Powder Science and Technology

HANDBOOK

OF POWDER

SCIENCE &

TECHNOLOGY

SECOND EDITION

edited by

Muhammad E. FayedLambert Otten

CHAPMAN & HALL

International Thomson Publishing

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Handbook ot powder science & technology / edited by M E Fayed, L Otten 2nd edp cm

Rev ed ol Handbook oi powder science and technoilogy cl984Includes bibliographical references and indexISBN 0-412-99621-9 (alk paper)1 Particles 2 Powders I Fayed, M E (Muhammad E ) II Otten, L (Lambert)III Title Handbook ot powder science and technology IV Handbook ot powderscience and technologyTP156P3H35 1997 97-3463620 43-dc21 CIP

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TO

My Late Parents,Fat-Hia HitataAl-Sawi Fayed

My Wife Carolynand my childrenMark and Susan Otten

All of whom have given us far too much without reservation

CONTENTSDedication vPreface xiiiAcknowledgments xvContributors xvii

1. PARTICLE SIZE CHARACTERIZATION 1

1.1. What Is the Size of a Powder Grain? 11.2. Obtaining a Representative Sample 31.3. Size Characterization by Image Analysis 71.4. Characterizing Powders by Sieve Fractionation 81.5. Characterizing the Size of Fineparticles by Sedimentation

Techniques 121.6. Diffractometers for Characterizing the Size of Fineparticles 141.7. Time-of-Flight Instruments 181.8. Size Characterization Equipment Based on the Doppler Effect 211.9. Stream Counters 231.10. Elutriators 241.11. Permeability Methods for Characterizing Fineparticle

Systems 261.12. Surface Area by Gas Adsorption Studies 281.13. Pore Size Distribution of a Packed Powder Bed 29References 32

2. PARTICLE SHAPE CHARACTERIZATION 35

2.1. Introduction 352.2. Dimensionless Indices of Fineparticle Shape 352.3. Geometric Signature Waveforms for Characterizing the Shape

of Irregular Profiles 392.4. Fractal Dimensions of Fineparticle Boundaries for Describing

Structure and the Texture of Fineparticles 442.5. Dynamic Shape Factors from a Study of the Catastrophic

Tumbling Behavior of Fineparticles 48References 52

vii

viii HANDBOOK OF POWDER SCIENCE

3. STRUCTURAL PROPERTIES OF PACKINGS OF PARTICLES 53

3.1. Introduction 533.2. Macroscopic Structure Parameters 543.3. Packing Structures of Equal Spheres 613.4. Packing Structures of General Systems 67References 90

4. FUNDAMENTAL AND RHEOLOGICAL PROPERTIES OF POWDERS 96

4.1. Packing Characteristics of Particles 964.2. Permeability of the Powder Bed 1164.3. Strength of a Particle Assemblage 118References 142

5. VIBRATION OF FINE POWDERS AND ITS APPLICATION 146

5.1. Introduction 1465.2. Literature Review 1485.3. Measurement of Dynamic Shear 1525.4. Dynamic Shear CharacteristicsSinusoidal Vibration

Excitation 1555.5. An Inertia Model for Vibration of Whole Shear Cell 1615.6. A Failure Criterion 1715.7. Boundary Shear and Wall Friction 1755.8. Random Vibration Excitation 1785.9. Compaction of Powders and Bulk Solids 1815.10. Application of Vibrations in Flow Promotion 1855.11. Transmission of Vibration Energy Through Bulk Mass 1905.12. Stress Waves in Three DimensionsSome Basic Concepts 1945.13. Concluding Remarks 196References 198

6. SIZE ENLARGEMENT BY AGGLOMERATION 202

6.1. Introduction 2026.2. Agglomerate Bonding and Strength 2066.3. Size Enlargement by Agglomeration in Industry 2276.4. Growth/Tumble Agglomeration MethodsAgitation Methods 2526.5. Pressure Agglomeration Methods 2956.6. Other Agglomeration Methods 3646.7. Acknowledgments 377

7. PNEUMATIC CONVEYING 378

7.1. Introduction 378

CONTENTS be

12. Relationship Between Major Pipeline Variables 3797.3. Basics of System Design 3817.4. Specification of Air Requirements 383References 388

8. STORAGE AND FLOW OF PARTICULATE SOLIDS 389

8.1. Introduction 3898.2. Definitions 3908.3. Types of Bin Construction 3908.4. Flow Patterns in Bins and Hoppers 3978.5. Stresses on Bin Walls 4058.6. Solids Flow Analysis and Testing 4168.7. Bulk Density and Compressibility 4248.8. Other Factors Affecting Flow Properties During Storage 4258.9. Design of Bins for Flow 4278.10. Effect of the Gas Phase 4368.11. Other Methods of Characterizing Solids Relevant to

Storage and Flow 4408.12. Particle Segregation During Storage and Flow 4468.13. Static Devices to Promote Gravity Flow from Bins 4538.14. Flow-Promoting Devices and Feeders for Regulating Flow 459References 480

9. FLUIDIZATION PHENOMENA AND FLUIDIZED BED TECHNOLOGY 487

9.1. Historical Development 4879.2. Advantages and Disadvantages of the Fluidized Technique 5029.3. Operating Characteristics and Design Procedures 514References 530

10. SPOUTING OF PARTICULATE SOLIDS 532

10.1. Introduction 53210.2. Minimum Spouting Velocity 53410.3. Maximum Spoutable Bed Depth 53510.4. Flow Distribution of Fluid 53610.5. Pressure Drop 53710.6. Particle Motion 53910.7. Voidage Distribution 54210.8. Spout Diameter 54210.9. Heat Transfer 54310.10. Mass Transfer 54510.11. Chemical Reaction: Two-Region Models 54610.12. Applications 54910.13. Modified Spouted Beds 55310.14. Practical Considerations 559References 562

X HANDBOOK OF POWDER SCIENCE

11. MIXING OF POWDERS 5 6 8

11.1. Basic Concepts of Powder Mixing 5 6 811.2. Different Mixing Machines 5 7 6References 5 8 4

12. SIZE REDUCTION OF SOLIDS CRUSHING AND GRINDING EQUIPMENT 586

12.1. Introduction 5 8 612.2. A Brief Review of Fracture Mechanics 58712.3. Size Reduction Machines 59812.4. The Analysis of Size Reduction Processes 60512.5. New Mills 62312.6. Future Work 631References 631

13. SEDIMENTATION 635

13.1. Introduction 63513.2. Theory of Sedimentation 63913.3. Thickening 65713.4. Clarification 66613.5. Nonconventional Sedimentation Processes and Equipment 672List of Symbols 676References 678

14. FILTRATION OF SOLIDS FROM LIQUID STREAMS 683

683685686688690695696698701719723723

727

15.1. Introduction 72715.2. Performance Characteristics 72815.3. Performance Modeling 731

14.1.14.2.14.3.14.4.14.5.14.6.14.7.14.8.14.9.4.10.4.11.

IntroductionPhysical Mechanisms of FiltrationFiltration TheoryFilter MediaMembranesFilter AidsStages of the Filter CycleLiterature and Information ReviewTypes and Description of Liquid Filter EquipmentCentrifugesFilter Equipment Selection

References

15. CYCLONES

CONTENTS Xi

15.4. Cyclone Design 743References 751

16. THE ELECTROSTATIC PRECIPITATOR: APPLICATION AND CONCEPTS 753

16.1. Introduction 75316.2. Factors and Effects 75716.3. Resistivity 75916.4. Operation and Maintenance 76316.5. Gas Conditioning 76816.6. Design and Performance Concepts 76816.7. Effect of Particle Size 769References 770

17. GRANULAR BED FILTERSPART I. THE THEORY 771

17.1.1. Introduction 77117.1.2. Total Bed Efficiency 77217.1.3. Collection Mechanisms in Deep-Bed Filtration 77317.1.4. Experimental Verification 77617.1.5. Concluding Remarks 778References 780

17. PART II. APPLICATION AND DESIGN 781

17.2.1. Introduction 78117.2.2. Purposes and Applications 78117.2.3. Porous Sintered Granule Beds 78317.2.4. Continuous Moving-Bed Filters 78417.2.5. Intermittent Moving-Bed Filters 78517.2.6. Fluidized Bed Filters 78817.2.7. Granular Bed Filters Mechanically Cleaned 78917.2.8. Granular Bed Filters Pneumatically Cleaned 79117.2.9. Technological Status of Systems Under Development and

Under Commercialization 792References 801Bibliography 801

18. WET SCRUBBER PARTICULATE COLLECTION 803

18.1. Introduction 80318.2. Power Consumption 81018.3. Collection Efficiency 81118.4. Scrubber Selection 81518.5. Atomized Spray Scrubbers (Venturi, Orifice, Impingement) 816

Xii HANDBOOK OF POWDER SCIENCE

18.6. Hydraulic Spray Scrubbers 82418.7. Wetted Packed Beds and Fibrous Mats 82518.8. Tray Towers 82718.9. Condensation Scrubbing 82818.10. Electrostatic Augmentation 83018.11. Demisters and Entrainment Separators 83318.12. Sundry Design Considerations 83618.13. Costs 837References 841

19. FIRE AND EXPLOSION HAZARDS IN POWDER HANDLINGAND PROCESSING 845

19.1. Introduction 84519.2. Principles of Dust Explosions 84619.3. Factors Affecting Dust Explosions 84919.4. Ignition Sources 85519.5. General Plant Design Considerations 85519.6. Dust Explosion Prevention and Protection Methods 85619.7. Applications to Industrial Processes and Equipment 863References 867

20. RESPIRABLE DUST HAZARDS 869

20.1. Introduction 86920.2. Specific Respirable Dust Hazards in Industry 876References 880

INDEX 883

PREFACE TO THE SECOND EDITION

Since the publication of the first edition ofHandbook of Powder Science and Technology,the field of powder science and technology hasgained broader recognition and its various ar-eas of interest have become more defined andfocused. Research and application activitiesrelated to particle technology have increasedglobally in academia, industry, and researchinstitutions. During the last decade, manygroups, with various scientific, technical, andengineering backgrounds have been foundedto study, apply, and promote interest in areasof powder science and technology. Many pro-fessional societies and associations have de-voted sessions and chapters on areas of parti-cle science and technology that are relevant totheir members in their conferences and careerdevelopment programs. Two of many refer-ences may be given in this regard; one is therecent formation of the Particle TechnologyForum by the American Institute of ChemicalEngineers. The second reference is the inten-sified effort given by the American Filtrationand Separation Society to define the areas ofparticle and particle fluid science and technol-ogy with the objective to promote the inclu-sion of courses on these topics at Americanuniversities, for undergraduate and graduatecircula. On the academic level, many universi-ties in the United States, Europe, Japan,

Canada, and Australia have increased teach-ing, research, and training activities in areasrelated to particle science and technology.

In addition, it is worth mentioning the manybooks and monographs that have been pub-lished on specific areas of particle, powder,and particle fluid by professional publishers,technical societies and university presses. Also,to date, there are many career developmentcourses given by specialists and universities onvarious facets of powder science and technol-ogy-

Taking note of all these developments, theeditors of this second edition faced the needfor evaluating and reorganizing, as well asupdating and adding to the content of the firstedition. In this edition, topics are organized ina logical manner starting from particle charac-terization and fundamentals to the many areasof particle/powder applications. Comprehen-sive upgrade of many of the first edition chap-ters were made and three more chapters wereadded: namely pneumatic conveying, dust ex-plosion, and fire hazard and health hazard ofdust.

The extent to which we have succeeded maybe judged from the authors contributions andthe contents of this book.

THE EDITORS

xiii

ACKNOWLEDGMENTS

We wish to thank Nadeem Visanji, senior student at Ryerson Polytechnic University, for hisassistance in preparing the index of this book.

We also would like to thank the Editorial and Production Staff of Chapman and HallPublishing Co., particularly Margaret Cummins, James Geronimo, and Cindy Zadikoff for theirattention and cooperation in the production of this book.

Last, but not least, we thank our families for their patience and understanding throughout thepreparation of this text.

CONTRIBUTORSLeonard G. Austin, Professor Emeritus, Department ofMineral Engineering, The Pennsylvania State Univer-sity, University Park, PA. (Ch. 12).Larry Avery, President, Avery Filter Co., Westwood,NJ. (Ch. 14).Wu Chen, The Dow Chemical Company, Freeport, TX.(Ch. 13).Douglas W. Cooper, Associate Professor, Departmentof Environmental Sciences and Physiology, School ofPublic Health, Harvard University, Boston, MA. (Ch.18).Francis A. L. Dullien, Professor Emeritus, Departmentof Chemical Engineering, University of Waterloo, Wa-terloo, ON, Canada (Ch. 3).Norman Epstein, Professor Emeritus, Department ofChemical Engineering, The University of BritishColumbia, Vancouver, B.C., Canada (Ch. 10).John R. Grace, Dean of Graduate Studies and Profes-sor, The University of British Columbia, Vancouver,B.C., Canada (Ch. 10).Stanley S. Grossel, President, Process Safety & DesignInc., Clifton, NJ. (Ch. 19).Donna L. Jones, Senior Engineer, ECI EnvironmentalConsulting & Research Co., Durham, NC. (Ch. 15).Mark G. Jones, Senior Consulting Engineer, Centre forIndustrial Bulk Solids Handling, Glasgow CaledonianUniversity, Glasgow, Scotland, U.K. (Ch. 7).Jacob Katz, Consultant, Coconut Creek, FL. (Ch. 16).Brian H. Kaye, Professor, Department of Physics andAstronomy, Laurentian University, Sudbury, Ontario,Canada (Ch. 1, 2, 11, 20).

David Leith, Professor, Department of EnvironmentalScience and Engineering, University of North Carolina,Chapel Hill, NC. (Ch. 15).

Wolfgang Pietsch, President, COMPACTCONSULT,Inc., Naples, FL. (Ch. 6).

Alan Roberts, Director and Professor, TUNRA BulkSolids Handling Research Associates, University of NewCastle, New South Wales, Australia (Ch. 5).

Keith J. Scott, (Deceased), Chemical Engineering Re-search Group, Council for Scientific and Industrial Re-search, Pretoria, South Africa (Ch. 13).

Kunio Shinohara, Chairman and Professor, Depart-ment of Chemical Process Engineering, Hokkaido Uni-versity, Sapporo, Japan (Ch. 4).

Gabriel I. Tardos, Professor, Department of ChemicalEngineering, The City College of The City Universityof New York, New York, N.Y. (Ch. 17).

Fred M. Thomson, Consultant, Bulk Solids Handlingand Storage, Wilmington, DE. (Ch. 8).

Olev Trass, Professor Emeritus, Department of Chemi-cal Engineering, University of Toronto, Toronto, On-tario, Canada (Ch. 12).

Frederick A. Zenz, Professor Emeritus, Department ofChemical Engineering, Manhattan College, Riverdale,N.Y. (Ch. 9, 17).

xvii

HANDBOOK

OF POWDER

SCIENCE &

TECHNOLOGY

1Particle Size Characterization

Brian H. Kaye

C O N T E N T S

1.1 WHAT IS THE SIZE OF A POWDER GRAIN? 11.2 OBTAINING A REPRESENTATIVE SAMPLE 31.3 SIZE CHARACTERIZATION BY IMAGE ANALYSIS 71.4 CHARACTERIZING POWDERS BY SIEVE FRACTIONATION 81.5 CHARACTERIZING THE SIZE OF FINEPARTICLES BY SEDIMENTATION

TECHNIQUES 121.6 DIFFRACTOMETERS FOR CHARACTERIZING THE SIZE OF FINEPARTICLES 141.7 TIME-OF-FLIGHT INSTRUMENTS 181.8 SIZE CHARACTERIZATION EQUIPMENT BASED ON THE DOPPLER EFFECT 211.9 STREAM COUNTERS 231.10 ELUTRIATORS 241.11 PERMEABILITY METHODS FOR CHARACTERIZING FINEPARTICLE

SYSTEMS 261.12 SURFACE AREA BY GAS ADSORPTION STUDIES 281.13 PORE SIZE DISTRIBUTION OF A PACKED POWDER BED 29REFERENCES 32

1.1 WHAT IS THE SIZE OF A POWDERGRAIN?

It must be firmly grasped at the beginning of adiscussion of techniques for characterizing thesize of fineparticles that for all except spheri-cal fineparticles there is no unique size param-eter that describes an irregularly shapedfineparticle.1'2

When an irregular grain of powder is stud-ied by various characterization techniques, thedifferent methods evaluate different parame-ters of the fineparticle. Thus in Figure 1.1various characteristic parameters and equiva-lent diameters of an irregular profile are illus-trated. When selecting a parameter of thefineparticle to be evaluated, one should at-tempt to use a method that measures the

2 HANDBOOK OF POWDER SCIENCE

Stokes DiameterProjected Area

ConvexHull

Sphere ofEqual Volume Aerodynamic

DiameterFigure 1.1. The size of a fineparticle is a complex concept for all but smooth, dense, spherical fineparticles.

parameter that is functionally important forthe physical system being studied. Thus, if oneis studying the sedimentation of grains of rocktailings in a settling pond one should measurethe Stokes diameter of the powder grains. TheStokes diameter is defined as the size of asmooth sphere of the same density as thepowder grain that has the same settling speedas the fineparticle at low Reynolds number ina viscous fluid. It is calculated by inserting themeasured settling velocity of the fineparticleinto the Stokes equation, which is:

where

v = the measured velocityds = Stokes diameterg = acceleration due to gravityrj = viscosity of the fluid

pP = density of powder grainpL = density of a liquid.

On the other hand, if one is measuring thehealth hazard of a dust one may need to

characterize the powder grains by two differ-ent methods. Thus, the movement of afineparticle suspended in the air into and outof the mouth of a miner is governed by theaerodynamic diameter of the fineparticle. Thisis defined as the size of the sphere of unitdensity that has the same dynamic behavior asthe fineparticle in low Reynolds number flow.However, when one is considering the actualhealth hazard caused by the dust fineparticles,one may want to look at the number of sharpedges on the fineparticle, in the case of asilocotic hazard, or the fractal dimension andsurface area of the profile, in the case of adiesel exhaust fineparticle. Furthermore, if oneis interested in the filtration capacity of arespirator, the actual physical dimensions of aprofile may have to be measured by imageanalysis. In recent years there has been a greatdeal of development work regarding the prob-lem of characterizing the shape and structureof fineparticles and this recent work is thesubject of a separate chapter in this book.

Many methods used for characterizingfineparticles have to be calibrated using stan-

PARTICLE SIZE CHARACTERIZATION 3

dard fineparticles. These are available fromseveral commercial organizations.3"6 TheEuropean technical community has evolvedsome standard powders for reference work.7Because different methods measure differentparameters of irregular fineparticles the datagenerated by the various methods are not di-rectly related to each other and one mustestablish empirical correlations when compar-ing the data from different characterizationproceedings. From time to time we discuss thisaspect of particle size analysis in this chapter.

It is useful to distinguish between direct andindirect methods of fineparticle characteriza-tion. Thus, in sedimentation methods, one di-rectly monitors the behavior of individualfineparticles and the measurements made aredirectly related to the properties of thefineparticles. On the other hand, in gas ad-sorption and permeability methods, the inter-pretation of the experimental data involvesseveral hypotheses. As a consequence, thefineness measurements should be regarded assecondary, indirect methods of generating theinformation on the fineness of the powderedmaterial.

1.2 OBTAINING A REPRESENTATIVESAMPLE

An essential step in the study of a powdersystem is obtaining a representative sample.Procedures have been specified for obtaining apowder sample from large tonnage material.In this chapter we concern ourselves mainlywith the obtaining of a small sample forcharacterization purposes for a sample ofpowder sent to a laboratory from theplant.1'2'8"10'11'12'13'14'15

For many years the spinning riffler has beenrecognized as a very efficient sampling devicefor obtaining a representative sample. Thispiece of equipment is shown in Figure 1.2a. Inthis device a ring of containers rotates under apowder supply to be sampled. For efficientsampling the total time of flow of powder intothe system divided by the time of one rotation

must be a large number. Although the spin-ning riffler is an efficient sampling device ithas two drawbacks. First, the total supply ofthe powder has to be passed through the sam-pling device to ensure efficiency; this cansometimes be inconvenient. Second, if thepowder contains very fine grains the rotaryaction of this sampling device can result in thefines being blown away during the samplingprocess. Both of these difficulties are avoidedif one uses the free fall tumbler powder mixershown in Figure 1.2b to carry out the samplingprocess. It has always been appreciated that ifa powder could be mixed homogeneously thenany snatch sample from the powder is a repre-sentative sample. However, there has beensome reluctance to use this approach to sam-pling because of the uncertain performance ofpowder mixers. Recent work has shown thatthe device shown in Figure 1.2b is a veryefficient mixer and that samples taken from acontainer placed in the mixer would normallyconstitute a representative sample.14'15 Themixing chamber is a small container in whichthe powder to be mixed or sampled is placed.In the case of the system shown in Figure 1.2ba cubic mixing chamber is used. The chambermust not be filled to capacity because thiswould restrict the movement of the powdergrains during the chaotic tumbling that consti-tutes the mixing process. Usually the containershould be half full. The lid of the chamber isremovable and contains the sampling cup on aprobe (rather like a soup ladle fixed to the topof the mixing chamber). The mixing chamberis placed inside the tumbling drum which iscoated with rough-textured foam to cause themixing chamber to tumble chaotically as thetumbling drum is rotated. This chaotic tum-bling of the mixing chamber results in thecomplete mixing of powder grains inside thecontainer. When the tumbling is completethe sampling cup attached to the roof of thechamber contains a representative sample. Thepower of the system to act as a mixer/sampleris illustrated by the data in Figure 1.3. Acrushed calcium carbonate powder nominally15 microns was sampled after tumbling a con-


a) Side View Top View

ControlValve

Drive Axis

b)Tumbling Drum

SampleCupSampleJar

Mixing ChamberRollers

DimpledLining

Motor

Figure 1.2. Systematic representative sampling of a powder can be achieved with a spinning riffler or chaosgenerating devices can be used to generate representative samples taken at random, (a) Side and top views of aspinning riffler. (b) The free-fall tumbling powder mixer can be used for powder homogenization and sampling.

tainer of the powder for 10 min. The samplewas characterized by the AeroSizer, an in-strument to be described later in the text. Themeasured size distribution and that of thesubsequent sample taken after a further 10min are shown in Figure 1.3a. In Figure 1.3bthe size distributions of a nominally 6 micronand 15 micron powder as measured by theAeroSizer are shown along with the size distri-bution of a mixture prepared of these twocomponents in the proportion 25%, 6 micronpowder to 75% of the 15 micron powder. In

Figure 1.3c the mathematically calculated sizedistribution of the mixture based on the knownsize distributions of the two ingredients is in-distinguishable from that of the mixture asobtained from the AeroSizer after the mixturehad been tumbled for 20 min in themixer/sampler. Because the powders were notfree flowing, the ability to mix these two pow-ders so that a representative sample matchedexactly the predicted structure of the mixtureis a good indication of the power of the systemto homogenize a powder that had segregated


NormalizedCumulative 0 5 - -

Volume

01 02 05 10 20 5 0 10 20 50 100Geometric Diameter

(u.m)

NormalizedCumulative 0 5-

Volume

01 02 0 5 1 0 2 0 50 10 20Geometric Diameter

50 100

Differential

01 02 05 1 0 2 0 50 10 20Geometric Diameter

50 100

Figure 13 If a powder is mixed well before sampling,any snatch sample is a representative sample (a) Sepa-rate samples of 15 micron calcium carbonate takenfrom a free-fall tumbling mixer, and characterized bythe Aerosizer, are nearly indistinguishable (b) Mea-sured size distributions of nominal 6 micron and 15micron calcium carbonate powders, compared with amixture of 25% of 6 the micron powder with 75% ofthe 15 micron powder (c) The measured size distribu-tion of the mixture in (b) is nearly identical to thepredicted size distribution (smooth curve) calculatedfrom the known size distributions of the constituentpowders

during previous handling.14'15 (See also dis-cussion on powder mixing monitoring inChapter 11)

Sometimes the fineparticles of interest haveto be sampled from an air steam, in which caseone can use several types of filters. Thus inFigure 1.4, three different types of filter areshown. The filter in Figure 1.4a is an exampleof a type of filter made by bombarding a

plastic film with subatomic particles with sub-sequent etching of the pathways in the plastic.This process produces filters with very preciseholes perpendicular to the surface of theplastic. This type of filter is available fromthe Nuclepore Corporation and othercompanies.16'17

When this type of filter is used to trapairborne fineparticles they remain on the sur-face of the filter so that they can be vieweddirectly for characterization by image analysis.The filter shown in Figure 1.4b is a depth filterof the same rating as that of Figure 1.4a. (Therating of the filter is the size of the fineparticlethat cannot pass through the filter.) It can beseen that there are much larger holes in themembrane filter and the trapped fineparticlesare often in the body of the filter and may notbe readily visible. To view the fineparticletrapped by the filter, the filters may have to bedissolved with the fineparticles being de-posited on a glass slide for examination. Theyare, however, much more robust than theNuclepore type filter and are generally of lowercost.

The third type of filter shown in Figure 1.4cis a new type of filter known as a collimatedhole sieve. These glass filter-sieves are madeby a process in which a fiber optic array isassembled and then the cores are dissolved togenerate orthogonal holes of closely con-trolled dimensions in the filter-sievingsurface.18 These glass sieves are available inseveral different aperture sizes and can bereused for many sampling experiments. Itshould be noted that when studying aerosols itis preferable to study them in situ rather thanafter filtering because the deposition of thefineparticles on a filter can change their na-ture. Thus if one is studying a cloud offineparticles it may be better to use a diffrac-tometer for in situ studies rather than to filterand subsequently examine the fineparticles. Ifone has to take a sample from a slurry streama sampler such as the Isolock sampler shouldbe used.19


C)

Figure 1.4. Various types of special filters are available for sampling aerosols to generate fields of view for use inimage analysis procedures, (a) The appearance of a Nuclepore surface filter, (b) Appearance of a cellulosicdepth filter, (c) Oblique view of a 25 micron "collimated hole" sieve.17

Once a representative sample of a powderhas been obtained, preparing the sample forexperimental study is often a major problem.If one is not careful the act of preparing thesample can change its structure radically. Forexample, some workers recommend that whenpreparing a sample for microscopic examina-

tion one places the powder to be studied in adrop of mineral oil and spreads it gently with aglass rod. From the perspective of the finepar-ticle the glass rod is many hundreds of timesbigger than itself and the pressure of the rodcan crush its structure into a myriad of frag-ments. Other workers sometimes use ultra-


sonic dispersion to create a suspension offineparticles and again such treatment can in-advertently change the structure of thefineparticle population. In general one shouldnot use a dispersion severity that is greaterthan that to which the system is going to besubjected in the process of interest. Thus if apharmaceutical powder is going to be stirredgently in a container of water then one shouldnot use ultrasonics to disperse the fineparti-cles. On the other hand if the substance is apigment such as titanium dioxide that is goingto be dispersed in a medium by processing itthrough a triple roll mill then one should use avery severe form of shear dispersion so thatagglomerates are broken down. Otherwise, agentle dispersion technique will leave agglom-erates untouched and give a false impressionof the fineness of the material when dispersedin a medium. The dispersion of powders inliquids is a very difficult task and requiresspecialist knowledge.20

1.3 SIZE CHARACTERIZATION BYIMAGE ANALYSIS

It is often assumed that image analysis is theultimate reference method because "seeing isbelieving." Unfortunately image analysis is of-ten carried out in a very superficial manner togenerate data of doubtful value. The firstproblem that one meets in image analysis isthe preparation of the array of fineparticles tobe inspected. If one uses a fairly dense arrayof fineparticles a major problem is decidingexactly what constitutes a separate fineparti-cle. Thus, in Figure 1.5a a simulated array ofmonosized fineparticles deposited at randomon a field of view to achieve a 10% coverage ofthe field of view is shown. It can be seen thatmany clusters exist in the field of view. Whenone inspects a filter through the microscopethere is no fundamental method of decidingwhether a cluster viewed has formed duringthe filtration process or existed in the cloud offineparticles that were filtered from the airstream. The only way that one can do this is to

repeat the sampling process at a series ofdilutions. As shown in Figure 1.5b even at 3%coverage of the field of view there are threeclusters that have been formed by randomjuxtaposition of the monosized fineparticles. Iffineparticles, which are really separate enti-ties, cluster in the field of view the loss of thesmaller fineparticles is described as primarycount loss due to the sampling process and thefalse aggregates, which are interpreted as be-ing larger fineparticles, are called secondarycount gain. (The whole question of clustering

a)

1

1 ,

1

1

a

1

11

.

m

1

r

1

H i

1

1

i

M 1

i%

_

if

i

*

I* '

|

1

1

1

m H

- ym u

f^ 1

b)

.'V

11

0

1

Pi

ft

1

I

m9

*

*

I

m

m

-

Figure 1.5. Random juxtaposition of fineparticles in afield of view can lead to false aggregates that distortthe measured size distribution of the real population offineparticles.21"23 (a) The appearance of a simulated10% covered field of monosized fineparticles. (b) Theappearance of a simulated 3% covered field of mono-sized fineparticles.


in a field of view by random chance is dis-cussed at length in Refs. 21, 22, 23.)

Many different automated computer-controlled image analysis systems have beendeveloped for characterizing fineparticle pro-files. If profiles contain indentations of thetype shown by the carbonblack profile of Fig-ure 1.6a the logic of the computer can haveserious problems as the scan lines of the tele-vision camera cross the indentations. To dealwith this problem many commercial image an-alyzers have what is known as erosion-dilationlogic.1 In the dilation logic procedure, pixelsare added around the profile with subsequentfilling in of the fissures of the profile as shownin Figure 1.6b. If the dilated profile is subse-quently stripped down by the erosion processthe resulting smoothed out profile can be eval-uated more readily by the scan logic of theimage analyzer. In Figure 1.6b the smoothingout of the profile by the addition of 32 layersof pixels in a series of operations is shown.Although the original purpose of the dilationfollowed by erosion was to create a smoothedout profile, the erosion logic can also be usedto strip down an original profile to see howmany components are in the original structureas shown in Figure 1.6c. The carbonblack pro-file of Figure 1.6a probably formed by agglom-eration in the fuming process used to generatethe carbonblack and the erosion strip down ofthe original profile suggests that it was formedby the collision of three to four original sub-sidiary agglomerates. Note that there is nosuggestion that the agglomerates of the car-bonblack were formed by deposition from theslide; in this case it probably was a real ag-glomerate formed in space during the fumingprocess.

The analyst must be very careful beforeusing erosion dilation logic to separate juxta-posed aggregates in a field of view being evalu-ated by computer-aided image analysis. A ma-jor mistake made by analysts when looking atan array of fineparticles is to over count thefiner fineparticles and the failure to search forthe rare events represented by the larger

fineparticles in the population to beevaluated.24'25 One should always use a strati-fied count procedure to increase the efficiencyof the evaluation process (See Exercise 9.1,pp. 411-414 of Ref. 22.)

1.4 CHARACTERIZING POWDERS BYSIEVE FRACTIONATION

In sieving characterization studies a quantityof powder is separated into two or more frac-tions on a set of surfaces containing holes of aspecified uniform size. In spite of the develop-ment of many alternate sophisticated proce-dures for characterizing powders, sievingstudies are still widely used and have the ad-vantage of handling a large quantity of pow-der, which minimizes sampling problems. It isa relatively low-cost procedure, especially forlarger free-flowing powder systems. There aremany different manufacturers of sieving ma-chines and of material from which the sievesare fabricated.1'2 Most industrial sieves usedfor fractionating powders are made by weavingwire cloth to create apertures of the typeshown in Figure 1.7a. For more delicate ana-lytical work one can purchase sieve surfacesthat are formed by electroforming or by otherprocesses.

Because there is a range of aperture sizeson a sieve in which theoretically all the aper-tures are the same size, fractionation is neverclear cut and it is necessary to calibrate theaperture range and effective cut size of anygiven sieve. This can be carried out either byexamining the apertures directly under a mi-croscope or by looking at near-mesh finepar-ticles that are trapped in the sieve surfaceduring a sieving experiment. These near-meshsizes are cleared from the sieve by invertingthe sieve, rapping it sharply on the surface,and collecting the particles that fall out on aclean sheet of paper. In Figure 1.7b the sizedistribution of the apertures of a sieve asdetermined by direct examination of the aper-tures, and by examining glass beads and sand


a)

b)

Original

Dilated profile after 32erosions(returned to original size)

24

Figure 1.6. Computer-aided image analysis system routines allow routine characterization of convoluted profiles.(a) A typical carbonblack profile traced from a high-magnification electromicrograph. (b) Dilation can be used tofill internal holes and/or deep fissures in a profile being evaluated. (The number indicates the number of dilationsapplied to reach this stage from the original profile.) (c) Repeated application of the erosion routine suggests thatthis cluster was formed by the collision of several subagglomerates. (The number indicates the number of erosionsapplied to reach this stage from the original profile.)


a)

b) 1.50-n

1.25-

NormalizedAperture 1.00-

Size

0.75-

0.50-

Direct MeasurementTrapped Glass BeadsTrapped Sand Grains

5 10 20 50 80I I I

90 95 9 8Percent of Apertures of the SAME or LARGER Size

Figure 1.7. A major problem in sieve characterization of powders arises from variations in the mesh aperaturesize. The aperture size range increases with sieve usage, (a) Magnified view of the apertures of a woven wire sieve.(b) Variations in aperture size can be determined either by direct examination of the apertures by microscope orby examining near mesh size fineparticles that were lightly trapped in the mesh during sieving and subsequentlyremoved by inverting the sieve and rapping it on a hard surface.

grains that were trapped in the mesh, is shown.It can be seen that the range of sizes trappedin the mesh depends on the shape of thepowder grains. Thus, in Figure 1.8a a typicalset of the sand grains used in the calibration isshown. The shape distribution of the sandgrains as determined from a study of the grainstrapped in the mesh is shown in Figure1.8c.26'27

(For a recent discussion of techniques forcalibrating sieves see Ref. 28. For a discussionof the various ways in which a sieve mesh canbe damaged and the subsequent changes ofaperture sizes monitored see the extensive dis-cussion given in Ref. 1.)

Apart from the uncertainty as to the exact

aperture size in the surface of a sieve, anothermajor problem when carrying out characteri-zation by means of sieve analysis is to deter-mine when the fractionation of the powder ona sieve with given apertures is complete.Methods have been developed to predict theultimate residue on a sieve from the rate ofpassage of materials through the sieve butthese techniques have not found wide accep-tance. The falling cost of data processingequipment, however, will probably lead to arenewed interest in automated characteriza-tion of powders by sieve fractionation.

When carrying out a sieve fractionationstudy one must carefully standardize the ex-perimental protocol and several countries have


a)

b)

NormalizedGrainSize

1.50-n

1.25-

1.00-

0.75-

Length Data set 1+ Data set 2

> 5 10 20

I

i1 i

501 i

80

Width Data set 1 Data Set 2

i i i90 95 98

Percent of Grains Smaller Than or Equal to Stated

c) 1.50-n

1.40 -

ElongationRatio

1.30-

i l5 10 20 80 90 95 98

Percent of Grains Smaller Than or Equal to StatedFigure 1.8. As a byproduct of calibrating a sieve mesh using trapped nneparticles, one obtains a subset of powdergrains, typical of the powder being characterized, which can be used to generate a shape distribution of thepowder grains, (a) Typical sand grains removed from a sieve mesh, (b) Length and width distributions of two setsof sand grains removed from a sieve mesh, (c) Distribution of the elongation ratio of two sets of sand grainsremoved from a sieve mesh.

prepared standard procedures for carryingout sieve characterization studies.29 Specialistsieve equipment is available from severalcompanies.30"35

Electrostatic phenomena can interfere withthe progress of a sieve fractionation of a pow-der. Thus, in Figure 1.9 the size distributionsof a plastic powder fractionated on a 30-meshASTM sieve are shown. (ASTM stands for theAmerican Society for Testing of Materials;this organization has specified a whole series

of tests for sieves. The mesh number refers tothe number of wires per inch with the wirediameter being the same as the aperture ofthe sieve.) The nominal size of a 30-mesh sieveis 600 microns. When the fractionated powderwas characterized by image analysis study therewere considerable numbers of fmeparticles lessthan 150 microns clinging to the coarser grains.On a mass basis, the fines do not constitute asignificant fraction of the weight of powder ofnominal size 600 to 1100 microns but their


a)

b)

6

" 8Size (microns)

0.6-

0.4-

0.2-

-

0.0-

1aS&si

}s9L-D

r &

aa

i

. .

Median " " Chunkiness afP

B m \a B

" m

*

a

1 I l l I l I l0.0 0.2 0.4 0.6

Normalized Size0.8 1.0

Figure 1.9. Electrostatic forces cause fines to cling to oversize fineparticles on the surface of a sieve, preventingthem from passing through the sieve apertures, (a) Size distribution of a sieved plastic powder showing a largenumber of fines still contained in the oversize fraction of the powder, (b) Chunkiness versus size domain for theplastic powder of (a). (Note that chunkiness is the reciprocal of aspect ratio.)

presence could severely modify the flow andpacking behavior of the powder. The finesclinging to the coarser grains had a widerrange of shapes as demonstrated by the chunk-iness size data domain of Figure 1.9b. Some-times the fines of such a powder can be re-moved by adding a silica flow agent into thepowder while sieving the powder. (For a dis-cussion of the effect of flow agents on thebehavior of a powder see the discussion inRef. 36.)

1.5 CHARACTERIZING THE SIZE OFFINEPARTICLES BY SEDIMENTATIONTECHNIQUES

As stated earlier in this chapter, in sedimenta-tion methods for characterizing fineparticlesthe settling dynamics of the fineparticles insuspension are monitored and the observeddata substituted into the Stokes equation tocalculate what is known as the Stokes diame-ter of the fineparticle. During the 1960s and


1970s sedimentation methods were the domi-nant techniques in size characterizationstudies and many different instrument con-figurations have been described.1'2 Severalinternational standard protocols for using sed-imentation equipment have been prepared.Recently the International Standards Organi-zation of the European Community has pre-pared standards for centrifugal and gravitysedimentation methods.37 In Figure 1.10 someof the basic instrument designs that have beenused to study the sedimentation dynamics of asuspension of fineparticles are shown. In in-struments known as sedimentation balancesthe weight of fineparticles settling onto a bal-

ance pan suspended inside the suspension, asshown in Figure 1.10a, is used to monitor thesettling behavior of suspension fineparticles.This type of instrument is known as a "homo-geneous suspension start" instrument. Thepresence of the pan in the suspension inter-feres with the dynamics of the settlingfineparticles but this interference can beallowed for in the interpretive equationsand minimized by specialized design of theequipment.

In an alternate method, the suspension offineparticles to be studied is introduced as alayer at the top of a column of suspension.The movement of the settling fineparticles

a) scale

Draft Shield

Suspension v

Inner Cylinder

Balance Pan N

Clear vrial P i s k \ Rotation ^Suspension

\

PhotodetectorArray

LightBeam

ScatteredLight

ForwardBeam

Detector

d) Homogeneous Suspension

LightBeam

'Clear 'Fluid

Photodetector

Figure 1.10. Sedimentation methods for characterizing the size distribution of powders uses the settling speed ofthe fineparticles in suspension and is interpreted as the size of the equivalent spheres using Stokes' law. (a) Insedimentation balances the fineparticles are weighted as they arrive at the base of the sedimentation column, (b)In a photosedimentometer, fineparticles are monitored by noting the scattering or extinction of light or X-rayspassing through the suspension, (c) In the linestart centrifugal method, a thin layer of suspension is injected ontothe surface of a clear fluid so that all the fineparticles start at the same distance from the wall of the disc, (d) Inthe homogeneous start centrifugal method the disc is filled with suspension.


down the column of clear fluid is monitoredusing a device such as a beam of light or abeam of X-rays as shown in Figure 1.10b.Workers started to use X-rays because of thecomplex diffraction pattern of irregular shapedparticles and the difficult interpretation ofconcentration data from the measured obser-vation of the light beam. Procedures in whicha layer of suspension was floated onto a col-umn of clear fluid are known as linestartmethods. Their advantage vis a vis the homo-geneous start method is the simplicity of datainterpretation; however, complex interactionof the fineparticles moving in a clear fluid cancause complications in interpretation of thesettling dynamics of linestart methods.

Overall, workers have preferred to work withthe homogeneous start method, especially be-cause the rapid development of low-cost dataprocessing instrumentation facilitated thecomplex data manipulations required for theinterpretation of homogeneous suspensionsedimentation procedures.

The Micromeretics Corporation of Georgiamanufactures an instrument for sedimentationstudies based on X-ray evaluation of concen-tration changes in a settling suspension knownas a Sedigraph.38 This instrument has beenwidely used, especially since some industrieshave written standard protocols for using theinstrumentation.2

Accelerated sedimentation of very smallfineparticles by means of centrifugal forcehas been the basic principle of several instru-ments for characterizing fineparticles. See, forexample, the trade literature of the HoribaCorporation.39

In recent years the favored technique fordoing centrifugal sedimentation studies uti-lizes the disc centrifuge. The basic construc-tion of this instrument is shown in Figure1.10c and l.lOd.40'41 Again the analyst has thebasic choice of using a homogeneous sus-pension at the start of the analysis or a linestart system.1'2 As with other sedimentationequipment light or X-rays can be used tomonitor the sedimentation dynamics in thecentrifuge.1'2'41

1.6 DIFFRACTOMETERS FORCHARACTERIZING THE SIZE OFFINEPARTICLES

Advances in laser technology have made itpossible to generate diffraction patterns froman array of fineparticles in a relatively simplemanner. It can be shown that if one has arandom array of fineparticles the resultantdiffraction pattern is the same as that of theindividual fineparticles times the number offineparticles. This is shown by the diagram inFigure 1.11a. The diffraction pattern gener-ated by a real fineparticle profile is dependenton the structure of the profile as shown by thediffraction patterns shown in Figure 1.11b. Inthe commercial instruments that measure sizedistributions from group diffraction patternsthe interpretation of the data is in terms ofthe spherical fineparticles of the samediffracting power as the fineparticles. As canbe seen from Figure 1.11b, sharp edges on theprofile will diffract light further out than thesmooth profile and this is interpreted bythe machines as being due to the presence ofsmaller fineparticles rather than correspond-ing smooth, spherical fineparticles of the samesize as the real fineparticles.52 The basic sys-tems of the various diffractometers are similarexcept that for very small fineparticles somesystems study side scattered light rather thanforward scattered light.42"48

One of the first diffractometers to becomecommercially available was developed by theCILAS Corporation to characterize the fine-ness of cement. The basic system used by theCILAS diffractometer is shown in Figure 1.12.The fineparticles to be characterized are dis-persed in a fluid and circulated through achamber in front of a laser beam. A complexdiffraction pattern generated by the light pass-ing through the suspension of fineparticles isevaluated by using a photodiode array. Inessence the smaller the fineparticle the furtherout the diffraction pattern from the axis of thesystem. The optical theory of software strate-gies behind the evaluation of the diffractionpatterns differs in complexity and sophistica-


a)

I ft

*

.> # *

jm # * '

b)

Figure 1.11. When interpreting the physical significance of the diffraction pattern data of a random array offineparticles, one should remember that the structural features and the texture of a fineparticle affect the lightscattering behavior of the fineparticle.52 (a) A random array of dots and its associated diffraction pattern, (b) Theeffect of shape and sharp points on the diffraction pattern of a single profile.

tion from machine to machine, but in essenceFraunhoffer or Mie theory of diffraction pat-tern analysis is used to interpret the diffrac-tion pattern. In the various presentations ofthe theory of the instrument, one is sometimes

given the impression that the deconvolution(the mathematical term for the appropriateprocess) of the diffraction pattern proceedswithout any basic assumptions. In practicemany diffractometers take short cuts in the


MechanicalStirrer

MeasurementCell

a) 1.0-1

* Output from arraysent ot computer

Figure 1.12. Schematic of the CILAS Corporation laserdiffractometer size analyzer. In this instrument the sizedistribution of a random array of flneparticles is de-duced from the group diffraction pattern. (Used bypermission of CILAS Corporation).43

data processing of their machines by curvefitting an anticipated distribution function tothe generated diffraction pattern data. Thecustomer should always inquire diligently as toany assumptions that are being made in thesoftware transformations of the patterns inany particular commercial diffractometer. Thefact that the shape and features, such as edges,on the flneparticles can contribute to thediffraction pattern has been used to generateshape information by comparing the data gen-erated by diffractometer machines with othermethods of particular size analysis.49"51

The way in which shape information can bededuced by comparing data from differentmethods is shown by the data summarized inFigure 1.13.53 The type of distortion that cancreep into size distribution information be-cause of the software used in the deconvolu-tion of a diffraction pattern is illustrated bythe data of Figures 1.14 and 1.15 taken fromthe work of Nathier-Dufour and colleagues.49These workers studied the size distributions ofthree food powders: a pulverized wheat flour,maize flour, and a soya bean meal. Whenthese were sized by means of a diffractometer(the Malvern size analyzer; see Ref. 44) thethree distribution functions were similar asshown in Figure 1.14. All three distributionsappear to be slightly bimodal, indicating that

0.5-Cumulative

Weight FractionFiner

0.2-

0.1-

Rounded Quartz

MICROTRAC Sedigraph

10 20Size

(J im)200

1.0n Irregular Limestone

0 . 5 Cumulative

Weight FractionFiner

0.2H

0.1-

MICROTRACSedigraphSedigraph translated bya constant shape factor

10 20Size

( J i m )

200

Figure 1.13. By comparing size distribution informa-tion derived from studies that evaluate different pa-rameters of the flneparticles, one can sometimesdeduce shape information factors.53 (Microtrac is aregistered trademark of Leeds and Northrup Co. andSedigraph is a trademark of the Micromeretics Corpo-ration.) (a) Sedimentation studies and diffractometerevaluations of particle size generate comparable datafor spherical flneparticles. (b) Sedimentation anddiffractometer data for angular crushed limestone canbe correlated by means of an empirically determinedshape factor. Thus:

mean size by Sedigraph 10mean size by Microtrac 7

the software being used to deconvolute thepattern was probably anticipating a bimodaldistribution. When the same flours were ana-lyzed by means of sieves the size distributionswere very different as illustrated by the data ofFigure 1.15. First, the wheat and maize floursdid indeed appear to be slightly bimodal butdid not have peaks in the positions corre-sponding to those calculated from the diffrac-tometer data. Note that all three size distribu-tions had ghost large and small fineparticlesthat did not exist according to the sieve char-acterization data. Further the peaks of thedistributions did not correspond to those cal-culated from the diffractometer. If one is onlywishing to compare a size distribution datathen the fact that the diffractometer seemed


a)

b)

Wheat flourd l aser = 792um

Particle Size (microns)20-18-:16-f

5 10-=I" 8i1 *\

A\

0

Maize flourdlaser = 7 5 4 ^ m

(O (O


tions to the sieve data of Figure 1.15 and infact the writer feels that a rush to fit distribu-tion functions to any size analysis data can bea self-defeating process. The analyst shouldreport the data that he finds even if it does notfit simple distribution functions. Distributionfunctions are of use only if one can interpretthe formation dynamics in terms of the distri-bution function produced by a given process.(For an extensive discussion of distributionfunctions that have been used for size analysis,see the first edition of this book and Ref. 2.For a discussion of the physical significance ofthe various distribution functions that havebeen used see the discussion in Ref. 54.) It isnot possible to give general guidance on howto interpret diffractometer data because thesoftware used by the various companies isconstantly changing. However, when reportingsize characterization data generated by dif-ferent diffractometers the research workershould specifically detail the year and modelof the equipment being used in their studies.If possible comment on the deconvolution al-gorithms being used to interpret the data. Inrecent years many manufacturers of diffrac-tion size analyzers have modified their equip-ment to be able to work with dry aerosolsand/or sprays. This has necessitated the de-velopment of systems for generating aerosolsfrom dry powder supplies prior to size analysis.This is not an easy task and the ancillaryequipment for generating the necessaryaerosol can be expensive. Again it is not possi-ble to give firm figures or exact descriptions ofthe equipment because manufacturers areconstantly modifying and changing the designof their equipment.

1.7 TIME-OF-FLIGHT INSTRUMENTS

The falling cost of data processing equipmentand the ready availability of lasers have gener-ated another family of instruments for sizecharacterization studies that can be called"time-of-flight instruments." In the first typeof instrument a narrow focused beam of laser

light explores an area of a suspension and thesize of the particles in suspension is measuredby the time it takes for the laser beam to trackacross the profile of the fineparticle. Sophisti-cated electronic editors are used to generatethe size distribution data from the informationgenerated by the scanning laser. The basicsystem of this type of instrument developed bythe Galai Instruments of Israel is shown inFigure 1.16. (Note that for many years thisinstrument was sold in the United States bythe Brinkman Instrument Company and somany publications in which this instrument isused refer to it as the Brinkman Size Ana-lyzer). The fineparticles to be characterizedare placed in the suspension and the laser isrotated by means of a rotating optical wedge.The system also incorporates a video camerafor inspecting the actual fineparticles beingmeasured. The logic of the Galai system canbe manipulated to provide shape information.It also provides logic modules for advancedimage analysis using the video camera datacollection system.55

Another time-of-flight analyzer that uses asystem similar to the Galai instrument isknown as the Lasentech Instrument. This sys-tem is portable and has been used for onlinemonitoring of fineparticles moving in the slurryor suspension as well as for size analysis in thelaboratory.56

Another time-of-flight instrument, theAeroSizer, is manufactured by Amherst Pro-cess Instruments Inc., in Massachusetts.57 Thebasic system of this instrument is shown in

Rotating/Wedge

Prism

SampleCell

Figure 1.16. The basic layout of the Galia laser-based"time-of-flight" particle size analyzer. (Used by permis-sion of Galia Instruments.)


Figure 1.17a. The aerosol flneparticles to becharacterized are sucked into an inspectionzone operating at a partial vacuum. As the airleaves the nozzle at near sonic velocity thefineparticles in the stream are acceleratedacross this inspection zone. It should be notedthat, as the aerosol stream emerges into theinspection zone, it is surrounded by a stream

of clean air that confines the aerosol stream tothe measurement zone. The use of a stream ofclean air to focus an aerosol stream to becharacterized is a widely used technique knownas hydrodynamic focussing. The term is some-what confusing because it was originally devel-oped with instruments employing liquidstreams to examine a series of flneparticles.

Aerosol to be studied Accelerating airstreamof aerosols

Timeof

Flight(US)

1 10 100Particle Diameter (urn)

c)(l) 1.00 . 8 -

Percent 0.6at Stated

Size 0 .4 -0 . 2 -0.0 I I I I

A A0.0 0.5 1.0 1.5 2.0 2.5 -

Size frim) 0.0 I I I I I T1.0 2.0Size

Figure 1.17. The Amherst Process Instruments Aerosizer is a "time-of-flight" size analyzer.57 (a) The basiclayout of the AeroSizer. (b) Calibration curves for materials of various densities, (c) The AeroSizer can distinguishthe various components in a mixture of standard polystyrene latex spheres, (i) Results for a mixture of 0.494 /im,0.806 jxm, and 1.037 fim latex spheres. (Density 1.05 g/cm3.) (ii) Results for 1.037 fim latex spheres alone.


Over the years the term was extended to cleangas sheaths that serve the same function toimprove the efficiency of the size characteriza-tion equipment. Inherently, the instrumentmeasures aerodynamic diameters directly;however, if the density of the fineparticles isknown, the data can be converted to geometricdiameters that are essentially Stokes' diame-ters because of the adjusted term involving thedensity of the fineparticle. The smaller thefineparticle, the faster the acceleration throughthe measurement zone. The individualfineparticles are characterized by the time theytake to travel across two laser light beams. Asthey pass through the laser beams, they scatterlight which is detected and converted intoelectrical signals by the two photomultipliers.A computer correlation establishes which peakfrom the second laser constitutes the matchingpeak to the initial peak as the fineparticlecrosses the first beam. This cross-correlationeditorial process enables the machine to oper-ate at very high fineparticle flow densities. Theequipment can measure fineparticles at a rateof 10,000/s. The instrument is calibrated us-ing standard fineparticles as shown in Fig.1.17b. The useful feature of the instrument isthat the system used to generate the aerosolfor inspection has variable shear rate disper-sion force so that one can study the forceneeded to disperse a given material into anaerosol. In Figure 1.18, some typical data gen-erated for a difficult cohesive powder areshown.57 The instrument allows the informa-tion on size to be printed out either in differ-ential or cumulative form and by number orvolume. The powder data in Figure 1.18 aretaken from a study of the size distribution ofpaint pigments. In the differential display ofthe data by number, the fines dominate thechart whereas if the data are presented byvolume, there appears to be a small amount ofagglomerated powder that may be dispersibleby higher shear dispersion study. The particu-lar sample of titanium dioxide used in thisexperiment had stood on a shelf for severalyears and it may well have agglomerated overthat period. It should be noticed that pigments

Differential rt_

Number 0 -5"

0.1 0.2 0.5 1.0 2.0 5.0 10 20 50 100Geometric Diameter

(urn)

Differential

0.1 0.2 0.5 1.0 2.0 5.0 10 20 50 100Geometric Diameter

Figure 1.18. Pigments can be characterized by time-of-flight instruments by making the powder into anaerosol.57 (a) Size distribution, by number, for a sampleof titanium dioxide as obtained from the AeroSizer. (b)Size distribution, by volume, for the titanium dioxide of(a) as obtained from the AeroSizer.

such as titanium dioxide are notoriously dif-ficult to disperse into a dry aerosol form andone needs to study the measured distributionof different shear rates before one can decidethe physical significance of data such as thatdisplayed in Figure 1.18.

Another time-of-flight instrument is manu-factured by TSI Incorporated.58 Their instru-ment is known as the Aerodynamic ParticleSizer (APS). This system operates at subsonicflow conditions and cannot tolerate as high aflux of fineparticles as the AeroSizer. The earlymodels also did not have a cross-correlatingeditor so that one had to operate at a flow ratethat permitted unique identification of a pairof light scattering peaks as the aerosolfineparticle crossed the inspection lasers. Con-stant developments are always underway at allthe instrument companies and the readershould check with vendor companies as to theoperating conditions and devices in theircurrent equipment.


1.8 SIZE CHARACTERIZATIONEQUIPMENT BASED ON THEDOPPLER EFFECT

In the time-of-flight instruments, the basicproperties of a laser that are exploited are theability of a laser system to concentrate highoptical power in a narrow nonspreading beamof light. In Doppler-based methods of sizecharacterization it is the monochromacity ofthe laser source that is exploited. The Dopplereffect is the shift in the frequency of a wavemotion caused by the relative motion betweena source of the wave motion and an objectreflecting those waves. It can be shown thatthe shift in the frequency caused by the rela-tive motion is related to the relative velocity ofthe source-reflector system. In Figure 1.19,one of the basic systems used to measure thesize of aerosol fineparticles by measuring theDoppler shift in light reflected off of a movingfineparticle is shown. Instruments using this

type of measurement are available fromseveral companies.58'61

The prime laser beam is split into two beamsand sent into the interrogation zone of theequipment at different angles by the lens asshown. The aerosol fineparticles to be charac-terized are sent across this beam in a singlestream using hydrodynamic focussing of thetype discussed in the previous section withrespect to the AeroSizer. In essence, the lightreflected from the two different beams suffersdifferent Doppler shifts. Thus the lower beamis heading into the direction of the air flowwhereas the upper beam is angled away fromthe flow of aerosols. The scattered light fromthe two beams therefore has slightly differentfrequency. When the reflected light is com-bined in the photomultiplier tube it generatesan interference frequency that is much lowerthan that of the laser light. This interferencefrequency is related to the speed at which theaerosol fineparticles are moving through the

FrequecyShifter " Sample Flow

Laser I.

Oscilloscope

Doppler Burst

High Filter0>

Low Filter

1Counter1 1

Multiplier

Gainoo

Data out toComputer

SignalProcessor

Figure 1.19. In the Doppler shaft-based technique of size characterization, the aerodynamic diameter of finepar-ticles is determined by accelerating the fineparticles through the inspection zone created by crossed laser beams.1


interrogation zone. As in the case of the time-of-flight instruments, the instrument is cali-brated with flneparticles of known size. Whenone reads the theory of the methods such asthat in Figure 1.19 it is sometimes hard todiscover how the Doppler effect is involvedbecause the interpretation of the data is some-times phrased in terms of movement of theaerosol flneparticles through the interferencefringes created by the two laser beams. In factthe optical arrangement of Figure 1.19 is iden-tical to that used in introductory physics labo-ratories to generate Newton's interferencefringes. The fringes constitute a series of lin-ear fringes perpendicular to the plane of thelight beam intersection and to the flow of theaerosol. Therefore to an external observerthe aerosol flneparticles appear to be movingthrough a series of interference fringes. Thespeed of the aerosol fineparticle is deducedfrom the frequency with which the aerosolfineparticle moves past the fringes (see dia-gram in Ref. 1). The interpretation of the datain terms of interference fringes is not strictlycorrect from a physical theory point of view,but can help one to intuitively understandwhat is happening to the interrogation zone.

If the fact that the method used in thesystem outlined in Figure 1.19 involves theDoppler method is difficult to understand frompublished discussions, then it is even moredifficult to track down the involvement of theDoppler shifts in a technique known as photoncorrelation spectroscopy (PCS). In this methodthe size of flneparticles in suspension undergo-ing Brownian motion are studied by looking atthe Doppler shifts of laser light scattered bythe wandering flneparticles. The technique isuseful for flneparticles several microns in di-ameter downwards. In particular it is widelyused to look at the size distribution of latexand colloidal flneparticles.62

In a recent review article Finsy makes thefollowing comments:

Originating some 20 years ago from a research toolin a form only suitable for experts, PCS has becomea routine analytical measurement for the determi-

nation of particle sizes. Its major strong point is thatit is difficult to imagine a faster technique for sizingsubmicron particles. Average particle sizes and dis-tribution width can be determined in a few minuteswithout elaborate sample preparation. However,reasonably accurate resolution of the shape of theparticle size distribution requires extremely accu-rate measurements over a period of ten hours andmore.64

The recent trend for this application is thedevelopment of measuring systems that allowthe control of production processes by on lineand in situ measurements in highly concen-trated dispersions. It should be noted that themethod is known by several names; thus it issometimes referred to as quasi elastic lightscattering (QELS) and DLS, standing for dy-namic light scattering. Commercial equipmentbased on PCS is available through severalcompanies.63

Another instrument that used Doppler shiftsto investigate the size of airborne flneparticlesis known as the E-SPART analyzer. This in-strument can measure aerosol sizes in therange 0.3 to 70 microns aerodynamic diameter.This instrument was developed by Mazumderand co-workers.65~67 The E-SPART analyzeris an acronym for the term the Electrical Sin-gle Particle Aerodynamic Relaxation Time an-alyzer. This instrument is used not only tomeasure size but also to measure the electro-static charge of aerosol flneparticles, a param-eter of importance when predicting the behav-ior of electrostatic copying machines andtherapeutic aerosol sprays used in the phar-maceutical industry. The basic system of theinstrument is shown in Figure 1.20. A knowl-edge of the electrostatic charge distribution onaerosol flneparticles is also of interest whenstudying the efficiency of crop dusting withpesticides and the electrostatic coating of ob-jects in industry such as the automotive indus-try.68 The instrument must be calibrated usingparticles of known particle size. Typical per-formance data for the E-SPART analyzer areshown in Figures 1.20b and 1.20c.

Focussinga) Aerosol in | Optics

Transducer,


Photomultiplier

Laser DopplerVelocimeter

Beams

b)

toComputer

Aerosol out

15 000-

12 5 0 0 -

10 0 0 0 -

7 5 0 0 -

5 0 0 0 -

2 5 0 0 -0 1 1 I ~ T

0.1 0.2 0.5 1.0 2.0 5.0Aerodynamic Diameter (u,m)

10

c)

Percent 15ParticleCount -JO

0.98 1.90 3.71 7.21 14.0Diameter (jim)

27.3

Figure 1.20. In the E-SPART analyzer, aerosols are oscillated in the inspection zone by acoustic waves. Differentsized fineparticles are accelerated at different rates and laser Doppler velocimetry (LDV) is used to derive thesizes.67'68 (a) The basic layout of the E-SPART analyzer, (b) Size distribution of 0.8 /im polystyrene latex (PSL)spheres used to calibrate the E-SPART analyzer, (c) Comparison of the size distributions obtained from a CoulterMultisizer and the E-SPART analyzer for dry ink powder, known as toner, used in laser printers and photocopiers.

1.9 STREAM COUNTERS

In a stream counter, as the name implies, thefineparticles to be characterized are passed ina stream through an interrogation zone wherethey change the physical properties of theinterrogation zone.69"73 (In instruments such

as the AeroSizer the fineparticles being char-acterized pass through the interrogation zonein the stream but the size of the fineparticlesis not monitored from the changes that theycause in the physical properties of the interro-gation zone; rather, they are deduced from ameasurement being made on the dynamics


of the fineparticle in the zone.) Thus in theCoulter Counter the inspection zone is a cylin-drical orifice between two electrodes placed ina conducting fluid as shown in Figure 1.21.The fineparticle, when it enters the zone,changes the electrical resistance of the columnof electrolyte in the zone and the measuredchanges in the properties of the zone are usedto deduce a size characteristic parameter ofthe fineparticle. In many discussions of theperformance of the Coulter Counter it isclaimed that the equipment measures the vol-ume of the fineparticle directly. This is not so,as can be easily shown by anyone who at-tempts to do a mass balance on the measuredsize distribution and number count when look-ing at flakes of gold. Such fineparticles spin asthey enter the zone, blocking off a larger vol-ume of the electroyte rather than the actualvolume of the flake of the material. Othersteam counters such as the Climet, HIAC, andthe Accusizer use optical signals to measurethe size of the fineparticles in the interroga-tion zone. Sometimes when looking at opaqueliquids sonic signals can be used to measurethe size of the fineparticle.1'2'69"71

A major problem with all stream countingdevices is the possibility of multiple occupancyof the interrogation zone. The fact that thenumber count of the small fineparticles is re-duced by the loss of the identity of the two ormore fineparticles in the interrogation zone isknown as primary count loss. The ensemble offineparticles in the interrogation zone is inter-preted by the machine as a pseudo largerfineparticle. These false fineparticles areknown as secondary count gain. Together theeffects of multiple occupancy are known ascoincidence effects. Some workers have at-tempted to deal with coincidence effects byusing statistics of probability of multiple occu-pancy but this requires assumptions about theknown size distribution being anticipated fromthe data, which is a somewhat dangerous wayof measuring an unknown size distribution.The safe way of dealing with coincidence ef-fects is to carry out a series of measurementsat a sequence of dilutions until further dilu-

Suspended Fineparticlesdrawn through Orifice

Figure 1.21. In stream counters, fineparticles to becharacterized pass through an inspection zone and thesize of the fineparticle is deduced from changes in thephysical properties of the inspection volume. Inthe Coulter Counter the inspection zone is a cylindricalorifice between two electrodes. A fineparticle in theorifice changes the electrical conductivity of the col-umn of electrolyte between the electrodes by an amountproportional to the size of the fineparticle.

tion of the suspension does not alter the mea-sured size distribution. Some modern streamcounters incorporate automated dilution tech-nology. Many stream counters incorporate hy-drodynamic focussing of the type discussed inthe previous section. Some of them employelectronic editors to reject signals fromfineparticles that do not travel down the cen-ter of the interrogation zone. It is sometimesclaimed that the signals from stream counterscan be interpreted from fundamental firstprinciples but in practice many of them arecalibrated using standard fineparticles such aslatex spheres. The type of resolution availablewith a light inspected stream counter is illus-trated by the data shown in Figure 1.22.74

1.10 ELUTRIATORS

The term elutriator comes from a Latin wordmeaning to wash out. In their earliest formelutriators were used to wash fine rock debris


14 000

12 0 0 0 -

10 0 0 0 -

Number 8 0 0 0 -of

Occurrences 6 000

4 0 0 0 -

2 0 0 0 -

10 20 50Size (urn)

100 200 500

Figure 1.22. The resolution of particle size information obtainable with light inspected stream counters, alsoknown as photozone stream counters, is illustrated by the data above, generated by the Particle Sizing SystemsAccusizer 770.63'74

away from heavier gold grains that settle downto the bottom of a container of moving fluid.Today the term elutriator refers to any devicein which powder fractionation is achieved bymeans of fluid movement with differential set-tling of the fineparticles. In the 1950s and1960s elutriators were some of the first devicesused to characterize fineparticles. In generalthey tend to have been displaced in moderntechnology by diffractometers and streamcounters. However, they are still the basicdevices for fractionating powders into differ-ent groups. For example, the preparation ofvarious grades of fine diamond polishing pow-der is still achieved using liquid elutriation.(See Blythe elutriator in Ref. 1.) Various con-figurations of elutriator have been devised asillustrated by the systems shown in Figure1.23. In the basic gravity elutriator, thefineparticles to be fractionated are placed in acylinder through which a liquid is moved. Thecut size of the elutriator is the size of finepar-ticle that cannot settle down the column butmust move out of the system with the fluid asit exits from the elutriator chamber. Complexflow takes place in the elutriator body. (Notonly is there a parabolic flow front because ofthe cylindrical structure of the chamber, butthe settling fineparticles interfere with the ris-

ing stream of liquid and the entrained smallerfineparticles.) It is difficult to predict the cutsize of an elutriator and the fractionation isnever clean cut. (See chapter on elutriators inRef. 1.) To accelerate the fractionation pro-cess, cyclones are often used. In a cyclone, asillustrated in Figure 1.23b, the fluid stream offineparticles entering the main body tangen-tially is made to spiral around the fractiona-tion chamber. Under the influence of centrifu-gal force the larger fineparticles are thrown tothe walls of the vessel and slide down into thebottom of the chamber. A tube placed axiallyinto the fractionation chamber accepts the re-turning fluid which is made to spiral out (vortexfinder of Figure 1.23b). The fluid dynamics ofcyclones is a complex subject and usually theexact cut size of the cyclone has to be estab-lished empirically. Part of the problem in pre-dicting the performance of the cyclone is thatthe concentration of fineparticles in the enter-ing fluid stream can effect the performance ofthe device. Personnel cyclones are widely usedto fractionate industrial dusts into respirableand nonrespirable hazards (see Chapter 20).Another type of elutriator that is widely usedto study aerosols and to sample aerosol sys-tems is the impactor shown in Figure 1.23c.An air stream containing suspended fineparti-


a)

Fineparticles ,are elutriatedup the body ofthe elutriator

Filter

Fines

Suspension qf_fineparticles tobe fractionated

Coarsefineparticles arethrown out andslide down thecone to thebottom

Fines VortexFinder

c)

Airstreamcontainingsuspendedfineparticles

Deposited fineparticles

Figure 1.23. Elutriators are devices in which fineparticles are fractionated by a moving fluid, (a) A gravityelutriator. (b) A centrifugal elutriator, also known as a cyclone, (c) In an impactor fineparticles are centrifugallydeposited on a slide as the jet of air is forced to turn by the slide.

cles is deflected by a glass slide or other col-lection surface. The turning fluid acts as acentrifugal system, throwing a certain size outonto the surface of the slide. The depositionof the fineparticles is controlled by the speedof the air jet and the distance from the de-flecting surface.75

1.11 PERMEABILITY METHODS FORCHARACTERIZING FINEPARTICLESYSTEMS

Thus far in our discussion we have been deal-ing with direct methods of fineness assess-ment. In this section we will study what are

known as permeability methods that are indi-rect techniques for studying the fineness of apowder. The basic concept of a permeabilitymethod for fineness assessment is that theresistance to flow offered by a compact of thepowder can be used to characterize the fine-ness of the powder.76 The permeability meth-ods for assessing fineness of substances suchas pyrotechnical powders, pharmaceuticalpowders, and cement powders was widely usedfor 50 years and is still a major technique inthe cement industry. The techniques havetended to fall into disuse in recent years be-cause of the availability of instruments such asthe diffractometer and the time-of-flight in-struments; however, they still have a role to


play in quality control of the heavy industriesparticularly since the sampling problems asso-ciated with permeability measurements aremuch less severe than those for diffractome-ters. Thus a sample of cement for assessmentwith a permeability instrument can be as largeas 200 g of powder as compared to the mil-ligrams of powder used in diffractometers. It ismuch simpler to obtain the 200 g as a repre-sentative sample than it is to go all the waydown to a few milligrams. The inherent cost ofpermeameters is also low. Studies aimed at theoptimization of permeability equipment forquality control situations would seem to offerthe potential for a renewed interest in thepermeability methods. One of the work horsesof industrial powder fineness measurementover the last 50 years was an instrument knownas the Fisher Subsieve Sizer. The basic instru-mentation of this device is shown in Figure1.24a. The components represent 50 year oldtechnology and newer pneumatic controldevices can be used in modern pneumaticcircuits.77'78

It can be seen that the basic pneumaticcircuit of the Fisher Subsieve Sizer is that ofmeasuring an unknown resistance with a po-tentiometer and a standard resistance. Thetwo taps, A and B, of the diagram representdifferent calibrated orifices for use in the com-parative circuitry.

In Figure 1.24b the basic pneumatic cir-cuitry of the Blaine fineness tester is shown.This equipment is widely used in the cementindustry to assess the fineness of cement. Be-cause of its widespread use, the fineness ofcement is often referred to as its Blaine num-ber, which is an arbitrary number derived fromthe performance of the equipment. The ce-ment to be calibrated is placed as a powderplug at the top of a U-Tube Manometer. Adriving pressure is established by closing tap Aand opening tap B. The time required for theair to flow through the plug of cement as themanometer decays from height Hj to H F ismeasured. This instrument is calibrated withcements of known fineness. It is necessary tohave a strict protocol for assembling the pow-

der plug; otherwise different operators usingdifferent pressures and assembly techniquecan change the apparent fineness of thepowder.79'80

In an alternative design of permeametercircuit suggested by Kaye and Legault, thepowder plug to be used in the studies is com-pressed using hydrostatic pressure. The use ofthe hydrostatic compression technique makesit possible to automate the loading and empty-ing of the permeability cell. The use of theequivalent of a wheatstone bridge circuit per-mits automated calibration of a feedback con-trolled instrument. Work is underway to com-pletely automate permeability control ofcement circuits using this design. Relating themeasured fineness of a cement or other pow-der to the constitution of the powder plug isnot a simple matter because the resistance toflow of the powder plug is related not only tothe fineness of the powder but also to the porestructure of the compact. This fact is illus-trated by the data in Figure 1.25. If the mea-surement made on the permeability was di-rectly related to the surface area, then whenone mixed two powders of comparable fine-ness the relationship between the measuredfineness of the mixture and the constitution ofthe mixture would be a linear relationship ofthe type shown for the mixture of aluminumpowder and molybdedum oxide powder shownin Figure 1.25a. However, when one attemptsto use the same interpretation for a mixture ofan aluminum powder and a vanadium pentox-ide powder there is a more complex curvewhich indicates that initially the vanadiumpentoxide filled the interstitial spaces of thepowdered aluminum, increasing its resistanceto air flow which was interpreted externally asan increase in fineness as shown in Figure1.25b. The opposite effect occurred when thealuminum powder was mixed with copper ox-ide powders as shown in Figure 1.25c. Thesecurves indicate, however, that although in somecases one could not follow the constitution ofa mixture from the measured permeability, thepermeability richness curves indicate whetherinterpacking or interference with the structure


a)

H|

I XXr-O-Z-

TapA

TapB

7Standpipe forsetting initial

pressure head

\Powder

Plug

c)

LevelAdjustment

\tCalibrated

Orifices

ControlValve

toVacuum

Pump

CompressedAir

AppliedPressure

NeedleValve

PressureDrop

acrossPowder

Plug

CompressedAir

\

PowderPlug

Water

ControlValve

PowderPlug

VolumeChange

FlexibleMembrane

Air Flow

Figure 1.24. In permeability methods for characterizing fineness of a powder, the resistance of a powder plug toair flow is related to the fineness of the powder.76 (a) Schematic of the Fisher Sub-Sieve Sizer. (b) Schematic ofthe Blaine Fineness Tester, (c) Schematic of the improved Kaye flexible wall permeameter.

of the powder plug is occurring. See discussionof these curves in Ref.76

1.12 SURFACE AREA BY GASADSORPTION STUDIES

The way in which Blaine fineness can be re-lated to data from other size characterizationtechniques is illustrated by the information

summarized in Figure 1.26. The surface areaof a powder can be measured directly by meansof gas adsorption studies. In these techniquesthe amount of gas or other molecular items,such as dye molecules, adsorbed onto the pow-der to form a monolayer is studied.82 (Seestudy of gas adsorption in Ref. 2.) In earlierdiscussions of gas adsorption (before 1977) itwas stated that one of the problems with gasadsorption studies was the uncertainty in the


4.0-

3.0-

2 .0-

0.0-

Theoretical Datao Experimental Data

b) 4.0-

3.0-

85" 2.0-

o 20 40 60 80 100Volume Percentage of Aluminum

1.0-

0.0-


0 20 40 60 80 100Volume Percentage of Aluminum

c) 4.0-

3.0-

2.0-

1.0-

0.0-


0 20 40 60 80 100Volume Percentage of Aluminum

Figure 1.25. The permeability of a powder compact is related to not only the fineness of the powder, but also tothe pore structure of the compact, as demonstrated by experimental data for several powders.76 (a) Permeametersurface area data for a mixture of molybdenum oxide and aluminum, (b) Permeameter surface area data for amixture of vanadium pentoxide and aluminum, (c) Permeameter surface area data for a mixture of copper oxideand aluminum.

knowledge of the cross-section area of theadsorbed molecule, which made estimates ofthe surface vary from gas to gas used in theadsorption studies. In recent years gas adsorp-tion studies of surface areas are being reinter-preted from the viewpoint of fractal geometry.It has been shown that the surface area mea-sured using a given gas depends on the acces-sibility of the rough surface to the particularmolecule being used, as illustrated by thesketch in Figure 1.26a. Avnir and co-workershave shown that if you plot a graph of thesurface area against the molecular size of theadsorbent gas or the molecule, one can draw a

straight line through the data to obtain afractal dimension descriptive of the rough sur-face as shown in Figure 1.26b.81 Neimark re-cently described a method for calculating thesurface area and surface roughness of a pow-der by studying capillary condensation of aliquid on a powder.83

1.13 PORE SIZE DISTRIBUTION OF APACKED POWDER BED

Sometimes when a powder has been made intoa compressed structure, or other packed pow-


b) 10.0-,

5 .0-

mMolesAdsorbed

2.0-

1.0-

OH

CH3 - C - CH3CH3

CH2CH3CH3CH2 - C - OH

CH2CH3

10 20 50Surface Area (A2)

Figure 1.26. Innovations in the interpretation of gas adsorption data allow the surface fractal dimension of asubstance to be deduced, (a) In gas adsorption the surface area is estimated from the number of a particularmolecule required to cover the surface. This e

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