a novel electrical-mobility-based instrument for total number concentration measurements of...

Aerosol Science 40 (2009) 439 -- 450

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Aerosol Science

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Anovel electrical-mobility-based instrument for total number concentrationmeasurements of ultrafine particles

Manish Ranjan, Suresh Dhaniyala∗

Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA

A R T I C L E I N F O A B S T R A C T

Article history:Received 16 September 2008Received in revised form26 December 2008Accepted 8 January 2009

Keywords:UltrafineElectrical mobilityConcentrationCompactMiniatureSensorAerosolTECSMEAS

A novel electrical-mobility-based technique to measure total particle number concentrationover a selected size range is presented. Charged particles are condensed out onto an electrodethat is shaped such that the product of its transfer function and the particle charging efficiencyis a constant, independent of particle size. The resulting total current is then proportional to thenumber concentration of the sampled particles over the collected size range. The theoreticalapproach for the calculation of the electrode shape function is described. The extension of thistechnique for measurement of highermoments of the particle size distributions over a desiredsize range is briefly discussed.This concept is used to design a new instrument, called the tailored electrode concentrationsensor (TECS). For validation of the theoretical concept, the collection electrode in the TECSinstrument is designed for concentration measurements over a size range of 30–90nm. Inthe TECS, the collection section is located downstream of an electrostatic precipitator section,where the sampled flow is split into aerosol and sheath flows, similar to the design of theMEAS[Ranjan, M., & Dhaniyala, S., (2007), Theory and design of a new miniature electrical-mobilityaerosol spectrometer, Journal of Aerosol Science, 38(9), 950–963]. This results in a compact, lowpressure drop instrument. Experimental results confirm that the response of the optimally-shaped electrode in the TECS system is only proportional to total number concentration overthe selected size range.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Ambient ultrafine particles (UFP, particle diameter, Dg < 100nm) make only a small contribution to the PM2.5 mass, butconstitute a significant fraction of particulate number (Westerdahl, Fruin, Sax, Fine, & Sioutas, 2005; Bukowiecki et al., 2002).UFPs are more likely to reach and reside in the gas-exchange region of the lung and present a greater interactive surface perunit mass of inhaled material than larger particles (Seaton, MacNee, Donaldson, & Godden, 1995; Oberdorster, Ferin, & Lehnert,1994). In urban areas, UFPs are predominantly formed due to combustion activities and, thus, have compositions that are likelyto adversely affect human health (Elder, Gelein, Finkelstein, Cox, & Oberdorster, 2000; Donaldson, Li, & MacNee, 1998; Peters,Wichmann, & Tuch, 1997; Ferin, Oberdorster, & Penney, 1992). It has been speculated that significant exposure to UFPs couldpossibly result in fibrosis and lung cancer (Mauderly, 1996), aggravating asthma, and inducing heart rate variability (Framptonet al., 2004; Frampton, 2001).

∗ Corresponding author. Tel.: +13152686574; fax: +13152686695.E-mail address: [email protected] (S. Dhaniyala).

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440 M. Ranjan, S. Dhaniyala / Aerosol Science 40 (2009) 439 -- 450

The short lifetimes of UFPs result in significant inhomogeneity in their spatial and temporal distribution (Martuzeviciuset al., 2004). Inparticular,UFPnumber concentrations canvary significantly over short distances (Zhuet al., 2002). This complicatesassessment of public exposure to ultrafine particles based on data from a few fixed monitoring sites (Violante et al., 2006; Kim,Okuyama, & Shimada (2002); Leung & Harrison, 1998). Estimating indoor exposures to UFPs is further complicated by thetransformation of these particles as they traverse the indoor-outdoor boundary and due to the presence of indoor sources (Zhuet al., 2005).

Complete characterization of exposure to UFPs will require measurements at a large number of locations (Eulerian mea-surements) or along all points of interest (Lagrangian). Accurate UFP number concentration measurements are possible withexisting commercial instruments such as the scanning mobility particle sizer (SMPS) and fast mobility particle spectrometer(FMPS; TSI Inc.). These instruments are, however, very expensive for large scale Eulerian measurements and their large size andneed for electrical power prohibits their deployment for Lagrangian measurements. Also, while these instruments provide highsize-resolution information, a single measure of total ultrafine number is, often, sufficient for monitoring and health assessmentstudies.

Total particle number measurements are possible with a portable condensation particle counter (e.g., TSI 3007 CPC). CPCmeasurements are, however, not limited to particles in the ultrafine size range. This might be possible by combining the CPCwithan upstream impactor of a 100nm cut-size. This instrument would, however, have a high pressure drop, and thus require a largerpump. Also the resultant lowering of internal pressure will negatively affect instrument performance. Also, portable CPCs havea size dependent counting efficiency, with low detection efficiency for particle sizes less than ∼30nm. This complicates totalnumbermeasurements with these instruments (Zhu, Yu, Kuhn, & Hinds, 2006). In addition, small fluctuations in CPC sample flowrate or pressure can result in complicating CPC operation due to liquid overflow (Birmili et al., 1997; Hermann & Wiedensohler,1996).Measurementswith portable CPCswill also be compromised by their lowupper concentration limit (105 cm−3). In addition,remote, long-term monitoring with CPCs is complicated by the need for regular maintenance to ensure that their working fluidlevels are maintained. There is an immediate need for a compact, portable, inexpensive, and easy to deploy UFP concentrationmeasurement instrument which could be used for large-scale indoor/outdoor monitoring and personal sampling studies.

Recently, the design and working of a compact instrument called the miniature electrical-mobility aerosol spectrometer(MEAS; Ranjan & Dhaniyala, 2007, 2008) was presented for ultrafine size distribution measurements. Here, we extend thatconcept to design a new compact, portable, instrument that can provide real-time total particle concentration over a desired sizerange.

2. Background

The design of a compact, portable total concentration sensor, called the tailored electrode concentration sensor (TECS) isintroduced, based on the concept of the MEAS instrument (Ranjan & Dhaniyala, 2007, 2008). The MEAS instrument consists ofthree sections—inlet; electrostatic precipitator (ESP); and a classifier section (Fig. 1). For sizing with MEAS, particles are chargedupstream of the instrument with a bipolar charger and enter the instrument through the inlet section. The inlet section isdesigned to ensure a uniform spatial distribution of particle concentration as they enter the ESP section. In the ESP section,particles pass through a set of parallel plate channels that are maintained at desired electric potential differences. Chargedparticles are electrostatically filtered from all channels, except one, the injection channel. The flow through this injection channelforms the aerosol flow in the classifier section, while the flow between the injection channel and the collection electrode acts assheath flow. In the classifier section, an electric potential difference is maintained to classify the injected particles based on theirelectrical mobility and particles are collected in a series of rectangular-shaped collection plates or electrodes that are connectedto electrometers. A size distribution can be obtained from the electrometer signals with the knowledge of particle collectioncharacteristics of the different electrodes (Ranjan & Dhaniyala, 2008).

The simple, open design of the MEAS results in a low-pressure-drop instrument, requiring control of just one flow. For real-time size distribution measurements with MEAS several electrometers are required; thus, potentially increasing its cost andcomplicating its operation. Often, a single measure of total particle number concentration over a desired size range, such as lessthan 100nm, is sufficient. For such applications, based on the MEAS design, a new TECS instrument is introduced, with a singlecollection plate and, hence, just one electrometer. The complication in the design of such an instrument is to ensure that theelectrometer signal is directly proportional to the particle number concentration over the desired size range.

Fig. 1. A cross-sectional view of the TECS/MEAS instrument. Charged particles are injected from one ESP channel (E3) and particles are classified by their electricalmobility in the classifier section.

M. Ranjan, S. Dhaniyala / Aerosol Science 40 (2009) 439 -- 450 441

3. Modeling and simulation

Measurement of total ultrafine number concentration based on particle electrical mobility is complicated by the size-dependent charging and collection characteristics of these particles. To ensure that the electrometer signal from capturedparticles is directly proportional to total particle number concentration, the collection plate or electrode in the TECS instrumentmust be shaped to obtain a size-independent kernel function or response function for the instrument. This collection plate shapewill likely depend upon the instrument operating conditions and geometry, such as: flow rate; classifier section dimensions; ESPand classifier plate voltages; ESP injection channel width, and particle charging characteristics. This paper presents a mathemat-ical approach to obtain such a collection plate shape for real-time total number concentration measurement over a targeted sizerange with the TECS instrument and provides preliminary experimental validation of the working of the instrument.

The net electrometer signal resulting from the capture of charged particles on a shaped collection plate is dependent onthe incoming particle size distribution (dN/d logDp), the size-dependent charging characteristics of the particles (�p), and thetransfer function of the shaped collection plate (�s), defined as the fraction of injection channel flowrate from which particlesare collected on the shaped-plate. The net signal (E) from the collection plate can be expressed as

E =∞∑p=1

peQ∫ ∞

0

dNd log Dp

�p(Dp)�s(Zp)d log Dp (1)

where p is the number of charges on a particle with diameter Dp, e is coulomb charge, Q is the flow rate through the instrument,and Zp is the particle electrical mobility. The transfer function of the shaped plate, �s, can be calculated as

�s =∫ xmax

Zp

xminZp

�(x, Zp)f (x)dx (2)

where�(x, Zp) is the collection efficiency per unit area of a rectangular plate at a location x along the flow direction and f(x) is thewidth of the collection plate at that location. The limits of the integral, xmin

Zpand xmax

Zp, represent the minimum and maximum of

the x-locationswhere particles ofmobility, Zp, are collected (as illustrated in Fig. 2). Eq. (2), thus, represents the net area-weightedparticle collection efficiency on a plate of width f(x), relative to that of a rectangle plate of width w. In the formulation of Eq. (2),it is assumed that particle collection is uniform along the width of the plate (i.e, there are no edge effects).

For ultrafine particles conditioned with a bipolar charger, only a small fraction of particles exist with more than one charge,and hence it is assumed that p = 1. Then, if the shape of the collection plate, f(x), could be chosen such that the product of theshaped plate transfer function (�s) and charging efficiency (�1; Wiedensohler, 1988) is a constant (�T), i.e.,

�1(Dp)∫ xmax

Dp

xminDp

�(x,Dp, p = 1)f (x)dx = �T (3)

where xmin,maxDp

are the same as xmin,maxZp

for singly charged particles, then the net electrometer signal from the shaped collectionplate (Eq. (1)) would be:

E = �TeQ∫ Dmax

p

Dminp

dNd log Dp

d log Dp = �TeQC. (4)

Thus, for a selected flow rate and collection-plate shape function, f(x), if Eq. (3) can be satisfied, then an electrometer signalresponse can be obtained that is directly proportional to the total number concentration (C) over a targeted size range (i.e.,between Dmin

p and Dmaxp ). Increasing the collection area of the shaped plate will scale the theoretical response function, �T,

resulting in an amplified electrometer signal.

Fig. 2. The collection locations of the particles with an electrical mobility Zp injected through the third injection channel. Dark plates are at high voltage andshaded plates are grounded.


X

f 1

f 2 f n

f n-1

f(x)

Plat

e sh

ape,

f(x

)Fig. 3. The discretized TECS plate shape function for the numerical solution of Eq. (8).

To determine the shape of the collection plate that results in a kernel-independent electrometer response, Eq. (3) can bewritten as

∫ xmaxDp

xminDp

�(x,Dp)f (x)dx = �T

�1(5)

As � = 0 for x < xminDp

and x > xmaxDp

, Eq. (5) can be rewritten with the integral limits changed from 0 to ∞ , without loss ofaccuracy. To solve for f(x), a numerical scheme is used, with the plate shape function discretized into (n–1) equally dividedintervals along the flow direction (x) (as illustrated in Fig. 3). Discretizing the plate shape function, Eq. (5) can be reduced to

n−1∑i=1

[�i(Dp)fmidi (xi − xi−1)] = �T

�1(6)

where fmidi and �i are the average values of f(x) and �, respectively, between the discrete x-locations xi and xi−1. An accurate

calculation of the plate shape function requires the solution to Eq. (6) with a large number of discrete collection plate locations,and, thus, transfer functions, making this approach computationally very intensive. The calculation of the optimum plate shapecan be simplified with the approach described below.

Based on observations of MEAS particle trajectories obtained from computational fluid dynamics simulations (Ranjan &Dhaniyala, 2007), it can be reasonably assumed that particles are captured uniformly over their collection locations. Therefore,over the collection locations (i.e., xmin

Dp< x < xmax

Dp) the local area-normalized collection efficiency [�(x,Zp)] is simply calculated as

�(x,Dp) = �tot(Dp)ADp

(7)

where �tot(Dp) is the net collection efficiency of a rectangular plate spanning (xminDp

,xmaxDp

) and of width, w; ADp is the collectionarea for the selected particle size, i.e., ADp = w(xmax

Dp− xmin

Dp). Then Eq. (5) reduces to

∫ xmaxDp

xminDp

f (x)dx =�Tw(xmax

Dp− xmin

Dp)

�1(Dp)�tot(Dp)(8)

The collection efficiency of a rectangular plate in the TECS geometry [�tot(Dp)] can be calculated using the method described inRanjan and Dhaniyala (2007). The shape function [f(x)] can be obtained using two approaches. In the first approach, the height ofthe ESP injection channel is assumed to be very narrow and hence the integral on the left hand side of Eq. (8) is further simplified.In the second approach, finite injection channel heights are assumed and a Simpson numerical integration technique is used tosimplify Eq. (8) into a series of linear equations. The solution procedure of the resulting ill-posed set of linear equations for theoptimum plate shape calculation is described below.

3.1. Assumption: narrow injection channel

If the ESP injection channel height is narrow relative to the height of the classifier section, then the charged particle flow isa small fraction of the total classifier section flow. It can then be assumed that particle collection will be over a narrow range oflocations, i.e., xmin

Dp≈ xmax

Dp. For this assumption, Eq. (8) reduces to

f (xmid) = f (x) = �Tw�1(Dp)�tot(Dp)

(9)

where xmid is the central location of particle collection, i.e., (xminDp

+ xmaxDp

)/2. As there is a unique relationship between particle

diameter and collection location, xmid, for the narrow injection channel assumption, an optimized collection plate shape that


Fig. 4. The collection plate geometry, f(x) calculated using Eq. (9) for a chosen set of ESP and classifier conditions. The scale corresponds to the diameter of theparticles collected on the plate.

Fig. 5. Normalized values of different parameters as a function of particle diameter for a narrow injection channel assumption. For the calculated plate shapefunction, f(x), the net electrometer signal is seen to be independent of particle size.

results in an electrometer signal only dependent on the total number concentration over the collected size range, can bedetermined using Eq. (9).

For preliminary calculations of f(x), the transfer functions (�tot) were theoretically obtained for a 3.4 cm long, 5 cm widerectangular collection plate located at a distance of 1mm from the ESP section exit (consistent with the MEAS classifier sectiondimensions; Ranjan & Dhaniyala, 2007). Particles are injected from the third injection channel with a total sample flowrate of 1LPM and the applied voltages on the classifier and ESP plates are set to 2kV and 200V, respectively (Ranjan & Dhaniyala, 2007).For these operating conditions, the collection plate geometry required to obtain a net electrometer signal proportional to totalparticle number concentration in the diameter range of 10–100nm (referred to here as the ultrafine range) is shown in Fig. 4.For this collection plate geometry, the product of particle fraction captured (�tot), charging fraction (�1), and the collection plateshape (f) results in an electrometer response (E) that is particle-size independent over the selected diameter range (Fig. 5). The netsignal from this collection plate will, therefore, be a true measure of the total UFP number concentration. The central assumptionin the above analysis is that the charged particles are injected over a narrow range of streamlines relative to the sheath flow.

3.2. No assumption: realistic case

In general, determining f(x) from Eq. (8) is equivalent to determining the shape function of an unknown curve with a knownarea between two points. While, there is a unique area between two points under a two-dimensional curve, the inverse problemrepresented by Eq. (8) has infinite possible solutions.


Fig. 6. (a) Transfer function (�tot) for the selected test case; (b) The calculated collection locations, xminDp

and xmaxDp

for different particle diameters. The ESP andclassifier voltages are 500 and 250V, flow rate is 1LPM, and particles are injected through the second injection channel.

The above analysis with the assumption of a narrow injection channel provides a good initial estimate of the collectionplate shape and an understanding of the plate shape function dependence on the different instrument parameters. In theTECS instrument, due to the physical limitations on the number of ESP channels that are possible, the narrow injection as-sumption cannot be easily satisfied. Also, as described in Ranjan and Dhaniyala (2007), the applied electric potentials in theESP and classifier sections will result in a non-uniform electric field within the instrument. In addition, the presence of theupstream and ESP plates in the flow region perturbs the flow field in the vicinity of the ESP section. The flow field per-turbation and electric field non-uniformity have been fully characterized and accounted for in the calculation of the par-ticle collection efficiency for the different injection channels and collection plates. The finite injection channel dimensionsand the electric and flow field non-idealities result in particle collection over a finite range of x-locations, and this mustbe considered for accurate plate shape calculation. The solution procedure for Eq. (8), under these conditions, is describedbelow.

For given operating conditions and instrument geometry—such as, flow rate, collection plate length, injection channel, andclassifier and ESP voltages—the transfer function for a rectangular collection plate can be obtained using the method of Ranjanand Dhaniyala (2007). Appropriate operating conditions can be selected such that collection efficiency over a target size rangeis non-zero. For different particle diameters in the targeted size range, collection efficiencies and collection locations (xmin

Dpand

xmaxDp

) can also be determined using the approach of Ranjan and Dhaniyala (2007). The integral term in the left hand side of Eq. (8)can be discretized using the Simpson numerical integration approach. All terms in the right hand side (RHS) of Eq. (8) are known,except �T. The constant �T determines the scaling factor for the plate width, which can be less than or equal to the width of theclassifier channel, and is initially chosen as 1. For n discrete values of the shape function (f), and m discrete values of particlediameter, Eq. (8) reduces to a matrix equation of the form, SF = A, where S is an m×n coefficient matrix, F is a column matrix oflength n, and A is a column matrix of length m consisting of the RHS values of Eq. (8). The nature of the integral Eq. (8) resultsin an ill-posed set of linear equations. The magnitude of the ill-posedness is typically measured by the condition number of thecoefficient matrix, which also represents the rate at which solution of f will change as a function of area matrix A. Small valuesof the condition number ( ≈ 1) represent a well conditioned linear set of equations and under these conditions, a solution fromdirect matrix inversion is possible. The inherent statistical error involved with the calculation of �tot, xmin

Dp, and xmax

Dp, and the

numerical errors with the Simpsonmethodwill, however, result in a coefficient matrix with a large condition number, and hencedirect matrix inversion will result in an extremely sensitive or “noisy” solution. A regularization routine (Ranjan & Dhaniyala,2008; Talukdar & Swihart, 2003) is, therefore, used to obtain plate shape functions that are practical (non-negative and relativelysmooth).

There are several parameters that influence the solution scheme including the number of unknowns in the equation (n),number of equations (m), the regularization parameter in the inversion routine (�), electrometer signal (E), electrometer error(�E), electrometer constant (�T), and the minimum collection plate width (�) that ensures that the shape function values arenon-zero and have a practical minimum value. For simplification, the number of equations and unknowns were assumed tobe equal (i.e., m = n). The optimal solution would minimize the electrometer error (�E) while maximizing the strength of theelectrometer signal (E).

For a test case, the ESP and classifier voltages were set to 500 and 250V, particles were injected from the second injectionchannel from the collection plate side (E2, Fig. 1), and the sample flow ratewas set as 1LPM. The collection plate lengthwas chosenas 7.6 cm, with a starting location of 0.079m from the entrance of the inlet section (Fig. 1). In Fig. 6, the resulting rectangular


plate transfer function (�tot) and the minimum and maximum diameter particle collection locations, xminDp

and xmaxDp

, are shown.In Fig. 6b, the beginning and end of the x-collection locations in the classifier section for different particle diameters are shownfor the selected TECS geometry.

The coefficient matrix of the test-case has a large condition number (3.1E6), prohibiting direct inversion of the linear matrixequation. To obtain a regularized solution, the area and coefficient matrices were input to the inversion routine and several platesolutions were obtained for regularization parameter (�) values varied logarithmically between 1E−10 and 10 in 101 steps. Forthe smallest value of �, the effect of smoothening is the least and the regularized solution is similar to that obtained from directinversion; for the largest � values, the effect of smoothening dominates and the accuracy of the solution is compromised. Todetermine an optimum value of �, an electrometer signal error parameter is introduced, which is defined as the percentage errorbetween the theoretical and predicted electrometer signals. For a selected particle size distribution and size range, the theoreticalelectrometer signal (ET) is obtained considering the theoretical response function (�T; Eq. (3)) while the predicted electrometersignal (EP) is obtained considering the final selected plate shape. The percentage electrometer error (�E) is, thus, calculated as

�E =∣∣∣1 − ET

EP

∣∣∣ ∗ 100 =

∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣

1 −peQ

∫ DpfDpi

dN(Dp)d log Dp

�T d log Dp

peQ∫ DpfDpi

dN(Dp)d logDp

�1�tot

⎡⎢⎢⎢⎢⎢⎣

∫ xmaxDp

xminDp

f (x) dx

w(xmaxDp

− xminDp

)

⎤⎥⎥⎥⎥⎥⎦d log Dp

∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣

⇒ �E =

∣∣∣∣∣∣∣∣1 −

∫ DpfDpi

dN(Dp)d log Dp

d log Dp

∫ DpfDpi

dN(Dp)d log Dp

�P

�Td log Dp

∣∣∣∣∣∣∣∣=

⎛⎜⎜⎝

∫ DpfDpi

dN(Dp)d log Dp

∣∣∣∣∣�P

�T−1

∣∣∣∣∣ d log Dp

∫ DpfDpi

dN(Dp)d log Dp

∣∣∣∣∣�P

�T

∣∣∣∣∣d log Dp

⎞⎟⎟⎠

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(10)

where Dpi and Dpf are the lower and upper diameter limits of detection interest, respectively, �P is the predicted responsefunction, i.e.,

�p = �1�tot

⎡⎢⎢⎣

∫ xmaxDp

xminDp

f (x)dx

w(xmaxDp

− xminDp

)

⎤⎥⎥⎦ (11)

obtained using the calculated collection plate shape function. The electrometer error (�E) must be minimized to obtain optimalvalues of the shape function f(x). The error in the electrometer signal is dependent on the size distribution, dN(Dp)/d logDp, andthe particle-size dependent ratio of the response function, �P/�T . The extent of deviation of the predicted response function fromthe theoretical value is calculated using the ratio (1+ |�P/�T − 1|), where a value of 1 is the best match with theoretical responsefunction.

In calculating the electrometer error for any plate shape, the choice of the size distribution of the incoming particles isimportant. In practice, infinite size distributions and associated infinite optimal plate shapes are possible. In the currentanalysis, as a practical compromise and to minimize any particle size bias, a size-independent (flat) number distribution(dN/d logDp = 1E5 cm−3) is used to represent the sampled aerosol. Simulations were performed for 10 different values of �T

varying from 1E−2 to 1E−1, and 11 values of � from 1mm to 4 cm. For each of the 110 combinations of �T and �, 101 plate shapeswere obtained for the varying � values. An optimum � value was identified corresponding to a minimum electrometer error (�E,Eq. (9)).

The percentage electrometer error as a function of � is shown in Fig. 7 for various values of �T. As expected, the predictedelectrometer error increases with increase in the minimum base width, �. Since the choice of � is an additional constraint on thesolution, higher values of � result in a greater error in the shape function determination. For smaller values of �, the percentageerror values are seen to range from 12% to 27% of the predicted electrometer signal. For the 110 optimum plate shapes obtained,the optimum value of �T and � was selected by analyzing the electrometer error, �E, and the electrometer signal, E.

Based on the minimum value of �E, the plate parameter values were obtained as: � = 1mm, and �T = 0.02. The optimumplate shape for these parameters is shown in Fig. 8a. Unlike the systematic variation in the plate shape obtained for the narrowinjection channel assumption, the optimum plate shape for the realistic case is not smooth because of the ill-posed nature of thegoverning equation (Eq. (8)). The calculated shape function shown in Fig. 8a is not a unique solution of Eq. (8), but is the best onefrom the obtained family of solutions. The ratio of predicted-to-expected response functions for different particle sizes is shownin Fig. 8b. Most of the values are ∼1, except at the edges due to finite slope of the transfer function. The absolute electrometererror for the selected shape function is calculated to be 12% of the theoretical electrometer signal which turns out to be 2 fA for aflat distribution with a dN/d logDp value of 1E5 cm−3.

Increasing the injection channel width (aerosol flow) increases the electrometer signal, and, thus, the instrument sensitivity.The above analysis is repeated to determine the influence of the injection channel width on the electrometer signal. Two test


Fig. 7. The variation of the electrometer error (Eq. (10)) with the minimum base width, �, for different values of theoretical plate shape factor, �T .

Fig. 8. (a) The plate shape function for � = 1mm, �T = 0.02; (b) The response function for the selected plate shape in comparison to the desired flat instrumentresponse over the selected size range.

cases were studied: particles injected from channels 2–3 and particles injected from channels 2–3–4. The electrometer signalerror for various values of � and �T are shown in Fig. 9.

The variation of �E with � and �T for these test cases is similar to that seen for the single injection channel case shown inFig. 7. For the multi-injection channel cases, the minimum error values are ∼20% of the theoretical electrometer signal, muchhigher than that with single-injection channel. This is because, in the TECS design, increasing the number of injection channelslowers the aerosol-sheath flow ratio and, thus broadens the transfer functions and complicates shape function calculation. Foraccurate measurements, therefore, the injection channel width should be minimized, and for experimental validation, a singleinjection channel is chosen.

4. TECS experimental validation

The optimal plate shape for the test case studied above (Fig. 8a) was fabricated for experimental validation of the TECSinstrument concept (Fig. 10a). For ease of testing, the TECS plate length and width were selected to fit the MEAS classifier section(Ranjan & Dhaniyala, 2008). Grounded complementary plates were located adjacent to the shaped collection plate, with a spacingof 1mm between them (Fig. 10b). The complementary plates help maintain uniform electric field throughout the TECS classifiersection. The shaped collection plate and the complementary plates were mounted on the collection plate holder and fitted withtriax connectors.

The experimental setup used for TECS testing is shown in Fig. 11, where a combination of particle sources—a spark aerosolgenerator (GFG-1000, Palas, Karlsruhe, Germany) for sub-100nm particles and a nebulizer with dioctyl sebacate (DOS) in


Fig. 9. Variation of the electrometer error with � and �T for injection from channels 2 and 3 and injection from channels 2–3–4. The classifier voltage is 250V,ESP voltage is 500V, and flow rate is 1 LPM.

7.6cm

5cm

7.6cm5cm

3.5cm

ESP section Inletsection

Classifier section

Outlet

Collection plate holder

TECS plate

Complimentary plate

Complimentary plate

Collection holder base

Fig. 10. (a) The TECS components and their important dimensions. (b) The collection plate holder with the TECS and the complementary plates.

isopropanol for larger particles—were used to generate particles over a broad range of sizes. The mixture of particles fromthese sources created a bimodal distribution, with one peak in the ultrafine particle range and the other peak above 100nm, withtheir relative strengths controlled by the fraction of their flowrates and the frequency of the spark generator. The aerosol flowfrom the particle generators was sent to a 20 L mixing volume chamber to dampen out fluctuations in the generated aerosol sizedistributions. The particle size distributions downstreamof the chamberwere continuouslymonitored using a SMPS (long columnDMA-TSI model 3071; aerosol flowrate—0.6LPM; and sheath flowrate—6LPM; water condensation particle counter [CPC]—TSIUltrafine CPCmodel 3786) operatedwith a scan time of 240 s and count data collected in 48 logarithmically-spaced size channels.The TECS classifier and ESP voltages were set to 250 and 500V, respectively, and the flow rate was maintained at 1LPM usinga highly stable mass flow controller (Alicat Scientific, Model MC-20SLPM). The TECS complementary plates were set at groundpotential and the collection plate was connected through a triax connector to an electrometer (Keithley source meter; Model6430), which was found to be very stable during previous experiments (Ranjan & Dhaniyala, 2008).

An automated data acquisition system was used to monitor the TECS electrometer signal, TECS flow rate, and the upstreamparticle size distributions. The background electrometer data was obtained by passing clean flow through the TECS instrument.The background signal was found to be largely invariant over the measurement duration (∼2.5 fA). With the test particles, the


Fig. 11. Experimental setup for testing of TECS performance.

electrometer signal responses varied from 2.5 to 50 fA depending on the upstream number concentration. Eight different sizedistributions were generated by varying the frequency of the spark generator and the operating pressure of the nebulizer. TheTECS signal measurements were made over 8min for each particle size distribution setting with an interval of 1min betweenconsecutive measurements. Two measurements of upstream size distributions were made with the SMPS system for each sizedistribution setting. The SMPSmeasurements were inverted to obtain particle size distributions and the average of the two SMPSmeasurements was used as the upstream size distribution. The total particle concentration of the test aerosol was obtained byintegrating the entire area under the SMPS size distribution curve, while the targeted particle concentration was obtained byintegrating the size distribution curve between the desired particle size limits (32–90nm).

A comparison of the TECS electrometer signal with the total and targeted particle concentrations from the SMPS instrumentis shown in Fig. 12. The TECS electrometer signal, which is representative of the number of particles collected on the shapedcollection plate, is seen to be linearly proportional to the targeted particle concentration, while being independent of the totalnumber concentration of the test aerosol. A closer examination of two test cases, labeled cases A and B in Fig. 12a is madeby comparing the upstream size distributions for these cases. The area contained within the vertical lines marked on the sizedistribution curves in Fig. 12b is the targeted particle concentration for the TECS instrument. In case A, the particle size distributionis mostly contained within the targeted size range and hence the difference between the targeted and total particle concentrationis small. In case B, the particle size distribution extends to sizes much larger than the targeted range and, hence, the totalparticle concentration is much larger than the targeted value. For both cases, the electrometer signal is only proportional to thetargeted particle concentration. This provides initial validation of the TECS concept. A direct experimental validation of the TECStheoretical response function (Fig. 8b) is not easily possible because of the difficulty of generating a high concentration of charged,monodisperse particles.

The detection limits of the TECS instrument is dependent on the length of the collection plate, distance between the ESP exitand start of the collection plate, maximum possible classifier voltage, maximum possible ESP voltage, and flow rate. The strengthof the electrometer signal can be increased by increasing the flowrate and the maximumwidth of the collection plate. The use ofthe existing MEAS components (Ranjan & Dhaniyala, 2008) for the TECS instrument, limited the detection range to 32–90nm. Tofabricate a TECS instrument version for total ultrafine concentrationmeasurements, a slightly longer classifier section is requiredand the collection plate should be located closer to the ESP section than in the current version.

5. TECS applications and limitations

In addition to total number concentration measurements over a desired size range, the proposed analysis can be extended todetermine electrode shapes that will result in signals that are proportional to a size-dependent collection curve (i.e., select �T tohave a desired size-dependence), such as the lung retention curve. Electrode shapes can also be obtained for measurements ofhigher moments of the number size distribution of the sampled aerosol. Also, the present analysis approach can be extended toelectrical mobility instruments with different classifier geometries, to arrive at collection electrode shapes that provide signalsproportional to desired measurement quantities.


Fig. 12. (a) Comparison of the detected TECS electrometer signal with the total and ultrafine particle concentrations of the test aerosol. The TECS electrometersignal is seen to be linearly proportional to the upstream ultrafine particle concentration and independent of the total concentration. (b) The size distributionsfor the cases A and B data points.

The detection limit and sensitivity of the instrument are dependent on the electrometer characteristics. For a typical elec-trometer with 1 fA lower detection limit, the current version of the TECS instrument can measure particle concentration down to∼1.1E5 cm−3. The TECS detection limit can be lowered by increasing the sample flow rate, scaling the collection plate width, andusing a higher sensitivity electrometer (e.g., Keithley 6430). Lowering the TECS detection limit will enable its possible applicationfor personal/ambientmeasurement. Also, for ease of deployment for ambient and personal measurements, it would be preferableto use a unipolar charger rather than bipolar charger upstream of the TECS. The calculation of a plate shape function with aunipolar charger would, however, be complicated by the presence of multiply-charged particles.

6. Summary

A novel instrument, called the tailored electrode concentration sensor (TECS), has been designed for real-time ultrafinenumber concentration measurement based on the design of the MEAS instrument (Ranjan & Dhaniyala, 2007, 2008). In TECS,an optimal collection-electrode shape is determined to provide total concentration measurements over a desired size range.A new computational approach was developed for the TECS plate design using the regularization technique developed for theMEAS size distribution calculations. Experimental results show that with an optimally-shaped collection plate, the measuredTECS-electrometer signals are linearly proportional to the integrated concentration over a targeted particle size range; validatingthe TECS calculation procedure and the working of the instrument.

Acknowledgments

The authors kindly acknowledge financial support from the National Science Foundation (Grant no. ATM-0548036) for thisresearch. The comments and suggestions by the editor, Dr. Gerhard Kasper, and two anonymous reviewers are also gratefullyacknowledged.


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