, weare not yet in a position to offer a thoroughly rigorous method of solution We have notgiven an account of the transportation of materials in such equipment as belt conveyors orbucket elevators, which we feel lie more distinctly in the field of mechanical engineering
In presenting a good deal of information in this book, we have been much indebted
to facilities made available to us by Professor Newitt, in whose department we havebeen working for many years The reader will find a number of gaps, and a number ofprinciples which are as yet not thoroughly developed Chemical engineering is a field inwhich there is still much research to be done, and, if this work will in any way stimulateactivities in this direction, we shall feel very much rewarded It is hoped that the form
of presentation will be found useful in indicating the kind of information which has beenmade available by research workers up to the present day Chemical engineering is in itsinfancy, and we must not suppose that the approach presented here must necessarily belooked upon as correct in the years to come One of the advantages of this subject is thatits boundaries are not sharply defined
Finally, we should like to thank the following friends for valuable commentsand suggestions: Mr G H Anderson, Mr R W Corben, Mr W J De Coursey,
Dr M Guter, Dr L L Katan, Dr R Lessing, Dr D J Rasbash, Dr H ski, Dr W Smith, Mr D Train, Mr M E O’K Trowbridge, Mr F E Warner and
Sawistow-Dr W N Zaki
xxvii
Trang 23The authors and publishers acknowledge with thanks the assistance given by the followingcompanies and individuals in providing illustrations and data for this volume and givingtheir permission for reproduction Everyone was most helpful and some firms went toconsiderable trouble to provide exactly what was required We are extremely grateful tothem all
Robinson Milling Systems Ltd for Fig 1.16
Baker Perkins Ltd for Figs 1.23, 2.8, 2.34, 13.39, 13.40
Buss (UK) Ltd, Cheadle Hulme, Cheshire for Figs 1.24, 14.24
Dorr-Oliver Co Ltd, Croydon, Surrey for Figs 1.26, 1.29, 7.15, 7.22, 10.8, 10.9.Denver Process Equipment Ltd, Leatherhead, Surrey for Figs 1.27, 1.30, 1.32, 1.47, 1.48.Wilfley Mining Machinery Co Ltd for Fig 1.33
NEI International Combustion Ltd, Derby for Figs 1.34, 1.35, 1.36, 1.37, 2.10, 2.20–2.24,2.27, 2.30, 14.18, 16.23
Lockers Engineers Ltd, Warrington for Figs 1.40, 1.41, 1.42
Master Magnets Ltd, Birmingham for Figs 1.43, 1.44, 1.45
AAF Ltd, Cramlington, Northumberland for Figs 1.54, 1.68, 1.70, 1.72
Vaba Process Plant Ltd, Rotherham, Yorks, successors to Edgar Allen Co Ltd for Figs 2.4,2.7, 2.13, 2.14, 2.29
Hadfields Ltd for Fig 2.5
Hosokawa Micron Ltd, Runcorn, Cheshire for Fig 2.12
Babcock & Wilcox Ltd for Fig 2.19
Premier Colloid Mills for Figs 2.33
Amandus– Kahl, Hamburg, Germany for Fig 2.35
McGraw-Hill Book Co for Fig 3.3
Norton Chemical Process Products (Europe) Ltd, Stoke-on-Trent, Staffs for Table 4.3.Glitsch UK Ltd, Kirkby Stephen, Cheshire for Figs 11.51, 11.52, 11.53
Sulzer (UK) Ltd, Farnborough, Hants for Figs 1.67, 4.13, 4.14, 4.15
Johnson-Progress Ltd, Stoke-on-Trent, Staffs for Figs 7.6, 7.7, 7.9, 7.10
Filtration Systems Ltd, Mirfield, W Yorks, for Fig 7.11
Stockdale Filtration Systems Ltd, Macclesfield, Cheshire for Fig 7.12, and Tables 7.1,7.2, 7.3
Stella-Meta Filters Ltd, Whitchurch, Hants for Figs 7.13, 7.14
Delfilt Ltd, Bath, Avon for Fig 7.16
Charlestown Engineering Ltd, St Austell, Cornwall for Figs 7.24, 7.25
Institution of Mechanical Engineers for Fig 1.59
Sturtevant Engineering Co Ltd for Fig 1.60
Thomas Broadbent & Sons Ltd, Huddersfield, West Yorkshire for Figs 9.13, 9.14
xxix
Trang 24Amicon Ltd for Figs 8.12.
P C I for Fig 8.9
A/S De Danske Sukkerfabrikker, Denmark for Fig 8.10
Dr Huabin Yin for Fig 8.1
Dr Nrdal Hilal for Fig 8.2
Alfa-Laval Sharples Ltd, Camberley, Surrey, for Figs 9.8, 9.10, 9.11, 9.12, 9.16, 9.17,13.37, 14.20
Sulzer Escher Wyss Ltd, Zurich, Switzerland for Fig 9.15
APV Mitchell Ltd for Fig 12.17
Davy Powergas Ltd for Fig 13.26
Swenson Evaporator Co for Figs 14.17, 14.18, 14.19, 14.20
APV Baker Ltd, Crawley, Sussex for Figs 14.21, 14.22, 14.23, 14.24, 14.25, 14.26
The Editor and Publishers of Chemical and Process Engineering for Figs 14.28, 14.30.
APV Pasilac Ltd, Carlisle, Cumbria for Figs 16.10, 16.11
Buflovak Equipment Division of Blaw-Knox Co Ltd for Figs 16.17, 16.18, and Table 16.3
Dr N Dombrowski for Figs 16.19, 16.22
Ventilex for Fig 16.29
Trang 25The understanding of the design and construction of chemical plant is frequently regarded
as the essence of chemical engineering and it is this area which is covered in Volume 6
of this series Starting from the original conception of the process by the chemist, it isnecessary to appreciate the chemical, physical and many of the engineering features inorder to develop the laboratory process to an industrial scale This volume is concernedmainly with the physical nature of the processes that take place in industrial units, and,
in particular, with determining the factors that influence the rate of transfer of material.The basic principles underlying these operations, namely fluid dynamics, and heat andmass transfer, are discussed in Volume 1, and it is the application of these principles thatforms the main part of Volume 2
Throughout what are conveniently regarded as the process industries, there are manyphysical operations that are common to a number of the individual industries, and may
be regarded as unit operations Some of these operations involve particulate solids and
many of them are aimed at achieving a separation of the components of a mixture.Thus, the separation of solids from a suspension by filtration, the separation of liquids
by distillation, and the removal of water by evaporation and drying are typical of suchoperations The problem of designing a distillation unit for the fermentation industry, thepetroleum industry or the organic chemical industry is, in principle, the same, and it ismainly in the details of construction that the differences will occur The concentration
of solutions by evaporation is again a typical operation that is basically similar in thehandling of sugar, or salt, or fruit juices, though there will be differences in the mostsuitable arrangement This form of classification has been used here, but the operationsinvolved have been grouped according to the mechanism of the transfer operation, so thatthe operations involving solids in fluids are considered together and then the diffusionprocesses of distillation, absorption and liquid-liquid extraction are taken in successivechapters In examining many of these unit operations, it is found that the rate of heattransfer or the nature of the fluid flow is the governing feature The transportation of asolid or a fluid stream between processing units is another instance of the importance ofunderstanding fluid dynamics
One of the difficult problems of design is that of maintaining conditions of similaritybetween laboratory units and the larger-scale industrial plants Thus, if a mixture is to bemaintained at a certain temperature during the course of an exothermic reaction, then onthe laboratory scale there is rarely any real difficulty in maintaining isothermal conditions
On the other hand, in a large reactor the ratio of the external surface to the volume — which
is inversely proportional to the linear dimension of the unit — is in most cases of a differentorder, and the problem of removing the heat of reaction becomes a major item in design
Some of the general problems associated with scaling-up are considered as they arise in
many of the chapters Again, the introduction and removal of the reactants may presentdifficult problems on the large scale, especially if they contain corrosive liquids or abrasive
xxxi
Trang 26solids The general tendency with many industrial units is to provide a continuous process,frequently involving a series of stages Thus, exothermic reactions may be carried out in
a series of reactors with interstage cooling
The planning of a process plant will involve determining the most economic method,and later the most economic arrangement of the individual operations used in the process.This amounts to designing a process so as to provide the best combination of capitaland operating costs In this volume the question of costs has not been considered inany detail, but the aim has been to indicate the conditions under which various types
of units will operate in the most economical manner Without a thorough knowledge ofthe physical principles involved in the various operations, it is not possible to select themost suitable one for a given process This aspect of the design can be considered bytaking one or two simple illustrations of separation processes The particles in a solid-solidsystem may be separated, first according to size, and secondly according to the material.Generally, sieving is the most satisfactory method of classifying relatively coarse materialsaccording to size, but the method is impracticable for very fine particles and a form ofsettling process is generally used In the first of these processes, the size of the particle isused directly as the basis for the separation, and the second depends on the variation withsize of the behaviour of particles in a fluid A mixed material can also be separated intoits components by means of settling methods, because the shape and density of particlesalso affect their behaviour in a fluid Other methods of separation depend on differences
in surface properties (froth flotation), magnetic properties (magnetic separation), and ondifferences in solubility in a solvent (leaching) For the separation of miscible liquids,three commonly used methods are:
1 Distillation — depending on difference in volatility
2 Liquid– liquid extraction — depending on difference in solubility in a liquid solvent
3 Freezing — depending on difference in melting point
The problem of selecting the most appropriate operation will be further complicated
by such factors as the concentration of liquid solution at which crystals start to form.Thus, in the separation of a mixture of ortho-, meta-, and para-mononitrotoluenes, thedecision must be made as to whether it is better to carry out the separation by distillationfollowed by crystallisation, or in the reverse order The same kind of consideration willarise when concentrating a solution of a solid; then it must be decided whether to stopthe evaporation process when a certain concentration of solid has been reached and then
to proceed with filtration followed by drying, or whether to continue to concentration byevaporation to such an extent that the filtration stage can be omitted before moving on todrying
In many operations, for instance in a distillation column, it is necessary to understandthe fluid dynamics of the unit, as well as the heat and mass transfer relationships Thesefactors are frequently interdependent in a complex manner, and it is essential to considerthe individual contributions of each of the mechanisms Again, in a chemical reactionthe final rate of the process may be governed either by a heat transfer process or by thechemical kinetics, and it is essential to decide which is the controlling factor; this problem
is discussed in Volume 3, which deals with both chemical and biochemical reactions andtheir control
Trang 27Two factors of overriding importance have not so far been mentioned Firstly, theplant must be operated in such a way that it does not present an unacceptable hazard
to the workforce or to the surrounding population Safety considerations must be in the
forefront in the selection of the most appropriate process route and design, and must also
be reflected in all the aspects of plant operation and maintenance An inherently safe plant
is to be preferred to one with inherent hazards, but designed to minimise the risk of thehazard being released Safety considerations must be taken into account at an early stage
of design; they are not an add-on at the end Similarly control systems, the integrity ofwhich play a major part in safe operation of plant, must be designed into the plant, notbuilt on after the design is complete
The second consideration relates to the environment The engineer has the
responsi-bility for conserving natural resources, including raw materials and energy sources, and
at the same time ensuring that effluents (solids, liquids and gases) do not give rise tounacceptable environmental effects As with safety, effluent control must feature as amajor factor in the design of every plant
The topics discussed in this volume form an important part of any chemical engineeringproject They must not, however, be considered in isolation because, for example, adifficult separation problem may often be better solved by adjustment of conditions in thepreceding reactor, rather than by the use of highly sophisticated separation techniques
Trang 28Particulate Solids
1.1 INTRODUCTION
In Volume 1, the behaviour of fluids, both liquids and gases is considered, with particularreference to their flow properties and their heat and mass transfer characteristics Oncethe composition, temperature and pressure of a fluid have been specified, then its relevantphysical properties, such as density, viscosity, thermal conductivity and molecular diffu-sivity, are defined In the early chapters of this volume consideration is given to theproperties and behaviour of systems containing solid particles Such systems are generallymore complicated, not only because of the complex geometrical arrangements which arepossible, but also because of the basic problem of defining completely the physical state
of the material
The three most important characteristics of an individual particle are its composition, itssize and its shape Composition determines such properties as density and conductivity,provided that the particle is completely uniform In many cases, however, the particle
is porous or it may consist of a continuous matrix in which small particles of a secondmaterial are distributed Particle size is important in that this affects properties such asthe surface per unit volume and the rate at which a particle will settle in a fluid Aparticle shape may be regular, such as spherical or cubic, or it may be irregular as, forexample, with a piece of broken glass Regular shapes are capable of precise definition bymathematical equations Irregular shapes are not and the properties of irregular particlesare usually expressed in terms of some particular characteristics of a regular shapedparticle
Large quantities of particles are handled on the industrial scale, and it is frequentlynecessary to define the system as a whole Thus, in place of particle size, it is necessary
to know the distribution of particle sizes in the mixture and to be able to define a meansize which in some way represents the behaviour of the particulate mass as a whole.Important operations relating to systems of particles include storage in hoppers, flowthrough orifices and pipes, and metering of flows It is frequently necessary to reduce thesize of particles, or alternatively to form them into aggregates or sinters Sometimes itmay be necessary to mix two or more solids, and there may be a requirement to separate
a mixture into its components or according to the sizes of the particles
In some cases the interaction between the particles and the surrounding fluid is of littlesignificance, although at other times this can have a dominating effect on the behaviour ofthe system Thus, in filtration or the flow of fluids through beds of granular particles, thecharacterisation of the porous mass as a whole is the principal feature, and the resistance
to flow is dominated by the size and shape of the free space between the particles Insuch situations, the particles are in physical contact with adjoining particles and there is
1
Trang 29little relative movement between the particles In processes such as the sedimentation ofparticles in a liquid, however, each particle is completely surrounded by fluid and is free tomove relative to other particles Only very simple cases are capable of a precise theoreticalanalysis and Stokes’ law, which gives the drag on an isolated spherical particle due toits motion relative to the surrounding fluid at very low velocities, is the most importanttheoretical relation in this area of study Indeed very many empirical laws are based onthe concept of defining correction factors to be applied to Stokes’ law.
1.2 PARTICLE CHARACTERISATION
1.2.1 Single particles
The simplest shape of a particle is the sphere in that, because of its symmetry, anyquestion of orientation does not have to be considered, since the particle looks exactlythe same from whatever direction it is viewed and behaves in the same manner in a fluid,irrespective of its orientation No other particle has this characteristic Frequently, thesize of a particle of irregular shape is defined in terms of the size of an equivalent spherealthough the particle is represented by a sphere of different size according to the propertyselected Some of the important sizes of equivalent spheres are:
(a) The sphere of the same volume as the particle
(b) The sphere of the same surface area as the particle
(c) The sphere of the same surface area per unit volume as the particle
(d) The sphere of the same area as the particle when projected on to a plane dicular to its direction of motion
perpen-(e) The sphere of the same projected area as the particle, as viewed from above, whenlying in its position of maximum stability such as on a microscope slide for example.(f) The sphere which will just pass through the same size of square aperture as theparticle, such as on a screen for example
(g) The sphere with the same settling velocity as the particle in a specified fluid.Several definitions depend on the measurement of a particle in a particular orientation.Thus Feret’s statistical diameter is the mean distance apart of two parallel lines which aretangential to the particle in an arbitrarily fixed direction, irrespective of the orientation ofeach particle coming up for inspection This is shown in Figure 1.1
A measure of particle shape which is frequently used is the sphericity, ψ, defined as:
ψ= surface area of sphere of same volume as particle
Another method of indicating shape is to use the factor by which the cube of the size ofthe particle must be multiplied to give the volume In this case the particle size is usuallydefined by method (e)
Other properties of the particle which may be of importance are whether it is crystalline
or amorphous, whether it is porous, and the properties of its surface, including roughnessand presence of adsorbed films
Trang 30Figure 1.1 Feret’s diameter
Hardness may also be important if the particle is subjected to heavy loading
1.2.2 Measurement of particle size
Measurement of particle size and of particle size distribution is a highly specialised topic,and considerable skill is needed in the making of accurate measurements and in theirinterpretation For details of the experimental techniques, reference should be made to aspecialised text, and that of ALLEN( 1) is highly recommended
No attempt is made to give a detailed account or critical assessment of the variousmethods of measuring particle size, which may be seen from Figure 1.2 to cover a range
of 107 in linear dimension, or 1021 in volume! Only a brief account is given of some
of the principal methods of measurement and, for further details, it is necessary to refer
to one of the specialist texts on particle size measurement, the outstanding example ofwhich is the two-volume monograph by ALLEN( 1), with HERDAN( 2) providing additionalinformation It may be noted that both the size range in the sample and the particle shapemay be as important, or even more so, than a single characteristic linear dimension which
at best can represent only one single property of an individual particle or of an assembly
of particles The ability to make accurate and reliable measurements of particle size isacquired only after many years of practical experimental experience For a comprehensivereview of methods and experimental details it is recommended that the work of Allen beconsulted and also Wardle’s work on Instrumentation and Control discussed in Volume 3.Before a size analysis can be carried out, it is necessary to collect a representativesample of the solids, and then to reduce this to the quantity which is required for thechosen method of analysis Again, the work of Allen gives information on how this isbest carried out Samples will generally need to be taken from the bulk of the powder,whether this is in a static heap, in the form of an airborne dust, in a flowing or fallingstream, or on a conveyor belt, and in each case the precautions which need to be taken
to obtain a representative sample are different
A wide range of measuring techniques is available both for single particles and forsystems of particles In practice, each method is applicable to a finite range of sizes andgives a particular equivalent size, dependent on the nature of the method The principles
Trang 31Pelleted products Particle size
(µm) Crystalline industrial chemicals
Granular fertilisers, herbicides, fungicides
Detergents Granulated sugars Spray dried products Powdered chemicals Powdered sugar Flour
Toners Powder metals Ceramics Electronic materials Photographic emulsions Magnetic and other pigments Organic pigments
Fumed silica Metal catalysts Carbon blacks
Figure 1.2 Sizes of typical powder products( 1)
of some of the chief methods are now considered together with an indication of the sizerange to which they are applicable
Sieving (>50 µm)
Sieve analysis may be carried out using a nest of sieves, each lower sieve being ofsmaller aperture size Generally, sieve series are arranged so that the ratio of aperturesizes on consecutive sieves is 2, 21/2 or 21/4 according to the closeness of sizing that
is required The sieves may either be mounted on a vibrator, which should be designed
to give a degree of vertical movement in addition to the horizontal vibration, or may behand shaken Whether or not a particle passes through an aperture depends not only uponits size, but also on the probability that it will be presented at the required orientation
at the surface of the screen The sizing is based purely on the linear dimensions of theparticle and the lower limit of size which can be used is determined by two principalfactors The first is that the proportion of free space on the screen surface becomes verysmall as the size of the aperture is reduced The second is that attractive forces betweenparticles become larger at small particle sizes, and consequently particles tend to sticktogether and block the screen Sieves are available in a number of standard series Thereare several standard series of screen and the sizes of the openings are determined by thethickness of wire used In the U.K., British Standard (B.S.)( 3) screens are made in sizes
Trang 32from 300-mesh upwards, although these are too fragile for some work The Institute ofMining and Metallurgy (I.M.M.)( 4) screens are more robust, with the thickness of thewire approximately equal to the size of the apertures The Tyler series, which is standard
in the United States, is intermediate between the two British series Details of the threeseries of screens( 3)are given in Table 1.1, together with the American Society for TestingMaterials (ASTM) series( 5)
Table 1.1 Standard sieve sizes British fine mesh
(B.S.S 410)( 3) I.M.M.( 4) U.S Tyler( 5) U.S A.S.T.M.( 5)
Nominal Nominal Nominal Nominal Sieve aperture Sieve aperture Sieve aperture Sieve aperture
in µ m in µ m in µ m in µ m
Trang 33instant Thus, if w is the mass of particles of a particular size on the screen at a time t, then:
Screening may be carried out with either wet or dry material In wet screening, material
is washed evenly over the screen and clogging is prevented In addition, small particlesare washed off the surface of large ones This has the obvious disadvantage, however,that it may be necessary to dry the material afterwards With dry screening, the material issometimes brushed lightly over the screen so as to form a thin even sheet It is importantthat any agitation is not so vigorous that size reduction occurs, because screens are usuallyquite fragile and easily damaged by rough treatment In general, the larger and the moreabrasive the solids the more robust is the screen required
Microscopic analysis (1 –100 µm)
Microscopic examination permits measurement of the projected area of the particle andalso enables an assessment to be made of its two-dimensional shape In general, thethird dimension cannot be determined except when using special stereomicroscopes Theapparent size of particle is compared with that of circles engraved on a graticule in theeyepiece as shown in Figure 1.3 Automatic methods of scanning have been developed
By using the electron microscope( 7), the lower limit of size can be reduced to about0.001 µm
Figure 1.3 Particle profiles and comparison circles
Trang 34Sedimentation and elutriation methods (>1 µm)
These methods depend on the fact that the terminal falling velocity of a particle in a fluidincreases with size Sedimentation methods are of two main types In the first, the pipettemethod, samples are abstracted from the settling suspension at a fixed horizontal level atintervals of time Each sample contains a representative sample of the suspension, withthe exception of particles larger than a critical size, all of which will have settled belowthe level of the sampling point The most commonly used equipment, the Andreasonpipette, is described by ALLEN( 1) In the second method, which involves the use of thesedimentation balance, particles settle on an immersed balance pan which is continuouslyweighed The largest particles are deposited preferentially and consequently the rate ofincrease of weight falls off progressively as particles settle out
Sedimentation analyses must be carried out at concentrations which are sufficientlylow for interactive effects between particles to be negligible so that their terminal fallingvelocities can be taken as equal to those of isolated particles Careful temperature control(preferably to±0.1 deg K) is necessary to suppress convection currents The lower limit
of particle size is set by the increasing importance of Brownian motion for progressivelysmaller particles It is possible however, to replace gravitational forces by centrifugalforces and this reduces the lower size limit to about 0.05µm
The elutriation method is really a reverse sedimentation process in which the particlesare dispersed in an upward flowing stream of fluid All particles with terminal fallingvelocities less than the upward velocity of the fluid will be carried away A completesize analysis can be obtained by using successively higher fluid velocities Figure 1.4shows the standard elutriator (BS 893)( 6) for particles with settling velocities between 7and 70 mm/s
Permeability methods (>1 µm)
These methods depend on the fact that at low flowrates the flow through a packed bed isdirectly proportional to the pressure difference, the proportionality constant being propor-tional to the square of the specific surface (surface : volume ratio) of the powder Fromthis method it is possible to obtain the diameter of the sphere with the same specificsurface as the powder The reliability of the method is dependent upon the care withwhich the sample of powder is packed Further details are given in Chapter 4
Electronic particle counters
A suspension of particles in an electrolyte is drawn through a small orifice on either side
of which is positioned an electrode A constant electrical current supply is connected
to the electrodes and the electrolyte within the orifice constitutes the main resistivecomponent of the circuit As particles enter the orifice they displace an equivalent volume
of electrolyte, thereby producing a change in the electrical resistance of the circuit, themagnitude of which is related to the displaced volume The consequent voltage pulseacross the electrodes is fed to a multi-channel analyser The distribution of pulses arisingfrom the passage of many thousands of particles is then processed to provide a particle(volume) size distribution
The main disadvantage of the method is that the suspension medium must be sohighly conducting that its ionic strength may be such that surface active additives may be
Trang 35Figure 1.4 Standard elutriator with 70-mm tube (all dimensions in mm)( 6)
required in order to maintain colloidal stability of fine particle suspensions as discussed
in Section 5.2.2
The technique is suitable for the analysis of non-conducting particles and for conductingparticles when electrical double layers confer a suitable degree of electrical insulation.This is also discussed in Section 5.2.2
By using orifices of various diameters, different particle size ranges may be examinedand the resulting data may then be combined to provide size distributions extending over
a large proportion of the sub-millimetre size range The prior removal from the suspension
of particles of sizes upwards of about 60 per cent of the orifice diameter helps to prevent
problems associated with blocking of the orifice The Coulter Counter and the Elzone
Analyser work on this principle.
Trang 36Laser diffraction analysers
These instruments( 8) exploit the radial light scattering distribution functions of particles
A suspension of particles is held in, or more usually passed across, the path of a mated beam of laser light, and the radially scattered light is collected by an array ofphotodetectors positioned perpendicular to the optical axis The scattered light distri-bution is sampled and processed using appropriate scattering models to provide a particlesize distribution The method is applicable to the analysis of a range of different particles
colli-in a variety of media Consequently, it is possible to examcolli-ine aggregation phenomenas
as discussed in Section 5.4, and to monitor particle size for on-line control of processstreams Instruments are available which provide particle size information over the range0.1–600 µm Light scattered from particles smaller than 1µm is strongly influenced bytheir optical properties and care is required in data processing and interpretation.The scattering models employed in data processing invariably involve the assumption
of particle sphericity Size data obtained from the analysis of suspensions of asymmetricalparticles using laser diffraction tend to be somewhat more ambiguous than those obtained
by electronic particle counting, where the solid volumes of the particles are detected
X-ray or photo-sedimentometers
Information on particle size may be obtained from the sedimentation of particles in dilutesuspensions The use of pipette techniques can be rather tedious and care is required toensure that measurements are sufficiently precise Instruments such as X-ray or photo-sedimentometers serve to automate this method in a non-intrusive manner The attenuation
of a narrow collimated beam of radiation passing horizontally through a sample ofsuspension is related to the mass of solid material in the path of the beam This attenuationcan be monitored at a fixed height in the suspension, or can be monitored as the beam israised at a known rate This latter procedure serves to reduce the time required to obtainsufficient data from which the particle size distribution may be calculated This technique
is limited to the analysis of particles whose settling behaviour follows Stokes’ law, asdiscussed in Section 3.3.4, and to conditions where any diffusive motion of particles isnegligible
Sub-micron particle sizing
Particles of a size of less than 2µm are of particular interest in Process Engineeringbecause of their large specific surface and colloidal properties, as discussed in Section 5.2.The diffusive velocities of such particles are significant in comparison with their settlingvelocities Provided that the particles scatter light, dynamic light scattering techniques,such as photon correlation spectroscopy (PCS), may be used to provide information aboutparticle diffusion
In the PCS technique, a quiescent particle suspension behaves as an array of mobilescattering centres over which the coherence of an incident laser light beam is preserved.The frequency of the light intensity fluctuations at a point outside the incident lightpath is related to the time taken for a particle to diffuse a distance equivalent to thewavelength of the incident light The dynamic light signal at such a point is sampled and
Trang 37correlated with itself at different time intervals using a digital correlator and associatedcomputer software The relationship of the (so-called) auto-correlation function to thetime intervals is processed to provide estimates of an average particle size and variance(polydispersity index) Analysis of the signals at different scattering angles enables moredetailed information to be obtained about the size distribution of this fine, and usuallyproblematical, end of the size spectrum.
The technique allows fine particles to be examined in a liquid environment so thatestimates can be made of their effective hydrodynamic sizes This is not possible usingother techniques
Provided that fluid motion is uniform in the illuminated region of the suspension,then similar information may also be extracted by analysis of laser light scattering fromparticles undergoing electrophoretic motion, that is migratory motion in an electric field,superimposed on that motion
Instrumentation and data processing techniques for systems employing dynamic lightscattering for the examination of fine particle motion are currently under development
1.2.3 Particle size distribution
Most particulate systems of practical interest consist of particles of a wide range of sizesand it is necessary to be able to give a quantitative indication of the mean size and of thespread of sizes The results of a size analysis can most conveniently be represented by
means of a cumulative mass fraction curve, in which the proportion of particles (x) smaller than a certain size (d) is plotted against that size (d) In most practical determinations of
particle size, the size analysis will be obtained as a series of steps, each step representingthe proportion of particles lying within a certain small range of size From these results
a cumulative size distribution can be built up and this can then be approximated by asmooth curve provided that the size intervals are sufficiently small A typical curve forsize distribution on a cumulative basis is shown in Figure 1.5 This curve rises from zero
to unity over the range from the smallest to the largest particle size present
The distribution of particle sizes can be seen more readily by plotting a size frequency
curve, such as that shown in Figure 1.6, in which the slope (dx/dd) of the cumulative
0
d
d
dx x
1
Figure 1.5 Size distribution curve — cumulative basis
Trang 38dx d
Figure 1.6 Size distribution curve — frequency basis
curve (Figure 1.5) is plotted against particle size (d) The most frequently occurring
size is then shown by the maximum of the curve For naturally occurring materials thecurve will generally have a single peak For mixtures of particles, there may be as manypeaks as components in the mixture Again, if the particles are formed by crushing largerparticles, the curve may have two peaks, one characteristic of the material and the othercharacteristic of the equipment
1.2.4 Mean particle size
The expression of the particle size of a powder in terms of a single linear dimension isoften required For coarse particles, BOND( 9,10)has somewhat arbitrarily chosen the size of
the opening through which 80 per cent of the material will pass This size d80 is a usefulrough comparative measure for the size of material which has been through a crusher
A mean size will describe only one particular characteristic of the powder and it isimportant to decide what that characteristic is before the mean is calculated Thus, it may
be desirable to define the size of particle such that its mass or its surface or its length
is the mean value for all the particles in the system In the following discussion it isassumed that each of the particles has the same shape
Considering unit mass of particles consisting of n1particles of characteristic dimension
d1, constituting a mass fraction x1, n2 particles of size d2, and so on, then:
Trang 39where ρs is the density of the particles, and
k1 is a constant whose value depends on the shape of the particle
Mean sizes based on volume
The mean abscissa in Figure 1.5 is defined as the volume mean diameter d v, or as the
mass mean diameter, where:
Another mean size based on volume is the mean volume diameter dv If all the particles
are of diameter dv, then the total volume of particles is the same as in the mixture
Mean sizes based on surface
In Figure 1.5, if, instead of fraction of total mass, the surface in each fraction is plotted
against size, then a similar curve is obtained although the mean abscissa d s is then the
surface mean diameter.
Thus: d s = [(n1d1)S1]
(n1S1) = (n1k2d13)
(n1k2d2) = (n1d13)
Trang 40where S1= k2d12, and k2 is a constant whose value depends on particle shape ds is also
known as the Sauter mean diameter and is the diameter of the particle with the same
specific surface as the powder
Substituting for n1 from equation 1.6 gives:
Mean dimensions based on length
A length mean diameter may be defined as:
The size analysis of a powdered material on a mass basis is represented by a straight line from
0 per cent mass at 1 µm particle size to 100 per cent mass at 101 µm particle size as shown in Figure 1.7 Calculate the surface mean diameter of the particles constituting the system.