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Aerosol Sampling


Aerosol Sampling

Science, Standards, Instrumentation and Applications

JAMES H. VINCENTDepartment of Environmental Health Sciences,

School of Public Health,University of Michigan,Ann Arbor, MI, USA


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For Christine


Contents

Preface xvii

A SCIENTIFIC FRAMEWORK FOR AEROSOL SAMPLING 1

1 Introduction 31.1 Aerosols 31.2 Particle size 41.3 Elementary particle size statistics 51.4 Aerosol measurement 81.5 Sampler performance characteristics 9

References 12

2 Fluid and aerosol mechanical background 132.1 Fluid mechanical background 13

2.1.1 Introduction 132.1.2 Equations of fluid motion 132.1.3 Streamlines and streamsurfaces 152.1.4 Boundary layers 162.1.5 Stagnation 182.1.6 Potential flow 202.1.7 Turbulence 20

2.2 Aerosol mechanics 222.2.1 Particle drag force and mobility 222.2.2 Drag coefficient 222.2.3 Slip 232.2.4 General equation of motion under the influence of an external force 242.2.5 Particle motion without external forces 252.2.6 Particle aerodynamic diameter 272.2.7 Impaction 282.2.8 Molecular diffusion 302.2.9 Turbulent diffusion 32References 33

3 Experimental methods in aerosol sampler studies 353.1 Introduction 353.2 Methodology for assessing sampler performance 35

3.2.1 The direct (trajectory) method 353.2.2 The indirect (comparison) method 363.2.3 Critique of the alternative methods 37


viii Contents

3.3 Scaling relationships for aerosol samplers 383.4 Test facilities 39

3.4.1 Moving air 403.4.2 Calm air 453.4.3 Slowly moving air 48

3.5 Test aerosol generation 503.5.1 Idealised test aerosols 503.5.2 Dry-dispersed dusts 523.5.3 Aerosol materials 573.5.4 Electric charge effects 59

3.6 Reference methods 603.7 Assessment of collected aerosol 603.8 Aerosol sampler test protocols and procedures 61

References 68

4 The nature of air flow near aerosol samplers 714.1 Introduction 714.2 Line and point sink samplers 714.3 Thin-walled slot and tube entries 73

4.3.1 Facing the freestream 734.3.2 Other orientations 74

4.4 Thick-walled tubes 754.5 Simple blunt samplers facing the wind 76

4.5.1 Two-dimensional blunt sampling systems 764.5.2 Axially symmetric blunt sampling systems 80

4.6 Blunt samplers with orientations other than facing the wind 824.6.1 A cylindrical blunt sampler 824.6.2 Flow stability 844.6.3 A spherical blunt sampler 86

4.7 More complex sampling systems 894.8 Effects of freestream turbulence 90

References 90

5 Aerosol aspiration in moving air 935.1 Introduction 935.2 Thin-walled tube samplers 94

5.2.1 Qualitative picture of aerosol transport 945.2.2 Impaction model for a thin-walled tube facing the freestream 965.2.3 Physical definition of impaction efficiency for aerosol sampling 985.2.4 Experimental studies for thin-walled tubes facing the freestream 985.2.5 Experimental studies for thin-walled tubes at other orientations 1045.2.6 Impaction model for other orientations 1055.2.7 Mathematical models 1095.2.8 Conditions for acceptable isokinetic sampling 114

5.3 Blunt samplers 1165.3.1 Impaction model for a blunt sampler facing the freestream 116


Contents ix

5.3.2 Experimental investigations of blunt samplers of simple shape facing the wind 1205.3.3 Blunt samplers at other orientations 1235.3.4 Mathematical and numerical approaches to blunt samplers 1255.3.5 Orientation-averaged conditions 126References 127

6 Aspiration in calm and slowly moving air 1316.1 Introduction 1316.2 Sampling in perfectly calm air 131

6.2.1 Qualitative description 1316.2.2 Experimental studies for sampling in perfectly calm air 1356.2.3 Analytical models for aspiration efficiency in calm air 1386.2.4 Descriptive modeling of aspiration efficiency 1446.2.5 Criteria for representative sampling in calm air 147

6.3 Slowly moving air 1496.3.1 Definition of calm air 1506.3.2 Intermediate conditions 152References 155

7 Interferences to aerosol sampling 1577.1 Introduction 1577.2 Interferences during aspiration 157

7.2.1 Effects of turbulence on aspiration 1587.2.2 Effects of electrostatic forces on aspiration 1627.2.3 External wall effects 165

7.3 Interferences after aspiration 1737.3.1 Deposition losses inside a straight sampling tube 1737.3.2 Deposition losses inside a bent sampling tube 1807.3.3 Deposition inside a thin-walled tube facing into the wind 1817.3.4 Deposition inside a thin-walled tube at other orientations 1847.3.5 Rebound of particles from internal walls 1857.3.6 More complicated systems 1867.3.7 Electrostatic effects 186References 188

8 Options for aerosol particle size selection after aspiration 1938.1 Introduction 1938.2 Elutriation 194

8.2.1 Vertical elutriation 1948.2.2 Horizontal elutriation 195

8.3 Filtration by porous foam media 1978.4 Centrifugation 2018.5 Impaction 205

8.5.1 Conventional impaction 2058.5.2 Low pressure and micro-orifice impaction 2098.5.3 Virtual impaction 209


x Contents

8.6 Diffusion 2118.6.1 Deposition by diffusion in laminar flow through tubes 2118.6.2 Deposition by diffusion in flow through screens 212

8.7 Other particle size-selective mechanisms 2138.7.1 Electrostatic precipitation 2138.7.2 Thermal precipitation 2148.7.3 Optical processes 215References 215

B STANDARDS FOR AEROSOLS 219

9 Framework for aerosol sampling in working, living and ambient environments 2219.1 Introduction 2219.2 Exposure to aerosols 222

9.2.1 The human respiratory tract 2239.2.2 Definitions of exposure 2259.2.3 Variability of exposure 227

9.3 Framework for health-related aerosol sampling 2279.3.1 Criteria 2279.3.2 Sampling instrumentation 2289.3.3 Analytical methods 2289.3.4 Sampling strategies 2299.3.5 Exposure limits 2329.3.6 Overview 233

9.4 Non-health-related aerosol standards 233References 235

10 Particle size-selective criteria for coarse aerosol fractions 23710.1 Introduction 23710.2 Experimental studies of inhalability 237

10.2.1 Early experimental measurements of inhalability 23710.2.2 Physical basis of inhalability 24110.2.3 Inhalability for very large particles 24210.2.4 Inhalability at very low wind speeds 244

10.3 Particle size-selective criteria for the inhalable fraction 24710.3.1 Early recommendations 24810.3.2 Modern criteria for the inhalable fraction 24910.3.3 Further recommendations 252

10.4 Overview 252References 253

11 Particle size-selective criteria for fine aerosol fractions 25511.1 Introduction 25511.2 Studies of regional deposition of inhaled aerosols 255

11.2.1 Framework 25511.2.2 Theories, simulations and models 258


Contents xi

11.2.3 Experiments for studying regional deposition 25911.2.4 Results for total deposition 26011.2.5 Results for extrathoracic deposition 26111.2.6 Results for tracheobronchial deposition 26211.2.7 Results for deposition in the alveolar region 26411.2.8 Results for the deposition of fibrous aerosols 26511.2.9 Results for the deposition of very fine and ultrafine aerosols 266

11.3 Criteria for fine aerosol fractions 26811.3.1 Historical overview 26811.3.2 Modern criteria for the thoracic and respirable aerosol fractions 27311.3.3 Criteria for the extrathoracic aerosol fraction 27511.3.4 Criteria for the tracheobronchial and alveolar aerosol fractions 27611.3.5 Criteria for very fine aerosol fractions 27811.3.6 Criteria for fibrous aerosols 27911.3.7 Criteria for ultrafine aerosols 280

11.4 Overview 28211.4.1 Summary 28211.4.2 Precision and tolerance bands 28311.4.3 International harmonisation of sampling criteria 284References 285

12 Health effects and Limit values 28912.1 Introduction 28912.2 Aerosol-related health effects 289

12.2.1 Diseases of the respiratory tract 29012.2.2 Diseases beyond the respiratory tract 291

12.3 The processes of standards setting 29212.4 Occupational exposure limits (OELs) 292

12.4.1 Health-based exposure limits 29312.4.2 Regulatory exposure limits 29312.4.3 OELs for aerosols 294

12.5 Ambient atmospheric aerosol limits 29712.5.1 Black smoke and fine particles 29712.5.2 Establishment of the EPA PM NAAQS limit values 29812.5.3 Limits for non-health-related aerosols 300

12.6 Special cases 30112.6.1 Fibrous aerosols 30212.6.2 Bioaerosols 30312.6.3 Ultrafine aerosols 304References 305

C AEROSOL SAMPLING INSTRUMENTATION 309

13 Historical milestones in practical aerosol sampling 31113.1 Introduction 31113.2 Occupational aerosol sampling 312


xii Contents

13.2.1 Sampling strategies and philosophies 31213.2.2 Indices of aerosol exposure 31313.2.3 Early gravimetric samplers for total aerosol 31313.2.4 Particle count samplers 31413.2.5 Emergence of gravimetric samplers for the respirable fraction 31613.2.6 Emergence of gravimetric samplers for total and inhalable aerosol 31713.2.7 Other aerosol fractions 31713.2.8 Sampling to measure aerosol particle size distribution 31713.2.9 Direct-reading instruments 31813.2.10 Overview 319

13.3 Ambient atmospheric aerosol sampling 31913.3.1 Sampling strategies and philosophies 31913.3.2 Indices of health-related aerosol exposure 32013.3.3 Indices for coarse nuisance aerosols 32213.3.4 Direct-reading instruments 32213.3.5 Overview 322References 323

14 Sampling for coarse aerosols in workplaces 32714.1 Introduction 32714.2 Static (or area) samplers for coarse aerosol fractions 327

14.2.1 Total aerosol 32714.2.2 Inhalable aerosol 328

14.3 Personal samplers for coarse aerosol fractions 33314.3.1 Total aerosol 33314.3.2 Inhalable aerosol 34414.3.3 Other samplers 351

14.4 Analysis of performance data for inhalable aerosol samplers 35214.4.1 Statistics 35214.4.2 Modeling 352

14.5 Passive aerosol samplers 354References 356

15 Sampling for fine aerosol fractions in workplaces 35915.1 Introduction 35915.2 Samplers for the respirable fraction 359

15.2.1 Early samplers 36015.2.2 Horizontal elutriators 36415.2.3 Cyclones 36815.2.4 Impactors 37615.2.5 Porous plastic foam filter samplers 37815.2.6 Other samplers 38315.2.7 Sampling for respirable fibers 385

15.3 Samplers for the thoracic fraction 38515.3.1 Vertical elutriators 38615.3.2 Cyclones 386


Contents xiii

15.3.3 Impactors 38715.3.4 Porous plastic foam filter samplers 388

15.4 Samplers for PM2.5 39115.5 Thoracic particle size selection for fibrous aerosols 39315.6 Sampling for very fine aerosols 394

15.6.1 Ultrafine aerosols 39415.6.2 Combustion-related aerosols 394

15.7 Simultaneous sampling for more than one aerosol fraction 395References 398

16 Sampling in stacks and ducts 40316.1 Introduction 40316.2 Basic considerations 40316.3 Stack sampling methods 404

16.3.1 United States of America 40516.3.2 United Kingdom and elsewhere 409

16.4 Sampling probes for stack sampling 41016.4.1 Standard probes 41016.4.2 Velocity-sensing probes 41116.4.3 Null-type probes 41116.4.4 Self-compensating probes 41216.4.5 Dilution 413

16.5 Sampling for determining particle size distribution in stacks 41416.6 Direct-reading stack-monitoring instruments 415

References 415

17 Sampling for aerosols in the ambient atmosphere 41717.1 Introduction 41717.2 Sampling for coarse nuisance aerosols 41717.3 Sampling for black smoke 42317.4 Sampling for total suspended particulate in the ambient atmosphere 425

17.4.1 Total aerosol 42517.4.2 Inhalable aerosol 431

17.5 Sampling for fine aerosol fractions in the ambient atmosphere 43217.5.1 PM10 43217.5.2 PM2.5 43517.5.3 Ultrafine aerosols 439

17.6 Meteorological sampling 440References 442

18 Sampling for the determination of particle size distribution 44718.1 Introduction 44718.2 Rationale 44718.3 Aerosol spectrometers 448

18.3.1 Horizontal elutriators 44818.3.2 Centrifuges 450


xiv Contents

18.3.3 Inertial spectrometers 45018.4 Cascade impactors 452

18.4.1 Outline 45218.4.2 Earlier cascade impactors 45418.4.3 Static cascade impactor-based samplers 45418.4.4 Personal cascade impactors 45918.4.5 Cascade impactors for stack sampling 46218.4.6 Inversion procedures for cascade impactors 463

18.5 Other spectrometers 46518.5.1 Parallel impactors 46518.5.2 Cascade cyclones 46618.5.3 Diffusion batteries 467

18.6 Particle size distribution analysis by microscopy 469References 470

19 Sampling for bioaerosols 47319.1 Introduction 47319.2 Standards for bioaerosols 47419.3 Technical issues for bioaerosol sampling 47419.4 Early bioaerosol sampling 47619.5 Criteria for bioaerosol sampling 47719.6 Inertial samplers 477

19.6.1 Passive samplers 47819.6.2 Single-stage impactors 47819.6.3 Cascade impactors 48119.6.4 Impingers 482

19.7 Centrifugal samplers 48519.7.1 Cyclones/wetted cyclones 48519.7.2 Centrifuges 485

19.8 Total and inhalable bioaerosol 48619.9 Other samplers 486

References 486

20 Direct-reading aerosol sampling instruments 48920.1 Introduction 48920.2 Optical aerosol-measuring instruments 490

20.2.1 Physical background 49020.2.2 Transmission/extinction monitoring 49220.2.3 Light scattering photometry 49420.2.4 Optical particle counters 49820.2.5 Particle size and shape 503

20.3 Electrical particle measurement 50320.4 Condensation nuclei/particle counters 50420.5 Mechanical aerosol mass measurement 50520.6 Nuclear mass detectors 50920.7 Surface area monitoring 510


Contents xv

20.8 Analytical chemical methods 51120.9 Bioaerosol monitoring 511

20.9.1 Fluorescence technology 51120.9.2 Particle size and shape for bioaerosols 51220.9.3 Hybrid systems 512References 513

D AEROSOL SAMPLE APPLICATIONS AND FIELD STUDIES 517

21 Pumps and paraphernalia 51921.1 Introduction 51921.2 Air moving systems 519

21.2.1 Pumps 52021.2.2 Personal sampling pumps 52221.2.3 Pulsation damping 523

21.3 Flow rate 52421.3.1 Flow control 52521.3.2 Flow measurement 525

21.4 Collection media 52621.4.1 Filters 52621.4.2 Filtration efficiency 52721.4.3 Mass stability 52821.4.4 Choices and applications 53121.4.5 Substrates 532

21.5 Analysis of collected samples 53321.5.1 Handling and transport of samples 53321.5.2 Gravimetric methods 53421.5.3 Chemical analysis 534References 535

22 Field experience with aerosol samplers in workplaces 53722.1 Introduction 53722.2 Personal and static (or area) sampling 53822.3 Relationship between total and inhalable aerosol 539

22.3.1 Side-by-side comparative studies 54022.3.2 The practical impact of changes from total to inhalable aerosol measurement 548

22.4 Converting particle counts to particle mass 54922.4.1 Respirable aerosol exposures in the coal industry 54922.4.2 Respirable aerosol exposures in hard rock mining 55222.4.3 Inhalable aerosol exposures in the nickel industry 554

22.5 Field experience with samplers for respirable aerosol 55822.5.1 Gravimetric mass sampling 55822.5.2 Workplace comparisons between optical and gravimetric aerosol samplers 559

22.6 Classification of workplace aerosols 56222.6.1 Particle size distribution 56222.6.2 Combined particle size measurement and chemical speciation 566


xvi Contents

22.7 Diesel particulate matter 56822.8 The future of workplace aerosol measurement 569

References 570

23 Field experience with aerosol samplers in the ambient atmosphere 57523.1 Introduction 57523.2 Nuisance dust 57623.3 Total suspended particulate and black smoke 57723.4 Black smoke and particle size fractions (PM10 and PM2.5) 58023.5 Transition to particle size-selective sampling 58223.6 PM10 58523.7 PM2.5 58923.8 Personal exposures to PM10 and PM2.5 58923.9 Classification of ambient atmospheric aerosols 593

23.9.1 Particle size distribution 59323.9.2 Chemical composition 59423.9.3 Bioaerosols 596References 596

Index 599


Preface

My first book, Aerosol Science: Sampling and Practice, was published by John Wiley & Sons, Ltd in1989. It had been conceived during a flight home to the United Kingdom from Australia in Decemberof 1987, the long hours of pondering and doodling producing an outline that subsequently changed littleas my notes evolved into a proposal and ultimately the book itself. Prior to that imposed period ofreflection I had had no intention whatsoever of ever undertaking the arduous task of writing a majorwork on the scale of a book. But it dawned on me that aerosol sampling was a central aspect of thestudy, characterization and surveillance of atmospheric environments and that it needed to be addressedscientifically in an integrated way in order that the results of aerosol sampling in the real world wouldhave any meaning. The book duly appeared at a time of burgeoning interest in aerosol sampling throughthe widening of the scope of health-related particle size-selective aerosol measurement, in particular theemergence of new criteria and standards, along with new instrumentation.

The field of aerosol sampling has moved forward dramatically during the past two decades, andthe time has now come for a re-evaluation and update. A second edition was discussed. Eventually,however, it was decided with the help of the publisher that so much has changed, so much hashappened, so much is better understood, that a new book is in order. Although written from scratch,Aerosol Sampling: Science, Standards, Instrumentation and Applications nonetheless clearly retains itsorigins in the earlier book, covering much of the same ground in the earlier parts, albeit in a way that hasmatured over the years of consideration and reconsideration. It still separates out the largely scientificfrom the largely practical elements since this most clearly defines, and best integrates, the scope ofwhat has been achieved. In addition to a complete review of the latest science of aerosol sampling andthe development of new instrumentation, major new ingredients in the latest book include extendedchapters on aerosol sampling criteria and standards, new chapters on bioaerosols and direct-readinginstrumentation, and a whole new section on field methods and applications. The first book had itsorigins in aerosol sampling science as it related to occupational exposure assessment. This is hardlysurprising since, at the time, I was working at the Institute of Occupational Medicine in Edinburgh andmy research team was consumed on a day-to-day basis almost entirely with such issues. But my movein 1990 to the University of Minnesota, and then on to the University of Michigan in 1998, launchedme into the wider world of aerosols and aerosol measurement. So the new book presumes to providea comprehensive review of the whole field of aerosol sampling, aimed at scholars, occupational andenvironmental hygiene practitioners, epidemiologists, engineers and instrument developers involved inall aspects of the study, development and application of aerosol exposure assessment methods.

A book like this demands a historical context, and I have attempted to provide one. It is an old clicheto say that how can we work out where we are going if we do not know where we have been? Importantwork from the 1800s and early 1900s is referred to. Even Charles Darwin gets a mention. But the greatmajority of what is described comes from the explosion of interest in, and concerns about, occupationaland living environments in the period post World War II. Indeed, it may be said that it was this periodthat gave birth to the disciplines that we now know as occupational and environmental hygiene.

Reading back what I have written, I see that the narrative in some respects has taken on the appearanceof a memoir, not just by virtue of my own journey through the field over nearly three decades butalso through my associations with a large number of people who, too, were players in what has taken


xviii Preface

place. This book is really about them. It follows, therefore, that I owe a great deal to the many peoplewith whom I have interacted over the years. The list has to begin with C.N. Davies and W.H. Walton,the doyens of aerosol sampling science and its applications to aerosol exposure assessment. They hadbeen together at the chemical and biological warfare research establishment at Porton Down in Englandduring World War II, and had been among the pioneers of what we now know as aerosol science. Afterthe war, Norman Davies, with the new British Occupational Hygiene Society, founded the Annals ofOccupational Hygiene, bringing to it the strong scientific rigor that came from his academic groundingin physics. After Davies eventually moved on to found the Journal of Aerosol Science, Henry Waltontook over the Annals, adding his own background in physics to further enhance the reputation of thatjournal as the leader in the field of what we can now refer to as occupational hygiene science. Infact, it may safely be argued that Henry Walton was one of a small number of ground-breaking, trueoccupational hygiene scientists, his contributions over time reaching beyond the physics of aerosolsand gases and into the realms of exposure assessment and occupational epidemiology. He was pivotal inthe development of aerosol sampling methods and exposure assessment in the context of coalworkerspneumoconiosis during his years with the National Coal Board and latterly the Institute of OccupationalMedicine in Edinburgh. The obituary that appeared in The Scotsman after his passing in 2000 at thegrand age of 87 contained the words It is not possible to estimate how many miners owe their livesand health to his innovations. There could have been no more appropriate epitaph. Henry Walton wasinstrumental in persuading me to come to the Institute of Occupational Medicine when he retired in1978, and that was the turning point that drew me into the field which is the subject of this book. Overthe years I learned that, in his inimitable quiet way, he had been the source of many ideas now taken forgranted in aerosol science, including the theories and development of aerosol dispersing devices suchas the spinning disc generator, respiratory protection devices and testing methods, and particle size-selective sampling devices such as horizontal and vertical elutriators. He was the driving force behindthe definition and measurement of respirable aerosol and latterly and less well-known inhalableaerosol and porous foam filtration. After his retirement, Henry was a regular and welcome presence inthe Institute, and would often drop by my office for a chat. It was during one of these, for example,that he was finally able to convince me how it was possible for the aspiration efficiency of an aerosolsampler to actually exceed unity! I last saw him when I visited him to discuss revisions to a paper wehad written together for Aerosol Science and Technology on the history of occupational aerosol exposureassessment. It was a Saturday, the day of the funeral of Princess Diana, and his eyes were glued to thetelevision as the event unfolded. We did not speak and, after a while, I left him to his thoughts. But in duecourse the paper duly appeared, sadly the only time our names appeared together on the printed page.

I am of course grateful to a very large number of others for their roles in my education about thescience and practice of aerosol sampling, most of whom feature many frequently as the pages areturned. There are those in my own research teams over the years, including my colleagues DavidMark, Alan Jones, Arthur Johnston, Rob Aitken, Harry Gibson and Gordon Lynch at the Institute ofOccupational Medicine; then later my faculty colleague Gurumurthy Ramachandran and doctoralstudents Perng-Jy Tsai, Mark Werner, Terry Spear and Avula Sreenath at the University of Minnesota;and subsequently my doctoral students Sam Paik, Wei-Chung Su, Laurie Brixey, Yi-Hsuan Wu andDarrah Sleeth at the University of Michigan. Then there are the scientists with whom I frequentlyinteracted, conversed, collaborated and shared research in Britain, including Richard C. Brown, SarahDunnett, Lee Kenny, Derek Ingham, Andrew Maynard, Trevor Ogden and Derek Stevens, to namejust a few. There are the many others in Europe and Scandinavia, including Lorenz Armbruster, PaulCourbon, Peter Gorner, Goran Liden and Vittorio Prodi, and many others. I owe special words toYngvar Thomassen for providing me with frequent opportunities to expound my thoughts at the manyexcellent symposia he organized, always in wonderful locations, as well as for his steady stream of


Preface xix

ideas and suggestions about how the results of all our researches could be applied in the real world. Ialso specially want to mention Jean-Francois Fabries. Paul Courbon introduced us over 25 years agoat an aerosols conference in Minneapolis, and we maintained scientific contact over all the years thatfollowed. He consistently made outstanding contributions to aerosol sampling science and its applicationsin occupational and environmental hygiene. It was a great loss to the whole aerosol science communitywhen this charming and modest colleague was taken from us prematurely only a few weeks before thisbook was completed after a long and brave battle with illness.

Upon my arrival in the United States on a frigid New Years Eve in 1990, my work and interests inaerosol sampling began a new phase, with expanded new opportunities for the funding of research and forthe applications of what had been learned in the laboratory to field applications. I owe a special debt toBen Liu, Virgil Marple, David Pui, Peter McMurry and others who encouraged indeed facilitated mymove to the University of Minnesota, undoubtedly one of the meccas of modern aerosol science. I amalso especially grateful for my long associations with Paul Baron, David Bartley, Nurtan Esmen, SergeyGrinshpun, Martin Harper, Bill Hinds, Mort Lippmann, Walter John, Mike McCawley, Bob Phalen,Klaus Willeke, and many others. There are at least two of these you know who you are where ourshared passion for music has exceeded even the joy of our scientific interactions! The work that some ofus carried out in the ACGIH Air Sampling Procedures Committee resulted in the important monograph,Particle Size-Selective Sampling for Particulate Air Contaminants that is widely considered a workingmodern framework for aerosol-related exposure standards.

I am also grateful for my long associations with those in the various commercial enterpriseswho along with names already mentioned have been in the forefront of the realization of practicalsampling instruments, including Debbie Dietrich, Bob Gussman, Pedro Lilienfeld, Eddie Salter, GilSem, and many others, including many that have kindly provided material for inclusion in this book.

The names I have listed above are all my friends. Overall, the list of distinguished aerosol scientists,occupational and environmental hygiene practitioners, and engineers who have contributed to what Ihave learned, and hence what is described in this book, is long. Sadly, many will have been inadvertentlyoverlooked. To those who are not mentioned through my oversight, my thanks to you too and my sincereapologies.

Of course, the actual writing of a book is only the first step in the process of bringing a work to fruition.In this case, in addition to all the individuals and organizations that provided various materials in theform of photographs and other pictures, I am especially indebted to the whole editorial and productionteam at John Wiley & Sons, Ltd, notably Jenny Cossham, Lynette James and Richard Davies and theirmany unnamed colleagues. I thank them all for their professionalism, patience and understanding.

Finally, it will be wryly noted by any reader who themselves have undertaken a large work that theeffort involves many hundreds of hours in solitude. Why do we undertake such projects? It is hardlythe search for immortality. That achievement is reserved only for the likes of Einstein and Newton. Foraerosol science, perhaps only Nikolai Fuchs has achieved that status. For the rest of us, the 99.999 %,we know that our contributions will fade soon after we have departed. What we hope for, therefore, is tobe able to integrate our knowledge in order to create a small new step in a field which can be the basisof further steps in the future by others. It is with this in mind that our thoughts turn to our families whohave been neglected so much for what might seem ultimately so little. In my case I am thereforegrateful to my children, Jeremy, David, Heather and Claire, now all grown up, for their encouragementof my crazy endeavour. Most especially, it could not have happened without the ongoing love andsupport of my wife Christine. In her 11 years as my editorial assistant when I was co-editor-in-chief(with Gerhard Kasper) of the Journal of Aerosol Science, she came to know the names and frequentlythe faces of very many of those same aerosol scientists that are featured in the book. Now, althoughher memory falters prematurely, she still remembers most of them.


Part AScientific Framework for Aerosol

Sampling


1Introduction

1.1 Aerosols

The scientific definition of an aerosol refers to it as a disperse system of liquid or solid small particlessuspended in a gas, usually air. It applies to a very wide range of particulate clouds encounteredterrestrially, including naturally occurring airborne dusts, mists, clouds, sandstorms and snowstorms,as well as the man-made smokes, fumes, dusts and mists that are found in our working and livingatmospheric environments. It also applies to airborne particles of biological origin, including pollens,spores, bacteria and viruses. Although there are some examples of beneficial aerosols, including thosespecifically generated for medicinal and therapeutic purposes (e.g. inhalers like those widely used bypeople suffering from asthma) and those that are generated in closed systems for the purpose of specificengineering applications (e.g. carbon black manufacture, nanotechnology), the primary focus of thisbook is with aerosols that have the potential to be harmful to human health. This alone has been thesubject of great and continuing interest. In this regard, many aerosols are regarded as pollutants andso are considered undesirable, especially if inhaled where they may be associated with adverse healtheffects in humans. It follows, therefore, that much occupational and environmental health research andpractice is concerned with aerosols that are regarded as hazardous agents.

Figure 1.1 summarises some aerosol classifications. It also includes some examples of aerosol typesencountered in occupational and environmental hygiene, reflecting wide ranges not only of chemistry andbiology but also of particle size. As indicated, the range of scale is enormous, across all of which particleshave the ability to remain airborne for significant durations in most environments and so be available forinhalation by humans. It will be a consistent theme throughout this book that particle size is one of themost important aerosol indices that influences the physical nature of aerosols including their manner oftransport in the air and in turn the intensity of human exposure and dose. By a similar token, particlesize is also extremely influential in all aspects of how aerosols are measured. But composition too is animportant consideration since this is largely what drives toxicological effects in aerosol-exposed people.It may vary greatly throughout the particle size range, from location to location, and from one set ofenvironmental conditions to another. This is especially the case for ambient atmospheric aerosols, whichare subject to more widely varying conditions than workplaces, where aerosol composition, althoughoften complex, is usually fairly constant. The continuing need to understand all these aspects of aerosolsposes difficult and interesting challenges to the science and practice of aerosol sampling.

Aerosol Sampling: Science, Standards, Instrumentation and Applications James Vincent 2007 John Wiley & Sons, Ltd


4 Aerosol Sampling

0.01 1 10 100 mm0.1

viruses

smoke

tobacco smoke pollens

atmospheric aerosol

bacteria

animal dander

asbestos fibers (length)

cooking related aerosols

asbestos fibers (width)

welding fume

coal dust

fly ash

cement dust

dust

spraymist

fume

Figure 1.1 Summary classification of aerosols, some types of interest in occupational and environmental health,and an indication of the relative range of scale of particle sizes

1.2 Particle size

For a particle that is spherical, its definition is straightforward, requiring specification only of a singledimension, the particle geometric diameter (d). This is what would be obtained if the particle were tobe observed and sized by reference to an appropriate calibrated graticule under a microscope. Fora particle that is not spherical, however, the microscopist has a dilemma. There is no single definingdimension. Although spherical particles may be found in carefully generated laboratory aerosols, mostaerosols in the real world with the exception of mists and sprays come into this second category. Ittherefore becomes necessary to find a metric of particle size that is not only consistent and accessiblebut is also relevant to the aspects of the behavior of the particles that are of specific interest. This leadsto the concept of equivalent particle size, for which there are several options. For example, equivalentvolume diameter (dV ) is the diameter of a sphere that has the same volume as the particle in question, andis physically relevant to some aspects of particle motion, including diffusion. The equivalent projectedarea diameter (dPA) and the equivalent surface area diameter (dA), are both physically relevant to someaspects of how particles interact with electromagnetic radiation, including visible light. However, aswill be seen later in Chapter 2 and beyond, none of these definitions is sufficient to fully describe theairborne behavior of the particle. From physical considerations, involving not only geometric size butalso particle density and shape, particle aerodynamic diameter (dae) emerges as a property of greatimportance relevant to airborne behavior.


Introduction 5

1.3 Elementary particle size statistics

Only rarely in practical cases do aerosols exist that consist of particles all of one size. When they do,they are referred to as monodisperse. More generally, however, aerosols consist of particles of manydifferent sizes, with particles usually belonging to populations with statistically continuous particle sizedistributions. These are referred to as polydisperse. For the purposes of most of what follows in thisbook, a rudimentary outline of particle size statistics provides sufficient background. More detaileddescriptions are available elsewhere (e.g. Fuchs, 1964; Hinds, 1999).

For particles whose size can be represented in terms of a single dimension (sometimes referred toas isometric), the fraction of the total number of particles with diameter falling within the range d tod + dd may be expressed as:

dn = n(d) dd (1.1)where

0n(d) d(d) = 1 (1.2)

and where n(d) is the number frequency distribution function. Alternatively, the mass frequency distri-bution function m(d) is given by:

dm = m(d) dd (1.3)and

0m(d) d(d) = 1 (1.4)

Other forms of expression for the particle size distribution may similarly be described. They are allinterrelated. Which form is actually used in practice depends on how the particle size is measured. Forexample, the counting and sizing of particles under a microscope yields distributions in the form ofn(d), while gravimetric methods, involving the weighing of collected samples on an analytical balance,yields them in the form of m(d). As a general rule, when discussing particle size statistics, it is prudentto indicate the method by which the particle size analysis has been achieved.

It is often helpful in particle size statistics to plot distributions in the alternative cumulative form, forexample:

Fraction of mass with particle diameter less than d, Cm(d) = d

0m(d) d(d) (1.5)

A typical particle size distribution is given in Figure 1.2, shown both as mass frequency and cumulativefunctions, m(d) and Cm(d), respectively. This figure contains a number of important features. Firstly,the median particle diameter, at which 50 % of the mass is contained within smaller particles and 50 %is contained within larger ones, can be read off directly from the cumulative distribution [Figure 1.2(b)and (c)]. Secondly, the frequency distribution [Figure 1.2(a)] exhibits a strong degree of asymmetrysuch that the peak value of m(d) lies at a value of d which is smaller than the median. The long tail inthe distribution that extends out to relatively large particles is very common indeed is ubiquitous inaerosols in the real world. Skewed frequency distributions like the one shown in Figure 1.2 are oftenwell represented by the log-normal function, given for example by:

m(dae) = Mdae

2 ln g

exp

[1

2

(ln dae ln MMAD

ln g

)](1.6)


6 Aerosol Sampling

0

0.05

0.1

0 10 20 30 40 50 60

m(d

)

0 10 20 30 40 50 60

d (micrometers)

0

0.5

1

Cm

(d)

1%2%5%10%16%25%

50%

75%84%90%95%98%99%

1 10 100

d (micrometers)

C(d

)

(a)

(b)

(c)

Figure 1.2 Typical aerosol mass-related particle size distribution: (a) frequency distribution; (b) cumulativedistribution; and (c) cumulative distribution on log-probability axes, indicative of a log-normal particle sizedistribution

for the mass distribution in terms of particle aerodynamic diameter. Here MMAD is the commonlyused acronym for the mass median aerodynamic diameter and g is the geometric standard deviationreflecting the width of the distribution (or degree of polydispersity), while M is the total mass containedwithin the sample represented by distribution shown. Particle count and surface distributions may bealso similarly represented. In Equation (1.6), g is given by:

g = d84%MMAD

= MMADd16%

(1.7)


Introduction 7

But for calculation purposes, especially when the cumulative distribution is required, involving numericalintegrations of m(d), application of Equation (1.6) becomes unwieldy. The alternative expression:

Cm(dae) = exp[a + b ln(dae)]1 + exp[a + b ln(dae)] (1.8)

provides a very good approximation to the cumulative log-normal function and is much easier to use.Here:

b = 1.658/ln(MMAD) and a = bln(g) (1.9)

For a perfectly monodisperse aerosol, g = 1. More typically, for aerosols like those found in manyworkplace situations, g ranges from 2 to 3. In such cases, when the cumulative distribution function isplotted on log-probability axes [as shown in Figure 1.2(c)], it appears as a straight line. Such behavioris easiest to interpret for scenarios where there are just single aerosol sources. But similar trends are alsofound for situations where there are multiple sources producing aerosols with essentially similar rangesof particle size. However, in situations where there are distinctly different types of aerosols generated intothe same space, the individual particle size distributions characteristic of each source type can be clearlyseen. The case illustrated in Figure 1.3 is typical of what might be found in a dusty workplace forexample, a coal mine where, in addition to the dust sources associated with the primary mechanicalmining operations, fine carbonaceous fume is also present in the form of diesel exhaust from miningvehicles. As will be seen later in this book, knowledge about particle size distribution can be extremelyimportant in understanding the distribution of the deposition of inhaled particles to different parts ofthe respiratory tract. Knowledge of how chemical species are distributed throughout the overall particlesize range is an important additional ingredient. Figure 1.3 therefore provides information that may beregarded as an aerosol fingerprint, containing much of the information needed for the estimation ofhealth related dose and, in turn, risk.

The particle size distribution of an aerosol in the ambient atmosphere is highly relevant to aerosolsampling in the outdoors environment. Here, because of the very diverse range of sources together withthe greater lifetime of some particles after they are released into the atmosphere, the picture is morecomplicated. Figure 1.4 contains a typical example, showing three clearly distinct regions. The first, the

010 20 30

d (micrometers)

F(d

)

dustfume

0

0.05

0.1

0.15

0.2

0 40

Figure 1.3 Example of a typical bi-modal particle size distribution in a workplace (e.g. coal mining) where bothdust and fume are being generated


8 Aerosol Sampling

.001 0.1 1 10 100.01d (micrometers)

F(d)

nucleation mode

accumulation mode coarse mode

Figure 1.4 Example of a typical particle size distribution for atmospheric aerosol

coarse mode, is for the larger particles that are generally associated with mechanically generated airborneparticles, including dusts from both natural and anthropological sources. The second, the nucleationmode, is for the finest particles that are generated as primary particles during combustion or other hotprocesses. Chemically, these are very different from those in the coarse fraction. In addition, followinggeneration, they continue to evolve through both chemical and physical processes. Through some ofthese processes, involving condensation and coagulation, a third population of particles is produced,the accumulation mode. The transition between the nucleation and accumulation modes takes placefor particle diameter around about 0.05 and 0.1 m, and that between the accumulation and coarsemodes around about 1.5 to 2.5 m. As will be discussed later, these transition regions have importantimplications for aerosol sampling.

1.4 Aerosol measurement

Interest in aerosol sampling is stimulated by practical needs to understand, qualitatively and quantita-tively, the properties of airborne particles in many occupational and ambient environmental situations.Such needs include the monitoring of emissions of particulate material to the atmosphere from industrialprocesses, assessment of the aerosol exposures of people for the purpose of epidemiology or risk assess-ment, and assessment of compliance with regulatory standards. In addition, there is the need in manysituations to measure aerosols for the purpose of monitoring and controlling certain types of industrialprocess, including clean rooms. Interest in aerosol measurement across this range of situations expandedrapidly during the postwar period, fueled in particular by increasing public awareness of the problemsassociated with air pollution, especially in relation to health effects, leading in turn to the introductionof wide-ranging clean air acts, emission control limits, and air quality and occupational health standardsin many countries. It has spawned a large and still growing body of scientific research, aimed atinforming us about how to make the process of measurement as relevant as possible to the reason formaking the measurement in the first place.


Introduction 9

The property of most common interest is the aerosol mass concentration (c) defined as the mass ofparticulate material per unit volume of air. It is usually expressed in units of micrograms or milligramsper cubic metre (g m3 or mg m3). Related properties of practical interest, used in some situations,include the number and surface area concentrations. Others include the distributions of particle size andchemical composition. The act of aerosol sampling involves the physical separation of particles froma given volume of the air so that they may be assessed in terms of these and other properties ofinterest.

Much of this book will be concerned with the process of aspiration whereby a known volume ofthe aerosol-laden air is extracted by sucking it (with the aid of pump) through one or more orificesin a solid casing which houses a sensing region which usually takes the form of a filter or someother substrate which may later be weighed, examined under a microscope or otherwise assayed. Theaerodynamic processes by which airborne particles enter the sampler along with the air itself are aswe shall see very complex, depending on many physical factors associated with the sampler itselfas well as its surrounding environment and particle properties. The important practical question is: forgiven sampling conditions, how representative is the aspirated sample of the aerosol of interest in theatmospheric environment outside the sampler? In the first instance this requires definition of what ismeant by representative, and this depends on the scientific rationale underlying the initial decisionto carry out the sampling. Secondly, the sampled aerosol concentration and/or particle size distributionare strongly affected by the physical sampling process itself. Since this in turn is governed by physicalprocesses dependent on particle size such that some particles will be sampled preferentially to others,the particle size distribution of the sampled aerosol will be biased and so will not properly reflect thatof the aerosol at large. It follows that the measured aerosol concentration will also be biased.

The matters of representative sampling and the physics of the sampling process have both been thesubjects of extensive discussion during recent decades. Industry and publicly funded research has beendirected towards the generation of what has now become a large body of applied research involvingapplications of both fluid mechanics and aerosol mechanics. This in turn has enabled considerableprogress towards the development of scientifically based practical methodologies.

1.5 Sampler performance characteristics

Scientific discussion of sampler performance at all levels can begin by referring to the diagram inFigure 1.5. It represents the air flow near a single-orifice sampler of arbitrary shape at arbitrary orien-tation with respect to a moving airstream. The sampler itself consists of an entry in a bluff body andan inner transition section leading to the sensing region, shown here as a filter on which the sampledparticles are collected. The flow pattern indicated represents the motion of the air near the sampler. Inparticular, the limiting streamline actually a streamsurface is the invisible surface which separatesthe sampled air from that which is not sampled. To aid the discussion, the incident plane is defined asan arbitrary plane sufficiently far upstream of the sampler for the flow pattern there to be undisturbed bythe presence or action of the sampler. The sampling plane is defined as the plane containing the samplerentry, and the filter plane defines the location of the sensing region inside the body of the sampler.

Under given particle size and air flow conditions, N0 is the number of particles passing through thatpart of the incident plane contained within the limiting streamsurface. Ns is the number passing throughthe sampling plane, having arrived there directly whilst airborne at all times. Nr is the number passingthrough the sampling plane which have undergone impaction with and subsequently rebounded (or beenblown off) from the external surfaces. It is important to note that both Ns and Nr may contain particlesthat were not included in the N0 originally contained within the sampled air volume. Of the particles


10 Aerosol Sampling

Area a

Incidentplane

aerosolconcentration c0

Samplingplane

cs

asa0

N0

Filterplane

P(Ns + N

r )

Nr

NF

Ns

Limiting

stream

surfa

ce

Limiting pa

rticle tr

ajectory

Figure 1.5 Representation of air and particle movement near a single-entry aerosol sampler of arbitrary shapeand orientation with respect to the external wind, identifying the important features needed on which to basea discussion about aerosol sampler performance. Reproduced with permission from Vincent, Aerosol Sampling:Science and Practice. Copyright (1989) John Wiley & Sons, Ltd

crossing the sampling plane, some may be deposited on the walls of the transition section so that thenumber reaching the filter (NF ) is:

NF = P(Ns + Nr) (1.10)where P is the fractional penetration of particles through the transition section. In what follows asthis book proceeds, it will become apparent that sampler performance needs to be described by morethan one parameter. Firstly, the aspiration efficiency (A) is the purely aerodynamic part of samplerperformance, determined only by the air and particle motions outside the sampler. This is given by:

A = NsN0

(1.11)

Next, the entry (or apparent aspiration) efficiency is:

Aapp = Ns + NrN0

(1.12)

Finally, the overall sampling efficiency (or sampling effectiveness) is

A = NFN0

= P(Ns + Nr)N0

PN sN0

= PA when Nr = 0 (1.13)


Introduction 11

This last metric of sampler performance is of special importance when a particular fraction of theaspirated aerosol needs to be consistently selected. For example, as will be discussed in detail later inthis book, this might be a sample that sets out to simulate a subfraction of particles inhaled by humansthat deposit in a particular part of the respiratory tract. In such cases, the transition region between theentry and the filter is designed with regard to geometry, as well as fluid and aerosol mechanics, so thatthe penetration, P , is consistent and known.

Particle concentration in an aerosol is a scalar quantity that, for practical purposes (and except forextremely low concentrations), may be described in terms of a continuous spatial distribution. Consideragain Figure 1.5. The limiting streamsurface encloses an area a0 in the incident plane. The samplingorifice has area as , outside which all particles either strike the external wall of the sampler or pass byin the freestream. The limiting particle trajectory surface, inside which all particles enter the plane ofthe sampling orifice, encloses a corresponding area a. Only for inertialess particles do the limitingstreamsurface and limiting particle trajectory surface coincide. Then a0 = a. Otherwise a0 > a. Theideal situation is the one where there are no external or internal wall effects on sampler performance,in which case Equation (1.11) for aspiration efficiency may be rewritten as:

A =

as

(cv) daa0

(cv) da(1.14)

where c and v are local values (over local elementary areas da) for particle concentration and velocity,both distributed continuously across the sampling and incident plane respectively. Here, terms of theform (cv ) are local particle fluxes, the numbers of particles flowing through unit area per unit time.Since, by continuity, the net flux of particles through a is the same as that through as , Equation (1.14)may also be expressed as

A =

a

(cv) daa0

(cv) da(1.15)

It is obvious from Equation (1.15) that A is dependent on the spatial distribution of both particleconcentration and velocity across the incident plane unless:

cv = constant (1.16)

over as or a, whichever is the greater. When Equation (1.16) is satisfied, Equation (1.15) reduces to:

A = a

a0(1.17)

and this is the form that underlies most theoretical and some experimental assessments of aspirationefficiency. In terms of particle fluxes, Equation (1.17) leads to:

A = csUsasc0Ua0

(1.18)


12 Aerosol Sampling

where U is the freestream air velocity at the incident plane and Us the mean air velocity across thesampling plane, and where as already defined cs and c0 are the mean particle concentrations at thesampling and incident planes, respectively. Continuity requires that:

Usas = Ua0 (1.19)

So, for aspiration efficiency, Equation (1.18) becomes:

A = csc0

(1.20)

It is important to reiterate that arrival at this familiar expression is entirely dependent on the assumptionof uniform spatial distributions of particle concentration and freestream air velocity upstream of thesampler.

It follows from Equation (1.13) that the efficiency by which particles arrive at the filter is

A = cFc0

(1.21)

where cF is the concentration of the particles reaching the filter.In the last two expressions, cs and cF are the measured quantities of interest. The first depends on

the aspiration efficiency of the sampler as reflected in A. This in turn is governed by the physics ofthe aspiration process so that for fixed geometrical and fluid mechanical variables, it is a function ofparticle size. As shown in Equation (1.13), the second depends both on A and on the similarly particlesize-dependent efficiency P by which particles penetrate through the internal section of the samplerbetween the inlet and the filter.

For a polydisperse aerosol where the non-normalized mass-based particle size distribution is givenby M(d), cs is given by:

cs =

0A(d)M(d) dd (1.22)

and cF by:

cF =

0P (d)A(d)M(d) dd (1.23)

As will become apparent, Equations (1.20)(1.23) are central to all discussions about the performancecharacteristics of aerosol samplers.

References

Fuchs, N.A. (1964) The Mechanics of Aerosols, Macmillan, New York.Hinds, W.C. (1999) Aerosol Technology: Properties, Behavior and Measurement of Airborne Particles, 2nd Edn,

John Wiley & Sons, Inc., New York.Vincent, J.H. (1989) Aerosol Sampling: Science and Practice, John Wiley & Sons, Ltd, Chichester.


2Fluid and Aerosol Mechanical Background

2.1 Fluid mechanical background

2.1.1 Introduction

The physics of air movement is fundamental to the behavior of suspended particles. At the microscopiclevel of an individual particle it defines the flow of air over and around the particle, and hence tothe drag and lift forces acting on it. So the fluid mechanics of what happens at this level are relevantto the way in which a particle may move relative to the air itself. At the macroscopic level they arerelevant to the behavior of larger-scale moving air systems in which aerosols move and in which theyare translated and, in some cases, arrive at surfaces. This in turn is relevant to the airflow close to andaround an aerosol sampler. It is not possible to have a discussion of the science of aerosol samplingwithout reference to both these aspects of fluid mechanics. In what follows, therefore, the aim is toprovide a succinct framework of rudimentary fluid mechanical ideas and concepts to aid the discussionof aerosol transport and sampler characteristics which will form the main thrust of subsequent chapters.For detail in greater depth and breadth, the reader is directed elsewhere to the many specialized textsthat are available (e.g. Schlichting and Gersten, 1999).

2.1.2 Equations of fluid motion

The starting point for describing the aerodynamic behavior of suspended particles is the set of equationsrepresenting the motion of the air itself. These are derived from applications of Newtons second lawto a three-dimensional, incompressible elementary air volume (see Figure 2.1). That is:

mass acceleration = sum of the forces acting (2.1)

in which the surface forces in question are normal forces associated with gradients in static pressurewithin the body of the fluid and shearing forces associated with gradients in fluid velocity and theattendant friction that occurs between adjacent layers of fluid moving at different velocities. By writingdown expressions for these forces in three dimensions, a set of dynamic equations is obtained fordescribing the fluid movement, one for each of the three spatial dimensions. In addition, in order that

Aerosol Sampling: Science, Standards, Instrumentation and Applications James Vincent 2007 John Wiley & Sons, Ltd


14 Aerosol Sampling

p dy dz

dx dz

dx

dy

dzshear

dy )dx dz( shear +sheary

(p + dx )dy dzppxx

Figure 2.1 Three-dimensional elementary air volume on which to base derivation of the fluid mechanicalequations of motion. Reproduced with permission from Vincent, Aerosol Sampling: Science and Practice.Copyright (1989) John Wiley & Sons, Ltd

mass is conserved, it is also necessary to ensure continuity. That is, the mass of air that flows into agiven volume must be equal to that leaving it. The combination of dynamic and continuity equationsprovides the well-known NavierStokes equations, expressed generally as:

DuDt

= grad p + 2uinertial pressure viscousforces gradient shearing

forces forces

div u = 0 (2.2)continuity

where the fluid is assumed to be incompressible, such that continuity of mass is equivalent to continuityof volume. Here, p is the local static pressure, u is the local instantaneous velocity vector, theair density and the air viscosity. The mathematical D-operator on the left embodies the substantiveacceleration that comes from changes in local fluid velocity in both time and space.

The NavierStokes equations may be nondimensionalised by setting U = u/U and X = x/D, andsimilarly for the y and z directions. In addition

Pr = ppr

(2.3)

In the above U is a characteristic air velocity representing the flow system as a whole, D is a charac-teristic dimension and pr is a reference static pressure. The set of equations of motion now becomes:

D uDt

= prD

grad Pr + DU

2U (2.4)

from which it is seen that mathematical solutions for describing the flow are unique if the coefficientfor the last term on the right-hand side is constant; that is, the nature of the flow is defined by the


Fluid and Aerosol Mechanical Background 15

dimensionless quantity (Re) where:

Re = DU

(2.5)

This is known universally as the Reynolds number, and its importance to aerosol science and in turnto aerosol sampling will soon become apparent.

2.1.3 Streamlines and streamsurfaces

Solutions of the NavierStokes equations can, in principle, allow determination of the pattern of the airflow for any set of boundary conditions and for a given value of Re. In practice, however, closed-formsolutions are not generally accessible except for very simple flows, most of which are not ultimately ofmuch use in practical applications. However, with the availability of powerful computers and appropriatesoftware based firmly on the physical fundamentals outlined above, numerical solutions for most situa-tions can now be obtained. There are many such routines developed specifically for research purposes byindividual investigators. Some will be mentioned elsewhere in this book. Commercial routines are moreaccessible to the less-specialised user, but these are usually expensive and still require a significant levelof expertise in engineering fluid mechanics in order to optimise the set-up and operation and, in turn,the quality of the results. Whether solutions are closed-form or numerical, flows with time-dependentbehavior (e.g. oscillations such as vortex shedding) are especially difficult.

The endpoints of solutions of the NavierStokes equations may take many forms, depending onthe desired goal of the enquiry. For present purposes, a solution that provides the shape of the flowpattern in a given situation is especially instructive. By way of illustration consider the simple case of aplane flow, two-dimensional in x and y only. Here, for steady flow, the NavierStokes equations fromEquations (2.2) may be expanded into the form:

uxux

x+ uy ux

y= 1

p

x+

(2ux

x2+

2ux

y2

)

uxuy

x+ uy uy

y= 1

p

y+

(2uyx2

+ 2uy

y2

)(2.6)

ux

x+ uy

y= 0

The pressure term may be eliminated by differentiating the first equation with respect to y and thesecond with respect to x and then subtracting. In this process, terms of the form of the left-hand sideof the third equation emerge which then vanish by virtue of continuity. If we now introduce the streamfunction (), where:

ux = y

and uy = x

(2.7)

then the air flow pattern is fully described by the single equation:

y

2x

x

2y

=

4 (2.8)

which may be solved for {x, y} for chosen constant values of for given boundary conditions and Re.Here, each set of {x, y} for a given value of defines a fluid trajectory, or streamline (or, perhaps more


16 Aerosol Sampling

Lines of equal y

Flow boundary

Convergence increasing air velocity

Figure 2.2 Typical flow pattern over a surface to illustrate the nature of streamlines. Reproduced with permissionfrom Vincent, Aerosol Sampling: Science and Practice. Copyright (1989) John Wiley & Sons, Ltd

appropriately, stream surface). A typical streamline pattern is shown by way of illustration in Figure 2.2.It is required that there can be no net flow of fluid across such lines. Therefore the volumetric flow ratebetween adjacent streamlines having different values for must remain constant. This in turn meansthat a divergence of the flow pattern is consistent with a decrease in fluid velocity; and vice versa forconvergence. Qualitatively, it also means that, for a given flow configuration, the pattern of streamlinesrepresents the trajectories of fluid-borne scalar entities moving in the absence of inertial or externallyapplied forces. The streamline pattern is therefore a vivid and instructive way of representing the natureof a fluid flow system, consistent with what would be observed in a flow visualisation, as for examplemight be achieved using a suitable visible tracer such as smoke.

Solutions for three-dimensional flow around a small spherical particle are particularly relevant in thecontext of this book. Some typical flow patterns for various ranges of Re are shown schematically inFigure 2.3. These show that, whereas the flow pattern at low Re(< 1) is symmetrical upstream anddownstream of the sphere, at higher Re (especially beyond 1) it tends to converge less rapidly on thedownstream side. This is due to the increased inertial behavior of the flow at higher Re. The higherthe value of Re, the greater will be the tendency of the flow in the wake of the sphere to separate (seebelow). Although this feature may not usually be applicable to the flow about aerosol particles, wherein almost all practical cases Re is less than or does not exceed unity, it may be relevant to air movementaround larger bluff obstacles (e.g. the body of an aerosol sampler) where Re is much higher.

2.1.4 Boundary layers

A boundary layer in a flow is defined as a region near a boundary (usually, but not always, a solid wall)where the influence of fluid viscosity is particularly important. For real fluids, the physical conceptof viscosity requires that the fluid velocity must fall to zero at the boundary itself. The boundarylayer, as shown in the schematic example in Figure 2.4, is therefore seen to be the region within



Re < 1

1 < Re < 20

Re > 20

Figure 2.3 General form of the air flow pattern near a spherical body for various ranges of Reynolds number(Re). Reproduced with permission from Vincent, Aerosol Sampling: Science and Practice. Copyright (1989) JohnWiley & Sons, Ltd

U

Boundary layer

Figure 2.4 Illustration of the flow in a boundary layer over a flat solid surface. Reproduced with permissionfrom Vincent, Aerosol Sampling: Science and Practice. Copyright (1989) John Wiley & Sons, Ltd


18 Aerosol Sampling

which the fluid velocity goes from zeroat the boundaryto the value corresponding to that whichwould be obtained by solving the NavierStokes equations for the zero-viscosity, so-called inviscid ,case. However, as we penetrate deeper and deeper into the boundary layer, frictional forces becomeincreasingly influential and, eventually at the wall itself, become dominant. In consideration of thegeneral nature of the flow, the extent to which the effect of viscosity is significant depends on thethickness of the boundary layer in relation to the scale of the bulk flow. It may be shown that theboundary layer thickness for flow over a large body is relatively small compared with that for a smallbody. This, of course, is consistent with the earlier discussion about the Reynolds numbernamely, thatRe for a large body, for given fluid velocity, is greater than for a smaller body. It is a fair workingassumption for the majority of aerosol sampling situations that the boundary layer at the sampler surfacemay be neglected and that potential flow models may be employed (see below). This in fact has beenthe assumption by many of the theoretical fluid dynamicists who have turned their attention to aerosolsampling.

For flow close to a solid surface, boundary layer properties are strong determinants of fluid behavior.For air flow over a smooth surface, energy is lost due to the friction in the boundary layer associatedwith the velocity gradient close to the surface. In the first instance, this is the source of the aerodynamicdrag on bodies placed in the flow. But, other than for flows characterised by very small Re (creepingflow with Re 1), the loss of energyand the associated change of local static pressuremay be suchthat the surface streamline can no longer remain attached to the surface, but rather may separate. Forhigh enough Re this may happen even for relatively smooth, slowly curved surfaces, as in the flowover a spherical body. But even at relatively small Re, for flow over a surface with a sharp change ingeometry, for example an abrupt step or a sharp-edged flat plate, the inertia of the flow in the boundaryplayer may be such that the flow cannot remain attached to the surface. So it suddenly detaches. Asshown in Figure 2.5, such flow separation is accompanied by flow reversal contained within a separationbubble which, depending on the flow geometry, may be more or less stable. Coherent vortex sheddingis very prominent for two-dimensional flows, less so for axially symmetric flows. As will be seen later,considerations of such flow separation have some relevance to aerosol sampling.

2.1.5 Stagnation

Along a given streamline, is constant and so the solution of the NavierStokes equations yields thewell-known Bernoulli expression:

p + 12u2 = constant (2.9)

which states that the sum of the local static pressure and the local velocity pressure is constant. This isequivalent to the conservation of energy. In effect it states that the sum of kinetic and potential energyis constant provided that there are no friction losses. From Equation (2.9) we see that, as the velocitydecreases, coinciding with the divergence of adjacent streamlines, the static pressure increases; andvice versa as velocity increases. Stagnation occurs when all of the velocity pressure is converted intostatic pressure and so the local velocity falls to zero. This is where the static pressure is highest. Thisusually but not always occurs at the surface of a bluff flow obstacle at points where a streamlineintersects with the body and its continuation follows the surface of the body itself (see Figure 2.6). Itis a particularly important concept in describing the flow near an aerosol sampler and will thereforefeature repeatedly in future chapters.



Separation

Reattachment

(a)

(b)

Figure 2.5 Illustration of some typical separated flows: (a) sphere with a relatively stable wake cavity enclosedwithin the separation streamlines (or bubble); and (b) surface mounted block, indicating separation andreattachment. The shaded areas represent turbulence that would be present if the Reynolds number (Re) is highenough. Reproduced with permission from Vincent, Aerosol Sampling: Science and Practice. Copyright (1989)John Wiley & Sons, Ltd

Stagnationpoint

Stagnationstreamline

Figure 2.6 Illustration of the phenomenon of stagnation in a typical streamline pattern over a body. Reproducedwith permission from Vincent, Aerosol Sampling: Science and Practice. Copyright (1989) John Wiley & Sons, Ltd


20 Aerosol Sampling

2.1.6 Potential flow

If friction forces are neglected, the flow is considered to be inviscid so that Equation (2.8) reduces to:

2 = 0 (2.10)In addition it is useful to introduce the closely related concept of velocity potential, , where:

ux = x

and uy = y

(2.11)

which satisfies:2 = 0 (2.12)

for inviscid flows. Described in this way, such flows are therefore widely referred to as potentialflows, in which lines of constant (streamlines) and constant (equipotentials) form an orthogonaltwo-dimensional network.

The particular value of the concept of velocity potential in relation to aerosol sampling is that itenables simple mathematical statements to be made about simple flows which may be combined inorder to create more complex (and more relevant) ones. The example of a two-dimensional line sink isdirectly relevant to aerosol sampling. Consider the case where the flow rate is Q per unit length placedin a uniform freestream whose characteristic velocity is U . For the line sink, the potential field in {x, y}coordinates, where the sink is located at the origin, is given by:

sink = Q2

ln(x2 + y2)1/2 (2.13)

For the uniform (freestream) flow:freestream = Ux (2.14)

These individual potential fields may now be superposed to provide the overall potential field associatedwith the line sink placed in a uniform freestream. Thus:

system = sink + freestream (2.15)which, with Equations (2.11), (2.13) and (2.14), yields the velocity components:

ux = U Qx2(x2 + y2)

uy = Qy2(x2 + y2)(2.16)

Much more complicated aspirating flows may similarly be constructed by superposing appropriate com-binations of such simple solutions in much the same way.

2.1.7 Turbulence

Flows in which the layers of fluid defined by the streamlines slide smoothly over one another arereferred to as laminar. However, when inertial forces become large enough in relation to viscous forces,



the flow may tend to become unstable, or turbulent. This was first demonstrated experimentally for theflow of water in pipes by Sir Osborne Reynolds (1883), who found that the transition from laminarto turbulent flow is governed by a dimensionless quantity involving the diameter of the pipe, the fluidflow rate and the density and viscosity of the fluid itself. This is, of course, the Reynolds number (Re)already referred to, and it was found that the transition occurred at around Re = 2300. Since thoseearlier experiments, corresponding transitions from laminar to turbulent fluid flows have been examinedby others for a wide variety of flow configurations, including internal flows in ducts and external flowsof water, air and other fluids around bluff bodies, in boundary layers, etc.

The subject of turbulence presents considerable theoretical difficulties for the study of air move-ments. All that needs to be said here is that the physical manifestation of the instability associatedwith turbulence appears as randomly fluctuating fluid motions superimposed on the mean flow. Tobegin to construct a physical model for explaining the consequences of this, each velocity term inthe NavierStokes equations may be replaced by its equivalent mean value plus the correspondinginstantaneous fluctuation from that mean. The resultant set of equations for the instantaneous flow iscomplicated, but may be rendered manageable by time-averaging. Then it is seen that, as one of itsconsequences, turbulence is accompanied by an apparent sharp increase in the viscosity of the fluid.Another consequence is that there is a corresponding increase in the rate of mixing of fluid properties(e.g. momentum) and of fluid-borne material.

The structure of turbulence may be described in terms of the spectral characteristics of the fluctuatingmotions that are superimposed on the mean flow. Eddy-like flow formations are created at the large,low-frequency end of the spectrum, having a scale comparable with that of the flow system in question,such as the dimension of the pipe or of the bluff body, and their energy is derived from the mean flow.By the process of vortex stretching, these eddies are broken down into progressively smaller andhigher frequency ones until the scale is reached where the energy may be dissipated viscously togenerate heat. There are two views of the statistical properties of those fluctuating velocities, reflectedin the Lagrangian and Eulerian microscales (L and E , respectively) which relate to the dimensions ofthe turbulence elements. The relationship between these quantities depends on how velocities in the fluidelements are correlated with one another. For instance, small L/E means that the velocities betweensuccessive elements are correlated; otherwise they are uncorrelated. This has important consequences inrelation to the motion of a suspended particle in a turbulent flow as it encounters a succession of suchelements.

Despite the physical complexity of turbulence, a useful, simplified picture may be obtained by describ-ing it in terms of (a) a characteristic integral length scale (L) typical of the eddies containing the bulkof the turbulent energy (and which is closely related to the microscales referred to above), and (b) acharacteristic energy or mean square velocity fluctuation:

e = u2x + u2y + u2z (2.17)

where ux , uy and uz are the components of the instantaneous velocity fluctuation in the three directionsindicated. If the corresponding velocities for the mean flow are Ux , Uy and Uz, respectively, then wemay also define the intensity of turbulence (Ix) for each of the three directions. Thus:

Ix = (u2x )

ux

1/2

(2.18)

describing the magnitude of the time-averaged velocity fluctuations of the turbulent motions as a pro-portion of the mean velocity for the x direction; and similarly for the y and z directions.


22 Aerosol Sampling

Mixing in turbulent flow may be described in terms of the transport of any scalar property, includ-ing airborne particles. The basic diffusivity of the turbulence itself may be expressed to a first-orderapproximation by:

Dt Le1/2 (2.19)where it is seen to be a property of the turbulence associated with the fluid flow and is not a fundamentalproperty of the fluid itself. Equation (2.19) is adequate in many cases for describing the turbulentdiffusion of airborne scalar properties that do not exhibit inertial or buoyancy effects. It is therefore auseful starting point for consideration of the turbulent mixing of aerosols.

2.2 Aerosol mechanics

The science of aerosol mechanics is concerned with the mechanical properties and transport of airborneparticles, and has been covered extensively in a number of well-known texts (Fuchs, 1964; Friedlander,1977; Hinds, 1999). This chapter sets out to provide an overview of those aspects that are importantfor describing aspiration and other processes relevant to aerosol sampling.

2.2.1 Particle drag force and mobility

The drag force acting on a macroscopic body moving relative to the air is a net result of the distributionand magnitude of the local static pressure and shearing forces over its surface. These forces may beobtained from solutions of the NavierStokes equations of motion for the air flowing over the particle,with relevant boundary conditions. As early as 1851, Stokes solved the equations of fluid motion for thevelocity and pressure distribution over the surface of the sphere of diameter d in a freestream where thevelocity is v. He calculated that the net fluid mechanical drag force is a combination of the integratedpressure forces (one-third) and the integrated shearing or friction forces (two thirds). This led to thenow-familiar expression of Stokes law:

FD = 3dv (2.20)for the conditions where the Reynolds number for the particle as given by

Rep = dv

(2.21)

is less than unity. This region (Rep < 1) is now widely known as the Stokes regime.Another quantity important for describing the airborne behavior of the particle, derived from Equation

(2.20), is its mechanical mobility () where:

= 13d

(2.22)

defines the ratio between the velocity of the particle and the external force associated with its motion.

2.2.2 Drag coefficient

The drag coefficient is given by

CD = FD/area12v2

24Rep

for Rep < 1 (2.23)



Stokes law

Rep

CD

102

10

1

101

101 10 102 103 104 1051

Figure 2.7 Drag coefficient (CD) for a spherical particle as a function of Reynolds number (ReP ) for the particle.Reproduced with permission from Vincent, Aerosol Sampling: Science and Practice. Copyright (1989) John Wiley& Sons, Ltd

where the denominator on the right-hand side normalises the force per unit area on the sphere withrespect to the velocity pressure in the fluid. For somewhat higher Rep just outside the Stokes regime,the problem becomes more complicated because the inertial terms in the equations of fluid motion canno longer be neglected. Oseen (1910) modified Stokes solution to take account of these conditions andobtained:

CD = 24Rep

(1 + 3

16Rep

)for 1 < Rep < 5 (2.24)

The problem becomes yet more complicated for still larger Rep > 5. The relationship between CD andRep for a sphere over the full range of conditions of interest to most aerodynamicists is shown inFigure 2.7, including the case for much higher Rep where the separated wake flow is turbulent and CDtends to level off. However, Rep values as large as this are largely irrelevant as far as the drag force onaerosol particles is concerned. Indeed, for airborne particles under many conditions of

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