Vol. 21 No. 4（2006） （47） 329

Research Paper J. Aerosol Res.，21（4），329-340（2006）

Aerosol Size Distribution Measurement Using Multi-ChannelElectrical Mobility Sensor

Panich INTRA＊ and Nakorn TIPPAYAWONG＊

Received 2 December 2005Accepted 26 July 2006

Abstract－Aerosol particles can be classified according to their electrical mobility. A multi-channel detector has been developed to classify electrically charged airborne particles under theinfluence of an electric field. The detector is capable of measuring the electrical mobility ofparticles in the sub-micrometer size range. It is compactly designed as an assembly of twoconcentrically-aligned cylindrical short electrodes with a fixed clearance. Sheath air and aerosolflows enter from one end, pass through the annulus and exit the other end. An electric field isapplied between the inner and outer electrodes. Particles with a given electrical mobility arecollected on a designated electrometer ring where electrical signals are measured to obtain sizedistributions. In this study, a mathematical model was developed to optimize the locations ofparticle detection sensors and the calculations of particle trajectories were performed for variousparticle sizes. A prototype detector constructed in the present work gave the particle sizes whichare in good agreement with those obtained by a scanning electron microscope. Signal currentfrom the detector was also analyzed to give number concentration of particles. Experimentalresults agreed well with the theoretical predictions. The proposed model was proven to be usefulin designing the detector and the prototype detector showed promising results for aerosol sizemeasurement.

Key Words： Aerosol, Electrical Mobility, Size Distribution, Spectrometry, Electron Microscopy.

1．Introduction

Aerosols are found in many human environmentsas well as processes in various industries such asfood, pharmaceutical and medical, electronic andsemiconductor industries. Governments and industrystress the importance of aerosol measurement, not onlyto protect the environment and health of their peopleas required by law, but also to improve industrialprocesses, increase productivity and gain competitiveadvantage. Information about the size spectrum ofthese fine particles is required if they are to be fully

understood and controlled. A widely used type ofdevice capable of measuring these ultra-fine particlesis an electrical mobility analyzer such as a differentialmobility analyzer（DMA）. A typical setup of theinstrument consists of a pair of parallel electrodesbetween which a potential is applied and a gas flows.An aerosol flow containing charged particles isintroduced adjacent to one of the electrodes. Aparticle-free sheath flow initially separates the aerosolflow from the opposite electrode. The electric fieldcauses charged particles to move toward the oppositeelectrode across the gap between the electrodes,according to their electrical mobility which is relatedto their size.

There have been numerous studies and developmentson the particle electrical mobility analyzer. Many

＊ Department of Mechanical Engineering, Faculty of Engineering,Chiang Mai UniversityChiang Mai 50200, Thailand

330 （48） エアロゾル研究

previous studies concern single size channel detection,improvements in performance and expansion ofmeasurement range 1～ 7）. Recent developments werereviewed by Flagan 8）. To measure particle size spectra,a DMA capable of single channel signal detection isconnected to a particle counter and operated in ascanning voltage mode, measuring a complete sizespectrum in about 30～60 s. Similar instruments withmulti-channel signal detection capability have recentlybeen under development by several workers. Tammetet al. 9）designed and developed an electrical aerosolspectrometer（EAS）which is able to classify particlesin similar fashion to, but faster than, a typical DMAdue to its multi-channel measurement capability.Graskow 10）developed a fast aerosol spectrometer tomeasure nanoparticles. Biskos et al. 11）later reporteda development of a differential mobility spectrometer（DMS）, derived from Graskow’s concept. Kulon etal. 12）described a bipolar charge aerosol classifierwhich uses electrostatic technique with differentclassifying sections operating at a number of appliedvoltages in series. The system is able to simultaneouslymeasure particle charge as well as size. The presentstudy focuses on development of a multi-channel sizeanalyzer able to measure aerosol size distribution nearreal time, based on similar principle to previouslymentioned instruments. Nonetheless, there werecollective differences between the present spectrometerand each of the existing instruments, which were asfollows ;（i）the concept of the present instrument was

based on a compact, inexpensive and portable unit.Short column classifier and a small number of detectionchannels were used to reduce diffusion effect of theparticle inside the classifier. Overall dimensions andweight were such that it was easy to handle and movearound ;（ii）the instrument adopted a tangentialaerosol inlet upstream of the first electrode ring toensure uniform particle distribution across the annularaerosol entrance to the classifier column ;（iii）ratherthan diffusion charging, the instrument employedunipolar corona（diffusion and field）chargingmethod ;（iv）the applied voltage was set to maintainat low level, well below the corona onset voltage, toavoid unintentional charging of the particles inside theclassifier ; and（v）the incompressible Navier-Stokesequation and Maxwell’s equations were numericallysolved in previous studies 13）to investigate flow andelectric fields inside the classifier and obtain appropriatedimensions, geometries and arrangement of the chargerand the electrostatic classifier in this instrument. Acomparison between the present instruments and theexisting instruments is shown in Table 1.

In this work, a simple model was developed topredict particle trajectories which influence theperformance of the detector and were used as a basisfor an aerosol size spectrometer system design. Theperformance of the spectrometer was examined usinga field emission-scanning electron microscopeobservation method with particle classification.Typical evaluation of number concentration and size

Table 1 Comparison between the present instrument and the existing spectrometers

EAS DMS BCAC EMS（Tammet et al. 9）） （Biskos et al. 11）） （Kulon et al. 12）） （This work）

Measurement technique Electrical mobility Electrical mobility Electrical mobility Electrical mobilitySize range 10 to 10,000 nm 5 to 1,000 nm ＜ 3,000 nm 10 to 1,000 nmConcentration range 108～1011 to 2× 104～ 1× 109 to 4× 1013 n / a 1011 to 1013 particles / m3

5× 107 particles / m3 particles / m3

Time response ＜ 1 s 200ms 10 s 30 sCharger type Corona charger Corona charger Corona charger Corona chargerCharging method Unipolar diffusion and Unipolar diffusion charging Bipolar diffusion charging Unipolar diffusion and

field charging field chargingParticle detector Electrometers Electrometers Electrometers ElectrometersElectrometer channels 26 26 10 10Aerosol inlet technique n / a n / a n / a Tangential inletAerosol flow rate 12 L / min 5 L / min 2 L / min 1 L / minSheath air flow rate 36 L / min 35 L / min 58 L / min 10 L / minOperating pressure n / a 25.3 kPa n / a 34.5 kPaElectrode applied voltage 800 V 5 kV to 10 kV 5 kV 500 V to 3 kVClassifier length n / a 700mm 2,000mm 131mmInner electrode radius n / a 12.5mm 1.5mm 10mmOuter electrode radius n / a 26.5mm 25mm 25mm

n / a : information not available

Vol. 21 No. 4（2006） （49） 331

distribution were also presented.

2．Aerosol Transport under Electric Field

Aerosol size spectrometry in this research study willbe based on differential electrical mobility classification.The model described in the following sections isapplicable to aerosol transport under a strong electricfield inside a concentric cylinder classifier. Solutions tothe simplified governing equations are proposed andpresented. Particle motions are dependent on externalforces applied to the particles, such as gravitationalforce, drag force, diffusion force and electrical force.The particles move in both axial and radial directions.The axial motion was influenced by the fluid velocityprofile in the axial laminar flow. The radial motion isdue to the electric force which is the dominant force.When the particles are introduced into the classificationcolumn, any charged particle under the influence ofan electric field will have an electrical mobility, Zp,defined as the velocity per unit field. The electricalmobility of charged particle can be derived by equatingthe electric field force, Fe＝ neE with the Stokes dragforce, Fd＝ 3 pµdpu / Cc and electrical mobility isgiven by :

（1）

where µ is air viscosity, u is the radial component ofparticle velocity, dp is the particle diameter, Cc isCunningham slip correction factors, e is charge ofelectron（1.6× 10－19 C）and n is the number ofcharge on the particle, E is electric field strength inthe gap between the concentric cylinders. It is assumedthat the air flow is axisymmetric, laminar, fullydeveloped, and incompressible. If the end effects areneglected, then the electric field for the concentriccylinders（the classifier）will have only a radialcomponent with intensity given by

（2）

Here V is applied voltage, r is radius, r1 and r2 are radiiof the inner and outer cylinder, respectively. Particlesmay become charged due to field charging, diffusioncharging, bipolar charging or photo charging. In thisstudy, combined field and diffusion charging isassumed as appropriate for fine particles. The averagecharge ndiff caused by the diffusion charging in a timeperiod t by a particle diameter dp can be found fromthe White’s equation 14）:

（3）

where e is the elementary unit of charge, c－i is the meanthermal speed of the ions（240 m / s）, k is theBoltzmann’s constant（1.380658× 10－23 J / K, forair）, T is the temperature, KE is the constant ofproportionality, Ni is the ion concentration, and t is theresidence time of the charger. For the corona-wirecharger 15）, an approximate expression for the Nitproduct can be derived :

（4）

where r1c and r2c are the radial position of the outerand inner charger cylinder, respectively, Ic is thecharging current, Zi is the mobility of ion（equal to0.00014m2 / V.s for the positive ion）, Ec（r）is thecharging electric field as a function of radial position,and Qc is the total flow rate through the charger. Thefraction charge per particle nfield caused by the fieldcharging in an electric field E derived by White 14）

and is given by

（5）

where e is the particle dielectric constant. Finally, bothfield and diffusion charging occur at the same time.This is known as continuum charging where particlecharge is the sum of the contributions from field anddiffusion charging. Fraction charged as a function ofthe particle diameter estimated from White’s theory isshown in Fig. 1. For the particle diameter less than

100

10

1

0.1

Mea

n ch

arge

per

par

ticle

Diffusion chargingField chargingCombined charging

Nit＝2.90×1014 ions・m－3 s－1

1 10 100 1000Particle diameter（nm）

Fig. 1 Fraction charged against particle diameter.

332 （50） エアロゾル研究

1 µm, the electric field existed in the charger has anegligible effect on the charging process 3）.

The most commonly used configuration for anelectrical mobility analyzer employs concentricannular flows. A flat velocity profile was commonlyassumed, even through the actual velocity profile inthe instrument’s annular cavity was a non-uniformdeveloping profile. Liu et al. 16）reported that thevalue of the electrical mobility calculated on the basisof a uniform flow with a flat velocity profile in theclassifier was approximately 12％ higher than thevalue calculated on the basis of a fully developed,non-uniform velocity profile. The transfer function wasapplied by Biskos et al. 11）to a multi-channel DMS.They noted that the transfer function shape would beinfluenced by the gas velocity profile within theannulus. In Biskos et al. analysis, a simplified modelthat masked these effects was used. Therefore, in thepresent study, rather than the widely adopted transferfunction method, the trajectory method that takes intoaccount the flow velocity profile was employed. Thissimple model is able to predict the particle motionbehavior, mobility range, and size classification of themulti-channel spectrometer. Additionally, the trajectorymethod is capable of showing how particles moveinside the annular gap which is useful in comparisonwith flow visuals.

For efficient performance of any electrical mobilityanalyzers, operation at laminar flow conditions isrequired so that particle trajectories can be accuratelydetermined. Neglecting gravitational effect andBrownian motion, the non-diffusive particle trajectoryis described by the system of differential equations.

（6）

（7）

where ur and uz denote the radial and axialcomponents of the air flow velocity. Similarly, Er andEz denote the radial and axial components of theelectric field. For a fully developed parabolic velocityprofile in the concentric annular, ur＝ 0, uz＝ uz（r）,Er（r）＝V /｛r ln（r2 / r1）｝, and Ez＝ 0. Substitutinginto Eqs.（6）and（7）gives the following differentialequations describing the trajectory of an aerosolparticle in an annular flow :

（8）

（9）

where :

dp / dz denotes the constant pressure gradient. UsingEqs.（8）and（9）, the trajectory of the particle in anannular flow is given by

（10）

Integrating Eq.（10）, the migration paths of the chargedparticles can be determined. Their landing locationdownstream of the aerosol inlet is given in terms oftheir electrical mobility, the mean velocity of the flow,and the electric field strength :

（11）

The particle entering the classifier at a radial positionof r1 has trajectory taking it to an axial position of z,which can be obtained as

（12）

and the expression for the trajectory of the particle thattake into account the flow velocity profile entering thespectrometer at a radial position of r1＋ d which hastrajectory taking it to an axial position of z and isgiven by

（13）

Once, the particle trajectories inside the instrument are

Vol. 21 No. 4（2006） （51） 333

known, size classification of deposited particles canbe determined.

3．Electrical Mobility Spectrometry

3.1 Spectrometer DescriptionA schematic of the aerosol size spectrometer used

in this research study is depicted in Fig. 2. Thespectrometer has one short column which consists ofcoaxially cylindrical electrodes. The advantage ofcylindrical geometry is that distortion of electric fieldbetween electrodes is minimal due to the absence ofcorners and edges. Operation and performance of theinstrument depend upon aerosol transport under theinfluence of flow and electric fields. It was importantto ensure that both flow and electric fields were laminarand uniformly distributed inside the classifyingcolumn. There are two streams which are the aerosoland sheath air flows. The two flows are regulated andcontrolled via mass flow controllers. The inside of theannular was constructed in such a way that smoothwall and turbulence free merging of the two gas flowswere ensured. Nonetheless, the flow field inside theapparatus was further investigated by solvingnumerically the continuity and Navier-Stokes equationsusing a commercial computational fluid dynamicsoftware package, CFDRCTM, reported in 13）. It wasshown that a parabolic velocity profile was establisheda few hydraulic diameters downstream from inlets,while negligible disturbances occurred at the pointwhere the two flows（aerosol and sheath air）merged.Flow simulation results showed similar trend to thoseby Chen and Pui 17）and Chen et al. 18）. For furtherchecking of the flow, the flow pattern inside theclassifier was examined using a similar flowvisualization techniques reported by Otani et al. 19）,Asai et al. 20）, and Myojo et al. 21）. It was possible toevaluate the extent of laminar and turbulent flowswithin the classifier. Flow visualization showed similarresults to those reported in the literature. The chargedparticles enter the analyzer column near the centralrod by a continuous flow of air. Since the central rodis kept at a positive high voltage, the charged particlesare deflected radially outward. They are collected onelectrically isolated electrometer rings positioned atthe inner surface of the outer electrode of the column.Electrometers connected to these electrodes measurecurrents corresponding to the number concentrationof particles of a given mobility which is related to theparticle size. Electrical current detection method wasconsidered to be easier and faster than direct particle

detection measurements. In addition, the applied highvoltage is maintained at a lower value than the coronaonset voltage to avoid unintentional charging of theparticles within the classifier. 3.2 Mobility and Size Classification

The theoretical background on aerosol transportpreviously described was used in designing thespectrometer system. In order to classify particlesize, the particle electrical mobility was considered.The design practice was similar to Kulon et al. 12）.The spectrometer was divided into a number ofwell-insulated virtual ground electrometer rings（R＞ 1012W）. Fig. 3 shows the principle of themobility classification. Intra and Tippayawong 13）

reported that the region between the inner electrodeand the electrometer rings on the outer wall exhibiteda uniform distribution of electric field that similar trendto those by Chen and Pui 17）and Chen et al. 18）. It cangenerally be considered to be a function of radius only.However, there were small non-uniformities close tothe wall between each electrometer ring gap whichwere made of electrical insulator. The effect wasdependent on ring width to ring separation ratio, aswell as ring separation. In this work, the arrangementwas designed in such a way that the effect of existenceof the insulator between neighboring electrodes is notsignificant. Each outer electrometer ring of thespectrometer represents one size classification channel

Sheath air flow（Qs）

Isolation housing Electrometer rings

High voltage central electrode Outlet

Isolation rings

Charged particles（Qa）

Outer Housing

Electrometers

i

ur

uz

Fig. 2 Schematic of an aerosol size spectrometer based onelectrical mobility technique.

Sheath airflow

zi ze, i

Zmax　p, i Zmin

　p, i

Aerosolflow

Fig. 3 Principle of mobility classification in the spectrometer.

334 （52） エアロゾル研究

and its axial location along the column depends on theparticle electrical mobility. Considering one particularelectrometer ring: the particle enters the spectrometerat the position immediately adjacent to the inner wall,and is deposited at the leading edge of the ring. In thiscase, the maximum mobility, Zmax

p, i , of particle to depositon this ring is

（14）

where zi is the axial position between the aerosol entrylocation and the leading edge of the electrometer ring.This equation can be used to determine the diameterof the particle where all the terms are known. UsingStoke’s law to classically define the electric mobility,Zp which can be written in terms of dmax

p, i , the particlediameter with the maximum mobility is given by

（15）

Similarly, the minimum mobility, Zminp, i , of the particle

that enters the spectrometer at the outer most radialposition of the aerosol inlet（at r＝ r1＋ d）anddeposits at the trailing edge of the ring is

（16）

where ze, i is the width of the electrometer ring, and dis the width of the aerosol flow inlet. The particle size,dmin

p, i , with the minimum mobility is given by

（17）

Only particles with electrical mobility between thesetwo limits Zmin

p, i＜ Zp, i＜ Zmaxp, i will deposit on this ring

and contribute to the measured signal. The range ofelectrical mobility is a function of the voltage appliedto the central electrode, flow settings, geometricalfactors of the spectrometer and particle size. Assuminga uniformly distributed particle concentration at theentrance, a constant electrometer ring width（12mm）,a given ring separation（1mm）and a fixed number ofelectrometer rings（10 rings）, relationships betweenthe predicted electrical mobility and each sizeclassification channel along the length（131mm）ofthe spectrometer column for a given operatingcondition（1.0 L / min aerosol flow, 10.0 L / minsheath air flow, 1.0 kV central rod voltage, 34.5 kPaoperating pressure）can be computed. Typical resultsare illustrated in Figs. 4 and 5 for mobility intervalsand their corresponding particle size bins, respectively.It was found that the mobility range for each channelwas not evenly distributed and there was a slightoverlap between adjacent channels in terms of theelectrical mobility predicted. For a better design of thespectrometer, these overlaps were minimized bymanipulation of the voltage applied to the centralelectrode, flow settings and the geometrical factors ofthe spectrometer.3.3 Number Concentration from Signal Current

MeasurementThe current from the deposition of charged particles

on each electrometer ring is magnified by the amplifierand measured by the sensitive electrometer. If themobility distribution function f（Zp）is defined as

10－5

10－6

10－7

Ele

ctri

cal m

obili

ty（m2

V－1

s－1 ）

Electrometer ring number

1 2 3 4 5 6 7 8 9 10

Fig. 4 Predicted electrical mobility range at each electrometerring（1.0 L / min aerosol flow, 10.0 L / min sheath airflow, 1.0 kV central rod voltage, 34.5 kPa operatingpressure）.

100 101 102 103

Particle diameter（nm）

Ele

ctro

met

er r

ing

num

ber

10

9

8

7

6

5

4

3

2

1

Fig. 5 Predicted particle size range at each electrometer ring（1.0 L / min aerosol flow, 10.0 L / min sheath air flow,1.0 kV central rod voltage, 34.5 kPa operating pressure）.

Vol. 21 No. 4（2006） （53） 335

（18）

where dNp is the number of aerosols in the mobilityrange dZp. For the spectrometer with sheath air flow,the signal current of a singly charged particles, Ie, canbe derived making use of the well known result thatthe rate at which particles are collected on the outerelectrode of the spectrometer is given by :

（19）

where Q is the sample flow rate, e is the value of theelementary charge, Zp is the particle electricalmobility（i.e. particle drift velocity / field strength）,and f（Zp）dZp is the number concentration of aerosol,Np, with mobility between Zp and Zp＋ dZp. For thepresent spectrometer, considering the critical mobilityin the range of Zmin

p, i ＜ Zp, i＜ Zmaxp, i , all particle are

measured, the signal current of a singly chargedparticles collected on the electrometer ring in channeli become

（20）

where Ie, i is the electrometer signal current measuredat channel i, and Qa is the sample aerosol flow rate.Therefore, the currents have the simple form as

（21）

where Np, i is the particle number concentration atchannel i. The signal current was then used toevaluate particle number concentration. Thus, theparticle number concentration of particles, Np, i, in themobility range from Zmin

p, i ＜ Zp, i＜ Zmaxp, i is related to

the signal current, Ie, i , as follows :

（22）

In fact, the aerosol contains not only singly chargedparticles of the desired particle size, but also multiplycharged particles of a larger particle size. Thus, themultiply charged particles must be applied to Eq.（22）,and can be rewritten to give

（23）

where n（dp）is the average number of elementarycharges carried by particles with diameter dp. To

obtain size distribution, the geometric midpointdiameter dmid

p, i , is calculated as :

（24）

where dminp, i , is the particle diameter with minimum

mobility in channel i, and dmaxp, i , is the particle diameter

with maximum mobility in channel i. The geometricmidpoint particle number concentration in channel ican be approximated as :

（25）

The measured size channel i distribution resultscorrespond to the channel concentration Np, i dividedby the channel geometric width :

（26）

4．Experimental Evaluation

4.1 Experimental SetupA test facility to evaluate a prototype of the aerosol

size spectrometer was constructed, as shown in Fig. 6.The system consists of a diode type corona particlecharger, a spectrometer, a signal detection system, aflow arrangement and a computer controlled interfacesystem. The combustion aerosol generator was used togenerate a polydisperse carbonaceous diffusion flameaerosol for this experiment. An aerosol flow rate of1.0L / min was used and a pre-filtered sheath air flowwas supplied at 10.0 lpm, controlled by flowcontrollers. The flow was delivered by means of avacuum pump. The flow was conditioned by placing aperforated screen upstream to ensure uniform laminarflow. The classifying column is comprised of astainless steel tube with 25mm diameter, a centralelectrode rod of 10mm diameter and 131mm inlength. A potential of 1.0 kV applied to the centralelectrode was used. The spectrometer system wasmaintained at 34.5 kPa in order to increase mobilityresolution for particle with diameter greater than100 nm 11）. The signal current from deposited chargedparticles on each electrode ring was measured with aKeithley 6517A electrometer and a Keithley 6522scanner card, interfaced to a personal computer via anIEEE-488 interface.4.2 Collection and Analysis for SEM

In this study, the deposited particles inside thespectrometer at each electrometer ring were analyzed

336 （54） エアロゾル研究

for their size using a scanning electron microscope（SEM）. The sampling was carried out using a 3mm

SEM copper tape placed on each inner surface of theelectrometer ring, as shown in Fig. 7. Aerosol sampleswere collected electrostatically for at least 30min ofoperation. Particle imaging was carried out using aJEOL JSM-6335F Field Emission Scanning ElectronMicroscope. During the SEM analysis, agglomerateswere selected and imaged randomly to minimize bias.Magnifications between 9,500 X and 80,000 X weretypically used, giving three to six particles per image.The SEM projected surface area distribution wasobtained first, by thresholding the original SEM imageand next, by calculating the projected surface area ofeach particle. Image processing was carried out usingImageJ, a public domain image analysis softwarewhich was developed at the National Institutes ofHealth（http://rsb.info.nih.gov/ij/）. A portion of theparticles were found to be non-spherical andcoagulated. It was known that the fraction ofcoagulated particles increased with an increase incollection time of the particles. In the procedures,highly coagulated particles were excluded to avoid theconfusion between the coagulation taking place duringparticle growth in the gas phase, or on the samplingplate during particle collection. For each data point,about 18～ 40 particle fields of view distributedthroughout the sampling plate were used for SEM

analysis to estimate particle surface area anddetermine the corresponding geometric mean projectedarea diameter. The equivalent mean projected areadiameter（dPA）can be calculated from the projectedsurface area（A）and is given by

（27）

It should be noted that in the free molecular regime（Kn≫ 1）, aerosol surface area is equivalent to

geometric surface area for spherical particles. Becauseparticle mobility and molecule attachment rate aregoverned by particle-molecule collisions, it is thereforetheoretically possible to use the mobility analysistechnique to measure the aerosol surface area 24）.Rogak et al. 25）demonstrated that for mobilitydiameters smaller than 400 nm（extending well intothe transition regime）, the equivalent sphere projectedarea diameter（the diameter of a sphere having thesame projected area）of particles scaled with the

Outer electrode

Inner electrode

3 mm SEM copper tape

Fig. 7 Schematic of the SEM sampler constructed.

Flowmeter

Corona chargerFlowmeter

Impactor Combustionaerosol

generator

External computer,data logging,user interface

Positive highvoltage supply

Positive highvoltage supply

Filter

Filter

Sheath airE

lect

rom

eter

rin

gs

Hig

h vo

ltage

ele

ctro

de

Kei

thle

y el

ectr

omet

er 6517A

＋Sc

anne

r ca

rd 6522

Excess air

Vacuumpump

E1 E2 E3 E4 E5 E6 E7 E8 E9 E10

Fig. 6 Experimental setup for the measurement system.

Vol. 21 No. 4（2006） （55） 337

particle mobility diameter for fractal-like particles. Itwas noted that the overall trend of the experimentalmeasurements showed close agreement with thatpredicted theoretically. Similar methods of particlesize comparison were conducted and reported byCamata et al. 26）, Hummes et al. 27）, Kuga et al. 28）,Seol et al. 29）, Ku and Maynard 24）. In free molecularregime, the electrical mobility of the charged particlebecomes

（28）

where l is the mean free path of the carrier gas. Thus,combining Eqs.（15）and（28）, it can be seen that inthe free molecular regime, the particle diameter withmaximum mobility is given by

（29）

Similarly, combining Eqs.（17）and（28）, the particlediameter with minimum mobility is given by

（30）

5．Results and Discussion

5.1 Size Comparison with SEM ResultsFig. 8 shows typical SEM images of the particles

collected on selected electrometer rings. Theclassification sizes were（a）177 nm,（b）191 nm,（c）262 nm,（d）314 nm,（e）363 nm, and（f）470 nmwith the inner electrode voltage of 1.0 kV, aerosol flowrate of 1.0 L / min, sheath air flow rate of 10.0 L / minand operating pressure of 34.5 kPa. The SEM data foreach individual data point is shown in Table 2. As canbe seen from Table 2 that after classification theparticles appeared to approximate monodisperse sizesystem, with calculated geometric standard deviations

of about 1.03～ 1.13. Fig. 9 provides comparison ofpredicted（geometric midpoint）mobility diameterwith average measured（geometric mean）equivalentsphere projected area diameter at each electrometerring in the spectrometer. The data represents particlesin the size range between 100～ 450 nm. From theresults obtained in this investigation, it was found thatthe diameter derived from projected surface area ofagglomerates analyzed by SEM agreed well withprediction from mobility analysis. The largestdifference observed was about 15％ at 150 nm. Atother sizes, the differences were within 5％. Theoverestimation by the present spectrometer was insimilar magnitude to that reported by Camata et al. 26）

using radial DMA, Hummes et al. 27）using short-type DMA, Kuga et al. 28）using low pressure DMA,Seol et al. 29）using very low pressure DMA, andDeppert et al. 30）using Vienna DMA. It should be

Table 2 Measured diameter data for each data point

Data Minimum Maximum Geometric mean Geometric standardpoint diameter（nm）diameter（nm） diameter（nm） deviation

1 148.69 207.80 177.61 1.052 178.44 213.15 191.91 1.033 198.02 349.00 262.89 1.084 198.67 432.62 314.08 1.135 273.73 481.38 363.00 1.076 332.54 499.55 407.58 1.06

（a）dg＝177.61 nm （b）dg＝191.91 nm

（c）dg＝262.89 nm （d）dg＝314.08 nm

（e）dg＝363.00 nm （f）dg＝407.58 nm

Fig. 8 Typical particle morphologies of agglomerates collected（1.0 L / min aerosol flow, 10.0 L / min sheath air flow,1.0 kV central rod voltage, 34.5 kPa operating pressure）.

338 （56） エアロゾル研究

noted that the difference between the size obtained bythese DMAs and the SEM observation from literaturewere slightly larger than that found in this work. Thepossible reasons for the difference in measurementsfrom SEM and the spectrometer were considered to bedue mainly to the irregularity of the particle shape andthe multiply-charged particles 26, 29）. It was known thatthe SEM-measured particle size was consistent withthe spectrometer-measured one in the case of sphericalparticles 27）. For the effect of the multiply chargedparticle, the multiply charged aerosols have the sameelectrical mobility diameter, and may therefore becollected on the same electrometer ring. Consequently,the electrical signal current measured at any givenelectrometer ring will be due to particles of differentphysical sizes. In other words, if the EMS is set toextract singly charged particle of 20 nm in diameter,then doubly charged particle of 29 nm in diameter, andtriply charged particle of 36 nm in diameter would beextracted because the mobilities of these particles arethe same. Another reason for the underestimation ofSEM may be attributed to the simplification of theSEM size measurements which were the lack of highquality focusing（which probably had 5～ 10％measurement uncertainty）, changes in particle sizesduring sampling, calibration errors, all the coagulatedparticles shown in these figure were formed on the SEMsampling plate, and difficulties in size determination.In case of coagulated particles, because the mobilityof a sphere having volume equivalent to such acoagulated particle was slightly greater than that ofthe coagulated particle 31）, the size of the coagulatedparticle classified by the spectrometer was slightlysmaller than the predicted size determined from thespectrometer. The detailed reasons for these differencesshould be investigated further. Overall, taking intoaccount the fact that the classification performance ofour EMS approximately followed the theoreticalprediction, the 15％ difference was considered tobe acceptable. It was thereby confirmed that thespectrometer was capable of correctly determiningparticle mobility diameter.5.2 Mobility and Size Distribution

Preliminary results were obtained and one typicalresult is depicted in Fig. 10. Signal current for thedistribution of the test aerosol size spectrum for eachelectrode was clearly shown, their values of the signalcurrent was in similar order of magnitude to thosereported by Graskow 10）. The signal current was thenused to evaluate number concentration and size

Part

icle

siz

e di

stri

butio

n dN

/ dl

og（d p）（

part

icle

/ m3 ）

3.5×1012

3.0×1012

2.5×1012

2.0×1012

1.5×1012

1.0×1012

5.0×1011

0.0

Particle diameter（nm） 10 100 1000

Fig. 11 Measured size distribution of aerosol（1.0 L / minaerosol flow, 10.0 L / min sheath air flow, 1.0 kVcentral rod voltage, 34.5 kPa operating pressure）.

Electrometer ring number

Ele

ctro

met

er c

urre

nt（pA）

30

25

20

15

10

5

01 2 3 4 5 6 7 8 9 10

Fig. 10 Measured electrical signals from the spectrometer（1.0L / min aerosol flow, 10.0L / min sheath air flow,1.0 kV central rod voltage, 34.5 kPa operating pressure）.

Theoretical predictionSEM measurement

Predicted electrical mobility diameter（nm）

Mea

sure

d eq

uiva

lent

sph

ere

proj

ecte

d ar

ea d

iam

eter（

nm）

500

400

300

200

100

00 100 200 300 400 500

Fig. 9 Predicted versus measured particle size in the classifier（1.0 L / min aerosol flow, 10.0 L / min sheath air flow,1.0 kV central rod voltage, 34.5 kPa operating pressure）.

Vol. 21 No. 4（2006） （57） 339

distribution. An example of data, representing sizedistribution of combustion aerosol measured by thespectrometer was shown in Fig. 11. The log normalnature of distribution was clearly illustrated.

6．Concluding Remarks

The operation of an aerosol size spectrometer designbased on electrical mobility determination techniquehas been studied. The instrument design concept isbased on electrical mobility analysis and multiple sizedetection channels. The system was developed withthe aim of measuring aerosol particles in the size range10～ 1,000 nm, and consisted of two coaxial cylindersas two opposite polar electrodes. Mathematicalmodeling for particle trajectory has been carried out.The operating parameters as well as geometricalfactors of the classifier section were designed basedon these mathematical investigation results togetherwith previous numerical modeling of flow and electricfields. A prototype of the spectrometer has been builtand tested. Its performance in evaluating particle sizeusing signal current to evaluate the numberconcentration of aerosol was compared with SEMresults. Experimental results were found to be in goodagreement with theoretical predictions and thespectrometer can be used successfully in obtainingaerosol size distributions. Nonetheless, the classificationperformance of the present instrument needs beexamined further with a system of monodisperseparticles from standard sized particles or generatedfrom a setup involving a tandem DMA. Futureverification experiments of the present instrumentalong side a standard DMA are planned.

Acknowledgments

This work was supported by the National Electronic andComputer Technology Center, National Science and TechnologyDevelopment Agency, Thailand.

Nomenclature

A : surface area （m2）c－i : mean thermal speed of ions （m / s）Cc : Cunningham slip correction factor （－）dp : particle diameter （m）dmax

p, i : particle diameter with maximum mobility （m）dmid

p, i : midpoint particle diameter （m）dmin

p, i : particle diameter with minimum mobility （m）dPA : equivalent projected surface area diameter （m）e : value of elementary charge on an electron （C）E : electric field strength （V / m）Ec : charging electric field strength （V / m）Er : radial components of the electric field （V / m）

Ez : axial components of the electric field （V / m）Ic : charging current （A）Ie, i : electrometer current （A）k : Boltzmann’s constant （J / K）KE : translational kinetic energy （N.m2 / C2）n : average number of elementary charges on the particle （－）ndiff : average charge of diffusion charging （－）nfield : average charge of field charging （－）Ni : ion concentration （ions / m3）Np, i : particle number concentration （particles / m3）Q : volumetric flow rate of gas （L / min）Qa : aerosol flow rate （L / min）Qc : total flow rate through the charger （L / min）Qs : sheath air flow rate （L / min）r : radial coordinate （m）r1 : inner radius of the annulus （m）r2 : outer radius of the annulus （m）T : absolute temperature （K）u : flow velocity （m / s）ur : radial components of the flow velocity （m / s）uz : axial components of the flow velocity （m / s）V : potential （V）zi : axial position （m）ze, i : electrometer ring width （m）Zi : ion electrical mobility （m2 / V.s）Zp : particle electrical mobility （m2 / V.s）Zmax

p : maximum electrical mobility of particle （m2 / V.s）Zmin

p : minimum electrical mobility of particle （m2 / V.s）

Greek Symbols

d : air density （kg / m3）e : dielectric constant （F / m）l : mean free path （m）µ : air viscosity （Pa.s）

Subscripts

a : aerosol

i : channel number

r : radial direction

s : sheath air

z : axial direction

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