Use of the Electrostatic Classification Method to Size OJ fxm SRMParticles A Feasibility Study

Transcription

1 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy [J. Res. Natl. Inst. Stand. Tehnl. 96, 147 (1991)] Use f the Eletrstati Classifiatin Methd t Size OJ fxm SRMPartiles A Feasibility Study Vlume 96 Number 2 Marh-April 1991 Patrik D. Kinney and David Y.H.Pui University f Minnesta, Minneaplis, MN and Gerge W. Mullilland and Nelsn P. Bryner Natinal Institute f Standards and Tehnlgy, Gaithersburg, MD The use f the eletrstati lassifiatin methd fr sizing mndisperse 0.1 (im plystyrene latex (PSL) spheres has been investigated experimentally. The bjetive was t determine the feasibility f using eletrstati lassifiatin as a standard methd f partile sizing in the develpment f a 0.1 (im partile diameter Standard Referene Material (SRM). The mean partile diameter was alulated frm a measurement f the mean eletrial mbility f the PSL spheres as an aersl using an eletrstati lassifier. The perfrmane f the lassifier was investigated by measuring its transfer funtin, nduting a sensitivity analysis t verify the gverning theretial relatinships, measuring the repeatability f partile sizing, and sizing NIST SRM 1691, [jtm and NIST SRM 1690, p-m partiles. Investigatins f the aersl generatr's perfr- mane fused n the effet f impurities in the partile-suspending liquid n the resulting partile diameter. The unertainty in partile diameter determined by eletrial mbility measurements is fund t be 3.3% t + 3.0%. The majr sures f unertainty inlude the flw measurement, the slip rretin, and a dependene f partile size n the aersl flw rate. It was fund that the lassifier uld be alibrated t indiate the rret size t within 0.1% fr bth SRM partile sizes if the defined lassiflatin length is dereased by 1.9%. Key wrds: aersl generatr; atmizers; ndensatin nulei unters; eletrial mbility; partile size; plystyrene latex spheres. Aepted: Nvember 20, Intrdutin This study assesses the auray f eletrstati lassifiatin fr measuring the diameter f 0.1 ^.m plystyrene latex (PSL) spheres prdued as an aersl by atmizing a suspensin f PSL spheres in water. The PSL spheres used in this study were prdued by emulsin plymerizatin by Dw Chemial Cmpany^ and the nminal size as mea- ' Certain mmerial equipment, instruments, r materials are identified in this paper t speify adequately the experimental predure. Suh identifiatin des nt imply remmendatin r endrsement by the Natinal Institute f Standards and Tehnlgy, nr des it imply that the materials r equipment identified are neessarily the best available fr the purpse. sured at Dw by transmissin eletrn mirspy is \hra. This study is mtivated by the need t develp an aurate 0.1 fj.m partile size standard. This size standard is imprtant fr imprving partile sizing auray by eletrn mirspy, light sattering, and by ther methds. A partile diameter f 0.1 jjtm is in the size range f mbustin generated partiles, ntaminatin partiles f nern in the semindutr industry, air pllutant partiulates, viruses, and varius manufatured partiulates suh as arbn blak and fumed silia. The eletrstati lassifier is a widely used instrument in aersl researh fr bth partile sizing and 147

2 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy fr generatin f mndisperse aersls ver the size range t 1.0 jim. The basi physial priniple f the lassifier is that the velity f a harged spherial partile in an eletri field is diretly related t the diameter f the partile. A harged aersl enters near the uter irumferene f the lassifier and partiles with a narrw range in eletrial mbility exit thrugh a slit in the enter eletrde. The mbility distributin is determined by measuring the number nentratin exiting the slit as a funtin f the eletrde vltage. The thery f the lassifier peratin and its perfrmane have been extensively studied [1-7]. In regard t sizing PSL spheres with the lassifier, Kusaka et al. [8], mpared measurements f PSL spheres made with the eletrstati lassifier t measurements made with a sedimentatin methd, and a balane methd using a Millikan type ell. The three measurements were fund t agree within a few perent fr 0.2 t 1 jim partiles, but measurements were nt nduted fr partiles smaller than 0.2 jj,m in diameter. The determinatin f the auray f a measurement methd requires that all the physial variables entering int the partile size equatin be aurately knwn. The tw key physial variables fr the eletrstati lassifier are the vlumetri flw rate and the eletrde vltage. The predure used at NIST fr these tw alibratins is desribed in setin An imprtant element in assessing the auray f an instrument is the verifiatin that the instrument behaves arding t the gverning equatin. The verifiatin predure utlined in setin inluded mparisn with the thery [1] and the use f tw lassifiers in tandem [9]. Further verifiatin f the lassifier perfrmane is ntained in setin 3.2.4, where the measured and predited sensitivity f the lassifier peak vltage t a hange in the flw vlume and the perating pressure are mpared. Anther way the auray f the lassifier was established was by measuring tw primary alibratin standards fr partile size: [xm (NIST SRM 1691) and ixm (NIST SRM 1690). The results f this mparisn are ntained in setin The methd fr generating the PSL sphere aersl invlved atmizing a suspensin f PSL spheres dispersed in water. The nn-vlatile impurities in PSL sphere suspensin result in a residue thikness n the PSL sphere. Signifiant effrt was invlved in minimizing the drplet size prdued by the atmizer system, setin 3.3.1, and in quantifying the amunt f impurity in the dilutin water, setin 3.3.2, and in the riginal, undiluted suspensin, setin In setin 4, the Disussin setin, a mparisn is made between the results f this study and tw ther studies [10,11] that fused n the aurate measurement f the same bath f Dw ixm PSL spheres. 2. Experimental Apparatus Figure 1. shws a shemati diagram f the instrumentatin used in this study. The majr mpnents are the atmizer, the eletrstati lassifier, and the ndensatin nuleus unter. A PSL aersl is prdued by atmizing a suspensin f PSL spheres in water. After nditining, the partiles are passed thrugh the eletrstati lassifier. By mnitring the number nentratin with the nuleus unter versus the mbility setting f the lassifier, the mean eletrial mbility f the partiles is determined. The mean size is then determined frm the partile size dependene f the eletrial mbility. A mre detailed desriptin f eah instrument fllws. 2.1 Aersl Generatin The PSL spheres are aerslized with an atmizer, shwn in figure 2, nsisting f a 15 psig air jet impinging n the end f a liquid feed tube. The ppsite end f the feed tube is submerged in a suspensin f PSL spheres in water. The vauum prdued by the air jet draws the partile suspensin thrugh the apillary tube and int the air jet. The jet atmizes the PSL partile suspensin prduing an aersl f drplets. Sme f the drplets prdued ntain PSL spheres while ther drplets are "empty." The drplets evaprate as they flw thrugh a diffusin drier and are diluted with lean, dry air. Drplets ntaining PSL spheres evaprate t frm a PSL sphere with a slight surfae residue. Drplets whih d nt ntain a PSL sphere evaprate and frm a small residue partile nsisting f nnvlatile impurities present in the riginal partile suspensin liquid. Thus, the resulting aersl nsists f ptentially dirty PSL spheres and small impurity partiles. When a drplet ntaining a PSL sphere evaprates, any nn-vlatile impurities in the liquid remain t frm a thin layer f residue n the partile surfae. The residue frmed n the surfae has a finite thikness and prdues a systemati errr in the measurement f partile diameter. T redue the nentratin f impurities in the partile suspensin, de-inized/filtered water was used t

3 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy s s s \ s \ s Dilutin Air IVIixing Chamber I Diffusin Drier Flw Meter Impatr Water Trap Atmizer PSL Suspensin Aersl Generatr b.'vvw>i. 15 psjg -*- r-isj- Exess Aersl ^S^- Exess Plydisperse Aersl Valve Plydlsperse Aersl Inlet -tj^ Eletrstati Classifier Sheath Air Inlet -th V7 Filter Diffusin Drier Pressure F^egulatr (\ 15 psig, 100 psig Mndisperse Aersl Oulet Exess Air Outlet I I Exliaust Clean, Dry Air Supply t Exess Mndisperse Aersl Valve Platinum Resistane Thermmeter Chilled-Mirrr Humidity Analyzer ^^ Exhaust Exhaust -*- Cndensatin Nuleus Cunter tjuzr strip Chart Rerder Figure 1. Apparatus fr partile sizing with the eletrstati lassifier. 149

4 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy Drplet Impatr Plate Drplet Aersl Aersl Outlet SS.-./ Air ( 15 psig ) Air Jet ^:i ^ji ^^ -fit ^j( -^ji ^X -^jt ry',^ ' Ji Ji ^Jt j^a ^J4 j^jt. Drplet Impatin Surfae Liquid Feed Tube Liquid Drain Impated Drplet Water Trap ^A'^A'^A-^A-^^-^^-^A ^. PSL Partile Suspensin Liquid Reservir Figure 2. Atmizer with drplet impatr. suspend the PSL spheres. The larger drplets evaprate leaving a larger impurity residue n the partile surfae. T minimize this effet, an impatr with a ut pint f abut 0.5 \xm was plaed at the utlet f the atmizer. The effet f impurity nentratin n the size f 0.1 ixm PSL spheres has been experimentally investigated in this study. 2.2 The Eletrstati Classifier The eletrstati lassifier used in this prjet is a mmerially available instrument (TSI, In., Mdel 3071). Figure 3 shws a shemati diagram f the instrument. The lassifying regin is bunded by a stainless steel uter ylinder with an inner diameter f m, and a axial, stainless steel enter rd with an diameter f m. The enter rd is nneted t a variable ( 0 t -11,000 V) negative d pwer supply, and the uter ylinder is grunded. By varying the enter rd vltage, the eletri field in the annular regin an be varied frm 0 t abut 11,000 V/m. Clean sheath air, after passing thrugh a finemesh flw straightening sreen at the tp f the lassifier, flws axially thrugh the annular regin alng the enter rd. A smaller, plydisperse aersl flw enters thrugh an axisymmetri pening alng the uter ylinder. The lean air flw fres the aersl t flw dwnward in a thin layer n the uter wall f the lassifying regin. It is essential that these tw streams merge smthly withut mbing. Near the bttm f the lassifying regin, a slit n the enter rd extrats a fratin f the air flw nsisting f near-mndisperse (single sized) aersl partiles. The remainder f the air flw exits thrugh the end f the annular regin as exess air. The length f the lassifying regin (44.44 m) is defined as the axial distane frm the aersl entrane t the aersl exit at the slit in the enter rd. Befre entering the lassifying regin, the partiles are sent thrugh a harge neutralizer. The neutralizatin urs thrugh interatin with bi-plar gaseus ins (psitive and negative ins) 150

5 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy Sheath Air (Q) HEP* Filtr Mass Flwmaler Kr-85 Charge NauUalizer Plydisperse Aersl ( Qa) High Vltage Pwer Supply Mndispersa Aersl Exit Slit Exhaust Air ^ Exess Mndisperss Aersl Vaivs Mndisperse Aersl (Qs) Figure 3. Eletrstati lassifier. prdued by radiative Kr-85. The ins impart a bi-plar harge distributin n the aersl partiles. Fr partiles with diameters arund 0.1 jim, abut 24% f the partiles arry a single psitive elementary harge and abut 4% arry a duble psitive harge [12]. When the partiles enter the lassifying regin, they are arried axially dwn the lassifying regin with the sheath air flw, and the partiles arrying a psitive harge mve radially twards the enter rd under the influene f the eletri field. Negatively harged partiles depsit n the inner surfae f the uter ylinder. Within the lassifying regin, a partile rapidly reahes a steady radial velity thrugh equilibrium between the eletri field fre, and the ppsing Stkes drag fre. The radial velity f the partile in the eletri field is determined by the partile's eletrial mbihty, defined as the velity a partile attains under the influene f a unit eletri field. 151

6 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy The eletrial mbility, Zp, f a singly-harged partile an be derived by equating the eletri field fre, Ft, with the Stkes drag fre, Fd: Stkes Drag Fre: Fi = ^^-.. ^ Eletri Field Fre: Ft = e Eletrial Mbility: Where F_eC(Dp) E Sir x Dp (1) V = radial mpnent f partile velity E = eletri field strength e = elementary unit f harge C(PP) = slip rretin ji = air vissity Dp = partile diameter. As seen frm eq (1), small partiles have high eletrial mbilities, and thus mve with high radial velities tward the enter rd and depsit n its surfae. Larger partiles, with lwer eletri mbilities, are swept further dwn the lassifying regin befre depsiting n the enter rd. Still larger partiles are swept ut the bttm f the lassifier with the exess air. The mndisperse utput f the lassifier is extrated thrugh a small slit n the enter rd shwn in figure 3. Only partiles with eletri mbilities within a narrw range have trajetries whih bring them t the entrane f the slit. Partiles reahing the entrane f the slit are remved frm the lassifying regin by the air flw entering the slit. In this way the lassifier extrats a narrw size range f partiles frm the brader size range f partiles entering the lassifying regin The Transfer Funtin Knutsn and Whitby [1] develped a thery fr the lassifier based n integrating the partile trajetry equatins. The majr result f their thery is an equatin fr the transfer funfin, H, whih is defined as the prbability an aersl partile that enters the analyzer will leave via the sampling flw given that the partile has a mbility Zp. A brief summary f their analysis is presented belw. Let r and z dente the radial and axial rdinates, respetively, within the mbility analyzer with z inreasing in the diretin f the main airflw. Let Ur{r;!:) and Ui(r/) be the radial and axial mpnents f the airflw velity. Similarly, let Er{rfi) and Ez(r,z) be the mpnents f the eletri field. Negleting partile inertia and Brwnian mtin, ne btains the fllwing tw first rder differential equatins fr the partile path: dr/df = Mr + ZpEr, dz/dt = «z + ZpEz. (2) (3) T demnstrate the njugate nature f the flw field and the eletri field, Knutsn and Whitby transfrmed t new rdinates, i /, the stream funtin, and <f), the eletri flux funtin.» ;(r,z) = <}>(r,z) = r r [ntrdz nizdr], [rerdz-rezdr]. (4) (5) They then demnstrate that the ttal differential f i j-t-zp4) is zer leading t the fllwing signifiant result: (J; = Zp(j) +nstant. (6) Quting Knutsn and Whitby [1] "The partile mves in suh a way that the rati f the number f streamlines rssed t the number f eletri field lines rssed is always equal t the partile eletri mbility, Zp." The advantage f this methd f analysis is that the stream funtin is lsely related t the vlumetri flw rate, whih is an experimentally ntrlled variable. Representative streamlines are indiated in figure 4 and the rrespnding flw variable is indiated belw: 2'ir(»]/2-v 'i) = aersl inlet vlume flw rate, ga 2T7(\\I4-\^2) = inlet sheath air vlume flw rate, Q^ 2'ir(i»4 - ips) = mndisperse aersl vlumetri flw rate, Qs 2ir(v i3 t /i) = utlet exess air vlume flw rate, 2m. With the initial nditin i ; =»]<! at <}> = 4)in, eq (6) fr the partile path bemes:»!/ = l(fm-zp((l)-^i ). (7) At < ) = (j)ut,» j has the value ^', given by: il/' = il;i -ZpA(j), (8) 152

7 1 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy where Atf) = <i)ut <!>«. The eletri field is vanishingly small in the aersl entrane and at the exit slip s that ( ) is a nstant j)in thrughut the entrane and 4>ut thrughut the exit slit. The transfer funtin, fl, is the prbability that the partile will leave via the sampling slit, whih an happen nly if l f3<tff'<l}(4. (9) Aersl Entrane a H Z 3 LU CO z < IT H MIN(1,Q3/QJ / \ 1 \ Q+ Qm s- Qal 2lt -Zp.Ad) ^ Oa + Qs ^ r^ 2r STREAMLINES PARTICLE PATHS Figure 5. The mbility analyzer transfer funtin. The dashed urve rrespnds t!2s = 2a. Fr unequal flw rate, the transfer funtin has a trapezidal shape. The rigin f the tp f the trapezid an be understd intuitively frm the fllwing example. Suppse the inlet aersl flw is less than the mndisperse sampling flw. Then there will be a range f vltages fr the enter rd fr whih all the inlet aersl with mbility Zp will be sampled by the mndisperse utlet. This implies that the transfer funtin is unity fr a range f vltages thus leading t a flat tp rather than a triangular shaped peak. The atual measurements f mbility are made versus the vltage setting f the enter rd. The relatinship between Af) and the vltage F an be btained using eq (5) and the expressin fr the radial and axial mpnents f the eletri field: Figure 4. Shemati representatin f mbility analyzer streamlines and partile paths. The prbabiuty, il, is therefre equal t the fratin f the interval (\\ii ZpA^,»!i2 ZpA( )) whih is interepted by the interval (i ;3,i f4). The results f arrying ut suh an analysis, whih is tedius but straightfrward, are presented in figure 5. There are several imprtant features f the transfer funtin apparent frm figure 5. If the aersl inlet flw and the mndisperse sampling flw are equal, Q^ = Q,, the transfer funtin has a triangular shape with a sharp peak rrespnding t a prbability ft f 1. This is the best nditin fr btaining aurate partile size.,=0,, = F/[rln(r2/A)]. (10) Perfrming the integratin yield the fllwing result: A(t) = KL/ln(/-2/ri), (11) The three features f figure 5 f greatest imprtane t the measurement f partile size are the entrid f the transfer funtin, and the upper and lwer widths f the transfer funtin. Expressing the results in terms f the mbility, Zp, Knutsn and Whitby [1] btained the fllwing expressin fr the entrid f the mbility band. 2p=ft?#inf'-^'-0. 4ITVL (12) 153

8 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy The range f the eletrial mbility, AZp, f partiles exiting thrugh the slit is given as: ^,=^%^^n(r^n)- I-XTVL (13) The range in AZp rrespnding t the upper prtin f the trapezld in figure 5, whih we dente as AZp* is given by ^^*=Sri^i"^^^'-')' where (14) Zp = partile eletrial mbility AZp = eletrial mbility width at base AZp* = eletrial mbilitywidth f plateau regin V = vltage n the enter rd L = length frm aersl inlet t exit slit r2 = radius f the uter ylinder (inside surfae) n = radius f the enter rd. Several assumptins were made in the develpment f these equatins. The flw field is assumed t be laminar, axisymmetri, and inmpressible; the eletri field is assumed unifrm, negleting field distrtins at the aersl entrane and the sampling exit slit; partile inertia and Brwnian mtin are negleted; and the influene f spae and image harges are assumed negligible Measurement f the Eletrial Mbility Distributin By varying the vltage n the inner rd f the lassifier, and measuring the nentratin f the aersl exiting thrugh the mndisperse aersl utlet, the distributin f the inlet aersl's eletrial mbility an be measured. The reslutin f this measurement an be ntrlled, as seen in eqs (12) and (13), by dereasing the rati f aersl flw rate t sheath flw rate. Using eq (1), the eletrial mbility distributin an be nverted t the size distributin f the inlet aersl. The lassifier is instrumented with an adjustable vltage pwer supply and three mass flwmeters whih ntrl the sheath air, exess air, and mndisperse aersl flw rates. The flwmeters perate by measuring the urrent needed t maintain a nstant-temperature ht-wire element in the air flw and are sensitive t the mass f air passing the sensing element. The alibratin f a mass-sensing flwmeter an take the frm f either an atual mass flw rate urve ([grams f air]/send vs meter vltage) r a vlumetri flw rate urve ([liters f air]/send at T,P vs meter vltage) where T and F are the air temperature and pressure during alibratin. As seen in eqs (12) and (13), measurements made with the lassifier depend n vlumetri flw rates. Sine the lassifier measures the flw rates using mass-sensing flwmeters, a rretin must be made if the temperature and pressure f the air in the lassifier differ frm the temperature and pressure f the air used fr the flwmeter alibratin. If the flwmeters are alibrated using dry air, the rretin t the alibratin fr dry air an be btained frm the ideal gas equatin, and is as fllws: Qval Qal ' atual I al -/"^atual (15) where Qv\ = vlumetri flw rate Qai = alibrated vlumetri flw rate at Tai./'ai Teal = alibratin temperature Peal = alibratin pressure Tatual = atual temperature inside lassifier Patuai = atual pressure inside lassifier. The rretin t the flwmeter alibratin fr wet air is slightly different, and is desribed in setin During peratin f the lassifier, the pressure, temperature and relative humidity f the air inside the lassifier were measured, and the vlumetri flw rate was alulated using eq (15). The temperature and relative humidity f the air inside the lassifier were fund by measuring the nditins f the air passing thrugh the exess air line. The temperature was measured using a platinum resistane thermmeter, and the relative humidity was measured using a hilled-mirrr humidity analyzer. The pressure inside the lassifier was abut 3.5xlCP Pa (36 m H2O) abve ambient fr 333 mvs (20 L/min) sheath air flw. T minimize the gage pressure in the lassifier, the exess air and mndisperse aersl valves were left fully pen, and flws were adjusted with the exess mndisperse aersl valve (see fig. 3). The elevated pressure inside the lassifier is required t exhaust the sheath flw thrugh the flw straightening header at the bttm f the lassifying regin. The pressure inside the lassifier is mnitred by measuring the pressure in the mndisperse aersl utlet line, and applying a slight rretin, 150 Pa (1.5 m H2O) fr a 33.3 mvs (2 IVmin) aersl flw, t aunt fr the pressure drp frm the interir f the lassifier t the pressure tap n the mndisperse utlet. 154

9 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy 2.3 The Cndensatin Nuleus Cunter Figure 6 shws a shemati diagram f the ndensatin nuleus unter (CNC) (TSI, In., Mdel 3020). The instrument samples aersl at a flw rate f 5 mvs and indiates the number nentratin f the aersl. The unting effiieny is nearly 100% fr partiles frm abut 0.02 t at least 0.1 [itn [13]. The aersl entering the unter passes thrugh a hamber ntaining nearly saturated butyl alhl vapr. The aersl-alhl vapr mbture is then passed thrugh a led ndensing tube ausing the alhl vapr t ndense nt the partiles. The ndensing alhl auses the partiles t grw t a size easily deteted with an ptial unter at the exit f the ndensing tube. In the ptial partile unter, the partiles pass thrugh a fused light beam and satter light nt a phtdetetr. In the single partile unting mde, used fr lwer partile nentratins, unting f individual pulses frm the phtdetetr prvides partile nentratin. In the nentratin mde, used fr high partile nentratins, the analg level f the phtdetetr is alibrated t prvide partile nentratin. In general, sine the single partile unting mde des nt require alibratin, its nentratin measurements are Partile Cunting Regin Aersl Inleti Saturatr Tube (35*0) Butyl Alhl Pl Figure 6, Cndensatin nuleus unter. 155

10 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy nsidered mre aurate. Fr sizing PSL spheres, the nentratin was kept lw enugh t use the single partile unting mde. The PSL partile nentratins dwnstream f the lassifier were maintained by adjusting the nentratin f the PSL suspensin used in the atmizer. 3. Experimental Methds and Results Fllwing a general desriptin f PSL partile sizing with the lassifier, the measurement methds fr defining the auray f partile size measurements by the eletrial mbility lassifier are presented. This setin inludes a detailed unertainty analysis f the lassifier perfrmane and an analysis f the effet f nn-vlatile impurities n the PSL sphere size as an aersl. 3.1 Predure fr Sizing Partiles with the Eletrstati Classifier Sizing the PSL spheres with the eletrstati lassifier is a relatively fast press. A suspensin f partiles is prepared, the PSL-partile aersl is generated, the lassifier is used t measure the vltage rrespnding t the mean eletrial mbility f the PSL spheres, and a straight frward data redutin press prvides a measurement f the mean partile diameter. Frm start t finish, the sizing press takes abut 15 min. The liquid suspensin f PSL spheres was prepared by diluting a nentrated suspensin with deinized-filtered water. The nentrated suspensin f the 0.1 xm PSL spheres nsisted f abut 10% by weight PSL spheres suspended in water. The Standard Referene Material partiles, 0.3 and 0.9 xm, were supplied in a suspensin f 0.5% by weight PSL spheres in water. The nminal dilutins and partile nentratins f the PSL suspensins used in the atmizer are as fllws: Partile diameter Drps f nentrated dilutin nentratin PSL suspensin vlume #/ml Q.l\im 3 f 10% by weight 250 ml 6x10"" 0.3 M.m 3 f 0.5% by weight 25 ml 2x10' 0.9 n,m 10 f 0.5% by weight 25 ml 2x10" While the 0.3 jtm and 0.9 (xm partile nentratins in the liquid suspensin were lwer than the 0.1 jxm partile nentratin, the mndisperse aersl nentratins were similar. The lwer liquid nentratins f the 0.3 jj-m and 0.9 p-m partiles is ffset by atmizing the suspensins withut the impatr. The atmizer prdues mre partile-arrying drplets withut the impatr. Fllwing a warm-up perid t allw the lassifier flwmeters t stabilize, the aersl was generated and passed thrugh the lassifier. During nrmal perafin, the sheath and exess air flw rates were kept equal, resulting in equal plydisperse and mndisperse aersl flw rates. T minimize the internal pressure f the lassifier, the exess air and mndisperse aersl valves were perated in a fully pen psitin. The sheath air flw rate was set by iterating with the tw valves upstream f the sheath air inlet, shwn in figure 1, until the pressure between the valves was abut 1.60x10'' Pa (160 m water) while maintaining the desired flw rate. The pressure upstream f the sheath air inlet was maintained at 1.60 x 10'' Pa t math the nditins existing during flwmeter alibratin. The exess plydisperse aersl valve and the exess mndisperse aersl valve were iteratively adjusted t prvide the rret exess air and mndisperse aersl flw rates. The flw rates used fr sizing the 0.1 ijim partiles were nminally 333 mvs (20 L/min) sheath air flws, and 33.3 mvs (2 L/min) aersl flws. Fr sizing the 0.3 i,m partiles, the flw rates were nminally 167 mvs (10 L/min) sheath flws, and 16.7 mvs (1 L/min) aersl flws. The 0.9 xm partiles were sized using nminally 50 m7s (3 L/min) sheath, and 5 mvs (0.3 L/min) aersl flw rates. Other flw rates were used t investigate the effet f flw rate n size measurements. One the flw rates in the lassifier were established, the enter rd vltage was varied t find the peak in the mbility distributin as measured by the ndensatin nuleus unter. The nentratin was then mnitred fr several minutes t insure a nstant aersl nentratin. The flutuatins in the partile nentratin were nsistent with a Pissn distributin f number nentratin; that is, the effiient f variatin, CV, defined as the rati f the standard deviatin in the number nentrafin t the average number nentratin, was in agreement with the predited CV fr a Pissn distributin. CV = \^ where CV = effiient f variatin fr a Pissn distributin N = average aersl number nentratin. 156

11 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy The nentratin rerded fr a given vltage setting was btained by mnitring several nseutive nentratin readings (ne reading every 3 s) and then estimating the average nentratin. When the nentratin flutuatins were bviusly larger than statistially predited, the measurement was disarded and effrts were made t stabilize the nentratin. Gradual nentratin hanges ver the urse f measuring the mbility distributin resulted in slight sizing unertainties and are inluded in the estimate f partile diameter measurement unertainty. After the aersl nentratin stabilized, the vltage n the enter rd f the lassifier was adjusted symmetrially abut the peak nentratin vltage. The nentratin was rerded fr eah vltage setting. A typial nentratin-vltage urve is shwn in figure 7. The quantity f primary interest in this study is the peak vltage whih is the vltage rrespnding t the peak in the nentratin-vltage urve. The peak vltage is mputed as the nentratin weighted average as fllws: neessary t iterate with eq (12) t determine the diameter. A simple iteratin rutine is used fr this purpse. The alulatin f partile diameter frm eqs (1) and (12), requires aurate values fr the vissity f air, p,, and the partile slip rretin, C The slip rretin used in the diameter alulatins is based n Allen and Raabe's [14] measurements fr PSL spheres using an imprved Millikan apparatus: C = l-f-i&i[l.l42-l-0.558expf ^^)1 (17) where C = partile slip rretin Kn = Knudsen number 2X Kn = jr-, where Dp is the partile diameter \ = mean free path f air. t^av where Fave = peak vltage Vi = measurement vltages Ni = nentratin rrespnding t K. (16) One the representative vltage f the peak is fund, the partile diameter an be alulated using eqs (1) and (12). Sine the partile slip rretin is dependent n partile diameter, it is Pressure and temperature rretins were made t the mean free path (\) [15]: where X = T = P = T = P = -^mi 110.4> 1+ T ; (18) xm, fr air at T, P referene temperature, K referene pressure, 1.01 x 10^ Pa (760 mm Hg) air temperature; Kelvin air pressure inside the lassifier. The effiient f vissity f air was alulated as [15]: Center Rd Vltage, vlts Figure 7. Number nentratin vs enter rd vltage fr 0.1 (im PSL splieres. ( T \'-^/ \,,, ^^ - ^'^"'^l 296l5 j I r } (^^) where X23-= X10-"/'. 157

12 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy 3.2 Verifiatin f Crret Classifier Perfrmane T ensure rret peratin f the eletrstati lassifier, alibratins were perfrmed and perfrmane tests were nduted. The vltage and flw meters were alibrated, the effet f humidity n vlumetri flw rate was measured, the transfer funtin f the lassifier was measured and mpared t the theretially predited transfer funtin. A sensitivity analysis was perfrmed t verify the theretial relatinships desribing the lassifier's dependene n the perating pressure and the flw rate. The repeatability f size measurements was heked and the lassifier measurements were tested with Standard Referene Material partiles Calibratin f the Flwmeters and Vltage Meter Vltage Meter Calibratin The enter rd vltage meter was alibrated with a preisin vltage meter apable f reading vltages up t 10,000 V. The auray f the alibrating meter is estimated as ±0.2%. The alibratin was amplished by nneting the alibrating vltage meter t the lead frm the pwer supply. The enter rd vltage meter was alibrated frm 1000 t 9,000 V. The alibratin indiated that the enter rd vltage meter was indiating vltages higher than were atually present by abut 2% at 4,000 and 3% at 9,000 V. Fr sizing 0.1 nm partiles using 333 mvs sheath air, a 2% errr in vltage at the nminal vltage peak f 3,800 V rrespnds t a 1% errr in partile diameter. Fr sizing 0.3 jim partiles using sheath air at abut 167 mvs, a 3% errr in vltage at a nminal vltage peak f 8,000 V rrespnds t a 2% errr in diameter. Flwmeter Calibratin Calibratins f the mass flwmeters used t ntrl sheath air flw, exess air flw, and mndisperse air flw were perfrmed t imprve the auray f the size measurement. The alibratins were perfrmed at the NIST flw alibratin faility using the "pistn prver" apparatus, maintained as the primary standard fr alibratin f gas flw meters. The apparatus nsists f a vlume displaement devie inrprating a merurysealed pistn inside f a glass ylinder. Fr alibratin f a flw meter, dry gas is passed thrugh the meter and int the alibratin ylinder. The pistn is displaed thrugh an aurately defined vlume in an aurately measured time. A bypass valve allws re-ruting f the gas stream s the pistn may be returned t its riginal nfiguratin between eah alibratin run. Measurements f temperature and pressure are rerded s that the mass flw rate an be determined. In rder t eliminate hanges in the flwfield experiened by the flwmeters, the alibratins were nduted withut remving the flwmeters frm the lassifier. The nfiguratin f the lassifier allwed simultaneus alibratin f either the sheath air meter and the exess air meter, r the sheath air meter and the mndisperse aersl meter. T alibrate the sheath air meter and the exess air meter, the mndisperse aersl utlet valve was lsed and the plydisperse aersl inlet was plugged. T alibrate the sheath air meter and the mndisperse aersl meter, the plydisperse aersl inlet was left plugged, the exess air valve was lsed, and the mndisperse aersl valve was left fully pen. The alibratins were perfrmed with the lassifier valves in their nrmal nfiguratin (exess air and mndisperse aersl valves fully pen). The valve n the sheath air inlet was adjusted t prvide an upstream air pressure f abut 1.60x10''Pa, and this pressure was maintained during nrmal peratin f the lassifier. During alibratin, the flw rate was apprximately seleted using the manufaturer's riginal alibratin. The meter readings were rerded, and the flw rate was measured using the "pistnprver" alibratin apparatus desribed abve. The flw rates hsen fr alibratin f the flwmeters were nminally 333, 167, and 50 mvs fr the sheath air and exess air flw rates. These flw rates were hsen t maximize the flw auray fr sizing 0.1 jjim, 0.3 ^i-m SRM, and 0.9 \im SRM partiles, respetively. Fr the mndisperse aersl flw meter, the alibratin flw rates ranged frm 33.3 t 4.2 mvs. The flw meters were alibrated at additinal flw rates in the viinity f the nminal values listed abve. Eah alibratin pint was repeated five times n tw nseutive days, and a partial alibratin was nduted 1 week later t hek fr meter drift. The auray whih is nrmally quted by the NIST alibratin faility is n the rder f ±0.25%, with 99% nfidene. As will be disussed later, the estimate f unertainty in the flwmeters used during peratin f the lassifier is nservatively estimated t be ±1% due t additinal unertainties in the meter setting and 158

13 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy the temperature and pressure whih are used t nvert the mass flw rate t the vlumetri flw rate [eq (15)]. The alibratin nduted a week after the initial alibratin did nt indiate a signifiant drift fr the higher flw rate alibratins (maximum shifts fr sheath and exess air: 0.05% at 33.3 mvs 0.14% at 167 m^/s, and.01% at 333 m7s). Drift assiated with the mndisperse aersl meter using lwer flw rates was slightly higher, with the maximum shift between the three alibratin days f abut 0.5% fr flw rate settings f nminally 33.3, 16.7, and 4.2 m'/s. The manufaturer's alibratin fr the sheath air meter indiated lwer flw rates by abut 5% at nminally 333 mvs and 3% at nminally 167 mvs mpared t the NIST flw rate alibratin. The manufaturer's alibratin fr the exess air meter was fund t be 8% lwer at nminally 333 mvs and 7% lwer at nminally 167 m7s. Fr sizing 0.1 \im partiles, an errr in the sheath air f 5% at 333 mvs rrespnds t a diameter errr f abut 3%. It shuld be nted that althugh the eletrstati lassifier was nt used until initiatin f this prjet in 1988, the alibratin is dated 7/83. Als, the larger unertainties seen in the exess air meter may be due t the unertainty in the meter setting aused by a signifiant amunt f rapid flutuatin in the meter reading Effet f Humidity n the Vlumetri Flw Rate Sine the mleular weight f a water mleule is less than the mleular weight f air, fr a given mass flw rate, the equivalent vlumetri flw rate f wet air shuld be higher than the vlumetri flw rate f dry air. Water vapr, prdued by the atmizer, leads t high humidities f the air exiting the atmizer. While the drying tube and dilutin f the atmizer aersl with dry air redues the humidity f aersl entering the lassifier, the resulting air humidity is still higher than the humidity f the air used during flwmeter alibratin. The air used fr sheath air is sent thrugh a diffusin dryer prviding relative humidities n the rder f 5%. The relative humidity f the aersl at the lassifier inlet an be high if lw dilutin air is used. The flw rate frm the atmizer withut dilutin is 83.3 m^s, and a typial dilutin air flw is abut 80 mvs. When the atmizer was used with the impatr, the relative humidity f the aersl at the inlet t the lassifier was measured t be arund 25% and abut 7% at the exess air utlet. Fr wet air, the vlumetri flw rate rretin made t the flwmeter alibratin is slightly different frm the rretin made fr dry air. Assuming flwmeter alibratins are nduted with dry air, the vlumetri flw rate rretin fr wet air, derived based n ideal gas nsideratins, is as fllws [mpare t eq (15)]: Gvi =Q, al ' atual leal al i'air+al20 Mair (20) <2vi = vlumetri flw rate f wet air Qai = alibrated vlumetri flw rate at TaiJ'eai Pair = partial pressure f air PHTP - partial pressure f water vapr MH20 = mleular weight f water Mair = mleular weight f air. The effet f relative humidity n vlumetri flw rate predited by eq (20) is summarized belw: R.H. (%) Gvi with R.H. rretin gvi n R.H. rretin (0.1%) (0.2%) (0.6%) (0.9%) (1.2%) Typial relative humidities f the exess air measured when sizing 0.1 nm partiles were 5-15%. The relative humidities existing when sizing the 0.3 and 0.9 \im SRM partiles were higher (when the atmizer is used withut the impatr, mre water vapr is prdued). The humidities were nt measured in these ases; hwever, an upperbund humidity f 25% is estimated based n 100% humidity f the inlet aersl and a fatr f 10 dilutin by the dry sheath air. Partile diameter measurements made withut rreting the flw rate fr relative humidity will result in an inrease in the measured diameter by a magnitude apprximately half the flw vlume ratis shwn abve. The effet f humidity n the vlumetri flw rate was experimentally investigated using a gas-test meter. Maintaining a given vltage n the mass flwmeter, the vlumetri flw rates were measured with different air humidities. It was fund that hanging the humidity frm 5% t 60% fr fixed mass flw rate inreased the vlumetri flw rate by less than 0.5%, whih was at the reslutin limit f the flw measurement. This finding is nsistent with eq (20), but the measurement reslutin is inadequate t prvide a quantitative test f the 159

14 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy equatin. In any event fr the 0.1 (xm PSL spheres with a humidity f 5-15%, the predited humidity rretin t the vlumetri flw rate is less than 0.2% Testing the Transfer Funtin T determine whether the lassifier is perating rretly, its perfrmane an be judged by mparing the theretial and experimental utput f the lassifier when lassifying a mndisperse aersl. Figure 8a shws a plt f nentratin vs enter rd vltage fr i,m PSL under the nditin f equal aersl flw rates. Als shwn n the urve is the theretial vltage-nentratin urve pltted abut the peak nentratin vltage. whih was btained frm figure 5 and eq (11) with (2 = 2m=167 m7s and Q^ = Qs = n m^/s. While Figure 8a indiates apprximately rret behavir, the slight unertainty in the peak nentratin auses unertainty in the plaement f the theretial transfer funtin. This unertainty is the result f the runding effet at the peak aused by slightly unequal aersl flw rates. A better mparisn is btained if the aersl flw rates are nt equal. The flw rate f the aersl entering the lassifier was redued by a fatr f tw, <2a = 8.5 mvs, while the sheath flw was inreased by 8.5 m^/s s g=175 mvs (fig. 8b). The data in figure 8b allws definite plaement f the theretial 4-* (0 k. 0) 1- a> S3 E 3 (1> _> Center Rd Vltage, vlts Figure 8a. Cmparisn f experimental and theretial respnse f the lassifier fr p.m partiles using equal aersl flw rates. -» n«e ^ in O a> L. 4-1 a> i- ^ C3 E Q. 3 Z r Center Rd Vltage, vlts Figure 8b. Cmparisn f experimental and theretial respnse f the lassifier fr ij,m partiles using different aersl flw rates. 160

15 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy transfer funtin and indiates rret lassifier utput. Slight differenes between the theretial transfer funtin and the experimental transfer funtin are due in part t the fat that the PSL is nt perfetly mndisperse. A send methd t hek fr rret perfrmane f the lassifier was develped by Rader and MMurry [9] and invlves the use f tw lassifiers in series. Suh a nfiguratin is alled a TDMA (Tandem Differential Mbility Analyzer). In this methd, a plydisperse aersl is sent thrugh the first lassifier t prdue a test aersl fr the send lassifier. The vltage n the first lassifier is held nstant while the vltage n the send lassifier is varied t trae the distributin f the test aersl. The nentratin-vltage data f the send lassifier is then mpared t the TDMA thery using a mputer algrithm whih estimates the rati f sheath t aersl flw rates by fitting the theretial relatinships t the vltage-nentratin data. Agreement between the atual flw rati and the fitted flw rati is an indiatin that the lassifiers are perating rretly. This methd was used t test the perfrmane f the NIST lassifier using a send lassifier f the same type and mdel t mplete the TDMA system. The send lassifier was prvided by the University f Minnesta Partile Tehnlgy Lab, The results f the TDMA test indiated the lassifier was perating rretly. (Fr a sheath t aersl flw rati f 10.0, the algrithm indiated a rati f 9.8 with the NIST lassifier used as the send lassifier in the TDMA system, and a rati f 10.0 with the NIST lassifier used as the first lassifier in the TDMA system.) A third test f the lassifier's perfrmane is t mpare the experimental peak nentratin at the utput f the send lassifier (Mut) t the nentratin at the input t the send lassifier (Nin). Frm the triangular shape f the inlet mbility distributin funtin (see fig. 5) and frm a similar triangular shape fr the sampling effiieny f the send lassifier, Kusaka et al. [7] derived the fllwing relatinship between Nzut and Nia fr the ase where the vltage f the send DMA is set equal t the first: N201U = (rwin. (theretial) ^^' (21) The fllwing experimental results indiate again that the lassifier perfrms as predited: N Ny /Vzut (theretial) r (!)« A^2li Nzut (theretial) The 7% t 8% differene between the atual and theretial dwnstream nentratins is due t partile wall lsses within the send DMA and t slight differenes between the atual and theretial transfer funtins Sensitivity Analysis T investigate the equatins gverning the size measurement f the PSL spheres, the perating nditins f the lassifier were varied slightly and then the PSL spheres were sized. If the equatins gverning partile size measurement are rret, the measured partile diameter shuld remain the same regardless f whih perating nditins are used. The experimental methd was straightfrward. The variables whih lend themselves t variatin are flw rate and perating pressure. The flw rate affets the relatinship between the enter rd vltage and the partile eletrial mbility [eq (12)], and the pressure effets the vlumetri flw rate [eq (15)] and the partile slip rretin [eq (17)] thrugh its effet n the mean-free path f air [eq (18)]. The measurement nsisted f first sizing 0.1 xm PSL using nminally 333 mvs sheath flw and exess flw rates, and a nrmal perating pressure f apprximately 3.5 x 10^ Pa abve ambient. The partile diameter measured with these perating nditins was mpared t the diameter measured when the flw rate r pressure were hanged. Equivalently, the gverning equatins an be used t predit the hange in the peak vltage whih shuld result when a different flw rate r pressure is used fr the measurement. The predited peak vltage an be mpared t the experimentally measured peak vltage. Operating Pressure Variatin The measurement using different perating pressures was dne by restriting the exess air valve s that the pressure inside the lassifier inreased frm the nrmal perating pressure f 3.5 xlo' Pa abve ambient t abut 1.27x10'* Pa abve ambient. The inrease in pressure results in a derease in the vlumetri flw rates [eq (15)], and a derease in the partile slip rretin fatr [eq (17)]. The gverning equatins [eqs (1) and (12) 161

16 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy tgether with the expressin fr the shp rretin] predit that the inrease in pressure shuld result in a derease in the peak vltage f abut 3%, whih was within 0.2% f the measured derease in the peak vltage, 3780 t 3685 V. The partile size measured with a pressure f 1.27 x 10* Pa was within 0.1% f the size measured using the nrmal pressure f 3.5 x 10^ Pa. The agreement between the tw measurements f partile diameter and the agreement between the predited and measured hange in the peak vltage indiate that the pressure variable is inrprated rretly int the gverning equatins f the partile measurement. Sheath Flw Variatin The sheath flw rate was dereased frm 333 t 300 m^s while keeping the exess air flw rate at 333 mvs. T maintain a flw balane, the plydisperse aersl flw rate was perated at 66 mvs, while the mndisperse aersl flw rate was perated at 33 m^s. In this ase, the gverning equatins predit a derease in the peak vltage f abut 6% whih was within 0.6% f the measured hange in peak vltage, 4240 t 4000 V. The differene between the partile size measured using the nrmal perating nditins and the varied-flw rate nditins was less than 0.3%. This differene is prbably aused by a dependene f measured partile diameter n the aersl flw rate, whih is disussed belw. Aersl Flw Variatin Partile sizing was als nduted using different aersl flw rates. In this ase, the thery predits a hange in the mbility width f the mndisperse aersl utlet partiles [eq (13)], but des nt predit a hange in the mean eletrial mbility r measured partile diameter. A high aersl flw rate rrespnds t a wide eletrial mbility range f the partiles sampled thrugh the slit in the enter rd. A lw aersl flw rate rrespnds t a narrw eletrial mbility range f the mndisperse aersl utlet partiles. T study the effet f the aersl flw rate n partile size, the sheath flw and exess flw rates were kept nstant and equal while the tw aersl flw rates were varied in tandem. Figures 9 and 10 shw the effet f aersl flw rate n the vltagenentratin urve fr p-m and 0.1 xm PSL spheres. The sheath flw and exess flw rates were 167 mvs fr the xm partiles and 333 mvs fr the 0.1 [xm partiles. Figures 9 and 10 shw the distributin pltted with bth atual nentratin and nrmalized nentratin. Pltting nrmalized nentratin allws diret mparisn f the peak vltage. Fr the 0.1 ixm distributin, the partile diameter inreases abut 1% as the aersl flw rate was dereased frm 33.3 t 5.0 mvs. The vltage peak was determined by averaging the nentratin-vltage data, using eq (16), fr nentratins greater than 0.6 A''max. Fr the xm PSL spheres, an inrease in diameter f abut 1% was als fund fr dereasing aersl flw rates. The reasn fr this inrease in partile size is nt presently knwn. The slight sizing dependene n aersl flw rate is negligible fr typial appliatins f the eletrstati lassifier. This effet apparently has nt been reprted in the literature. Fr this wrk, the inrease in measured diameter fr dereasing aersl flw rates is inluded as an unertainty in the measured diameter Sizing Repeatability The 0.1 j,m PSL size measurement was repeated eight times n ne day and six times abut a week later. The 14 measurements are shwn in table 1. The sheath flw and exess flw rates used fr these measurements were 340 and 330 mvs fr the first and send days, respetively, while aersl flw rates were nminally 33 mvs. The effiient f variatin (CV) f the 14 measurements is 0.2%. The size measurements fr runs 1-3 n day 1 are thught t have been affeted by a gradually hanging inlet nentratin. If runs 1-3 n day 1 are disarded, the CFf the measurements is 0.1% Measurement f Standard Referene Material Partiles As a test f the sizing auray f the lassifier. Standard Referene Material partiles ( NIST SRM 1691 at 0.269±.007 [im, and NIST SRM 1690 at 0.895±.008 p.m) were sized. The resulting size measurements are shwn in table 2. The measurements were made immediately fllwing the flwmeter alibratin and inlude the vltage alibratin. The xm SRM partiles were measured using sheath flw and exess flw rates f 167 mvs and aersl flw rates f 17 mvs. The ^,m SRM partiles were measured using sheath flw and exess flw rates f 41.7 mvs and aersl flw rates f nminally 5 mvs. The (xm SRM partiles, measured fr the SRM reprt using eletrn mirspy, were measured with the lassifier t have a mean diameter f xm, whih is 1.6% larger than the SRM reprted diameter. The unertainty in the diameter f the (i,m partiles is 2.6%. The [im SRM partiles, measured fr the SRM reprt using a light sattering tehnique, were measured with the lassifier t have a mean diameter f j,m, whih is 1.7% larger than the SRM reprted diameter. The unertainty in the diameter f the jim partiles is ±0.9%. 162

17 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy 400 Legend Aersl Symbl Flwrale 2.5 L/min 1.0 Umin O.S L/min Center Rd Vltage, vlts Figure 9a. Vltage vs experimental nentratin fr (i.m partiles fr three different aersl flw rates. CO <u u 1- Q E z > Center Rd Vltage, vlts Legend Aersl Symbl Flwrate 2.5 L/mIn 1.0 L/min 0.5 L/min Figure 9b. Vltage vs relative nentratin fr 0,269 ^.m partiles fr three different aersl flw rates. While bth measurements are larger than the SRM reprted diameters by a similar perentage, the measurement f the (jm partiles lies within the unertainty quted fr the SRM measurement, but the measurement f the xm SRM partiles is utside f the errr band quted fr the SRM measurement. It shuld be nted that the measurement f the [im SRM partiles was nduted using signifiantly different flw nditins (41.7 mvs) than thse used fr the 0.1 and jim SRM partiles (333 and 167 mvs sheath flws, respetively). The xm partile measurement an be repeated using higher sheath flws by measuring multiply harged partiles. This methd is desribed belw in setin

18 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy 40Q Legend Aersl Symbl Flwrate 2.0 L/mJn 1.0 Umin 0.3 Umin Center Rd Vltage, vlts 4600 Figure 10a. Vltage vs experimental nentratin fr 0,1 jim partiles fr three different aersl flw rates. CO 1- ^-» 0) O i 0) Legend Aersl Symbl Flwrate a L/mln 1.0 Umin 0.3 L/mln > ra Center Rd Vltage, vlts 4600 Figure 10b. Vltage vs relative nentratin fr 0.1 (jim partiles fr three different aersl flw rates Calibratin f the Eletrstati ClassiHer Using Standard Referene Material Partiles One pssible explanatin fr the differene between the eletrial mbility results fr partile size and the ertified partile size is an errr in the definitin f the length f the lassifier. Reall that the length dimensin is used in eq (12) t alulate the partile eletrial mbility frm whih the partile size is alulated using eq (1). At present, the length is defined as the distane frm the midpint f the mndisperse aersl exit slit t the midpint f the aersl inlet (see fig. 3). This hie f length 164

19 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy Table 1. Repeatability f 0.1 Fim partile diameter measurements Day 1 (May 27) Day 2 (June 1) Run Measured Run Measured number diameter number diameter )i.m (im D (Am D = im <r -i (jlm (0.2%) O-n-l = M.m (0.1%) Cmbined Analysis D = (j.ra 0>i-l = M.m (0. 2%) Table 2. Summary f measurements f 0.3 and 0.9 (im Standard Referene Material partiles Standard Referene Material (im partiles Measured diameter p,m _ D = ^l.m. _, = (im (0.1%) D" = ± Jim (±2.6%) D -De = tjim(1.6%) Standard Referene Material jim partiles Measured diameter iim _ D = 0,9103 nm a-.j = (JLm (0.3%) O" = ± M.m (±0.9%) 5 - D = (im (1.7%) ' Certified diameter fr NIST Standard Referene Material ' Certified diameter fr NIST Standard Referene Material

20 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy is nsistent with the analysis by Knutsn and Whitby [1] assuming axisymmetri and laminar flw and a unifrm eletri field in the axial diretin. These nditins will be vilated t sme extent at the aersl entrane and exit t the lassifying lumn. These effets might be inrprated in eq (12) as a rreted length f the lassifier. If the length used in the alulatins is taken as 1.9% shrter than the presently defined length, (44.44 m hanged t m), the lassifier measurements f bth SRM partile sizes agree within 0.1% with the SRM reprted diameters. The length dimensin was measured in this study t be m whih is in lse agreement with the m measurement reprted by the manufaturer. While the length an be adjusted s the lassifier indiates the rret size fr bth SRM partile sizes, the required hange in length may be t large t laim that the measurement differenes are due t an errr in the length definitin. Adjusting the length definitin as suggested abve is ne methd f alibrating the eletrstati lassifier fr measurement f the 0.1 xm partiles. A mre rigrus apprah fr alibrating the lassifier, whih is suggested fr future nsideratin, is t measure the and (xm SRM partiles using the same sheath and aersl flw rates as used fr the measurement f 0.1 xm partiles. The alibratin tehnique invlves measuring the eletrial mbility f multiply harged and p-m SRM partiles. Sine a multiply harged partile has a higher eletrial mbility than a singly harged partile, a higher flw rate an be used in the lassifier t measure the mean partile mbility and partile diameter. By measuring the multiply harged SRM partiles with the same flw nditins as the 0.1 jim partiles, a alibratin fatr (suh as hanging the length definitin) an be inluded in the gverning equatins whih fres the SRM partile measurements t be in agreement with the reprted diameters. This methd f alibratin is thught t be mre rigrus sine all the partiles are measured with the same flw nditins. 3.3 Investigating the Effet f Impurities As was disussed in setin 2.1, impurities in the water used t suspend the PSL spheres prdue a layer f residue n the surfae f partiles after the PSL-arrying atmizer drplets evaprate. This residue results in a systemati errr in partile diameter measurements sine it inreases the apparent partile diameter. The impurities in the PSL partile suspensin me frm impurities existing in the water used t dilute the nentrated PSL partile suspensin and frm the impurities in the liquid used in the nentrated PSL partile suspensin. T estimate the thikness f the impurity residue n the PSL sphere, it is neessary t knw the impurity nentratin in the PSL partile suspensin and the diameter f the partile-arrying drplet. Assuming all f the nn-vlatile impurity frms a unifrm residue shell arund the partile, the fllwing relatinship between the thikness f the residue n the partile and the impurity nentratin, partile diameter, and drplet diameter is btained: where /=impurity additin t diameter ( xm) C=vlumetri nentratin f impurities Dd PSL-arrying drplet diameter befre evapratin iy-va) Dp = PSL partile diameter (txm). (22) T estimate the effet f impurities n the partile size, measurements were perfrmed t determine the PSL partile-arrying drplet diameter befre evapratin, the nentratin f impurities in the water used t dilute the PSL partile suspensin, the impurities in the diluted PSL partile suspensin, and the impurity nentratin effet n partile diameter Charaterizing the Atmizer As seen in eq (22), the PSL-arrying drplet diameter strngly influenes the effet f impurities n partile diameter. The drplet distributin was determined by atmizing a slutin ntaining a knwn nentratin f NaCl, and measuring the resulting residue partile size distributin using the lassifier. 166

21 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy The drplet size distributin an then be determined using the simple relatinship between the impurity nentratin, C, residue partile size, Dp, and the drplet size, Da. Dj, = Dd C^""^. (23) The atmizer an be used in tw nfiguratins. First, fr sizing the 0.1 \im partiles, an impatr is used at the utlet f the atmizer t remve large drplets (see fig. 2). Withut the impatr the larger drplets, apable f arrying larger PSL spheres, are allwed t pass thrugh the utlet f the atmizer. Figure 11 shws the number distributin f drplets prdued with and withut the impatr. With the impatr in plae, the mde f the number distributin is arund 0.7 ^.m. Withut the impatr, the mde f the number distributin is arund 0.8 p,m, with signifiantly mre large drplets than exist with the impatr. The effet f the impatr is mre bvius if the drplet distributin is weighted by mass r vlume as shwn in figure 12. lu a> SI E 3 Z O > Dp (la m) Figure 11a. Drplet number distributin with impatr. 1 ^ 1.0 T = 0.8. / *^» O A \ ' E /. \ Relative 9 J r-t- 1 1 r- S^.., Dp (nm) 10 Legend NaCI Symbl Cnentratin 530 ppm 108 ppm 52 ppm Figure lib. Drplet number distributin withut impatr. 167

22 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy 1.2 O '^ 1.0. a O (0 CO CO r 0.6 " S (1) 0.4 r > m DC n. A iist Dp (n m) 10 Figure 12a. Drplet mass distributin with impatr. Symbl Legend NaCI Cnentratin 530 ppm 108 ppm 52 ppm Dp(jim) Figure 12b. Drplet mass distributin withut impatr. Similar measurements f an atmizer's drplet distributin using this tehnique, reprted by Niida et al. [16], suggest that the drplet distributins measured in this wrk are biased tward larger partiles beause f diffusinal lsses f small residue partiles upstream f the lassifier. The measured drplet distributins are nly qualitatively representative f the atual distributins. The drplet distributin f the atmizer suggests that sizing PSL spheres withut the impatr in plae will result in larger PSL partile-arrying drplets, and mre signifiant impurity effets Measuring the Cnentratin f Impurities in the Water Used t Dilute the PSL Partile Suspensin The vlumetri impurity nentratin was measured fr tap water and distilled, deinized water using three methds. The tap water impurity nentratin measurements were nduted fr mparative purpses. Tw mea- surement methds invlved evaprating drplets and measuring the resulting residue partile size. The third methd invlved gravimetri measurements f evapratin residue. Classifying Atmized DI Water In the first methd used t estimate water impurities, the water was atmized withut PSL r ther additives. The atmizer was used withut the impatr s that larger residue partiles were frmed. The drplets frmed frm the atmizatin were dried and the resulting residue partiles were sized using the lassifier. This measurement was dne fr tap water and distilled, deinized (DI) water, and the resulting mass distributins are shwn in figures 13a and 13b alng with the residue partile distributins prdued by atmizing a knwn slutin f NaCl. 168

23 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy +- i.n /ap\ re ^ r I / (U 0.8 u 11 \ \ T I \ \ r f 1 \ 11 R \ O \ Y tf) / / \ en rf / \ \ CO S 0.4 // a> / / \ \ > ^ / \ \ _// \ \ V fv^ou^ \ \ rr -rtsi^^''^ > 0.0 Q 0=^ r 1 r T-i i-t^ Dp{txm) Symbl D Legenf Residue Tap Water % NaCl Figure 13a. Cmparisn f residue partiles fr tap water and 0.010% NaCl. Legend Syinbl Residue 01 Water % NaCl Dp(iim) Figure 13b. Cmparisn f residue partiles fr deinized water and % NaCl. The alulatin f impurity nentratin is amplished by mparing the means f the mass distributins f the water residue and NaCl residue partiles. The DI water residue partiles were mpared t the residue partiles prdued frm a slutin f % NaCl by vlume. The tap water residue partiles were mpared t the residue partiles prdued frm slutin f % NaCl by vlume. The impurity nentratins were alulated frm the fllwing expressin derived frm eq (22): where / -^p NaCl mde \.^ /^ water " itt \ ^ *-'NaCl M^ water mde / (24) Cwatet = vlumetri impurity nentratin in water CNSCI = vlumetri nentratin f NaCl I>pNaamde = mde f the NaCl residue distributin IJp water mde = md f the whtr residue distributin. The result f the impurity measurement fllws frm figures 13a and 13b: Atmizer slutin Residue partile mde ((ira) % NaCl 0.11 Dl-water % NaCl 0.15 Tap water 0.20 Vlumetri impurity nentratin % (52 ppm) % (2 ppm) % (108 ppm) 0.026% (260 ppm) Unertainty ± 1 ppm" ±70 ppm " Unertainties resulting frm estimatin f mde diameter. One prblem with sizing the residue partiles frm the DI water is the lss f partiles dwnstream f the atmizer befre being lassified. T redue eletrstati lsses a Kr-85 biplar harge neutralizer was added at the utlet f the atmizer fr the DI water residue partiles and the % NaCl residue partiles. Evidene f these lsses is apparent frm the bservatin that the number 169

24 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy nentratin f residue partiles fr the % NaCl slutin is abut 30 times greater than the nentratin f the residue partiles prdued frm the DI water. This wuld suggest that the mde f the number distributin f the residue partiles frm the DI water is utside the range f the lassifier. The mde f the mass distributin f the residue partiles appears t be within the range f the lassifier. Classifying Residue Partiles Frm the Vibrating Orifie The send methd used t determine the vlumetri nentratin f the impurity in the water again invlved sizing the residue partiles prdued by evaprating large water drplets f knwn size. In this methd the Vibrating Orifie Mndisperse Aersl Generatr (VOAG) (TSI, In., Mdel 3450) was used t prdue large mndisperse water drplets. The vibrating rifie generatr was perated withut a filter n the liquid pump s that impurities were nt remved frm the slutin being tested. The VOAG was used t prdue 39 iitn drplets f the DI water. The resulting residue partiles were sized with the lassifier. Exept fr a sendary peak rrespnding t dubly-harged partiles, the residue partiles were mndisperse with a size f abut 0.27 ^JLm. Using eq (22), the nentratin f impurities in the water is alulated t be 0.3 ppm. This same methd was used t estimate the level f impurities in nrmal tap water and lab distilled water. Using the lassifier t size the residue partiles fr nrmal distilled water, the impurity nentratin was alulated t be 5 ppm. Fr nrmal tap water, the residual partiles were t large t size using the lassifier. Instead the TSI Mdel 3310 Aerdynami Partile Sizer (APS) was used. The resulting distributin is shwn in figure 14 t have a peak partile aerdynami diameter f abut 2.7 xm. Fr a unit density partile, the aerdynami diameter is equal t the gemetri diameter, and the vlumetri impurity nentratin an be estimated using eq (22) t be 330 ppm. Impurity Measurements using a Gravimetri Methd A third attempt at measuring the vlumetri impurity nentratin f the water was t evaprate a knwn mass f water and measure the resulting impurity mass. This methd did nt wrk fr the distilled water r the DI water beause the impurity mass was t lw. The methd did wrk fr the Oi 0) Si.-.-^^ JL Aerdynami Diameter, ( iim ) 8 10 Figure 14. Tap water residue partiles prdued by the vibrating rifie and measured with the aerdynami partile sizr. tap water and indiated a mass nentratin f abut 220 ppm. The three methds fr measuring the impurity nentratin are qualitatively in agreement. Fr the deinized/filtered water, the methds indiated impurity nentratins n the rder f 1 ppm. The impurity nentratin measurements f the tap water were nduted t mpare the different methds. The measurements made with the VOAG-APS and the gravimetri methd are in qualitative agreement, with best agreement urring if unit density impurity is assumed. Fr unit density impurity, the VOAG-APS indiates 330 ppm vlumetri impurity and the gravimetri methd indiating 220 ppm vlumetri impurity. As stated abve, the tap water impurity was measured by sizing residue partiles frm the atmizer t be abut 260 ppm Estimating the Impurity Cnentratin in the PSL Partile Suspensin In the previus setin, the impurity nentratin in the water used t dilute.the PSL suspensin was measured. The send sure f impurities, the nentrated PSL suspensin, is nsidered belw. The ttal nnvlatile impurity nentratin in the diluted suspensin is estimated in this setin and als the predited effet f the impurity n the partile diameter is mpared with measurements. Calulatin f the Impurity Cnentratin Cnentratins f impurities in the slids mpsing PSL partile suspensins have been reprted t be frm abut 1 t 7% [17]. If the nentrated PSL partile suspensin is nt suffiiently diluted with water, these impurities will have a signifiant 170

25 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy effet n the resulting partile size. Fr the 0.1 (xm partiles, the perentage f slids in the nentrated PSL suspensin was abut 10%. Dilutin f the nentrated suspensin was nrmally abut 1 t 2500 with DI water. Assuming an impurity nentratin in the PSL slids t be 3% (in the middle f the range reprted by Raabe [17]), the resulting PSL partile suspensin, inluding 1 ppm impurity in the dilutin water, will have an impurity nentratin f abut 2.2 ppm. Using eq (22) with a drplet diameter f abut 0.9 ^,m, the resulting residue thikness (in diameter) is abut nm r abut a 0.05% additin t the diameter. The same alulatin fr the \im SRM partiles ntaining 0.5% slids and 50 ppm f biide in the nentrated PSL partile suspensin, (assuming 3% impurities in the PSL slids, a dilutin f 1 t 250, and a larger drplet diameter f 2.5 xm sine sizing urs withut the impatr n the atmizer), indiates that an inrease in diameter f xm r abut 0.06% wuld be expeted. Measurement f the Impurity Cnentratin Measuring the nentratin f impurities in the atual PSL suspensin is diffiult. As disussed in setin 2.1, the aersl prdued by the atmizer nsists f bth PSL spheres and impurity partiles resulting frm evapratin f drplets whih d nt ntain a PSL partile. Measurement f the impurity nentratin in the PSL suspensin was made by lassifying the entire distributin f partiles existing in the PSL partile aersl, and mparing the distributin f impurity partiles t the distributin f partiles prdued by atmizing a slutin with a knwn nentratin f NaCl. In figure 15, the entire distributin f the 0.1 \im PSL aersl is shwn. The sendary peaks in the viinity f the main PSL partile peak are the result f dubly harged singlet partiles and varius multiplet partiles. The distributin f impurity partiles is learly identified. The mde f the impurity partile mass distributin was mpared t the mde f residue partiles prdued frm a % NaCl slutin indiating the impurity nentratin t be abut 6 ppm. This same tehnique was used t estimate the impurity nentratin existing in the SRM partiles using a typial dilutin f the nentrated PSL suspensin by abut 1 t 300 with DI water. The resulting impurity residue partiles were mpared t impurity partiles frm a % NaCl slutin. The measurement indiated an impurity nentratin f abut 52 ppm. This result is signifiantly higher than the estimated nentratin using Raabe's estimates f impurities in the PSL slids. Effet f Impurities n the SRM Partile Measurements A simple methd f determining whether r nt the impurities in the PSL slids are ntributing t measurement errrs is t size the PSL spheres using a very dilute PSL partile suspensin, and mpare the measurement t that resulting frm a very nentrated PSL partile suspensin. If the impurities in the undiluted PSL suspensin are ausing signifiant measurement errrs, the diameter measured using a very dilute suspensin shuld be smaller 1.2 <u n E z > 2 Dp()im) Figure 15. Number nentratins vs partile diameter fr 0.1 p,m PSL partiles and assiated impurity residue partiles. 171

26 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy than the diameter measured using a nentrated suspensin. This measurement was nduted fr the jim SRM partiles. The nentratin f the PSL suspensin was varied by ver a fatr f 15 (frm 3 drps f undiluted PSL in 500 ml f DI water t 10 drps f undiluted PSL in 100 ml f DI water), and n systemati hange in the diameter measurement was ntied. An attempt was als made t size the nm SRM partiles using an impatr n the atmizer in an effrt t redue the effet f impurities in the suspensin. The diameter measured with the impatr was similar t the diameter measured withut the impatr giving strng evidene that impurities are nt influening the measurement. It is nted, hwever, that atmizing the jim partiles with the impatr leads t extremely lw partile nentratins beause mst f the partiles are remved by the impatr. As disussed in setin 3.1, if the nentratin f the PSL spheres in the aersl is t lw, signifiant unertainties result. Based n these tw measurements, it is nluded that impurities inrease the partile diameter fr the p,m SRM by less than 1%. Effet f Impurities n Measurements f the 0.1 xm Partiles T investigate the relatinship between impurity nentratin and partile size, the nminally 0.1 (xm PSL spheres were sized using aqueus NaCl slutins f knwn nentratin. In this measurement, the atmizer was used with the impatr in plae beause withut the impatr the nentratin f NaCl partiles vershadwed the PSL distributin. The partiles were first sized using lean water fr suspensin and then sized using several different NaCl slutins. Figure 16 summarizes the results. One f the data pints used in the figure is the result btained when the PSL is lassified with tap water. Here the impurity nentratin f the tap water was 0.033% as measured by sizing the residue partiles prdued by the Vibrating Orifie Generatr with the Aerdynami Partile Sizer. This data an be used t predit the effetive PSL partile-arrying drplet diameter. The predited inrease in diameter by eq (22) fr a drplet diameter f 0.9 ixm is seen t be in gd agreement with the data in figure 16. This diameter an be used, with an estimate f the impurity nentratin in the PSL suspensin, t alulate the expeted residue thikness added t a partile. Assuming an impurity nentratin in the 0.1 xm partile suspensin f abut 10 ppm as alulated = 0.04 u s a. E 0.01 Equatin 22 Pltted With Dj( = 0.9 urn Inrease in Diameter ( ^m) Figure 16. Impurity nentratin vs inrease in diameter fr 0.1 ^.m partiles in a NaCl slutin. and as measured, eq (22) is used t estimate the impurity residue inrease in diameter t be abut 0.2%. Several data pints taken with NaCl nentratins f abut 900 ppm, indiating thiknesses f abut 0.01 n-m, were nt inluded in Figure 16. This data indiated muh lwer thikness than wuld be expeted pssibly due t lumping f the residue n the surfae f the partile. This data als did nt agree with drplet distributin data btained using lwer NaCl nentratins, pssibly beause the NaCl residue partiles were frming as hllw lumps. A final methd fr estimating the effet f impurities invlved sizing f dilute and nentrated PSL suspensins. Fr PSL nentratins f 3 drps per 1000 ml t 3 drps per 25 ml f DI water, n ntieable size shift urred. This wuld suggest that impurities are nt influening the measured diameter f the 0.1 p-m partiles. If eq (22) is used with the previusly estimated impurity nentratin f 6 ppm, and partile-arrying drplet diameter f 0.9 ]x,m, the resulting inrease in diameter an be estimated t be xm r 0.15%. The unertainty estimate is apprximate and we duble the value given abve s that the verall unertainty frm impurities is xm r 0.3%. The use f an impatr immediately dwnstream f the atmizer further redues the impurity effet by remving the larger drplets. The impatr redues the peak vltage f the mbility distributin f the 0.1 xm partiles by abut 130 V as indiated in figure 17. This rrespnds t abut an j.m (2%) redutin in the partile size. Fr the estimated impurity nentratin f 6 ppm, a drplet 172

27 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy size f 2.2 jiin is estimated using eq (22). Thus it is fund t be very imprtant t use an impatr t minimize the drplet size in additin t using high purity dilutin water ,1 Randm Errr The randm mpnent f the unertainty assiated with the measurement f the average partile size an be btained frm the 14 repeat measurements f the partile size (se ). The average f these 14 measurements and the assiated standard deviatin, a, are and jim, respetively. The randm mpnent f the unertainty, R, is given by Center Rd Vltage, vlts Center Rd Vltage, vlts O withut Impatr With Impatr O withut Impatr a with Impatr Figure 17. Effet f impatr n partile mbility. Estimates f Unertainty in the ClassiHer Perfrmane in the Partile Diameter Measurements lui the previus setin, results were presented regarding the preisin assiated with repeat measurements and unertainties assiated with the quantities appearing in the gverning equatins, eqs (1) and (12), inluding flw rate, vltage, and slip rretin. In this setin, a summary is presented f all the unertainties and an estimate f the verall unertainty is given fr the eletrial mbility lassifier. An verall estimate f the unertainty in measuring the 0.1 \Lm. PSL spheres is btained by mbining the tmertainty assiated with the impurity effet and the unertainty assiated with the use f the lassifier. R =t.i (0.025) <j/(n) 1/2 (25) where n is the number f repeat measurements, 14, and t -i (0.025) is the Student (-value fr n -1 degrees f freedm and fr 95% nfidene level (fi3 (0.025) = 2.16). The value f R is xm, whih rrespnds t a relative errr f 0.1% Unertainty in the Flw Rate The flw rate unertainty reprted in table 3 represents a mbinatin f flw meter alibratin auray, preisin f flw rate seletin, the unertainties in the pressure and temperature rretin t the flwmeter alibratin, and the effet f humidity n the flw alibratin. The preisin f flw rate seletin is estimated t be ±0.4% refleting the stability f the flw rate after it is set, and the preisin f the initial flw rate setting. This value was alulated fr the sheath air meter at nminally 333 mvs by estimating the preisin f flwmeter vltage setting t be ±.002 V fr a vltage setting f V. The unertainty in vltage was nverted t unertainty in flw rate using the alibratin urve. The unertainty in the alibratin, nrmally quted by the NIST flw alibratin faility, is ±0.25% with 99% nfidene. Unertainties in the flw rate prdued by the temperature and pressure rretin, given by eq (15) result frm unertainties in the temperature and pressure. The unertainty in pressure is estimated as ± 3 mm Hg due t unertainties in the barmetri pressure reading, and unertainties in measuring the pressure inside the lassifier. The unertainty in temperature is estimated as ±0.5 C. The resulting unertainty in vlumetri flw rate due t temperature and pressure unertainties is estimated as ± 0.4%. The effet f humidity n the vlumetri flw rate is estimated t be 0.2% in setin The sum f all the flw related unertainties is 1.25% and the sum in quadrature is 0.5%. We use as an verall unertainty in the vlumetri flw rate an intermediate value f ±1.0%. 173

28 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy Table 3. Summary f unertainties" assiated with measurement f partile diameter Resulting Unertainty unertainty Variable in variable in diameter j2 = sheath air flwrate 1.0% 0.6% j2m = exess air flwrate 1.0% 0.6% rj = uter radius 03% 0.26% n = inner radius 0.2% 0.16% L = length 0.5% 0.30% V = enter rd vltage 0.45% 0.26% e = elementary unit f harge negligible 0.025% ^i. = vissity f air 0.04% 0.025% C = slip rretin 0.9% 0.5% T = temperature 0.2% 0.01% P = pressure 0.4% 0.16% Wrst ase estimate frm eqs (1) and (12) ±2.4% Randm errr, R ±0.1% Residual unertainty assiated with effet f aersl flwrate n apparent size ±0.5% Ttal unertainty assiated with lassifier ±3.0% Impurities related unertainty +0%/-0.3% Ttal unertainty lassifier+residue layer + 3.0%/-3.3% " The unertainty in partile diameter determined by eletrial mbility measurements arises frm the unertainties in the variables used in eqs (1) and (12). Zp = ec(dp)/(3tt xdp) Zp = (Q + e ) In (r^/n) / (4 -ir VL) (1) (12) Unertainty in Gemetri Measurements The unertainty in tiie values f the enter rd radius, n, the uter ylinder radius, ri, and the lassifiatin length, L, listed in table 3 are estimates f hw aurately the measurements an be made. Fr the inner radius, n, the unertainty f ±0.2% represents abut ±0.04 mm in diameter, whih inludes the variability f the diameter ver the length f the enter rd and the differene between the diameter indiated by the manufaturer (1.874 m) and the single measurement made during this prjet (1.870 m). The unertainty in r2 is estimated as 0.3% in a similar manner t n, althugh its larger value represents the inreased diffiulty in measuring the inner diameter f the ylinder. The unertainty in length is estimated as 0.5% refleting bth the unertainty in measuring the length (manufaturer's measurement was m mpared t m measured in this study), as well as the distrtin f the eletri and flw fields at the entrane and exit f the lassifier lumn Unertainty in Peak Vltage The unertainty in vltage rrespnding t the peak is estimated as ±0.25% rrespnding t ±10 V fr the nminal 0.1 xm peak vltage f 3750 V when 333 mvs sheath air is used. This value f unertainty was estimated by nsidering the data used during the repeatability measurement. It represents twie the vltage spread fr the send day f the repeatability measurements (the repeatability measurements are shwn in table 1). The unertainty in vltage reading due t alibratin auray is estimated as ±0.2%. Summing bth unertainty levels, the verall unertainty in the vltage is estimated as ±0.45% Unertainty in Slip Crretin The unertainty in the slip rretin fr 0.1 urn partiles is estimated t be ± 0.4% based n a reent study by Allen and Raabe [14]. Hwever, there is a 2.4% differene between the slip rretin mputed by Allen and Raabe [14] fr a Knutsen number f 1.3 ( 0.1 jxm diameter sphere at ambient pressure) and 174

29 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy their earlier mputatin [15] based n a reanalysis f Millikan's il drp data [18,19]. Allen and Raabe [14] attribute this disrepany t the differene in the surfae ammdatin fr the slid PSL spheres in their study mpared t the Hquid drplet surfae in Millikan's studies. Beause f this large differene (2.4%) and beause there have been n slip rretin measurements n 0.1 ixm spheres, an intermediate estimate f the slip rretin unertainty f ±0.9% is used Pressure, Temperature, and Vissity The effets f the unertainty in the temperature and pressure measurements n the flw alibratin and flw measurements has been inluded in the flw unertainty. Hwever, the temperature and pressure als affet the mean free path f the gas eq (18), whih in turn affets the slip rretin, and the temperature affets the vissity eq (19). The unertainty in the vissity f air itself is abut 0.04% [20,21] Additinal Unertainties Aersl Flw Rate and Impurity Effet All f the unertainties disussed abve diretly affet the quantities appearing in the gverning equatins. The unertainty assiated with varying the aersl flw rates in tandem is nt aunted fr by prpagating the unertainty thrugh the gverning equatins. In fat, as pinted ut in se , the partile size mputed frm eqs (1) and (12) is nt affeted by hanging the aersl flw rates as lng as they are kept equal. In setin the unertainty assiated with the aersl flw rate is estimated t be ±0.5%. The unertainty assiated with impurities in the water des nt affet the measuring auray f the lassifier itself, but it des lead t a systemati inrease in the PSL partile diameter as an aersl mpared t the atual size f the PSL sphere withut any impurity ating. The impurity unertainty is estimated t be 0/-0.3% based n the effet f impurity nentratin n the residue thikness tgether with the effet f an impatr n the PSL partile diameter (se ) Ttal Unertainty in the Partile Size Measured by the Classifier All f the varius sures f systemati unertainty in regard t the eletrstati lassifier are listed in table 3. A nservative measure f the mbined systemati unertainty is t nsider the wrst-ase situatin in whih eah variable is ffset by its unertainty t prdue an extreme value f the diameter. The estimate is made by alulating the diameter using the nminal variable values and mparing t the diameter alulated if all the variables are ffset by the magnitude f their unertainty with the signs hsen s that the ttal unertainty is a maximum. The perent hange in the diameter is ±2.4%. Adding t this the randm errr, R, an verall errr f ± 2.5% is btained. There is ne additinal unertainty that must be inluded and this is the unertainty assiated with the aersl flw rate, ±0.5%. Adding this value t the wrst ase ttal, we arrive at ur best estimate f the unertamty in measuring partile size with the eletrstati lassifier as [/= ±3.0% Ttal Unertainty in the Measurement f the 0.1 fim PSL Spheres T btain the ttal unertainty in sizing the 0.1 ixm diameter PSL spheres with the lassifier, we must inlude the irjipurity effet. While impurities in the water and in the partile suspensin d nt affet the perfrmane f the lassifier, they d ause the size f the PSL sphere t be slightly larger as an aersl mpared t the size f the PSL sphere itself. In this ase the errr is nly in the minus diretin; that is, this errr auses the measured size t be t large by up t 0.3%. Adding this errr t the wrst ase estimate fr U given abve, we btain a ttal unertainty fr the 0.1 p-m PSL spheres f + 3.0%/-3.3%. This rrespnds t the fllwing range in terms f partile diameter: Diameter = p,m. 4. Disussin One way f assessing the validity f the unertainty estimates is t mpare the lassifier results fr the 0.3 and 1.0 \im SRMs with the ertified values. In bth ases the diameter btained by the lassifier methd is larger than the ertified value, by 1.6% fr the xm SRM and by 1.7% fr the ixm SRM. The imprtant pint is that the perent differene between the SRM values and the ertified values are smaller than the perent unertainty ( + 3.0/-3.3) that we have estimated fr the 0.1 j,m partile diameter. In a reent study, Knllenberg [10] summarized ther measurements fr the same bath f PSL sphere and reprted p-m ±0.007 (im (Knllenberg, light sattering) and ixm (Yamada, [11], eletrn mirspy). There are unreslved issues abut the auray f size measurements by eletrn mirspy beause f the unertainties in 175

30 Vlume 96, Number 2, Marh-April 1991 Jurnal f Researh f the Natinal Institute f Standards and Tehnlgy the determinatin f the magnifiatin and in defining the edge f the partile [22], Yamada's study [11] has quantified the effet f the eletrn beam expsure time n the hange in the partile diameter. The gd agreement between the lassifier measurements and the eletrn mirspy is enuraging but nt nlusive beause f the undefined unertainties in the eletrn mirspy results. In KnUenberg's study, the light sattering intensity f 0.1 (xm PSL sphere is mpared with that f xm SRM spheres fr wavelength large enugh that the sattering is in the Rayleigh regime. In this ase the primary sure f errr is the unertainty in the SRM partile itself. The size reprted by KnUenberg [10], ixm, is utside the unertainty limits f the lassifier measurement; hwever, the unertainty limits fr the light sattering measurement are brad (±0.007 jj-m) and inlude the jim average size btained by the lassifier. T further redue the unertainty assiated with the lassifier methd, it is prpsed that the lassifier be alibrated with the p,m SRM, whih has an unertainty f ±0.9%. Bth the 0.1 (im PSL and the xm SRM wuld be measured using the same flw nditins in the lassifier t remve the large flw unertainty. By analyzing the multiply harged xm partiles, a high flw rate an be used in the lassifier thus minimizing the unertainties assiated with perating the lassifier at lw flw. It is believed that the unertainty in the determinatin f the average partile size fr the 0.1 (xm PSL an be redued t abut 1.5% by using this predure. Aknwledgment This study was supprted by Natinal Institute f Standards and Tehnlgy, Cntrat 43NANB807219, and by the Partile Cntaminatin Cntrl Researh Cnsrtium at the University f Minnesta. Ken Bensn and Gerge Mattingly f NIST assisted with the flw alibratins and Martin Misakian perfrmed the vltage alibratin. 5. Referenes [1] Knutsn, E. O., and Whitby, K.T., J. Aersl Si. 6, 443 (1975). [2] Knutsn, E. C, in Fine Partiles, Liu, B. Y. H. ed.. Aademi Press, New Yrk (1976) p [3] Hppel, W. A., J. Aersl Si. 9, 41 (1978). [4] Fissan, H. J., Helsper, C, and Thielen, H. J., J. Aersl Si. 14, 354 (1982). [5] Plmp, A., ten Brink, H.M., Spelstgra, H. and van de Vate, J. F., J. Aersl Si. 14, 363 (1982). [6] Sheibel, H. G., Hussin, A., and Prstendrfer, J., J. Aersl Si. IS, 372 (1983). [7] Kusaka, Y., Okuyama, K., and Adahi, M., Aersl Si. Tehnl. 4, 209 (1985). [8] Kusaka, Y., Okuyama, K., Shimada, M. and Ohshima, H., J. Aersl Si. 4, 501 (1988). [9] Rader, D. J., and MMuny, P, J., J. Aersl Si. 17, 771 (1986). [10] KnUenberg, R. G., J. Aersl Si. 20, 331 (1989). [11] Yamada, Y., Miyamt, K., and Kizumi, A., Aersl Si. and Teh. 4, 227 (1985). [12] Uu, B. Y. H., Pui, D. Y. H., J. Cllids Interfae Si. 49, 305 (1974). [13] Agarwal, J. K., and Sem, G. J., J. Aersl Si. 11, 343 (1979). [14] Allen, M. O., and Raabe, O. G., Aersl Si. Tehnl. 4, 347 (1985). [15] Allen, M. O., and Raabe, O. G., J. Aersl Si. 13, 537 (1982). [16] Niida, T., Kusaka, Y., Oda, S., Part. Syst. Charat. 5, 139 (1988). [17] Raabe, O. G., in Fine Partiles, Liu, B. Y. H., ed., Aademi Press, New Yrk (1976) p. 57. [18] Millikan, R. A., Phys. Rev. 15, 544 (1920). [19] Millikan, R. A., Phys. Rev. 22, 1 (1923). [20] Birge, R. T., Am. J. Phys. 13, 63 (1945). [21] Millikan, R. A., Eletrns (+ and - ), Prtns, Phtns, Mestrns, and Csmi Rays., The University f Chiag Press, Chiag (1947). [22] Swyt, D. A., A lk at tehniques fr the dimensinal alibratin f standard mirspi partiles. Natl. Bur. Stand. (U.S.) Spe. Publ (1983). Abut the Authrs: Patrik D. Kinney was a guest wrker at NIST while a graduate student in Mehanial Engineering at the University f Minnesta and is urrently emplyed at SAES Pure Gas In., San Luis Obisp, CA. David Y. H. Pui is an Assiate Prfessr in Mehanial Engineering and is a member f the University f Minnesta Partile Tehnlgy Labratry, Minneaplis, MN. Gerge W. Mulhlland is a researh hemist and Nelsn P. Bryner a hemial engineer in the Fire Measurement and Researh Divisin f the NIST Building and Fire Researh Labratry. 176