Particle Deposition onto Enclosure Surfaces

Transcription

1 AEROSPACE REPORT NO. TR-2009(8550)-2 Partile Depsitin nt Enlsure Surfaes 20 August 2009 De-Ling Liu Spae Materials Labratry Physial Sienes Labratries Prepared fr: Spae and Missile Systems Center Air Fre Spae Cmmand 483 N. Aviatin Blvd. El Segund, CA Authrized by: Engineering and Tehnlgy Grup APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED Assuring Spae Missin Suess

2 This reprt was submitted by The Aerspae Crpratin, El Segund, CA , under Cntrat N. FA C-0001 with the Spae and Missile Systems Center, 483 N. Aviatin Blvd., El Segund, CA It was reviewed and apprved fr The Aerspae Crpratin by G. F. Hawkins, Prinipal Diretr, Spae Materials Labratry; and D. C. Marvin, Prinipal Diretr, Researh and Prgram Develpment Offie. Cl. David E. Swansn was the prjet ffier fr the Missin-Oriented Investigatin and Experimentatin (MOIE) prgram. This reprt has been reviewed by the Publi Affairs Offie (PAS) and is releasable t the Natinal Tehnial Infrmatin Servie (NTIS). At NTIS, it will be available t the general publi, inluding freign natinals. This tehnial reprt has been reviewed and is apprved fr publiatin. Publiatin f this reprt des nt nstitute Air Fre apprval f the reprt's findings r nlusins. It is published nly fr the exhange and stimulatin f ideas. Cl\David E>Swansn SMC/EA SC-1629(2, 5654, 58, JS)

3 REPORT DOCUMENTATION PAGE Frm Apprved OMB N Publi reprting burden fr this lletin f infrmatin is estimated t average 1 hur per respnse, inluding the time tr reviewing instrutins, searhing existing data sures, gathering and maintaining the data needed, and mpleting and reviewing this lletin f infrmatin Send mments regarding this burden estimate r any ther aspet f this lletin f infrmatin, inluding suggestins fr reduing this burden t Department f Defense, Washingtn Headquarters Servies, Diretrate fr Infrmatin Operatins and Reprts ( ), 1215 Jeffersn Davis Highway, Suite 1204, Arlingtn, VA Respndents shuld be aware that ntwithstanding any ther prvisin f law, n persn shall be subjet t any penalty fr failing t mply with a lletin f infrmatin if it des nt display a urrently valid OMB ntrl number PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES VERED (Frm - T) TITLE AND SUBTITLE Partile Depsitin nt Enlsure Surfaes 5a. NTRACT NUMBER FA C b. GRANT NUMBER 5. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER De-Ling Liu 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) The Aerspae Crpratin Physial Sienes Labratries El Segund, CA SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Spae and Missile Systems Center Air Fre Spae Cmmand 483 N. Aviatin Blvd. El Segund, CA PERFORMING ORGANIZATION REPORT NUMBER TR-2009(8550) SPONSOR/MONITOR'S ACRONYM(S) SMC 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Apprved fr publi release; distributin unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT In spae appliatins, the main nern f partile depsitin arises frm the undesirable effets f surfae bsuratin n ntaminatin-sensitive surfaes. The develpment f effetive mitigatin strategies t minimize paniulate ntaminatin requires the understanding f partile transprt and depsitin as well as the assiated physial fatrs affeting the presses. The knwledge gleaned frm the state-f-the-art literature review presented here an be applied t an enlsure sale as small as a spaeraft paylad avity, r as large as a lean rm in a manufaturing/pressing faility. The insights frm studying the physial presses that influene the rate f partile depsitin within an enlsure are expeted t prvide a strng sientifi fundatin t benefit varius aspets f aerspae ntaminatin ntrl needs. 15. SUBJECT TERMS Partile depsitin, Partile transprt. Paniulate ntaminatin 16. SECURITY CLASSIFICATION OF: a. REPORT b. ABSTRACT UNCLASSIFIED UNCLASSIFIED. THIS PAGE UNCLASSIFIED 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 58 19a. NAME OF RESPONSIBLE PERSON De-Ling Liu 19b. TELEPHONE NUMBER (inlude area de) (310) Standard Frm 298 (Rev. 8-98) Presribed by ANSI Std

4 Aknwledgments This wrk was supprted under The Aerspae Crpratin's Missin Oriented Investigatin and Experimentatin prgram, funded by the U.S. Air Fre Spae and Missile Systems Center. The authr thanks Prfessr William W Nazarff at UC Berkeley fr prviding valuable mments. 111

5 Cntents 1. Intrdutin I 2. Bakgrund Relevane t Cntaminatin Cntrl in Spae Appliatins Nature f Air Flw and its Near-Surfae Charateristis Evaluating Partile Depsitin: Depsitin Flux 5 3. Mehanisms f Partile Transprt Brwnian Diffusin Turbulent Diffusin Drag Fre Gravitatinal Settling Thermphresis Eletrstati Fre Turbphresis Parameters fr Partile Depsitin Charaterizatin Depsitin Velity, v d Partile Depsitin Rate, P Cmparisn f v d and fi Methds fr Measurement f Partile Depsitin Measuring Partile Depsitin Rate, p Measuring Partile Depsitin Velity, v d Review f Experimental Studies Partile Charateristis Affeting Partile Depsitin Airflw Charateristis Affeting Partile Depsitin Fred Cnvetin Natural Cnvetin 24

6 6.3 Surfae Charateristis Affeting Partile Depsitin Surfae Orientatin: Hrizntal vs. Vertial Surfae Texture: Smth vs. Rugh Surfae Temperature: Warm vs. Cld In the Presene f an Eletri Field Mdeling Partile Depsitin and Experimental Validatins Hmgeneus Turbulene Mdel Three-Layer Mdel Mass Transfer Mdel Summary Appendix 45 Referenes 51 Figures 1. Shemati f the re zne and the bundary layer in enlsures f different gemetrial shapes 5 2. An illustrative example f aersl nentratin deay measurements f varius partile diameters as a funtin f time in a 165-L ylindrial hamber Cmparisn f experimentally btained partile depsitin rates as a funtin f partile diameter Dependene f experimentally measured partile depsitin rates n the degree f airflw turbulene, as haraterized by the fan stirring rate (in rpm) and the air-exhange rate (inming airflw rate divided by the enlsure vlume, with the unit f h~') Cmparisn f experimentally measured partile depsitin rates as a funtin f partile size under natural nvetin nditins Cmparisn f experimentally measured depsitin velity fr surfaes f varius rientatins in a ubi hamber under natural nvetin The dependene f experimentally measured partile depsitin rates n the surfae rughness 27 VI

7 8. Experimentally measured depsitin velities t the vertial walls f a 1.2 x 1.2 x 1.2 m enlsure as funtins f partile diameter and surfae-t-air temperature differene Cmparisn f measured partile depsitin rates in a 60 m Tefln smg hamber with mdeling preditins by Crump and Seinfeld Experimentally determined partile depsitin rates as a funtin f partile diameter under varius influenes f eletrstati attratins Preditins f partile depsitin rate as a funtin f partile diameter in the three-layer mdel in Lai and Nazarff 25 mpared with experimental data Mass transfer rrelatin f partile diffusinal depsitin in smth walled stirred hamber, with Sherwd number (Sh) pltted as a funtin f Re^S" 3 42 Tables 1. Partile Reynlds Numbers (Re p ) Calulated fr Partiles f Different Diameters Falling at Their Terminal Settling Velities in Air at 20 C, Pressure = 1 atm, and Gravitatinal Aeleratin = 980 m s~ Distributin f Charge n Aersls at Bltzmann Equilibrium Relative Cntributins f Partile Depsitin Flux Experimentally Determined fr the Hrizntal and Vertial Surfaes as a Funtin f Partile Diameter in Byrne et al Summary f the Values f n and ke Determined frm Varius Partile Depsitin Experiments Summary f Equatins Used fr Partile Depsitin Analysis in the Three-Layer Mdel.. 39 vn

8 1. Intrdutin The study f partile depsitin frm aersl flw nt surfaes in enlsed spaes has attrated nsiderable attentin in the past few deades wing t its signifiane in a great variety f tehnlgial appliatins, suh as mirntaminatin ntrl in the semindutr industry, 1 ' 2 aersl prdutin in hemial reatrs, 3 indr air pllutin, 4-6 and siling f artwrks, 7 as well as nulear reatr safety analysis. 8,9 Bth desirable and undesirable utmes may result frm the presses f partile depsitin. Fr instane, the thin-film ating tehniques used t generate unique surfae prperties are an appliatin f the desirable utme. 10 ' 11 In ntrast, there are many examples f undesirable partile depsitin, whih auses surfae ntaminatin r even material damage. One f the wellknwn examples is the redued yield f integrated iruits in the wafer manufaturing press. Partiulate ntaminatin n ritial surfaes f a spae telespe leading t ptial bsuratin due t light sattering and hene degrading perfrmane is anther unwanted nsequene. 12 T develp effetive strategies t ntrl either desirable r undesirable depsitin f partiles, a sund understanding f the underlying partile transprt mehanisms and the assiated physial fatrs influening the presses is required t gain insights int partile depsitin behavirs. A signifiant bdy f sientifi researh has been devted t studying the dynami behavir f partiles under well-defined nfiguratins and air flw nditins examples inlude aersl-laden air flwing thrugh fibrus filters, 1314 partile depsitin frm turbulent hannel flw, 1516 and partile depsitin frm laminar, vertial flw nt a irular plate. 2 ' 1719 In ntrast, nt many published studies nsider partile depsitin nt surfaes in a three-dimensinal nfined spae, prbably due, in part, t the mplexity f airflw patterns assiated with enlsures f varius gemetrial shapes. The gal f this reprt is t prvide a state-f-the-art literature review nerning partile depsitin nt surfaes within an enlsed vlume. The knwledge gleaned frm the available sientifi publiatins presented here an be applied t an enlsure sale as small as a spaeraft paylad avity, r as large as a lean rm in a manufaturing/pressing faility. The surfaes f interest fr partiles t depsit n uld be walls, the flr, the eiling, r any ntaminatin-sensitive surfaes within an enlsed vlume relevant t varius engineering appliatins. The reprt begins with the haraterizatin f airflw adjaent t a surfae and hw it relates t the re regin f an enlsure. Partile depsitin flux, a parameter used t evaluate the rate f depsitin nt surfaes, is briefly intrdued as the nept will be mentined thrughut the hapter. Next, the fundamental physial presses gverning the transprt f partiles are disussed, and the definitin f the parameters mmnly reprted in the literature fr haraterizing depsitin are intrdued, alng with the available experimental tehniques fr their measurement. The dependene f partile depsitin rate n partile size, airflw, and surfae harateristis are examined frm the existing published experimental investigatins relevant t enlsures. Lastly, mdeling develpments fr prediting the rate f partile depsitin and assiated experimental validatins are presented.

9 2. Bakgrund Knwledge f partile transprt and depsitin within an enlsed vlume has been applied in numerus pratial senaris. In the beginning f this setin, speial attentin is given t the relevane f partile depsitin t ntaminatin ntrl in the ntext f spae appliatins. Sine aersl partiles are transprted t the viinity f surfaes by air urrents, understanding the nature f air flw and its near-surfae harateristis is the first step t gain insights int the presses f partile depsitin nt surfaes. In additin, a quantitative apprah using the nept f flux and the underlying physial mehanisms that gvern partile depsitin are briefly desribed. 2.1 Relevane t Cntaminatin Cntrl in Spae Appliatins In spae appliatins, the nern f partile depsitin n ntaminatin-sensitive surfaes arises frm the undesirable effets f surfae bsuratin. Fr ne thing, the presene f partiles n ptial refletive surfaes, e.g., mirrrs and fal planes, interferes with the prper transmissin f light t the next ptial mpnents, hene reduing the signal strength. Partiles residing n an absrptive surfae, suh as baffles inside a telespe assembly, auses light sattering.whih, in turn, verwhelms the signal and ultimately may even damage ther ptial mpnents. The presene partiles n thermal ntrl surfaes auses alteratins f slar absrbane and/r emissivity, whih leads t an altered equilibrium temperature, and may further deterirate the thermal ntrl funtin. In light f the adverse effets due t paniulate ntaminatin, the aim f ntaminatin ntrl is t prevent perfrmane degradatin by minimizing the depsitin f partiles n ritial and sensitive surfaes f spaeraft mpnents. Meeting this bjetive is partiularly imprtant fr high-prfile remte sensing spaeraft, suh as the Hubble Spae Telespe. As a nsequene, tremendus effrts and resures are dediated t ntaminatin ntrl during varius phases f spaeraft pressing: design, manufaturing, assembly, testing, integratin, strage, shipping, launh site grund ativities, and in-flight peratins. The develpment f effetive mitigatin strategies t minimize partile ntaminatin requires knwledge f partile transprt and depsitin as well as the assiated physial fatrs affeting the presses. Spaeraft surfae ntaminatin as a result f partile fallut may take plae at any level f engineering pratie, fr instane, mpnent fabriatin in a leanrm, system assembly and testing within a paylad avity, and spaeraft integratin inside payladfairing. Nte that the terms in italis refer t the rrespnding enlsed vlumes under the example senari nsidered; thus, ne an see that the study f partile depsitin nt surfaes in enlsures is f strng relevane t a variety f irumstanes in spae appliatins. The insights frm studying the physial presses that influene the rate f partile depsitin within an enlsure are expeted t prvide a strng sientifi fundatin t benefit varius aspets f aerspae ntaminatin ntrl needs.

10 2.2 Nature f Air Flw and its Near-Surfae Charateristis Inside an enlsed vlume, air is mixed thrugh tw mehanisms: natural nvetin and turbulent mixing (fred nvetin). Natural nvetin is driven by temperature gradients, i.e., temperature differene (AT) arss the spae inside the enlsure, indued by heat transfer at surfaes. Turbulent mixing r fred nvetin, n the ther hand, is assiated with external energy input int a system, suh as fan mixing r fluid flushing. In an enlsure withut the mehanism f fred nvetin, natural nvetin bemes the nly ause fr fluid mixing. Small temperature variatins within the enlsure may indue nvetive urrents, whih, in turn, ause aersl nentratin t beme mixed thrughut the vlume. It is estimated that the nvetive flw velity an reah apprximately 1 m/s in a 1-m-high hamber when the flr r wall surfaes are warmer than the air by 0.01 C. 20 Study als has shwn that a AT f 0.1 C an indue hmgeneus mixing fr partiles up t 15 (im in diameter. 21 On the ther hand, buyany an als impede mixing. Fr instane, a warm eiling and l flr will prmte stratifiatin f air masses within an enlsure. Sme empirial evidene abut near-surfae airflws in rms an be fund in referene [22] One widely aepted apprah t mdel air flw in enlsures is t assume that the air in the re regin is hmgeneusly and istrpially turbulent, behaving like an ideal nnvisus fluid. Adjaent t the interir surfae, the air is assumed t behave as a visus fluid within a thin layer, whih is als knwn as the bundary layer. Inside the mmentum bundary layer, the fluid velity drps sharply t zer at the surfae frm its mainstream peak value. The thikness f the mmentum bundary layer depends n the mmentum diffusivity f the fluid. Fr instane, the typial thikness is abut 1 t 2 m fr rm air mtin, 6 given air kinemati vissity f 0.15 m 2 s~ at 293K and 1 atm. The bundary layer nept an als be used t apture the near-surfae harateristis in terms f thermal and ntaminant nentratin prfiles. Fr air, the thikness f the thermal bundary layer is mparable t that f the mmentum bundary layer beause the thermal diffusivity (~0.2 m 2 s~" fr air) is f the same rder f magnitude as the mmentum diffusivity. Fr gaseus ntaminants with mleular weights lse t thse f N 2 and 0 2, the thikness f the nentratin bundary layer wuld be similar t that f the mmentum and thermal bundary layer beause the mleular diffusivities are mparable t mmentum and thermal diffusivities. Airbrne partiles, hwever, have small diffusivities (r diffusin effiients) mpared t mleular ntaminants, whih leads t muh thinner* partile nentratin bundary layers than the mmentum and thermal bundary layers. Okuyama et al. 23 estimated, frm their experiments in a 2.6-L nn-stirred ylindrial tank, the partile nentratin bundary layer thikness t be apprximately 0.3 m when the partile diffusivity is 10-3 m 2 s~. Cnsiderable infrmatin abut partile nentratin bundary layer thikness an be fund in referenes [24] and [25]. In additin t aersl diffusivities, the nature and the intensity f the near-surfae air flw als play a rle in determining the thikness f the nentratin bundary layer. Sale analysis 26 that is used t apprximate partile bundary layer thikness adjaent t surfaes indiates that, given the same diffusivity, the bundary layers are thinner when the fluid utside them is fast mving, and thiker when the fluid mves slwly. As will be shwn later in Subsetin 6.3.2, the impliatin f a thinner nentratin bundary layer is that small-sale surfae rughness an play a signifiant rle in affeting partile transprt arss the bundary layer, but have negligible effets n mmentum and heat transfer.

11 In general, the air within an enlsure f arbitrary shape an be visualized t nsist f tw parts: a re zne where the air is well mixed, and a thin quiesent bundary layer adjaent t the inside surfae f the enlsure where little air mtin exists in the diretin perpendiular t the surfae (see Figure 1). In the re zne the partile nentratin is ften assumed t be spatially unifrm due t well-mixed air flws, and large-sale turbulent (r eddy) diffusin is respnsible fr bringing aersls t the viinity f the surfae fr subsequent depsitin.* Upn arrival at the bundary layer, aersls may migrate thrugh the thin layer t the surfae by mehanisms suh as Brwnian/turbulent diffusin, gravitatinal settling, thermphresis, inertial drift, and eletrstati attratin. These transprt presses, as will be disussed in Setin 3, mmnly ntrl the rate f partile depsitin nt surfaes in enlsures. In summary, the bundary layer nept used t haraterize aersl transprt presses frm mainstream fluid nt surfaes has been applied with great suess in a large variety f air flw senaris, suh as external flws arund ylinders r spheres, laminar and turbulent pipe flws, and enlsures with quiesent r turbulent flws. Theretial develpments based n this bundary layer nept t evaluate the extent f partile depsitin within an enlsed vlume alng with the assiated experimental validatins will be disussed in mre details in Subsetin Evaluating Partile Depsitin: Depsitin Flux The rate f partile transprt nt a surfae is mmnly quantified in terms f a depsitin flux, with the dimensins f mass (r number) per unit time per unit area. In the event that transprt thrugh the bundary layer is dminated by the mbined effets f turbulent and Brwnian diffusin, the flux f partiles nt a smth, isthermal, and eletrially neutral vertial surfae an be haraterized by the fllwing ne-dimensinal steady-state ntinuity equatin. Flux = -(e D +D), v dy (1) well-mixed re zne r quiesent bundary layer quiesent bundary layer Figure 1. Shemati f the re zne and the bundary layer in enlsures f different gemetrial shapes. Als knwn as "hmgeneus turbulene mdel," and its theretial representatins will be addressed in Subsetin 7.1.

12 where Ep and D are the turbulent (r eddy) and Brwnian diffusivities fr aersls, respetively; C is the aersl nentratin in air; and y is the distane frm the surfae. Equatin (1) an be viewed as a mdified frm f Fik's first law f diffusin, whih desribes the linear relatinship between the flux f aersls and the nentratin gradient dc/dy, with the term ( p+ D) being the prprtinality nstant. Physially, this suggests that the net transprt f partiles, due t diffusin nly, always takes plae frm regins f high t lw partile nentratin. Equatin (1) has lng been used t evaluate partile depsitin flux. Sine the air flw utside the bundary layer is assumed t be hmgeneusly mixed, a partile nentratin gradient nly exists within the bundary layer. Other assumptins fr this theretial representatin inlude: (1) partiles are mpletely retained ne they llide nt the surfae, i.e., the surfae ats as a perfet sink fr partile depsitin; and (2) n mehanisms f agulatin, ndensatin, and evapratin are invlved during the transprt press (i.e., there are n sures r sinks fr partiles within the bundary layer); thus, the partile flux is nstant thrughut the partile nentratin bundary layer. In the presene f partile transprt mehanisms ther than diffusin, the partile flux an be evaluated by adding terms t aunt fr external fre fields ating n the partiles, and that gives Flux = -(e + D) v e C, (2) dy where v e is the partile steady-state drift velity under the atin f external bdy fres unterated by fluid drag. The external fre fields f mst interest in partile depsitin presses inlude gravitatinal, eletrial, and thermal (generated by a temperature gradient in the fluid), as will be presented in the next setin.

13 3. Mehanisms f Partile Transprt Airbrne partiles are transprted nt surfaes thrugh a variety f physial presses, s-alled depsitin mehanisms. The fundamental physis behind partile transprt r mvement frm ne pint t anther is universal, regardless the nfiguratins f the system, fr instane, dust aumulatin in ventilatin duts, gas leaning by partile lletin n fibrus filters, and savenging f partiulate matter frm the atmsphere. Belw, the underlying physial presses gverning partile mtin in air are addressed. 3.1 Brwnian Diffusin Brwnian diffusin is the harateristi randm wiggling mtin f small airbrne partiles in still air, resulting frm nstant bmbardment by surrunding gas mleules. Suh irregular mtins f pllen grains in water were first bserved by the btanist Rbert Brwn in 1827, and later similar phenmena were fund fr small smke partiles in air. In the early twentieth entury, the relatinships haraterizing Brwnian diffusin based n kineti thery f gases were first derived by Einstein in the early 1900s, and later verified thrugh experiments. 20 The Brwnian diffusivity, D (r diffusin effiient), whih relates the gas prperties and the partiles thrugh fluid drag, an be evaluated by the Stkes-Einstein expressin. 27 ' 28 D, %-. (3, 3*pd p where k is Bltzmann's nstant (1.38 x 10~ 23 J K 1 ), T is the abslute temperature in K, p, is dynami vissity f air, d p is partile diameter, and C is a slip rretin fatr fr small partiles (see Subsetin 3.3 fr details). The value f D depends n the partile size and fluid prperties. Fr instane, the diffusivity f a 0.01-pm aersl partile is 20,000 times higher than that f a 10 pm aersl partile. The larger the value f D, the mre rapid the mass transfer press t drive partiles mving frm regins f high t lw nentratin. Brwnian diffusin is the dminant partile depsitin mehanism fr small partiles (<0.1 urn) ver shrt distanes. 3.2 Turbulent Diffusin Fr partile transprt n greater physial sales (i.e., larger distane), turbulent diffusin is far mre effetive than the thermal-based Brwnian diffusin. Mass transfer f partiles frm ne pint t anther by turbulent (r eddy/nvetive) diffusin is analgus t mmentum transfer by flutuating velity mpnents in turbulent flws. Unlike mmentum transfer inside the thin stagnant layer f air adjaent t a surfae where visus fres are dminant and turbulene flutuatins are negligible, mass transfer f partiles is attributed t the mbinatin f turbulent and Brwnian diffusin. A

14 general expressin fr the partile flux t the surfae due t bth turbulent and Brwnian diffusin was desribed in Eq. (1), with the derivatins shwn in referene [27]. ( Intuitively, the partile turbulent diffusivity, e p, inside the bundary layer is expeted t vary with distane frm the surfae, y, wing t the physial nstraints impsed by the surfae. In fat, it is extremely diffiult t determine the value f Ep expliitly beause it is strngly assiated with the degree f turbulene with respet t the air flw struture in the system, as well as with the size f partiles (e.g., heavy partiles annt faithfully fllw the fluid eddies). Hinze 29 has shwn that ver a suffiiently lng time sale, the partile turbulent diffusivity equals the fluid turbulent vissity by slving the equatin f mtin fr a partile in a hmgeneus turbulent flw field. A similar argument made by Fuhs 20 is that the mtin f larger partiles is mre persistent due t their larger mass, whih, in turn, ntributes t the nearly idential average distane traveled by large and small partiles ver a lng time limit. Additinally, numerial simulatin f turbulent diffusin f partiles als indiated that partile and fluid turbulent diffusin are mparable fr partiles smaller than apprximately 170 urn. 30 Therefre, it is a fair statement that the turbulent diffusivity fr partiles an be reasnably apprximated as the same rder f magnitude as that f gas fluid (~ 1 (T 1 m 2 s~), whih is far greater than the partile Brwnian diffusivities. In ther wrds, partiles tend t migrate lser t the surfae by turbulent diffusin befre Brwnian diffusin bemes imprtant. In essene, partile turbulent diffusivity gradually diminishes in the partile nentratin bundary layer t zer at the surfae. Thrughut the re f an enlsure, turbulent diffusivities an vary ver large ranges in ardane with the intensity f air mtin. 3.3 Drag Fre Fluid drag n a partile is the resistane fre exerted by the surrunding fluid when there is relative mtin between the partile and the fluid. In ther wrds, the drag fre is always present as lng as the partile is nt travelling in a vauum. The net effet f the drag fre is t redue the aeleratin f partiles. The drag fre, F D, n a spherial partile an be haraterized by Stkes's law: Fr^TIilVdp, (4) where V is the partile speed relative t the lal fluid speed. Stkes's law is derived frm the slutin f the Navier-Stkes equatins, assuming* that inertial fres are negligible mpared t visus fres and that the fluid speed at the partile's surfae is the same as the partile's. Owing t the lw velities and small partile sizes invlved, mst aersl mtins ur at lw partile Reynlds numbers (Re p «1), where Re p = d p V/v, expressing the rati f inertial t visus fres n partiles. Other assumptins inlude: inmpressible fluid, n walls r ther partiles nearby, nstant mtin, zer fluid velity at the partile's surfae, and rigid spherial partiles. These assumptins wrk well in mst ases fr aersls. See Hinds fr mre detailed disussins.

15 Table 1 shws the alulated Re p fr spherial partiles f different sizes falling at their steady-state settling velity in air due t gravity. By lking at Re p, Stkes's law learly hlds true fr partiles smaller than 20 u.m. Fr aersls that are relatively large and mve thrugh a fluid rapidly, the inertial fres beme dminant mpared t visus fres; thus, the drag fre exerted t the partile is alulated as F D-4 d P ^ (5) where C d is the drag effiient, given by referene [31] 24 Re Re«1 (Stkes's law) C = < 24 Re 1+ Re+ Re2 ln(2re) <Re<2 (6) (l+0.15f Re v 2 < Re < <Re<2xl0 5 When the size f an aersl partile apprahes the mean free path f gas mleules (0.066 am fr air at 1 atm and 20 C), the assumptin f zer relative fluid velity right at the partile surfae fails, whih uld lead t signifiant errrs. In this ase, the atual drag fre is smaller than predited by Stkes's law. A rretin parameter, the Cunningham rretin fatr, C, is intrdued t rret fr this "slip" phenmenn fr small partiles, and the rreted Stkes's law bemes F D = 37iixVd p (7) Table 1. Partile Reynlds Numbers (Re p ) Calulated fr Partiles f Different Diameters Falling at Their Terminal Settling Velities in Air at 20 C, Pressure = 1 atm, and Gravitatinal Aeleratin = 980 m s~ Partile diameter, im Re p x x10^ x x

16 =i+ d p exp (8) where X is the mean free path f gas mleules. The empirial frmula f Eq. (8) allws the extensin f Stkes's law t aersl size belw 0.01 urn. It is imprtant t inlude the slip rretin fatr fr partiles whse diameter is smaller than abut 10 times the mean free path f gas mleules. 3.4 Gravitatinal Settling Gravity impses an verall dwnward drift n partiles, whih ntributes an enhaned depsitin flux n surfaes with an upward mpnent t their rientatin. The gravity fre exerted n a partile is F g=f d p 3 (Pp-Pa)g, (9) where g is the aeleratin due t gravity (9.81 m s~ 2 at the Earth's surfae), and p p and p a are partile and air densities, respetively. The buyany effet usually an be negleted beause p a is mmnly muh smaller than p p. The terminal settling velity f a partile, v, is established when the gravity fre is balaned by the fluid drag fre, and it is expressed as 27 ' 28 C Ppd p 2 g v^^ (10) As suggested in Eq. (10), the partile terminal settling velity inreases rapidly with partile size sine it is prprtinal t the square f partile diameter fr supermirn partiles (where C = 1). Assuming unit partile density, fr instane, the settling velities fr 1 u.m and 10 p.m partiles are 3.50 x 10~ 3 m/s and 3.05 x 10 _1 m/s, respetively. 3.5 Thermphresis In the presene f a temperature gradient, aersl partiles are driven frm the high t lw temperature regins; this transprt press is knwn as thermphresis. The phenmenn was first reprted in the 19 th entury, 32 and its quantitative desriptins were published by Watsn in and Zernik in Thermphreti fre arises frm asymmetrial interatins f an aersl with the surrunding gas mleules in a temperature gradient, where gas mleules n the warm side bmbard the partile with 10

17 higher average mmentum than thse n the ler side. Ating in the diretin f dereasing temperature, thermphreti fre an be expressed as 35 37qi 2 d p H d T Fth= TT^^-- (H) Pa T dy where dt/dy is the temperature gradient, and H is the thermphreti fre effiient, given by H = 2.34 k a /k p A/dp (12) l X/d p JI l + 2k a /k p +8.72X/d p where k a and k p are the thermal ndutivities f air and the partile material, respetively. When the thermphreti fre n a partile is balaned with fluid drag, the thermphreti velity is btained as C vhdt... v t n= ^r~t- T dy (13) Cntrary t gravitatinal settling and Brwnian diffusin, whih are strng funtins f partile size, the thermphreti velity is nearly independent f partile size fr partiles smaller than 1 lm. This urs beause bth the thermphreti fre and fluid visus drag have apprximately the same dependene n partile diameter. Fr larger partiles, the thermphreti velity dereases with inreasing partile size in a manner that depends n the relative thermal ndutivities f the partile and f air. 3.6 Eletrstati Fre A harged partile migrates in an eletrial field due t the Culmb fre F, whih is given by F =qe = n e ee, (14) -* where q is the harge n the partile, E is the eletri field strength, n e is the number f eletrns f deviatin frm the eletrially neutral state (inluding sign), and e is the harge f a single eletrn (- 1.6xl(T 19 C). In the absene f an eletrial field, harged aersls will migrate twards r away frm a nduting surfae, wing t the image fre, dieletri fre, and diple-diple fre, althugh these fres are muh weaker than the Culmb fre. The verall eletrstati fre n a harged partile an be predited by 36 11

18 qed. 3Te 0 d 6 p E 2 F E =qe- 167i 0 y 16y 128/ (15) where e 0 is the permittivity f air (8.86 x KT 12 C 2 N _l m~ 2 ), and y is the nrmal distane frm a surfae. The terms n the right-hand side f Eq. (15) aunt fr the Culmb fre, image fre, dieletri fre, and diple-diple fre, respetively. When an eletrial field is present, the Culmb fre dminates, and bth the dieletri and diple-diple fres are negligible. In the absene f an eletri field, hwever, the nly eletrstati fre respnsible fr partile mtin is the image fre, as suggested in Eq. (15). The image fre, whih nly urs near a nduting surfae, is always direted tward a surfae and may dminate ver Brwnian diffusin and turbulent dispersin when extremely lse t a surfae. On eletrially insulating materials, harges may aumulate n the surfaes, giving rise t eletri fields, whih, in turn, affet depsitin f harged partiles. It shuld be nted that aersl partiles aquire r lse their harges thrugh randm llisins with airbrne ins, whih are frmed by ubiquitus inizing radiatin. In the absene f an eletrial field, the presses f aersl aquiring and lsing harges will eventually lead t an equilibrium harge state alled Bltzmann equilibrium. The maximum number f harges arried by a partile depends n the size f the partiles. Table 2 shws the distributin f harges arried by aersls at Bltzmann equilibrium. Take 10-u.m partiles, fr example. At equilibrium, nly 4.3% f the partiles are eletrially neutral, and nearly 70% f the aersl partiles arry mre than 3 harges n a single partile (either psitive r negative). Fr highly harged aersls in an eletrial field, the drift velity resulting frm eletrstati fres n partiles an be thusands f times greater than that frm the gravitatinal fre. Table 2. Distributin f Charge n Aersls at Bltzmann Equilibrium (Reprdued with permissin frm Hinds, 1999, Jhn Wiley & Sns, In. 28 ) Partile Diameter Perentage f Partiles Carrying the Indiated Number f Charges (urn) < >

19 3.7 Turbphresis Turbphresis is a phenmenn in whih the net migratin f partiles urs frm regins f high t lw turbulene intensity, i.e., tward surfaes where the turbulent velity flutuatins derease t zer. Physially, partiles in regins f high turbulene intensity aquire suffiient flutuating velity mpnents, whih enable them t drift t regins where the turbulene intensity is t lw t send them bak with suffiient mmentum fr the return jurney. Based n the analgy between Brwnian mtin and turbulent diffusin, as well as energy transfer frm the fluid t the partile, the mathematial expressin fr turbphreti velity V, was first prpsed by Capralni et al. 31 as C Pp d p 2 d(^f Vt= iir A (,6 > 18(i dy where v' y is the flutuating partile velity nrmal t the surfae. Reeks 38 dedued the term fr the turbphreti effet and arrived at the same expressin in a muh mre rigrus apprah (a speial lsure f Liuville partile equatin f mtin). Distintly different frm turbulent diffusin, turbphresis is attributed t the interatin between partile inertia and the inhmgeneus turbulent flw field, and the mass transfer takes plae against the gradient in turbulene intensity, even in the absene f a nentratin gradient. The effet f turbphresis is nly signifiant fr partiles with suffiiently high inertia, and is typially nly relevant in the viinity f a surfae where the gradient in turbulene intensity is high. Fr near-surfae inertial partiles under highly turbulent flw senaris, partile transprt mdels aunting fr turbphresis have shwn gd agreements with experimental measurements. 39 "^1 13

20 4. Parameters fr Partile Depsitin Charaterizatin T haraterize the rate f partile depsitin in an enlsure, depsitin velity (v d ) and partile depsitin rate (P) are the tw parameters mmnly reprted in the literature. Here, their definitins, derivatins, and physial impliatins, as well as the distintins between P and v d are disussed. 4.1 Depsitin Velity, v d Partile depsitin, a mass transfer press f airbrne partiles nt surfaes, urs by a first-rder, irreversible mehanism. Being "first-rder" suggests that partile depsitin flux is linearly prprtinal t the airbrne nentratin, and being "irreversible" means that partiles simply adhere ne they llide with surfaes. The aersl depsitin rate an be parameterized in terms f a mass transfer effiient, knwn as the depsitin velity, v d. It is nsidered as the prprtinality nstant between the net aersl flux J and the free-stream airbrne nentratin, C,. J r l mass / area time r i length v d = W : [=J (17) C mass/vlume time The aersl nentratin, C, is determined at a psitin suffiiently far away frm the surfae, i.e., re zne in an enlsure, s that the nentratin shuld nt vary greatly with psitins. With dimensins f length per time, depsitin velity appears t represent an effetive velity, whih inrprates all f the mplexities f the partile depsitin press. In ther wrds, depsitin velity, as an aggregated term, mprises every aspet f partile depsitin presses, inluding (1) aerdynami transprt f partiles by turbulent diffusin frm the well-mixed re regin t the thin bundary layer f air adjaent t the surfae; and (2) mass transfer f partiles arss the bundary layer, and subsequent uptake by the surfae thrugh a variety f partile depsitin mehanisms. The magnitude f the depsitin velity depends n fatrs that gvern partile transprt: partile size, the near-surfae air turbulene, surfae harateristis inluding rientatin and texture (smth vs. rugh), air-surfae temperature differene, and the presene f an eletrial field near the surfae. A literature review f the existing experimental findings nerning the influene f these fatrs n partile depsitin is presented in Setin 6. 15

21 4.2 Partile Depsitin Rate, 0 Anther mmn parameter used t quantitatively haraterize the partile depsitin rate (3 in an enlsure is defined as: 20 dc(d p,t) = -PC, (18) dt where C(d p,t) is the aersl number r mass nentratin as a funtin f time, t, in the re regin f the enlsure, and P is the partile depsitin rate with the unit f time -1 (e.g., s _1 ). Partile depsitin rate is als mmnly referred t as the aersl remval rate r wall lss rate beause the depsitin press remves partiles frm the gas phase nt the available wall surfaes. Equatin (18) is written in the frm f mass balane f partiles suspended in air within an enlsure, with the fllwing nditins: (1) n r negligible sures fr partile generatin (suh as partile influx in the inming air flw and nuleatin); (2) n partile size hange due t agulatin,* ndensatin, and evapratin; and (3) depsitin nt surfaes is the nly partile lss mehanism. Nte that the partile depsitin rate is expeted t be a funtin f partile size, as is the ase fr partile depsitin velity. Als nte that Eq. (18) nly aunts fr partile lss attributable t depsitin. In an enlsure, there are typially ther presses urring in parallel, suh as air exhange, that influene the partile nentratin and shuld be taken int aunt. 6 Experimentally, the aersl nentratin deays with time as expressed by Eq. (18) after initial mixing f aersls in an air-tight enlsure. Mathematially, the rearrangement f Eq. (18) gives C t =C 0 e-p\ (19) where C 0 is the initial aersl nentratin in the enlsure, C, is the aersl nentratin at time t. When the air is well-mixed, pltting InC as a funtin f time gives rise t a linear plt, with the negative f the slpe yielding the partile depsitin rate, p. Figure 2 represents an example f partile nentratin deay as a funtin f time and the assiated depsitin rate. Similar t partile depsitin velity v d, P inrprates all the depsitin presses that remve aersls frm being suspended in the enlsure. 4.3 Cmparisn f v d and p The majr distintin between v d and p is that v d depends n surfae rientatins with respet t gravity (a "lal" parameter), while P represents an average term ver all available surfaes fr depsitin within an entire enlsure (a "glbal" parameter). Fr instane, in the ntext f a Partile agulatin, whih ntributes t aersl size distributin hange, urs when the aersl nentratin is suffiiently high. When that urs, agulatin may be an imprtant mehanism t inrprate in Eq. (18), as seen in Okuyama et alp 16

22 0.305 urn urn Time, hr Figure 2. An illustrative example f aersl nentratin deay measurements f varius partile diameters as a funtin f time in a 165-L ylindrial hamber (reprinted with permissin frm Chen et al. A2 ). The partile depsitin rates, btained frm the values f the slpe, were 0.058, 0.14, 0.088,0.28, 0.44,0.71 h~' fr partile diameters f 0.305, 0.073, 0.91, 1.74, 2.02, and 2.99 um, respetively. retangular enlsure, the magnitude f v d fr supermirn partiles varies strngly with surfae rientatin, i.e., v d,nr > v d,waii > v d.eiiing> wing t the dminant ntributin f gravitatinal settling ver diffusin and ther mehanisms. The value f P an be related t the values f v d fr all enlsure surfaes. By material balane, the depsitin rate, p, is the surfae-area-averaged v d multiplied by the surfae-t-vlume rati (S/V) f the enlsure: dc?± = -± fv d (s)ds = -C-v d =-0C, dt V J V (20) where v d (s) is the partile depsitin velity nt the surfae s. The integratin is t be arried ut ver all the enlsure interir surfaes with the ttal surfae area S, and v d is the area-weighted mean 17

23 depsitin velity. It an be learly seen that p\ unlike v d, eliminates the expliit spatial dependene f partile depsitin. 18

24 5. Methds fr Measurement f Partile Depsitin Owing t its imprtane fr numerus engineering systems, the presses f partile depsitin n surfaes have been widely studied experimentally. Here, the general apprah fr measuring P and v d with respet t an enlsed system is presented with the aim f helping t gain insights int the experimental findings that will be presented in Setins 6 and 7, respetively. 5.1 Measuring Partile Depsitin Rate, p Experimentally, the partile depsitin rate P as a funtin f partile diameter is inferred frm aersl nentratin deay ver time, fllwing Eq. (18) and as shwn in Figure 2. T d s, mndisperse aersls are usually generated in elevated nentratins s that suffiient time is available t take multiple data pints n aersl nentratins during the urse f depsitin experiments. When the test aersls are plydisperse, the aersl measuring instruments will need t have the partile size-reslved apability in rder t determine the nentratin deay rate as a funtin f partile diameter. The peratin priniples fr sme mmn partile sizing instruments, e.g., ptial partile unter, time-f-flight aersl spetrmeter, eletrial aersl mbility analyzer, as well as aersl generatin methds, an be fund in referenes [28,43,44]. Nte that the degree f air turbulene plays an imprtant rle in influening the rate f partile depsitin. Therefre, the stirring f air within the experimental hamber, by either impeller mixing r flushing, shuld be ntrlled nsistently thrughut the experiment. The sheme f determining partile depsitin rate by mnitring airbrne partile nentratin deay ver time des nt invlve diret measurements f depsited partiles n surfaes, thus the measured depsitin rate is "inferred." This type f experiment is relatively simple t arry ut, and data analysis is straightfrward. Hwever, the drawbak f this indiret apprah is the inability t differentiate the ntributin f partile depsitin n surfaes with respet t rientatins and latins. 5.2 Measuring Partile Depsitin Velity, v d As suggested in Eq. (17), partile depsitin velity is determined by nrmalizing the depsitin flux with the average aersl nentratin ver the duratin f partile depsitin. Distint frm measuring the depsitin rate nstant, p, evaluating v d requires a diret measurement f partile depsitin, whih invlves the simultaneus determinatin f partile depsitin flux and airbrne partile nentratin. In ther wrds, the depsited partile mass will need t be revered frm the surfae (r therwise deteted and quantified), and the aersl nentratin utside the bundary layer during the urse f depsitin will als need t be determined. Fr the typial experiment f this type, mndisperse aersls need t be generated and injeted int the experimental hamber t prvide the size-speifi depsitin flux. T btain the depsitin velity as a funtin f partile diameter, the same experimental predures are repeated fr ther partile sizes f interest. The 19

25 advantage f this diret measurement, albeit time-nsuming and labr-intensive, is that spatially reslved partile depsitin an be determined. A key hallenge f this apprah, hwever, is the need t aurately determine trae amunts f partiles depsited n surfaes. The earliest methd was perfrmed by mirspially unting the partiles n a small area f a test surfae. 45 Despite the reent rapid advanement f ptial and digital imaging tehniques, it remains a tedius task t perfrm the unting, nsidering that nly a very small surfae area is available per mirspi frame, whih, in turn, limits the pssibility f sampling larger surfae areas. T quantitatively determine depsited partile mass n surfaes, aersls an be labeled t failitate subsequent surfae analysis. Tw types f traer aersl detetin tehniques have been emplyed fr suh purpses: (1) fluresene spetrspy, and (2) neutrn ativatin analysis (NAA) r prtn-indued X-ray emissin (PIXE). With respet t the frmer methd, mndisperse aersls are generated with fluresent materials. After depsitin, the fluresent partiles n the test surfae are extrated with a slutin f knwn vlume. The resulting fluresene intensity f the slutin is prprtinal t the lleted partile mass frm the surfae. 46^8 In rder t aumulate suffiient fluresent partile mass fr analysis, the experimental depsitin time, partiularly fr submirn partiles, uld easily exeed 100 h. 46 Cntrary t the hemistry-based fluresene tehnique, NAA r PIXE relies n the physis f atms in the aersl materials. In NAA, the energy f the indued radiativity thrugh neutrn bmbardment is harateristi f a partiular element, while PEXE invlves the measurement f the harateristi X-ray emissin via high-energy prtn exitatins f the elements in the sample. Methds using NAA and PIXE are semi-invasive; i.e., nly the partile-bearing surfae needs t be remved fr the analysis frm the test hamber, and remval f depsited partiles frm the partile-bearing surfae is nt required. T minimize interfering effets frm varius elements, rare earth elements suh as dysprsium ( l64 Dy) and indium ( II5 In) an be inrprated int the aersls fr the purpse f subsequent NAA analysis. 49 " 51 Owing t the extremely high sensitivity, fr instane, a 164 Dy mass f the rder f 10"' g an be easily deteted; hene, the experimental depsitin time an be signifiantly redued (e.g., min). 50 The drawbak f this tehnique, hwever, is that speialized failities, suh as a nulear reatr fr neutrn ativatin, is required. 20

26 6. Review f Experimental Studies A signifiant bdy f experiments has been devted t explring partile depsitin in enlsures sine the late 1940s due t the relevane t material deteriratin and the impliatins t human health risk, et. Table Al in the Appendix highlights a hrnlgial summary f the labratry investigatins pertaining t partile depsitin in an enlsed envirnment. The presses f partile depsitin nt surfaes are mplex, multifaeted phenmena sine they vary strngly depending n the harateristis f partiles and airflw patterns, as well as surfae prperties. In brief, the presses f partile depsitin nsist f tw mehanisms in series: (1) partile transprt frm the re regin in the enlsure t the bundary layer adjaent t the surfae, and (2) subsequent depsitin nt the surfae. Cnsequently, bth prperties f airflw and the surfae play a ruial rle in gverning the rate f partile depsitin in steps (1) and (2), respetively. The degree f airflw turbulene ntrls hw rapidly partiles migrate t the prximity f a surfae, while the surfae harateristis, suh as rientatins and rughness, determine hw readily partiles interat with the surfae. As will be seen sn, partile size is the mst imprtant parameter gverning the mtins f partiles in a gas phase assiated with the transprt prperties. Here, the imprtant physial fatrs that influene partile depsitin nt enlsure surfaes are summarized frm the existing literature. 6.1 Partile Charateristis Affeting Partile Depsitin Partile size is key in the determinatin f partile depsitin. The dimensin f partiles in the gas phase is mmnly haraterized in terms f aerdynami diameter, whih refers t an equivalent diameter f a unit density spherial partile with the same terminal settling velity as the partile being measured. 27 Therefre, the nept f aerdynami diameter has taken partile shape and density int aunt, and it has suessfully aptured the aerdynami behavir f airbrne partiles in many systems f interest.* The ntin f aerdynami diameter has been mmnly used in the aersl literature, inluding this review. Figure 3 illustrates the harateristi V-shaped urves f experimentally determined partile depsitin rates as a funtin f partile diameter. The large variability f the data, whih an be up t 2 rders f magnitude, reflets the fat that ther fatrs, suh as airflw turbulene and surfae harateristis, als play a signifiant rle in influening the extent f partile depsitin in enlsures. As mentined earlier, when partiles are nt eletrially harged, the rate f partile depsitin is gverned by gravitatinal settling and Brwnian mtin f partiles, as well as the turbulent mtin f the fluid in whih partiles are entrained. Fr partiles smaller than 0.1 im, Brwnian and turbu- The behavir f nnspherial partiles in shear flws might nt be prperly haraterized using the nept f aerdynami diameler wing t their mplex rtatinal and translatinal mtins nt aunted fr in spherial partiles. Thus, the preditin and measurement f depsitin using aerdynami diameters fr nnspherial partiles under this senari wuld be an average utme ntributing frm their sthasti behavirs in the turbulent flw. 21

27 10- ' 1 CD 10- : 10" : ' ; e 6 D Crump etal. [71], 3.8 Ipm. _ Crump etal. [71], 2.1 Ipm 1 & : O Okuyama et al. [23], 0 rpm V 0 < : Okuyama et al. [23], 500 rpm V a Okuyama et al. [23], 2000 rpm # A Shimada et al. [55], 500 rpm A f y 8 A 0 Shimada et al. [55], 3000 rpm O '. A 2 A! *S Chen et al. [42], AT = 0 C VT T V Chen etal. [42], AT = 10 C V A V Cheng [56], 0 rpm? Cheng [56], 300 rpm T J D V Cheng [56], 1000 rpm <* 1 0 Cheng [56], 1800 rpm D 0 % V Figure Partile diameter, im Cmparisn f experimentally btained partile depsitin rates as a funtin f partile diameter. The values f partile depsitin rale 3 exhibit distint minima fr a.m partiles, as indiated in the V-shaped urves. lent diffusin ntrl partile depsitin. On the ther hand, gravitatinal settling bemes dminant in remving partiles frm the gas phase with the inrease f partile size, e.g., >1 urn. As a result, a minimum f partile depsitin rate urs fr partiles f u.m, whih are generally referred t "aumulatin mde" partiles, when neither f the mehanism wrks effetively t ause partile depsitin (Figure 3). With respet t partile mpsitin, experiments have shwn that the material f partiles makes n differene in the measured partile depsitin rates. 23 Als, as seen in Table Al, varius aersl materials have been emplyed fr partile depsitin experiments, and the hie f aersl mpsitins des nt alter the utme. 6.2 Airflw Charateristis Affeting Partile Depsitin Carried by large-sale eddy urrents, airbrne partiles are brught frm ne pint t anther by turbulent diffusin. Eddy urrents an be indued by natural nvetin (e.g., temperature gradient), and fred nvetin (e.g., mehanial stirring and fluid flushing) Fred Cnvetin Early experimenters bserved that inreasingly turbulent air mtin in an enlsed spae was related t enhaned partile depsitin nt surfaes, and the empirial parameters desribing suh phenmena were btained as a funtin f the air stirring intensity. 5 Crner and Pendlebury 5- later explained these empirial bservatins based n the theretial grunds, and nluded that air turbulene was ne imprtant fatr that influened the rate f partile depsitin. 22

28 Subsequent experiments help t shed light n the dependene f partile depsitin rates n the air turbulene level in the enlsures. Figure 4 represents fur labratry results f partile depsitin rates with respet t different air mixing senaris. It an be seen that enhaned partile depsitin is attributed t inreased air turbulene, whih was prdued by either fluid flushing (Nmura el al: ) r fan stirring (Okuyama et al. 23, Shimada et al. 55, and Cheng 56 ). The enhanement f partile depsitin nt enlsure surfaes results frm mre effetive aerdynami mass transfer at higher airflw turbulene, whih brings aersl partiles mre rapidly tward a surfae. In additin, as the turbulent flutuatin f air mtin bemes signifiant, partile inertia may ntribute t partile depsitin, and inertial transprt f partiles thrugh the bundary layer uld be ptentially enhaned by near-surfae turbulent bursts. 41 Inertially indued turbulent depsitin uld be partiularly imprtant fr large partiles. A 'en 10' 2 A O s re 10-3 Depsiti Okuyama et al. [23] 2.6 L ylindria tank S/V = 47 m" 1 0 A A a DA O 0 0 O O A D 6 B fi D A 0 rpm 500 rpm 1000 rpm 2000 rpm A 8 - CD 2 CL 0) Q 10=" 10 3 Shimada et al. [55] 2.6 L ylindrial tank S/V = 47 rrf rpm 1000 rpm 3000 rpm Partile diameter, urn 10 10' Partile diameter, urn 10 Cheng [56] 161 L spherial hamber 0 t 0 rpm 300 rpm 10-2 S/V = 9 m" 1 D 1000 rpm A A 1800 rpm CD A "S10 3 i Depsitin D O A e D 10" Figure 4. A AS A D O e 6 B D 'en s D D ^lo 2 CD 0 s O i_ U *^ Q_ CD Q 0 Nmura et al. [54] 0.8 h" L retangular hamber 1.7 h" 1! S/V = 6.4 rrf D 2.4 h" 1 in Partile diameter, urn Partile diameter, urn Dependene f experimentally measured partile depsitin rates n the degree f airflw turbulene, as haraterized by the fan stirring rate (in rpm) and the air-exhange rate (inming airflw rate divided by the enlsure vlume, with the unit f h"'). The interir surfae area-t-vlume rati, S/V, is indiated fr eah test hamber. Within the same experimental system, enhaned partile depsitin is nsistently bserved at higher air turbulene levels. D 23

29 6.2.2 Natural Cnvetin Natural nvetin arises frm temperature differenes amng air parels, r heat transfer at surfaes (i.e., surfae-t-air temperature differene). In the absene f fred nvetin, natural nvetin bemes the nly means f air mixing inside enlsed spaes. Cheng 5 nduted partile depsitin experiments under isthermal and still air nditins with n apparent air mvements deteted* in the hamber, but still fund the depsitin data well desribed by the hmgeneus turbulene mdel, assuming the re regin was well-mixed (see Subsetin 7.1 fr mre disussin). Figure 5 shws a mparisn f partile depsitin rates as a funtin f partile size under natural nvetin nditins frm different experiments ,56-58 First, ntie that partile size remains the predminant parameter gverning the depsitin rates, as indiated by the distint V-shaped urves. Sendly, the satter f the data in these experiments may be attributed t (1) the S/V rati, as higher surfae area nrmalized by vlume translates t mre surfaes available fr partiles t depsit n, and (2) temperature gradient within the enlsure, as it ditates the extent f nvetive mixing. Chen et al 4 and Cheng 56 speifially dumented the temperature measurements inside their test hambers, ensuring that the experimental systems were either isthermal r therwise reprted. The temperature data frm the ther depsitin measurements are either insuffiient r unavailable t draw any useful infrmatin. 6.3 Surfae Charateristis Affeting Partile Depsitin After airbrne partiles enter a bundary layer, they may be transprted t the surfae by means f a variety f depsitin mehanisms, as desribed in Setin 3. It remains a gd apprximatin and has been demnstrated experimentally that adhesin f mirmeter-sized (r smaller) partiles is Okuyama et al. (1986), S/V = 47 m" 1 Van Dingenen et al. (1989), S/V = 7.9 m' 1 Chen et al. (1992), S/V = 9.1 m ', AT = 0 C A Chen et al. (1992), S/V = 9.1 m"\ AT = 10 C «> Cheng (1997), S/V = 8.8 m" 1 O Van de Vate (1972), S/V = 7 m ' Figure 5. Partile diameter, urn Cmparisn f experimentally measured partile depsitin rates as a funtin f partile size under natural nvetin nditins. The interir surfae area t vlume rati, S/V, is indiated fr eah experimental hamber. AT in Chen et al.* 2 refers t the temperature differene between the tp and bttm walls (e.g., T b - T, = 10 C) f the test hamber. The detetin limit in these experiments was abut 1 m/s. 24

30 mplete and irreversible ne they me int ntat with a surfae." The Van der Waals fre is the predminant adhesin fre between an aersl partile and any surfae (inluding anther partile), althugh eletrstati and apillary fres may be imprtant as well. 28 Surfae harateristis play a rle influening partile depsitin as they ften affet partile-surfae interatins within the bundary layer. The dependene f partile depsitin n surfae harateristis has been explred experimentally by manipulating varius fatrs suh as surfae rientatins and rughness. Belw, an verview is prvided nerning experimental depsitin studies with respet t varius surfae harateristis Surfae Orientatin: Hrizntal vs. Vertial The effet f gravity ntributes t the majr differene in terms f partile depsitin flux nt surfaes f varius rientatins, e.g., a hrizntal upward-faing surfae (flr) as ppsed t a vertial (wall) r a hrizntal dwnward-faing surfae (eiling). Briefly, the mehanism f gravitatinal settling is primarily respnsible fr partile depsitin nt the flr, while turbulent and Brwnian diffusins are dminant depsitin presses t walls and eiling. Partile flux with respet t surfaes f varius rientatins an nly be studied by means f spatially reslved depsitin velity measurements as desribed in Subsetin 5.2. Byrne et al. 49 emplyed the NAA tehnique t rever the partile mass depsited n varius surfaes under fred nvetin in their ubi test hamber (2x2x2 m 3 ). They reprted that prprtinately mre f the verall partile depsitin flux was fund n the flr (and thus less n walls) as partile size inreases, as summarized in Table 3. Thather et al 4b used fluresent traer partiles t measure partile depsitin velity with respet t different surfaes under natural nvetin flw nditins in their ubi enlsure (1.2 x 1.2 x 1.2 m 3 ). In additin t examining the effet f different surfae rientatins, the interir surfae temperatures f the hamber were independently ntrlled at fixed surfae-t-air temperatures t investigate the thermphreti effets n partile depsitin (see Subsetin fr mre disussin). In brief, the experimental hamber was heated n the flr and ne vertial wall, and led n the eiling and the ppsite wall. As lng as the surfae-t-air temperature differene is kept idential, the thermphreti effet is nsidered t be very similar, allwing mparisns t be made nerning partile depsitin n surfaes f different rientatins. Table 3. Relative Cntributins f Partile Depsitin Flux Experimentally Determined fr the Hrizntal and Vertial Surfaes as a Funtin f Partile Diameter in Byrne et al. 49 Partile size Flux n hrizntal surfae Flux n vertial surfae Average depsitin velity* (urn) (flr) (ne wall) (m/s) % % % % aunted fr partile depsitin t all hamber surfaes. 9% 4.1x10 6 8% 6.2x10" 5 7% 1.1X10" 4 5% 2.0x10" 4 25

31 Figure 6 presents a mparisn f partile depsitin velity experimentally btained frm vertial and hrizntal surfaes at the same temperature [+1.5K in (a) and -1.5K in (b) relative t the air temperature]. One f the distintive features in Figure 6(a) is that partile depsitin velity nt the hrizntal upward-faing surfae (i.e., flr) inreases as partile size inreases, in agreement with theretial preditins and experimental results in Byrne et a/. 49 Als nte in Figure 6 (a) that the measured depsitin velities nt vertial surfaes (i.e., wall), were inreasingly lwer than thse n the flr by 1 t 3 rders f magnitude with the inrease f partile size. Due t the diminishing ntributin frm gravitatinal settling, the depsitin velity t the hrizntal dwnward-faing surfae (i.e., eiling) als dereases fr inreasing partile size, as shwn in Figure 6(b) Partile diameter, urn Partile diameter, \un Figure 6. Cmparisn f experimentally measured depsitin velity fr surfaes f varius rientatins in a ubi hamber under natural nvetin. The surfae temperatures in (a) and (b) were kept at 1.5K higher and 1.5K lwer than that f air, respetively. The values f depsitin velity pltted here were btained frm Table 2 in Thather et al. 46 The symbl f * in (b) dentes that the depsited partile mass n the eiling was under the detetin limit. 26

32 : Surfae Texture: Smth vs. Rugh Surfae texture mpliates the press f partile depsitin. The mirsale rughness elements an alter the near-surfae turbulent strutures and redue the bundary layer thikness, whih, in turn, influenes partile depsitin. Rughness an als influene diffusive depsitin even when the fluid-mehanial prperties are nt disturbed. The rughness elements an extend int and arss the partile nentratin bundary layer (whih an be muh thinner than the visus sublayer), and this an expse the elements t higher partile nentratin, thus enhaning the depsitin rate. In additin, partile depsitin may be further enhaned by mre sites within the rughness elements available fr impatin prvided that partile inertia is suffiient. Experimental data regarding the effet f surfae rughness n partile depsitin within an enlsure are sparse. Nnetheless, a large lletin f literature exists fr partile depsitin nt smth and rugh pipe walls, allwing sme lues t be inferred. Sippla " prvides an exellent review f this issue. Based n sme assumptins and the measurements frm a stirred 2.6-L ylindrial hamber, Shimada et <a/. 60 prpsed a semi-empirial mdel t explain the dependene f surfae rughness height n partile Brwnian and turbulent diffusive depsitin, and t estimate the rate f partile depsitin. Figure 7 illustrates the influene f surfae rughness level n the experimentally measured depsitin rates fr (Xm partiles under the same turbulent mixing nditins (500 rpm). They nluded that as the surfae rughness bemes signifiant, partile depsitin tends t be influened by the turbulent diffusin very lse t the surfae, leading t the enhanement f partile depsitin. Later, Shimada et al. 62 further refined the mdel, and reprted that the experimentally determined depsitin rates agreed well with thse reprdued in mdel alulatins when the twdimensinal nfiguratin f surfae rughness was taken int aunt in alulating partile nentratin abve a rugh surfae. Sine their mdeling apprah fused n diffusive depsitin fo u.m partiles, the mehanisms f gravitatinal settling and inertial impatin were nt inluded. 10' U5 CD im Q- CD Q 10 ; 10 : 10-" 0 * i A Shimada et al. [60], 11.2 urn Shimada et al. [60], urn Shimada et al. [60], urn A Abadie et al. [61 ], linluem A Abadie et al. [61], smth wall paper a Abadie et al. [61], rugh wall paper * Abadie et al. [61), arpet 10' Partile diameter, urn Figure 7. The dependene f experimentally measured partile depsitin rates n the surfae rughness. The length sale f 11.2, 119.2, and u.m in Shimada et al. 60 refers t the average height f rughness f the sandpapers plaed n the interir surfae f the enlsed tank. The S/V ratis f the experimental hamber in Shimada et al. and Abadie et al. are 47 and 10 m~', respetively. 27

33 Thather and Nazarff 47 studied the influene f different surfae rughness n partile depsitin under natural nvetin in a 1.8 nr ubi enlsure. They fund that depsitin f small partiles (-0.2 pm) was relatively insensitive t surfae textures, but mre prnuned effets were bserved with inreasing partile size. In their experiments, the measured depsitin nt the rughest vertial* surfae fr 1.3 pm partiles was 5 times greater than depsitin t a vertial smth surfae. They als nted that the surfae rughness had mre substantial effets fr vertial surfaes than hrizntal, and fr warm surfaes than l. Varius wall treatments n all interir surfaes were furnished in a ubi hamber (0.6 x 0.6 x 0.6 m 3 ) t measure depsitin rates in Abadie et al 6] fr partiles f 0.7, 1.0, and 5.0 urn under fan mixing nditins. As shwn in Figure 7, the measured partile depsitin rates were fund t inrease with the fllwing rder f inreasing surfae rughness level: linleum, smth wall paper, rugh wall paper, and arpet. Lai et a/. 63 nduted depsitin experiments in an 8-m 3 test hamber under different fan speeds using mndisperse partiles frm 0.7 t 5.4 pm. They bserved that, at the highest fan speed, the average rati f partile depsitin flux nt a vertial rugh surfae ver smth surfae inreased frm 1.05 fr 0.7 pm partiles t 1.1, 1.6, and 2.4 fr partile sizes 2.5, 4.3, and 5.4 pm, respetively. Sine gravity des nt play a rle in partile depsitin nt vertial walls, surfae rughness and perhaps partile inertia fr larger partiles, are believed t ntribute t the enhaned partile depsitin in the experiments. Thather et al. M reprted n the influene f partile depsitin rates upn different furnishing levels (bare, arpeted, and fully furnished with hairs, urtains, et.) in a rm-sized setting (2.2 x 2.7 x 2.4 m 3 ) fr partile sizes frm 0.5 t 10 pm. The use f arpeting and furniture an be nsidered t inrease the average rughness f surfaes (althugh the airflw pattern will be different fr the furnished senari due t additinal bstrutins inside the rm; als inreased surfae area t vlume rati). Arss all partile sizes measured, the measured depsitin rates were bserved t have the nsistently desending trend with respet t the furnishing r rughness level: furnished > arpeted > bare. Lai and Nazarff 48 plaed glass plates and sandpapers f different grades n the vertial walls f a 1.8-m 3 ubi hamber t measure the depsitin velities f supermirn partiles under fred nvetin nditins. They reprted that the experimentally determined depsitin velity appeared t reah a fairly steady value fr partiles larger than 7 pm. In additin, the depsitin velity was bserved t inrease with inreasing rughness grade, albeit the inrements with inreasing surfae rughness were nt as signifiant as the influene f partile size n depsitin Surfae Temperature: Warm vs. Cld As disussed in Subsetin 3.5, thermphreti fres n airbrne partiles an be indued by temperature differenes between a surfae and air. In the presene f a temperature gradient, partiles always mve tward the diretin f lwer temperature. As a nsequene, partiles tend t preferentially depsit nt a ld surfae ver a warm ne due t thermphresis. Vertial surfaes are studied t exlude the diret influene f gravity n depsitin. 28

34 Numerus experimental studies have examined the effetiveness f expliting thermphresis t minimize partile depsitin n silin wafers fr mirntaminatin ntrl. " Hwever, experimental data fr partile depsitin n ld and warm surfaes with respet t an enlsed vlume are sparse. The experiments perfrmed by Thather et al. prvided valuable insights int partile depsitin under the influene f surfae-t-air temperature differenes within an enlsure. Figure 8 represents the experimentally measured depsitin velity t the vertial surfaes as a funtin f the 10" l wall warm wall 10' 10' i-" 0.1 urn i «10' 4 in Si 10' - E 0.5 urn \ i- 4 5 $ 'iti 0) Q lo"' 10' 10" 0.7 urn J Experimentally measured depsitin velity Theretial preditins fr islated vertial flat plate 10' 10' l- 4-10' 10' \ \ 1.3 Jim \ "is * 2.5 urn \ \ i f Figure Surfae-t-air temperature differene, K Experimentally measured depsitin velities t the vertial walls f a 1.2 x 1.2 x 1.2 nr enlsure as funtins f partile diameter and surfae-t-air temperature differene (reprinted with permissin frm Thather et al 46 Depsitin velities predited theretially by Nazarff and Cass 65 fr a vertial islated flat surfae are als pltted fr mparisn. Eah diamnd symbl represents the average value btained by 10 lal surfae extratins ver the entral prtin f the l r the warm wall frm a single experiment. The errr bars span the maximum and minimum values f measurements at eah latin, while an arrw is used t indiate that the lwer limit f the 95% nfidene interval fr the mean was less than the detetin limit. The symbl * dentes that the depsited partile mass was under the detetin limit. 29

35 surfae-t-air temperature differene (±1.5K and ±10K, respetively) fr five different partile sizes. The depsitin velity predited theretially by Nazarff and Cass 24,65 was als pltted fr mparisn. As shwn in Figure 8, the thermphresis effet n depsitin velity appears t be diminishing as partile size inreases. Fr instane, the experimentally btained depsitin velity t the l vertial surfae (-10K) fr 0.1 (im partiles is mre than 3 rders f magnitude higher than t the warm vertial surfae (+10K). On the ther hand, the measured depsitin velities t the l and warm walls fr larger partiles (1.3 and 2.5 p;m) are apprximately the same. Furthermre, fr partiles larger than 0.5 ixm, the measured depsitin velity n the warm wall at +10K is higher than at +1.5K. This bservatin is unterintuitive sine a warmer surfae is antiipated t enhane thermphreti repulsin thus reduing partile depsitin. In summary, the depsitin velity determined experimentally in Thather et al.^ shws relatively gd agreements with the preditins fr all five partile sizes studied when the wall surfae temperature is ler than the air. In ntrast, the depsitin velity t the warm wall btained in the experiments appears t be muh higher than predited, partiularly fr inreasing partile size. The disrepany between experimental findings and theretial preditins may be attributed t the fat that the existing mdel des nt aunt fr all the fatrs influening partile depsitin under the settings f the experiments. The surfae-t-air temperature differene influenes nt nly partile thermphreti velity, but als the near-surfae airflw pattern, whih further intrdues mre mplexities tward understanding f the depsitin presses. The mpliated airflw pattern and flw instability in their hamber experiments are believed t play a rle in ntributing the variatins f the depsitin velity measurements. Other fatrs suh as partile inertia and the effet f rners n airflw nt being addressed in the mdel may be f imprtane t influene the depsitin press In the Presene f an Eletri Field Eletrstati fres may play an imprtant rle in influening partile depsitin. When the interir surfae f an enlsed vlume has the tendeny t aquire eletrstati harge (e.g., made f pr nduting materials), a lal near-surfae eletri field may develp, whih, in turn, enhanes the depsitin f harged partiles.* Early experiments have shwn that the presene f eletri harges n surfaes an intrdue additinal variability t partile depsitin measurements. 66 MMurry and Rader 67 demnstrated in their 60-m 3 Tefln hamber experiments under natural nvetin that the enhaned depsitin fr \xm partiles was attributed t eletrstati effets, as seen in Figure 9. In anther set f Tefln film bag (250 L) experiments, the depsitin rates f singly harged partiles uld be signifiantly inreased as mpared t partiles at Bltzmann distributin, 67 as shwn by the symbls V and T in Figure 10. Fr instane, a nearly 30 times depsitin enhanement was bserved fr the 0.1 u.m singly harged partiles in mparisn t partiles with Bltzmann harge distributin. In additin, their experimental data indiated that the depsitin rates As mentined in Subsetin 3.6, airbrne partiles beme harged by llisin with air ins and arry ertain harges depending n their partile size arding t Bltzmann distributin. 30

36 10 i i i i i -n-rr ed OJ *- E 10" 1/1 Q. OJ Q Crump and Seidfeld Mdel E = 0 f_ = 0.12s' Mdel inluding eletrstati 9 60 m 3 Tefln smg hamber data effets (6 experiments) E = 38v/m (r t = 0.12 s 1 10' J l_l Mil J ''''' I I I i i i i I t. 0) OJ Q Partile diameter, urn Figure 9. Cmparisn f measured partile depsitin rates in a 60 m Tefln smg hamber with mdeling preditins by Crump and Seinfeld. 68 E and k dente the estimated average eletri field strength n the hamber interir surfae and the parameter f airflw turbulene intensity, respetively. Nte that the experimental data exeeded predited values fr urn partiles when eletrstati effets were nt taken int aunt. Reprinted with permissin frm MMurry and Rader ' T 10' : en ««S <D 2 10"! CL O 10-4 ffi * 0 8 O T r T T v MMurry and Rader [67], Bltzmann distributin (n = 0) T MMurry and Rader [67], singly harged aersls (n = 1) Shimada et al. [69], * = 0 Shimada et al. [69], <t> = 50 V Shimada et al. [69], <I> = 100 V Shimada et al. [69], «= 200 V Partile diameter, urn Figure 10. Experimentally determined partile depsitin rates as a funtin f partile diameter under varius influenes f eletrstati attratins. The data pints f MuMurry and Rader 67 were btained in a 250-L Tefln film bag (natural nvetin; S/V = 10.6 irf 1 ), in whih the average eletri field was estimated as 45 V/m via data fitting t their mdel. The eletrstati attratins in Shimada et al. 69 were established by applying knwn vltage (<I>) at the bttm f the enlsed tank (fred nvetin; S/V = 47 m" ). 3 I

37 were nearly idential fr ppsitely harged partiles f the same size. The labratry results agreed satisfatrily with their mdel that inrprated eletrstati drift as an additinal transprt mehanism. As explained in the mdel, depsitin fr partiles larger than 1 urn and smaller than 0.05 urn were still dminated by gravitatinal settling and Brwnian/turbulent diffusin, respetively; while eletrstati effets were imprtant fatrs influening depsitin f j.m partiles. Shimada et al. 69 perfrmed depsitin measurements fr (im partiles in a stirred metal tank where the turbulene intensity and the eletri field uld be ntrlled. They fund n differene in depsitin rates fr harged and unharged partiles when the surfaes were grunded. As the eletri field strength inreased, hwever, the enhanements f partile depsitin rates were bserved, as indiated in Figure 10. By diretly lleting partile depsitin mass nt vertial surfaes in a 1.8-m 3 ubi hamber, Lai 70 reprted that the measured partile depsitin velities nt aetate sheets fr xm partiles were mre than an rder f magnitude higher than thse nt glass and pper plates, wing t the eletrstati effets. The labratry data indiated that depsitin velities fr bth glass and pper surfaes were mparable, and the use f anti-eletrstati spray n the surfaes was fund t lead t redued partile depsitins by minimizing the Culmbi effet. 32

38 7. Mdeling Partile Depsitin and Experimental Validatins Tw majr types f mdels, bth theretial-based and semi-empirial, have been prpsed t quantify, predit, and explain partile depsitin in enlsures. The first type, as will be disussed in Subsetins 7.1 and 7.2, invlves first mdeling the air turbulent struture adjaent t the enlsure surfaes, and partile transprt is subsequently frmulated aunting fr gravity, diffusin, and ther depsitin mehanisms. One key hallenge in this mdeling apprah lies in the determinatin f the near-surfae partile eddy diffusivity, whih is pstulated t be related t the air turbulene intensity within the enlsure as well as the distane t the wall. The send type f mdeling apprah, as will be desribed in Subsetin 7.3, applies the well-knwn analgy between mass and heat transfer, and depsitin rate f partiles frm the gas phase t the surfae due t diffusin is estimated via the mass transfer rrelatin. In this setin, the mdeling develpments based n these tw apprahes fr prediting partile depsitin rates in enlsures are summarized, tgether with the available experimental investigatins t mpare against the mdeling analyses as well as the limitatins assiated with these mdels. 7.1 Hmgeneus Turbulene Mdel Mdeling effrts fr studying partile depsitin frm turbulent flw nt enlsure surfaes were initiated in the early 1950s. Crner and Pendlebury 53 develped the first theretial mdel aunting fr partile depsitin nt the surfaes f hrizntal and vertial rientatins in a retangular enlsure where the air was hmgeneusly turbulent. Their mdel was derived based n the fllwing key assumptins: (1) the air utside the bundary layer is hmgeneusly turbulent, and aersl nentratin is unifrm (as illustrated in Figure 1); (2) within the bundary layer f thikness S, the fluid mtin is turbulent with randm flutuatins, but the mean fluid mtin is parallel t the surfae; (3) the velity gradient is linear within the bundary layer; (4) the mehanisms f gravitatinal settling, Brwnian/turbulent diffusin are respnsible fr partile transprt thrugh the bundary layer; (5) turbulent diffusin dminates Brwnian mtin at the edge f the bundary layer; and (6) partile transprt is quasi-steady-state in the bundary layer. Under the abve assumptins, the aersl nentratin in the bundary layer adjaent t the surfae is gverned by d_ dy dc ^>f, dc «-v te k = 0, (21) dy where k is the unit nrmal vetr in the vertial diretin. The first and send terms f Eq. (21) aunt fr the presses f turbulent/brwnian diffusin and gravitatinal settling, respetively. The bundary nditins fr the abve equatin are 33

39 C = 0 at y = 0 C = CL at y > 8 (22) where CL is the bulk aersl nentratin utside the bundary layer. The partile nentratin prfile in the bundary layer an thus be slved frm Eqs. (21) and (22). In the Crner and Pendlebury mdel, the partile eddy diffusivity is apprximated using Prandtl's mixing length thery as E p =k e y 2, (23) where kg is the turbulene intensity parameter used t haraterize the degree f turbulent mixing inside the enlsure. There is n a priri way t estimate the values f kg with available data; hene, it is usually determined empirially by fitting experimental data int the thery. Crner and Pendlebury 53 suggested that kg be evaluated as k e = K^, (24) dy where K is the vn Karman's nstant (usually taken as 0.4), and U is the mpnent f the mean flw velity parallel t the surfae. The velity gradient, du/dy, is apprximated by means f fluid drag fre balane fr a flat plate in Crner and Pendlebury's mdel. Fllwing the seminal wrk f Crner and Pendlebury, 53 several additinal mdel extensins have been prpsed. Crump and Seinfeld 68 derived expressins fr estimating partile depsitin rate in an enlsure f arbitrary shape, and the analytial slutins fr a spherial vessel were speifially frmulated. They shwed that, in an enlsure having nly hrizntal and vertial surfaes, the transprt presses f gravitatinal settling and diffusin an be treated independently by vetrially summing the gravitatinal settling velity t the depsitin velity assiated with the diffusin press. Fr the inlined surfaes f a sphere, hwever, their derivatins indiated that these tw mehanisms are always intimately upled t eah ther and annt be separated. They prpsed that the value f ke an be evaluated frm the fluid energy dissipatin rate, instead f velity gradient in the bundary layer as suggested in Crner and Pendlebury. 53 Mrever, Crump and Seinfeld 68 derived the partile depsitin rate with a mre general frm f p = ke y n, where n an be any number, whih uld be btained by empirially fitting experimental data. They als demnstrated that the use f the expnent n = 3, as suggested by Friedlander, 27 uld prdue analytial expressins t predit depsitin that are analgus t thse with n = 2. In summary, Crump and Seinfeld 68 alulated the partile depsitin velity nt the surfae f an enlsure t be 34

40 i(e)=exp v^se _ (25) nv,s0/ nsin?/k e e n-l -P where v, s is the partile terminal settling velity, and 6 is the angle between nrmal vetr f wall and gravity diretin (rad). T validate their wn theretial derivatins, Crump et a/. 71 perfrmed partile depsitin experiments in a spherial vessel. By fitting the data and using n = 2, the turbulene intensity parameter k,; in their study was evaluated in terms f the vlumetri air flwrate int the hamber, whih was related t the turbulent energy dissipatin rate, as suggested in Okuyama et al. 12 The experimental results in Crump et al. shwed gd agreement with the analytial expressins with respet t the dependene f partile depsitin rates n partile size and turbulene intensity. Based n the existing mdel develped by Crump and Seinfeld, 68 MMurry and Rader 67 inrprated eletrstati effets as an additinal partile depsitin mehanism t evaluate the partile depsitin rate in an enlsure. Experiments were als perfrmed t measure the depsitin rate f neutral and singly harged aersls in a 250-L Tefln bag and a 60-m 3 Tefln smg hamber, respetively. A gd fit between the experimental results and the mdel preditins was btained by setting n = 2 and adjusting the values fr k,, and the mean eletri field. Okuyama et al 27, studied the depsitin lss f mndisperse aersls with partile diameters f t 2 (im in a stirred ylindrial vessel. The turbulene intensity parameter ke in their experiments was alulated by the average energy dissipatin rate per unit mass f air, and the parameters f K and n were btained by fitting the experimental data. The experimental depsitin rates mpared well with the mdel alulatins by Crump and Seinfeld 68 when the eddy diffusivity was assumed t be prprtinal t the 2.7 lh pwer f the distane frm the surfae (i.e., n = 2.7). In additin, mre deviatins frm the mdel were bserved fr inreasing partile size r flw turbulene intensity, and this is likely attributed t effets f enhaned partile inertia, whih was nt nsidered in the mdel. Cheng 56 measured the partile depsitin rates f mndisperse partiles ranging frm t 2 fim in a spherial hamber. Bth the hamber temperature and air velity prfiles under varius turbulene nditins were measured. The turbulene intensity in the experiments evaluated using bth methds, inluding the velity gradient as shwn in Eq. (24) and energy dissipatin rate, 23 ' 72 gave reasnable estimates f ke as well as the partile depsitin rates. The data were well explained by Crump and Seinfeld's mdel, 68 exept that the best-fitted estimate f n was apprximately 2.8, instead f n = 2 as supprted in Crump et al., 11 MMurry and Rader, 67 and Chen et al* 2 The expressin k e <* {elvy suggested in Okuyama el al. 12 riginates essentially frm the Prandtl's mixing length frmula, where [elv)' is prprtinal t the r.m.s. velity gradient in the bundary layer. The symbl refers t the turbulene energy dissipatin rate and v is the kinemati vissity f the fluid. 35

41 By vetrially adding the depsitin flux, Nazarff and Cass 65 inrprated the thermphresis effet int the mdel by Crner and Pendlebury 53 t estimate depsitin velity nt a vertial islated flat plate in the presene f surfae-t-air temperature differene. Their analysis shwed that, as partile size inreases, an inreasingly prnuned differene in depsitin velity is predited fr the vertial warm relative t the l walls. The experimental findings in Thather et a/. 46 indiated that the mdel appeared t greatly underestimate the depsitin velity fr a warm surfae, espeially fr supermirn partiles, as was explred in Subsetin In summary, the existing experimental data agree reasnably well with the thery by Crner and Pendlebury, inluding its extensins. Hwever, there are still sme issues that must be arefully examined befre applying the mdel t varius senaris. Fr example, an ke and n be determined in any partiular enlsure, withut resrting t fitting the results f sphistiated partile depsitin experiments? These tw parameters are key and vary with experimental nditins; they ultimately influene the magnitude f the partile eddy diffusivity p, whih diretly affets the alulatin f depsitin rate and flux t the surfae. Table 4 summarizes the values f n and k<, determined frm varius partile depsitin experiments. The senari f n = 2 is regarded as the "lassial" frm f Crner and Pendlebury 53 and Crump and Seinfeld. 68 This is als supprted by sme experimental data (Crump et al.; 1] MMurry and Rader; 67 Chen et a/. 42 ). In ther experimental findings, hwever, the best fit f the data t the mdel urs at n = (Okuyama et al.; 23 Van Dingenen et al.; 51 Hlub et al.; 13 Cheng, 56 ), lse t n = 3 as suggested by Friedlander 27 as well as Pandian and Friedlander 74 based n a theretial perspetive f the analgy between mass and heat transfer. In the definitin f partile eddy diffusivity (in m 2 s~', p = k^y ) when n = 2, the dimensin f k e (s _1 ) 2 n 1 has the dimensins f a rate nstant. Nn-integer values f n leads t ke with a dimensin f L T, whih nt nly laks a slid physial fundatin but als auses neptual and pratial prblems when ke is t be evaluated based n infrmatin f velity gradient r turbulent energy dissipatin rate (bth methds assuming n = 2). Based n the rules f dimensinal analysis, Benes and Hlub 75 suggested a mdified frmulatin t avid the dimensinal innsisteny prblem: P = M 2 8. (26) where S\s the bundary layer thikness. Using this new expressin has shwn t yield gd agreements with data frm ne experimental study. 56 Hwever, it remains unreslved with respet t the evaluatin methd fr n. Nevertheless, Crump and Seinfeld 68 nted that the hie f n value is f little imprtane frm the standpint f their theretial derivatins. Van Dingenen et a/. 57 suggested that, after re-examining the data by Crump et al. lx and MMurry and Rader, 67 the exat value f n is trivial as lng as an apprpriate ke is determined in an independent way, fr instane, the evaluatin f energy dissipatin rate r near-surfae velity gradient, as suggested in Okuyama et al n 36

42 1 -,- Q. x LU C u D 5 a. IS. => O i > -a ai N <. g> T > 0) Q E 6 «> O 3.1 «~ S3 ^~1 * I en JtO I d (0 s i p- X uj TO CD Q. a- 3 DC Q r 3 2 (M O O J3 O <D = I- O 5= in a> eg h- N 05 R CM CD 0) T 0) a. a> a: a) CD ra Q) Q X t > a CL CM d d CM d n. C_ r 0) (!) CD r CJ 5 CM li a> E sz CL-C: en E ra IT n O! CM 0) ID \i >, b n en r u en r <? -B W m!s <? CTi 01 CM O m d CD Cl F r ( u F b _ F _J ra _J CD a. en T a - a x> il * 0) 0)1.b: ^ E > OJ t (D > > 3 ' «<B 2 > Q. ^E I 82 g r,g >^ >, _. CD ra ra r- X E 0) ".i X O E r P T3 2r r : i> CD > U) _ X CJ F r 3 r CD m r: T) 3 r (0 3 <0 > 0) S S T3 JS E T3 3 & r r -a ra M ra T> n F = T F a. m «~ 2 get ra 11 r ~ E r S* "fi C a= S 2 15 r Q.-D "> ST" r. g) di <=>. O a; D r 1 eg tm ^x 5 CD -O 7~ CM O ^ *- ra <1 CM _> (i a n t > it V E r t r CM CM CD i- E E ' Sen ^- Q. <p ra a CD a ra^r «D W i s 2. ^? ra d.e CM 37

43 7.2 Three-Layer Mdel Inrprating the infrmatin n the struture f near-surfae turbulent diffusivity, Lai and Nazarff 25 prpsed a mdel in whih nly ne parameter, fritin velity, u*, is required t evaluate partile depsitin under hmgeneusly turbulent nditins. The fritin velity is defined by u = V Ka J 1/2 du dy y=j y/2 (27) where T w is the shear stress at the surfae, p a is the air density, and V is the kinemati vissity f air. The parameter u* is intended t apture the turbulent harateristis in the viinity f the surfae. As suggested in Eq. (27), the fritin velity is related t the velity gradient at the surfae, du/dy, whih an be evaluated by a freestream air speed LL and a harateristi length f enlsure surfaes L: 76 du dy y=0 PaV Pa U LT L -1/5 (28) Anther apprah f estimating fritin velity is t measure the velity prfile in the lgarithmi flw regin near the surfae, i.e., the Clauser-plt methd. 77 Within the turbulent bundary layer, the time-averaged velity, U, as a funtin f distane frm the surfae y is expressed by U LT 2.5u, f In LL yu 0 + A, (29) where A is a nstant. Thus, the fritin velity an be inferred frm the slpe f the line by pltting measurements f U/LL versus the lgarithm f (yu /v). Cmmnly knwn as the law f the wall, a turbulent bundary layer nsists f three distint znes arding t the velity distributin as a funtin f the distane perpendiular t the wall. The apprah used by Lai and Nazarff t analyze partile depsitin frm turbulent flw is t examine the turbulent flw struture zne by zne, and t frmulate partile transprt equatins fr eah zne, assuming (1) gravitatinal settling and Brwnian and turbulent diffusin are respnsible fr the partile depsitin presses; (2) nstant partile flux in the nentratin bundary layer; (3) partile eddy diffusivity well represented by fluid turbulent vissity; and (4) negligible surfae rughness effets. Arss the bundary layer, the expressin fr the depsitin velity was then integrated fr eah zne. The depsitin velity was evaluated fr vertial, upward, and dwnward hrizntal surfaes, and the first-rder depsitin rates were prvided fr retangular and spherial avities, respetively. This apprah is smewhat mpliated, but remains pratial t use. 38

44 Table 5 summarizes the equatins required fr alulating partile depsitin alng with explanatins f parameters used in the mdel. Their mdel preditins mpared well with published experimental data fr depsitin f pm partiles in a spherial enlsure (Cheng 56 ), as seen in Figure 11. Lai and Nazarff " indiated that their mdel alulatins yield the best agreement with the mdel by Crump and Seinfeld 68 with n = 2.95, very lse t n = 3, whih is used t haraterize nvetive heat transfer. 74 It is expeted that the analgy between heat and mass transfer shuld hld when partile inertia is insignifiant. Table 5. Summary f Equatins Used fr Partile Depsitin Analysis in the Three-Layer Mdel (reprinted with permissin frm Lai and Nazarff 25 ) Parameters Equatins Integral l = [~3.64S 2/3 (a-b)+39l a = In SC" 1 ' S" V3tan -l 8.6-I0.92SC 1/3 / SC" 1 / 3 b = In 2 (l0.92s~ /? + r H S ' x10 4 r + V3tan 2r SC" 1 ' 3 y S" 1/? Depsitin velity vertial surfae v d,v = ~r Depsitin velity upward hrizntal surfae Vd.u I - exp v tr l Depsitin velity dwnward hrizntal surfae Vd.d = vts exp - vts' Depsitin rate, retangular enlsure Depsitin rate, spherial enlsure 1 Vd,yA v + Vd, u A u + Vd,dA<j where x = &- Nmenlature: S = v/d = partile Shmidt number v = kinemati vissity f air D = Brwnian diffusivity f partiles i* = d p u'/2v dp = partile diameter u = fritin velity v, s - terminal settling velity f partiles A v = area f vertial surfaes A u = area f upward-faing surfaes Ad = area f dwnward-faing surfaes V = rm vlume R = radius f spherial enlsure D,(x) = Debye funtin defined by "*> *&: -dt I ' The integral is evaluated analytially under the apprximatin that Brwnian diffusivity, D, is negligible mpared with eddy diffusivity fr y* t 4.3, where y* is the nrmalized distane frm the surfae. This apprximatin is aurate t 1% r better fr partile diameters larger than 0.01 pm. Fr smaller partiles, the integratin must be arried ut numerially. See the fllwing fr results. 39

45 Partile diameter, d p (urn) Integral, I (-) In the limit f small partiles {negligible influene f gravitatinal settling), the expressin simplified t p 1 = 3u'(RI) '. In the limit f large partiles (negligible influene f Brwnian diffusin), the expressin simplifies t [i = 3vfe;(4R)" 1. Lai and Nazarff [25] Cheng [56] u*= 0.9 m/s 0RPM u*= 1.2 m/s 300 RPM u*= 3.1 m/s 1000 RPM * 1800 RPM Figure Partile diameter, jim Preditins f partile depsitin rate as a funtin f partile diameter in the three-layer mdel in Lai and Nazarff 25 mpared with experimental data (Cheng 6 ). Reprinted with permissin frm Lai and Nazarff Lai and Nazarff 48 perfrmed labratry experiments t measure depsitin f Lim partiles frm turbulent flw nt vertial surfaes f a ubi aluminum hamber. The experimentally measured partile depsitin velities fr 9-Lim partiles were higher by a fatr f as mpared t their wn mdel preditins fr fritin velities f m/s. The hamber walls were grunded; thus, eletrstati fre was nsidered negligible. They nte that the disrepany between experimental bservatins and mdel alulatins is attributed t the inadequaies f the mdel, in whih the key transprt and depsitin presses fr supermirn partiles may nt be addressed apprpriately. Fr example, partile inertia and shear-indued lift fre* A partile in a shear flw field may experiene a lift fre perpendiular t the main flw diretin. This life fre arises wing t partile inertia and is imprtant fr large partiles. Lai and Nazarff' 5 pstulated that shear-indued lift fre may be imprtant in their experiments, in whih signifiant velity gradient adjaent t the surfae is expeted wing t the parallel airflw pattern alng the vertial walls f the hamber. 40

46 are pstulated t be ptentially imprtant players t enhane transprt f larger partiles thrugh the relatively thin bundary layers and lead t subsequent surfae depsitin. Lai 78 later inrprated the mehanism f partile inertia int the three-layer mdel by adpting the mmnly aepted eletrial resistane analgy in atmspheri dry depsitin mdeling, 31 t simulate supermirn partile depsitin frm turbulent flw t a vertial surfae. Treating the fritin velity as the fitting parameter and inrprating analyses aunting fr surfae rughness effets, 79 the agreements between experimental data and mdeling alulatins were gd fr smth surfaes, but less satisfatry fr rugh surfaes. The influene f eletrstati drift was nsidered as an additinal partile depsitin mehanism in the inertia-inrprated three-layer mdel by Chen and Lai. 80 The experimental findings invlved with eletrstati effets in Lai 70 again demnstrated that the partile depsitin is a mpliated press, partiularly when mehanisms mre than diffusin and gravitatinal settling are invlved. Mre detailed experiments r numerial simulatin n near-surfae airflw struture will be helpful t shed light n the dynamis f partile transprt. 7.3 Mass Transfer Mdel As mentined in Subsetin 4.1, partile depsitin velity is equivalent t a mass transfer effiient with the units f length per time (LT 1 ). Based n the analgies fr mass and heat transfer, 81 the rrelatins fr transfer effiients in mass and heat transprt shuld be f the same frm fr partile mass transfer frm turbulent flw t the enlsure surfaes by diffusin, and fr nvetive heat transfer in jaketed vessels, assuming that the average rughness heights are immersed within the visus sub-layer (i.e., fr smth walls). Fllwing this analgy, Pandian and Friedlander 74 prpsed a semi-empirial mass transfer expressin t estimate the rate f partile depsitin due t turbulent and Brwnian diffusin in the frm f Sherwd-Reynlds- Shmidt rrelatin: Sh=a(Re) 2 / 3 (S)'/ 3, (30) where Sh is the Sherwd number = k m D/D, k m is the mass transfer effiient r partile depsitin velity (m s 1 ), D is the hamber diameter (m), D is partile diffusivity (m 2 s" 1 ), Re is the Reynlds number fr stirring = NDA, N is the impeller speed (rpm, revlutins per minute) in a stirred hamber, D s is the stirrer diameter (m), V is the kinemati vissity f fluid in the hamber (m 2 s '), S is the partile Shmidt number = v/d, and a is a nstant. By fitting the experimental data in Okuyama et a/. 23 t Eq. (30), Pandian and Friedlander 74 btained a = 0.63 as the best fit fr partiles smaller than 0.1 u.m in diameter and Re n greater than Other labratry results were als used t mpare with Eq. (30), and gd agreements were fund, as shwn in Figure 12. Using different sets f data, the values f fitted a have been fund t be slightly different. By equating the expressin f partile depsitin rate in Crump and Seinfeld 68 t Eq. (30), Cheng 56 shwed that the mass transfer equatin prpsed by Pandian and Friedlander 74 has an equivalent frm as the Crump and Seinfeld mdel with n = 3. 41

47 n 2/3 r 1/3 Re S Figure 12. Mass transfer rrelatin f partile diffusinal depsitin in smth walled stirred hamber, with Sherwd number (Sh) pltted as a funtin f Re^S" 3. The dash line f a = 0.63 was btained frm fitting the data in Okuyama et al., 23 and the straight line f a = 0.54 was btained frm fitting the data in Okuyama et al. 2i and Cheng. 56 Reprinted with permissin frm Cheng. 56 The partile depsitin rate estimated frm the mass transfer rrelatin thus an be estimated as P = a AA Re 2/3 S 1/3. D V (31) where S and V are the interir surfae area and the vlume f the hamber, respetively. Nte that this mass transfer rrelatin indiated in Eq. (30) is nly appliable fr evaluating partile depsitin rate in the diffusinal regime (e.g., d p < 0.1 u.m) in small ylindrial r spherial vessels with smth surfaes, assuming that Re an be defined as stated in Eq. (30). Fr larger partiles and higher fluid turbulene, deviatins frm Eq. (30) were bserved beause diffusin was n lnger the nly mehanism fr depsitin and ther presses, suh as inertial drift, may ntribute t partile transprt t the surfaes. 42

48 8. Summary The phenmenn f partile depsitin nt surfaes in a nfined envirnment is frequently enuntered in numerus industrial and envirnmental settings, either as a desirable r an undesirable utme. This reprt presented a literature review n the imprtant physial fatrs that influene partile depsitin in enlsures, as well as the available experimental tehniques and mdeling apprahes used fr haraterizing the rate f partile depsitin. Experimental findings mpared with the mdel alulatins were presented, and the aveats with respet t the mdels were disussed. As was already knwn, and is further substantiated by the sientifi evidene presented here, the press f partile depsitin is a mpliated phenmenn. Transprt behavir f partiles t surfaes is gverned by the nature f airflw near surfaes, inluding the turbulene intensity, the surfae harateristis, and, imprtantly, partile size. The experimental studies reviewed in this reprt have revealed that the depsitin rate varies bradly arss nditins, and the measurement results are affeted by varius fatrs ating simultaneusly. Diret measurements f partile depsitin nt surfaes f interest are a hallenging task t perfrm, and the ntributin frm varius ptential depsitin mehanisms under realisti irumstanes makes mdeling wrk diffiult. Nevertheless, further prgress t eluidate the presses f partile depsitin will require ntinued effrts t ndut mre arefully ntrlled experimental investigatins, in whih the partile size, near-surfae air flw nditins, and the nature f surfaes are well haraterized. 43

49 a E 3.!= > UJ u PJ (A OX 1 feus - The lgarithm f the aersl mass nentratin was fund t derease linearly with time due t depsitin t hamber surfaes. - The rate f partile depsitin shwed dependene n turbulent flw nditins. - The presene f eletri harges n pr nduting surfae (e.g., plasti) an intrdue additinal variability in partile depsitin measurements. - The partile bundary layer thikness (0.85 mm) was estimated frm the partile nentratin deay measurements, assuming aersls were depsited by gravity and diffusin nly. - Partile depsitin rates were fund t depend n the surfae rughness (rugh latex paint vs. smth aluminum fil surfae) - Partile nentratin bundary layer thikness was fund t be funtins f partile size and surfae rughness - The dependene f depsitin rates n partile size and turbulent intensity were shwn t agree well with the theretial derivatins by Crump and Seinfeld [68]. - A single value f turbulene parameter ke x prvided a mderately gd fit t the measurement results fr um partiles. C3 O a e xs S E S natural nvetin and turbulent mixing natural nvetive mixing natural nvetive mixing natural nvetive mixing turbulent mixing (ntinuus flw) X C Q n a! > a a 2 3 < a eletrstati and thermal preipitatin Si u 1 a. O B &, u eletrstati preipitatin and mirspy light sattering partile unter eletrial aersl analyzer fr partile < 0.2 um and ptial partile unter fr larger partiles 1 s OS 0 H 2 3 U m LLuite sphere ef- C II - E 58 x 58 x58 m 3 plywd hamber rughly spherial glass vessel with a vlume f 118 L Partile mpsitin E 3 D " e 'C B _0 E 2 ea E p a qi E 3 plystyrene latex partiles (PSL) plystyrene latex partiles NaCl and plystyrene latex partiles la 19 E plydisperse 1 t 8 urn ft <* - P E ri- mndisperse t 2.02 um mndisperse t um g 2 S3 60 a 8 > a 1 < Langstrth and Gillespie, Lieberman and Rsinski, al CB > 8- ^ OS B (ft s l2 * a &= B rn

50 plate-ut experiments fllwed by a-ativity measurements ndensatin nuleus unter (CNC) turbulent and natural nvetive mixing natural nvetive mixing turbulent mixing and n mixing turbulent mixing - The measured depsitin velities fr Rn and Th prgenies with the fan n (turbulent mixing) were signifiant higher than thse measured with the fan ff (nvetive mixing). - Gravitatinal setting is the predminant partile lss mehanism fr partiles > 1 um. - Brwnian and turbulent diffusin is the dminant mehanism fr remving partiles < 0.05 urn. - Eletrial fres were shwn t ntribute partile depsitin signifiantly fr smaller harged partiles ( um), depending n the field strength near the surfae. - Psitive and negative partiles were lst t the surfae at the same rate when eletrial fre was the dminant transprt mehanism. - N differene in depsitin rate due t partile materials - Enhaned depsitin rates were bserved with inreasing fluid turbulent intensity - Partile depsitin rates exhibit a strng funtin f partile size with minimum depsitin rate at 0.2 (n mixing) t 0.6 um (vigrus mixing) - Gd agreements between mdel and experiments were btained fr um partiles, and fr k> -10 s" 1. - Diffusin bundary layer thikness inreases prprtinally with 1/3" 1 pwer f Brwnian diffusin effiient. - Enhaned partile depsitin nt rugh surfaes was fund mpared t that nt smth surfaes. - The enhanement f partile depsitin, aused by turbulent diffusin very lse t the surfae, was mre prnuned with inreasing turbulent intensity and partile size. *-» E v 250 L Tefln film bag and 60 m 3 Tefln film smg hamber light sattering partile unter fr partiles > 0.5 um; partile size magnifier and light sattering partile unter fr partiles < 0.5 um ylindrial tank with a vlume f 2.6 L; aryli resin interir L ylindrial tank with sandrughened interir walls radn and thrn prgeny attahed t airbrne partiles 9 z mndisperse um mndisperse t 2 um NaCl, diethylhexyl sebaate (DEHS), and plystyrene latex partiles NaCl, diethylhexyl sebaate (DEHS) mndisperse 0.01 t 0.2 um» 00 0 i 73 r- * OO k_i *- S u a 2 s *-* S 00 ea r~ 73 OO ea <3\ E - IS f 00 a 46

51 u 3 "> C 6 u 8 S & 1"8 5 S M sis E 2.2.2» 3 ">?! s? TJ «> i-8 «> 2 t 43 ^ "Ufa H 2 '5 a TJ "5 4> T-T i_ u 4> 4> X D. 60 w D 1-.2.N "3 *w 3 <u.«60 S. S3 a a 4> S3.5 B X! 3= J ^ a 4) E 2.2 *-* -2 *-- 'a 2 «S 1. ^ ^4 3 NO a 01 a. n 00 ~ E \s x: K i) - 0) TJ 2 a l- -s O -a "8 * > ^> S pi. <u 4> x: t- E TJ 73 u «s,a _4> *- TJ -=. s «^ >» g>3 - a fa a>,0 3 -a "a, 2-3?> *> 2 E 1) ID 2 I pa P" 2 u g, ID TJ TJ 4> O 3 I JB CA E g t8 A 2 E «> <u a t g E O. 1).- u "O 73 <2i*.2 m "> 1 - «*-".5 " 2.9 & 4> E e.1 2.S 3 a g x:.p. Q. u n m 4> 3 TJ U 0. u O 4) U 3 S SI 8.-S u 4) 5 i. E X) C s> X u >. D O C3 f 4> <U E O C 3 TD u 60 E i x; 0 (1) u 0 r u_ u B -a 4J 5 g «, JJ 4J.2 & 4> T3 * S 1 S3 13 x: 2 1 4J > C x: 4>? Q 60 C s Gfl <D a i V 8 8 -S S3 4) «X^T3 ~ 4> 3 4> B 4) si sl I S3 P " PQ ^ s 4) x: 00 3 O 8S «2 B 3 B 6X.U ill 2 ^ It- 0.2 rt T3 fl P ^ T3 «60 B si 4> 00 S SS a O T3.a, I I Q. 5 U 4> r- ^ 8 ^ 4) S? ^ 2 ^ E O 4) *! 2 > 5 4> '& e- 'C s- a. x - 4> _ <4-l 2 0 fj 11 4) 1 4) 4> fa OS 3 E 4> X) X «- xi u 3 ^ 4i 6O1-J S O *.a ^ B - 4) P x B _4) 60 ii "3.5 "S xi x S. 3 'E E 3 'S" 'S.5 > g 41 s X) U z u u 4. Z 73 S 2 <= 5. 3 O (J y aj O 3 3 (8 O ^ GA E O Z O 3 (J!< *^ d x: I11 a* en B* O - w E U 1- li s a 4) O y J5.5 xi 0 "3 B E r- O O 4) 5 S3 J 73 ^ g x^.2 5 m a.- > 2 «[fl > N - 8 T3 s 4) x) XI 4) *~^ ^ in m y "x^s Z^B E -3 i: MO'p O " fa x^ a, E x: 4> E!a 1 i Q. S-. X U 0 D. J2 z 8-S "g 2 E < E d E 3. E 3. m d 1 8 E ~ O E d T3 O S3-4) v. P 60 -S3 CM fa 5 CN O O * U 3 E E 0 4) ^t S.CN "^ j O ad., C N«E 3. O OOO E d d d ^ > CS 00 T3 00 a E - 3 ~J w> a XI P 3 00 n x2 ^> in a s T3 00 a a\ 2-3 -J n a ^ \D C3 Ov TJ 00 CB ON E - 3 ~J 00 a CJ ON 00 4) ON 60 47

52 O O t-s Q, S SP 1 s t- > s «u T <u X! U 4> 0 S 1 = «O g rt E Q s >r a. 2ES x " 3 ra 3 E?> e y s i. 3 8 J «-» t <<-. < «-8 ^ C v- E s U«- a. x 2 3 'S C/5 i 8* II Si rt 5 S 8 C <x. l ill -PS D T3 T3 ea "^ feb «s a- i JO 9 II B.2 S as X u,u t Tt 00 i P B /5 a. E U >> X a O u X I S3 - ^ (D 5(5 5 " 3 4> p u 5 >> 8 a E.9 x > >> 8.2 i) II _ B CL. U - 41 > X si t/5 T3 O ti t S C E s 2 I J e «U C J «> 1> 1^1» ^> 5 USB, 7t.- C at <u u fi t S -SP C«-i C _t a E A O -a _j) il b Q.,0 w C >.2 6b ">' & > j= ~ O BJ,1) C SB «flg 1 f F (Q «C w i.sp CL* > </> E.2 ««4J 3 7 x: s > a S w I p j u E C ill 0 -H.y +?. J' 08 IT i E y b 5 U ' U > if '5 F C u 0) > 0). 3 O 5 tl. T3 S S u -a -a a.~ y - OJ l'? *-* "8.s Q. U T3 ed a E I.si 4) fid > C i '5 > 1) bo 3.5 X> X 3 O 3 S X X 1 i g i g 2 y 60 s 1 1 u 2 i < > < 4> W I 11 a. 9 u ' u t t S i.-.2 «"3 JJ S 1 «S :! 1 R * S <U -a 3 g 3 U X> t t^ >1 a u "S 1) Q, 1) S3 S wt: 4> O C X, t 1) llll w.a Si.* J? j u.s S i J3 Cl* XI O Q,, >> 1) in S J > E i N 1J J 4) "O E ^ 3 l O II S E. I x E X u Is i» ^r n * - *Oi ".. - (s -k m - -. O 0O VC O «N 2 <N Tt i~- -OOO-N u it r- 8 9 E d I is a xi.8 S L.9 "0 E d i 4) 60 O O " B.'H «U i a. u E 3 B = t d 8 E i ^ E <=> a. IT) IT) d i O -J u2 a ON 2 4>-» P ON i^on a g ON 48

53 -a s j O TO 1» >- Ji 5 '5 3 '2 u 2. <«SS ^3,* Cut 8.S i P 2-2 ' It E g a = - a CN 3 5 is a a <" (U O *B «2 «> -a ' "j O I- j a Q 3 O C O O CJ N CJ «i 'a ex 73 s S U J s ^ 2 j 3 _; :a*s g 8 S.J s" 5 < 3 Efl U [A ">!» ^. _ T: * 2 b ^ g5 El «= x: S5P I.n N u 8 s CJ 3 IS B._ u i) 'C S * j,c0 8 S U. i O a «If "* 5 1 a CJ a CJ j O <N t vq CN II =: B *-* 2 ^ a s. 3d - > X3 feel s.i = 5 5 Civs CJ O T3 0< _ JH C TJ C a -a 5 ^ CJ r 2 «J ^ E O si A 3 b A 3 T3 w O V 5 5 * «00 1 * B 2 s I» feb g 15 =L 6 -a 09 CJ M 5 a a «3f j CJ Ix. C JB S-S OJ 3 w - a CJ T-1 00 a CJ u 2S x X) j U S "««? s a M a CJ CJ S 4i a.h C u- en e u «>.2.ts 'P «J 5» "I «j 3 ^ ^ '3 e p4 w B.T) O f j 2 C X! 3 a; C5 TJ CJ IM 0 2 I S e CJ 0 a> 3 -n Xl u e CJ 5 E 5 3 ^ "8 > J en ta 6?. t- nj CJ a t S«S «j e IC CJ CJ 00 u g t 3 Q. J= -C *5 00 # O CJ CJ d a. (M 8t. g 1 si * a S j j g > N Sip P 2 O CJ 60 j 2 CJ a > j CJ = 0 X> X &T3 X ' P IS a ^ X) O g, CJ 00 3 C 11 I S 5 CJ e>0 3.S P X U X^ *B a a a <= &, O O O -a, a TJ rt T^ «-^ u S b.a b &>- 5, u a I e w & E -g 5 s 5 -a a 3 -Q 3.<«a X) 7) <+- C Cu 0!a 1 S X) =3 U 1 u a 2 8, 3 u z 1 u rn part Aerdyn tide Size _CJ CJ I a P "a ^ 3 v -^ g 5 a-.a U -2 A 115 _CJ CJ 1 a. 3 ^ a. j a ^ S <*- E -a ^ a <1 Q. "S 3 W5 a T-i n «= -.52 e s 'u O «C CJ CJ a "a f> = - ^ a a u a - 01 ^ $ CN W g e X! x X! a. 1 *0 ^ X! a 0 00 x'5. r-: 11 0 E E E - CJ ES Cd V- E.S 3 CJ ~ ' > S "> O j 5 E 3 a B 0 -: E O 3- T3 a a > a j *> S3 1 «5 rt D- CJ e S 5 1 8, ' ^ -s "7 I 9 b - -a ta a O > E Q. ^ CX u g 12 b e Ed ii3 O O u S a Z a hlf X O 3 n a QQ a. CJ n i. 3. E 5 CN O ' C <N E T3 a a CJ S * CJ ^ O v. 8,-g E J3 "5 en p 1- O CN a. r~- Ed e g *0 m - - ; eax_- >, E a. X! gr- 2 a t- 2 S <* ESz2 a E - zw u CJ_ < CN 853 M CN a Q a J CN 49

54 J-. OJ P I.5. T3 Q OJ <D S 3 S <u a 1 a I C I «.2 en.n,. s 0 = TJ g. S? <u X u ">.a ET 7J S D.-S u a u > O OJ OJ ~^ ;n et ' as a. O j.9*8 a 03 OJ _ u > u a -a u 3 E a _ e F- 1 OJ i p _ "S > <u O u \s S."= sal fill.5-3 -> p p 1) C fa -Biff.a e 3 fi u R a e O.H.5 OJ > a CJ OJ a <u 3 t j C a 2 >i a fe u» * j a <u u j x: a _3J M g, 3 Oj C U <*«a O >- S u S T3 5 OJ ~ "* OJ (O s s i T3 L, OJ,0 U C«1 «OS is a, a» a j XI S ~ n d ' a t>0 Dij OJ u e QJ T3 -e J= Q, OJ s E t CL XI «a w S >» s g x> a) BO 73 5-S II > s e.a OJ CJi 3.S P x a OJ 00 ft- gp l! II xi n 8 JJ OJ OJ 8 i -8 i 1 a a a e a, O O D. 3.1 u - fi a. CJ 73 OJ OJ «s i r OJ eg ^ O ^ 2 <2 O u *_ C^H CL OJ S 7t in a C,. M 'X! OJ y P.5? -P w a OJ IS a X) 15 OJ OJ 1 E * 8 t> y g S 3 3 J E r- (N X E 3 <N ^ in X E J5 U fn CN (N CN E x E fn CN CN CN I X! OJ E a. -i -n ^, e t D- O S.CN r- q_ 5 -. P - -«1 Oi a... \ in E en r-^ =3 3. >n E en a. «J 3t -N x: 8 CN a f _. - H a It S Z CN 3 3 u 50

55 10. Referenes 1. D. W. Cper, "Paniulate Cntaminatin and Mireletrnis Manufaturing: An Intrdutin," Aersl Si. Tehnl. 5, 287 (1986). 2. B. Y. H. Liu and K. H. Ahn, "Partile Depsitin n Semindutr Wafers," Aersl Si. Tehnl. 6, 215 (1987). 3. S. E. Pratsinis, T. T. Kdas, M. P. Dudukvi, and S. K. Friedlander, "Aersl Reatr Design: Effet f Reatr Type and Press Parameters n Prdut Aersl Charateristis," Ind. Eng. Chem. Press Des. Dev. 25, 634 (1986). 4. J. D. Spengler and K. Sextn, "Indr Air Pllutin: A Publi Health Perspetive," Siene 111, 9 (1983). 5. A. V. Ner, "Cntrlling Indr Air Pllutin," Sientifi Amerian 258, 42 (1988). 6. W. W. Nazarff, A. J. Gadgil, and C. J. Weshler, "Critique f the Use f Depsitin Velity in Mdeling Indr Air Quality," in Mdeling f Indr Air Quality and Expsure, ASTM STP 1205, N. L. Nagda, Ed., ASTM, Philadelphia, (1993). 7. W. W. Nazarff and G. R. Cass, "Prteting Museum Clletins frm Siling Due t the Depsitin f Airbrne Partiles," Atmspheri Envirn. 25A, 841 (1991). 8. A. Wright, "Primary System Fissin Prdut Transprt and Release," Reprt NUREG/CR- 6193, ORNL/TM-12681, Oak Ridge Natinal Labratry, Oak Ridge, TN (1994). 9. F. Gelbard, "Maers User Manual," U.S. Nulear Regulatry Cmmissin, Washingtn, DC (1982). 10. F. E. Kruis, H. Fissan, and A. Peled, "Synthesis f Nanpartiles in the Gas Phase fr Eletrni, Optial, and Magneti Appliatins - A Review," J. Aersl Si. 29, 511 (1998). 11. T. T. Kdas, "Generatin f Cmplex Metal Oxides by Aersl Presses: Supernduting Cerami Partiles and Films," Adv. Mater. 1, 180 (1989). 12. A. C. Tribble, Fundamentals f Cntaminatin Cntrl, SPIE Press, Bellingham, WA (2000). 13. B. Y. H. Liu and K. W. Lee, "Experimental Study f Aersl Filtratin by Fibrus Filters," Aersl Si. Tehnl. 1, 35 (1981). 14. L. Spielman and S. L. Gren, "Mdel fr Prediting Pressure Drp and Filtratin Effiieny in Fibrus Media," Envirn. Si. Tehnl. 2, 279 (1968). 15. M. R. Sippla, "Partile Depsitin in Ventilatin Duts," Ph.D. dissertatin, University f Califrnia at Berkeley, Berkeley, CA (2002). 51

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61 PHYSICAL SCIENCES LABORATORIES The Aerspae Crpratin funtins as an "arhitet-engineer" fr natinal seurity prgrams, speializing in advaned military spae systems. The Crpratin's Physial Sienes Labratries supprt the effetive and timely develpment and peratin f natinal seurity systems thrugh sientifi researh and the appliatin f advaned tehnlgy. Vital t the suess f the Crpratin is the tehnial staff's wide-ranging expertise and its ability t stay abreast f new tehnlgial develpments and prgram supprt issues assiated with rapidly evlving spae systems. Cntributing apabilities are prvided by these individual rganizatins: Eletrnis and Phtnis Labratry: Mireletrnis, VLSI reliability, failure analysis, slid-state devie physis, mpund semindutrs, radiatin effets, infrared and CCD detetr devies, data strage and display tehnlgies; lasers and eletr-ptis, slid-state laser design, mir-ptis, ptial mmuniatins, and fiber-pti sensrs; atmi frequeny standards, applied laser spetrspy, laser hemistry, atmspheri prpagatin and beam ntrl, LIDAR/LADAR remte sensing; slar ell and array testing and evaluatin, battery eletrhemistry, battery testing and evaluatin. Spae Materials Labratry: Evaluatin and haraterizatins f new materials and pressing tehniques: metals, allys, eramis, plymers, thin films, and mpsites; develpment f advaned depsitin presses; nndestrutive evaluatin, mpnent failure analysis and reliability; strutural mehanis, frature mehanis, and stress rrsin; analysis and evaluatin f materials at rygeni and elevated temperatures; launh vehile fluid mehanis, heat transfer and flight dynamis; aerthermdynamis; hemial and eletri prpulsin; envirnmental hemistry; mbustin presses; spae envirnment effets n materials, hardening and vulnerability assessment; ntaminatin, thermal and strutural ntrl; lubriatin and surfae phenmena. Mireletrmehanial systems (MEMS) fr spae appliatins: laser mirmahining; laser-surfae physial and hemial interatins; mirprpulsin; mir- and nansatellite missin analysis; intelligent mirinstrumenis fr mnitring spae and launh system envirnments. Spae Siene Appliatins Labratry: Magnetspheri, aurral and smi-ray physis, wave-partile interatins, magnetspheri plasma waves; atmspheri and inspheri physis, density and mpsitin f the upper atmsphere, remte sensing using atmspheri radiatin; slar physis, infrared astrnmy, infrared signature analysis; infrared surveillane, imaging and remte sensing; multispetral and hyperspetral sensr develpment; data analysis and algrithm develpment; appliatins f multispetral and hyperspetral imagery t defense, ivil spae, mmerial, and envirnmental missins; effets f slar ativity, magneti strms and nulear explsins n the Earth's atmsphere, insphere and magnetsphere; effets f eletrmagneti and paniulate radiatins n spae systems; spae instrumentatin, design, fabriatin and test; envirnmental hemistry, trae detetin; atmspheri hemial reatins, atmspheri ptis, light sattering, state-speifi hemial reatins, and radiative signatures f missile plumes.

62 (A) AEROSPACE The Aerspae Crpratin 2310 E. El Segund Bulevard El Segund, Califrnia U.S.A.