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A new miniature electrical aerosol spectrometer (MEAS): Experimental characterization
Aerosol Science 39 (2008) 710 – 722 www.elsevier.com/locate/jaerosci
A new miniature electrical aerosol spectrometer (MEAS): Experimental characterization Manish Ranjan, Suresh Dhaniyala∗ Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA Received 12 September 2007; received in revised form 8 April 2008; accepted 9 April 2008
Abstract Design and theory of a new compact ultrafine particle sizing instrument, called the miniature electrical-mobility aerosol spectrometer (MEAS), was recently introduced [Ranjan, M., & Dhaniyala, S. (2007). A new miniature electrical spectrometer: Theory and design. Journal of Aerosol Science, 39, 950–963]. In the MEAS, electrostatic precipitation technique is used for both generation of sheath flow and classification of particles based on their electrical mobility. An electrometer-array, connected to the collection electrodes in the classifier section, is used to measure the number of particles collected in the different mobility channels, and these data are inverted using MEAS transfer functions to obtain particle number size distributions. Design of a prototype MEAS and the experimental approach to validate the performance of the individual components of the instrument are presented. Particle size distributions obtained from MEAS measurements compare well with those obtained using a scanning mobility particle sizer (SMPS; TSI 3936), validating theoretical calculations of instrument transfer functions. The operational limits of MEAS are determined from the calculation of error in the inverted size distribution as a function of total particle concentration. This analysis suggests that the designed MEAS can be used for applications such as personal and ambient monitoring under conditions of moderate to high particle concentrations. 䉷 2008 Elsevier Ltd. All rights reserved. Keywords: Electrical mobility; DMA; MEAS; Miniature; Compact; Aerosol instrument; Electrometer; Size distribution; Experiments; Personal sampler
1. Introduction A compact real-time size distribution measurement instrument is essential to study spatial and temporal variation of particle concentration in the ambient atmosphere and our microenvironment. Commonly used electrical-mobilitybased particle characterization instruments include scanning mobility particle sizer (SMPS; TSI Inc.), electrical aerosol spectrometer (EAS; Tammet, Mirme, & Tamm, 2002), and differential mobility spectrometer (DMS; Biskos, Reavell, & Collings, 2005a). SMPS uses a differential mobility analyzer (DMA; Knutson & Whitby, 1975) to classify particles based on electrical mobility and a condensation particle counter (CPC; Agarwal & Sem, 1980) or a Faraday cup electrometer to count them. The EAS and DMS use inside-out classification columns with a set of electrometers for sub-second particle size distribution measurements. These instruments are most suitable for site-specific, highresolution particle size distributions, but these instruments are large in size, expensive, and complicated to use due to ∗ Corresponding author. Tel.: +1 315 268 6586; fax: +1 315 268 6695.
E-mail address: [email protected] (S. Dhaniyala). 0021-8502/$ - see front matter 䉷 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2008.04.005
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Fig. 1. A schematic diagram of the MEAS instrument illustrating the injection of particles from one ESP channel (E3) and the subsequent electrical-mobility-based classification of particles in the classifier section.
multiple flow controls and several size classification channels. There is an immediate need for a compact, portable, inexpensive, and easy to deploy instrument which can measure the real-time size distribution with reasonable accuracy. Recently, design of a new compact electrical-mobility-classification instrument, called the miniature electricalmobility aerosol spectrometer (MEAS; Ranjan & Dhaniyala, 2007), was introduced (Fig. 1). MEAS consists of three major parts: inlet, electrostatic precipitator (ESP), and classifier sections (Fig. 1). For sizing with MEAS, particles are charged upstream of the instrument with a bipolar or a unipolar charger and enter the instrument through the inlet section. The inlet section is designed to ensure a uniform spatial distribution of particle concentration over the ESP entrance cross-section. The ESP section consists of a series of narrow channels maintained at desired electric potential differences. As particles move through the ESP section, they are electrostatically filtered from all channels, except one, the injection channel. Particles and flow traversing through the selected injection channel into the classifier region form the aerosol flow, while the rest of the flow acts as sheath flow. In the classifier section, an electric potential difference is maintained to classify the injected particles based on their electrical mobility. Collection electrodes in the classifier section are connected to electrometers and the signals obtained from the collection of charged particles are used to determine the size distribution of the sampled particles, considering the transfer function of the collection plates. The MEAS design is advantageous over other existing electrical-mobility measurement instruments, as it requires control of only one flow. The relatively open MEAS geometry results in a low-pressure-drop instrument and the option of varying the injection channel permits measurements over a broad range of particle sizes. The compact and simple design of the MEAS makes it inexpensive to manufacture. The rectangular geometry permits easy scaling of MEAS dimensions to optimize its response based on sampling conditions. 2. Design description A prototype MEAS (Fig. 2) was fabricated for experimental validation of theoretical predictions. The MEAS inlet section is designed to transition flow from the circular entrance to the rectangular cross-section of the ESP section. To minimize flow recirculation regions, the cross-section of the inlet section gradually changes from a circle to a rectangle with an expansion angle of ∼18◦ over a length of 10 cm. While an optimal expansion angle would be ∼7◦ , to keep the inlet section short a larger expansion angle is chosen with additional pressure drop generated by placing a wire mesh in the center of the inlet section length. To minimize the particle loss within the instrument due to charge effects, the MEAS inlet and outlet were both cast out of aluminum. In the prototype MEAS, the ESP section is designed with five parallel electropolished stainless steel plates that are 2 cm long, 5 cm wide, 0.7 mm thick, and spaced 2 mm apart. An ultraminiature voltage amplifier (EMCO Model Q40-5) is used to set the voltage on the ESP plates. The ESP plate voltages are chosen such that charged particles are electrostatically filtered through all the ESP channels except one selected injection channel. For typical operation, the potential difference in the ESP channels must be below the breakdown limit, while resulting in the capture of all charged particles of measurement interest. The potentials on the individual ESP plates are maintained using a single high-voltage source via a distributor setup. For handling safety, the ESP and classifier sections are housed in an external insulated unit made of Delrin䉸 . The classifier section of the MEAS consists of a set of seven collection plates, spaced 1 mm apart, located across a classifier plate maintained at high voltage. Electropolished stainless steel rectangular plates of 1 cm length, 5 cm width, and 0.7 mm thickness are used as collection plates.
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Fig. 2. The MEAS prototype that was built and tested.
The MEAS particle capture characteristics are complicated by the non-uniform nature of the electric and flow fields in the classifier section. The details of the calculation of the electric and flow fields in the MEAS are provided in Ranjan and Dhaniyala (2007) and only a brief overview is given here. The classifier section flow field at the vicinity of the ESP section exit must be accurately modeled for accurate particle trajectory calculations. For this, the assumed parabolic velocity profiles in the individual ESP channels are combined using a Heaviside step function to represent the classifier section velocity profile near the ESP exit. In the rest of the classifier section a single parabolic velocity profile over the entire channel is assumed. For the non-uniform electric potential field in the MEAS classifier section, space charge effects are neglected and the Laplace equation is solved with appropriate boundary conditions. The resultant electric flux () and stream () functions in the classifier section are then analytically calculated and contours of + Zp are used to determine particle trajectories in the MEAS instrument. The instrument transfer functions were calculated as the fraction of charged aerosol particles entering the ESP injection channel that are captured on the collection plate. With known transfer functions, appropriate data inversion routines can be used to determine size distribution of the sample aerosol from the electrometer signals. In addition to the theoretical modeling, the MEAS performance is also obtained from computational fluid dynamics (CFD) simulations using the software FLUENT (FLUENT Inc., NH). A user-defined function (UDF) code is used to accurately account for slip correction and the effect of electric field on particle trajectories in the instrument (Ranjan & Dhaniyala, 2007). The numerically calculated transfer functions are seen to compare well with theoretical predictions. 3. MEAS performance validation Validation of theoretical and numerical predictions of MEAS performance requires a number of different experiments. In the first test, the overall collection efficiency of the classifier section is measured. For this test, all ESP plates are grounded, thus permitting the injection of charged particles from all ESP channels into the classifier section. The total collection efficiency can be determined from measurement of particle concentrations upstream and downstream of the instrument and compared with the theoretically predicted collection efficiency. In the second test, the ESP plate voltages are set such that particles are injected through one channel and corresponding classifier section collection efficiencies are experimentally obtained. In the third test, electrometers are connected to collection plates and the response is measured for varying flowrates and injection channels. Particle size distributions measured with MEAS in this test are compared with measurements with commercial instruments.
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4. Performance evaluation of the MEAS classifier section The experimental setup used for testing the performance of the classifier section is shown in Fig. 3. The combination of a particle source (nebulizer; NaCl in H2 O), compressed air (∼50 psi) dried with silica gel, and a long column DMA (TSI Model 3071, aerosol flowrate—0.9 LPM and sheath flowrate—10 LPM, recirculated) was used to generate particles over a narrow range of electrical mobilities. The aerosol flow from the nebulizer was sent to a chamber (volume—10 L) to dampen out fluctuations in the generated aerosol size distributions. Particle size distributions downstream of the chamber were continuously monitored using a fast mobility particle spectrometer (FMPS; TSI 3091) and were observed to be largely uniform over a 2-h interval (total concentration mean: 7.93E4 cm−3 , upper 95% confidence interval: 7.99E4 cm−3 , lower 95% confidence interval: 7.88E4 cm−3 , geometric mean: 124 nm, geometric standard deviation: 1.54). Downstream of the DMA, charged monodisperse particles were passed through the MEAS. Particle concentrations upstream and downstream of the MEAS were measured using two CPCs (TSI CPCs 3025 and 3786) to calculate the MEAS collection efficiency as a function of the classifier plate voltage. With two particle counters, temporal variations in monodisperse particle concentrations can be accounted for in the collection efficiency calculation. For efficiency measurements, the classifier plate voltages were varied over 4-min intervals and particle counts were recorded at 1 Hz on a computer. For MEAS operation with grounded classifier and ESP plates (i.e., no controlled particle collection in MEAS), a slight discrepancy was observed between the upstream and downstream CPCs. The average of the median values of the ratio of particle concentrations measured by the upstream (CPC 3025; ref ) and the downstream (CPC 3786; C ref ) counters was found to be 1.1 with the standard deviation of 0.035 for Cup down two tested particle diameters (136 and 164 nm). This constant factor is due to the combination of small difference in the detection efficiencies of the two CPCs, particle loss within the MEAS, and slight noise in the voltage source. This factor is accounted for in all subsequent collection efficiency measurements. A comparison of the experimentally measured collection efficiency with the theoretical predictions of the classifier section collection efficiency is shown in Fig. 4 for the two test sizes. The error bars in the plot represent the standard deviation of the collection efficiency calculated using the uncertainty propagation method. The parameter Vte Ac /Q is used for the comparison tests, where Vte is the electrostatic terminal velocity (Hinds, 1999), Ac is the collection area of the entire classification section, and Q is the flowrate through the instrument. This parameter represents the collection efficiency for a uniform electric field and plug flow condition. The experimental results are seen to compare well with the numerical and theoretical predictions. At zero classifier voltage, small collection efficiency is observed, possibly because of particle loss due to exposure to the Delrin䉸 housing over a small area. The overall result of this test validates the performance of the classifier section without considering the ESP voltages.
Fig. 3. Schematic diagram of the experimental setup used for testing the individual components of MEAS.
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Fig. 4. Comparison between theoretical and experimental collection efficiencies of the classifier section with the grounded ESP section using 136 and 164 nm test particles.
5. MEAS collection efficiency evaluation In the next test, the collection characteristics of the classifier section with the ESP operated to permit injection through one channel are evaluated. Particles are injected through the third injection channel and the penetration through the classifier section is measured as a function of applied potential difference. The experimental setup shown in Fig. 3 is again used for these experiments. Particles of 134 nm diameter are selected to be output from the DMA. The MEAS classifier section voltage is varied and the collection efficiency of the classifier section is measured as before. A comparison of measured MEAS particle penetrations and theoretical predictions is shown in Fig. 5. The experimental penetration through the third injection channel was found to be 16.4%, while the ESP penetration in the theoretical calculation was assumed to be 16.6%. The theoretical collection efficiencies are seen to largely match experimental data and the error bars are calculated as explained in the previous section. A slight difference between theory and experiments for collection efficiency in the presence of ESP plate voltages is likely due to simplifications made in the calculation of non-uniform electric and flow fields in the classifier section.
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Fig. 5. Comparison between theoretical and experimental collection efficiencies with 350 V on the ESP section and 135 nm particles are passed through the third injection channel of the ESP section. Theoretical ESP penetration is 16.67% ( 16 th) and experimental penetration was measured to be 16.4%.
6. Measurement and comparison of particle size distribution by MEAS To test the performance of the integrated MEAS instrument, the transfer function of the different collection stages must be experimentally determined and compared with theoretically predicted results. Direct transfer function measurements are very difficult for electrometer-based instruments due to the difficulty of generating charged particles over a narrow size range at concentrations that are high enough for electrometer detection but lower than the upper limit of an upstream counter. Moreover, electrostatic capture of charged particles for sheath flow generation in the ESP channels of MEAS reduces the charged aerosol concentration available for detection to 16 th of the entrance concentration. Validation of MEAS transfer function calculation is, therefore, made by comparing size distributions determined from measured MEAS electrometer signals with those obtained from other instruments. Due to the availability of only one electrometer, the size distribution measurements were made by varying one of the instrument parameters controlling the collected mobility range. In the MEAS, the detected mobility range depends on the classifier plate voltage, the operating flowrate, the choice of collection plate number, and the selection of injection channel. Changing the classifier plate voltage was observed to result in electrometer noise as the classifier channel acts as a large capacitor with a certain time constant. This also slows the electrometer response time. Size distribution measurements obtained by varying the ESP injection channel and the collection plate will be limited by the number of ESP channels and collection plates. Also, changing ESP voltages increases electrometer noise. For measurements with a single electrometer, varying the flowrate is most suitable. For measurements of particles in the ultrafine size range, flowrates were stepped up gradually over a range of 0.1–5 LPM. For this operating range, the flow in the instrument is laminar and uniform throughout the instrument. Size distribution measurements were performed by different combinations of flowrates, injection channel, and collection plates. Initial experiments with the electrometer were to test the linearity of the signal response to upstream particle concentration. The experimental setup used for this test is shown in Fig. 6. The electrometer (Keithley sourcemeter, Model 6430) was connected to the seventh collection plate from the ESP channel side. The ESP plates were set to 500 V with the injection channel chosen as the fourth channel above the collection plates. The classifier plate was set to 450 V and flowrate through the instrument was 1 LPM. Particle size distribution upstream of the MEAS was monitored with an FMPS system and the MEAS electrometer signal was recorded at 1 Hz. The upstream particle concentrations were varied and the expected number of particles captured on the seventh collection plate was calculated by convolving the theoretical transfer function (Ranjan & Dhaniyala, 2007) with the FMPS particle size distribution. A comparison of the expected concentration and the measured electrometer signal is shown in Fig. 7. The fluctuation in the FMPS size distribution measurement has been accounted in the expected particle concentration calculation. Upper and lower
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Fig. 6. Experimental setup used for the tests of electrometer signal variation and measurements of size distributions with MEAS.
Fig. 7. Comparison of raw electrometer signal with expected particle concentration on the collection plate.
95% confidence interval limits for the FMPS size distribution are used for error calculation in the expected particle concentration. Electrometer signal was recorded every second and the 95% upper and lower confidence intervals for the 30 s steady-state electrometer signal are also shown in Fig. 7. Excellent error values are attributed to the highly stable nature of the aerosol flow through the chamber outlet and the highly stable signal measured by the sourcemeter (Keithley, 6430 with preamp) operated at slow speed (10 plc) with three stage internal filtering system. As expected, the electrometer signal varied linearly with the change in upstream particle concentration. This test provides a validation of the consistency of the electrometer signal response to captured particle concentrations. 7. Size distribution measurement with flowrate variation For size distribution measurements, the flowrate through the instrument was stepped from 0.25 to 1.5 LPM. The classifier and the ESP voltages were set to 500 and 700 V, respectively. An experimental setup similar to that shown in Fig. 8 is used for this test. The flowrate through the instrument was controlled by an adjustable valve placed downstream of the instrument. The electrometer data were continuously acquired via an RS232 port using a LabView code.
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Fig. 8. Experimental setup used for size distribution measurements with MEAS.
Fig. 9. Particle size distribution comparison of MEAS and SMPS using laboratory-generated aerosol.
To calculate particle size distributions, the discretized linear inversion equations are solved with a first order inversion routine considering the theoretical instrument transfer functions. A large upstream particle concentration was used to reduce the effect of electrometer noise on the signal and the flowrates were chosen to ensure minimal overlapping of transfer functions. This facilitates easy size distribution calculation using first order direct inversion. Size distribution measurements with MEAS are seen to compare well with those made using an SMPS (Fig. 9). The large concentrations used in this test ensured sufficient electrometer signal strengths in the range of 30–400 fA. Highly stable flow measurement device (Alicat Scientific, Model MC-20SLPM) and minimal electrometer fluctuation cause negligibly small variation in the measured size distribution. A more stringent test of MEAS performance requires measurements with lower particle concentrations and at higher resolution. Increasing the number of measurement channels results in overlapping of transfer functions and complicating data inversion. For such data sets, advanced data inversion techniques are required and our approach is outlined below.
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8. Data inversion methodology The electrometer response is related to the upstream size distribution and the instrument transfer function as follows: ∞ ∞ (nf (n, Dp )i (n, Dp )) d log Dp , (1) N (log Dp ) Ei = Qe 0
n=1
where Ei is the ith channel electrometer current, N is the particle size distribution entering the instrument, n is the number of elementary charges on the particle, e is the charge on an electron, f is the particle charge distribution, i is the MEAS transfer function, and Dp is the particle diameter. This equation is commonly referred to as the Fredholm integral equation of the first kind and its inversion is an ill-posed problem that is further complicated by overlapping set of transfer functions (Ranjan & Dhaniyala, 2007). Data inversion for an ill-posed system of equations is discussed by Talukdar and Swihart (2003), Kandlikar and Ramachandran (1999), Lesnic, Elliot, and Ingham (1996), Wolfenbarger and Seinfeld (1990), Busigin, Vooren, and Phillips (1980), and Cooper and Spielman (1976) among others. The ill-posed inversion equation is commonly solved with a regularization technique to obtain a best estimate of the size distribution (Bashurova, Koutzenogil, Pusep, & Shokhirev, 1991; Lloyd, Taylor, Lawson, & Shields, 1997; Phillips, 1962; Talukdar & Swihart, 2003; Wolfenbarger & Seinfeld, 1990, 1991). A regularization technique balances the accuracy of inversion result with the smoothness of the solution using a regularization parameter. One efficient method to determine the regularization parameter is the L-curve optimization technique (Hansen & O’Leary, 1993) used for inversion of DMA data (Hansen, 1992; Talukdar & Swihart, 2003; Wahba, 1990; Wolfenbarger & Seinfeld, 1991). An inversion routine based on the L-curve regularization technique is developed for size distribution calculation with the MEAS. In the L-curve technique, the optimal value of the regularization parameter is obtained by a maximum curvature approach (Hansen, 1992). To test the performance of the MEAS inversion routine, the theoretical MEAS transfer functions are convolved with an assumed size distribution to calculate the expected electrometer signal (Ei ) in terms of total particle concentration. To account for signal errors, we consider two types of noise: a Poisson-type pois counting noise (Ei ) inherent with the expected particle concentration on the collection electrodes and a Gaussian spectrum (Ei εi ) with mean zero and standard deviation of (Ei ) to account for the electrometer noise. For inversion tests, the expected electrometer signal is obtained as follows: noisy
Ei
pois
= Ei
+ E i εi ,
i = 1, N ,
(2)
noisy
where Ei is the electrometer current with noise in channel i. To estimate the accuracy of inversion for different starting size distributions, the difference between the inverted and actual distributions is represented as percentage area error, area , calculated as follows: ⎤ ⎡ Df |N − N | dD p inv D ⎦ ∗ 100, (3) area = ⎣ i D f Di N dDp where Ninv is the inverted size distribution. The percentage area error as a function of total particle concentration for a lognormal distribution [ = 70 nm, g = 1.35] is shown in Fig. 10. As expected, the area error reduces with increasing total concentration. This analysis provides an estimate of the operating limits of the fabricated MEAS. Similar analysis can be extended to determine the dimensions and the operating conditions of an MEAS design for a desired minimum concentration detection limit. 9. Field testing To test the performance of the instrument for low particle concentrations and in field conditions, the MEAS was tested at the mobile emissions test facility at the New York State Department of Environmental Conservation (NYSDEC), Albany, NY. An experimental setup similar to that shown in Fig. 8 is used. A diesel generator (Genset), with a dilution flow of 1:150 and operating at different load conditions was used as a source of particles. A bipolar neutralizer (Kr85 ) was used as a particle charger. An electrometer (Keithley sourcemeter, Model 6430) was connected to the third collection
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Fig. 10. Percentage area error after inversion as a function of total particle number concentration.
Fig. 11. Comparison of MEAS and SMPS measurements of particle size distributions from a diesel generator.
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plate from the ESP channel side. The ESP and classifier plate voltages were set to 200 and 500 V, respectively. Particles were injected from the third ESP injection channel. A valve was used downstream of MEAS to change the flowrate through the instrument. Since the detected electrometer signals were low (0.1–1.5 fA) and in the same order of magnitude as RMS noise of the electrometer (0.1–0.2 fA), the background signals were obtained for all flowrate conditions. The signal due to particle collection was obtained as the difference of the measured and background signals. Flowrates were selected such that the transfer function can span the size range of the aerosol distribution. The size bins for the inversion were selected to be the median diameter for the transfer functions except the extreme points which are the maximum and minimum mobilities collected for the minimum and maximum flowrates, respectively. The linearized inversion equation, considering only singly charged particles, equates the electrometer signal with the product of a coefficient matrix and the discrete size distribution. Elements of the coefficient matrix represent the area under the transfer function in various size bins. The theoretical MEAS transfer function, including the 16 th ESP penetration factor, for the various test flowrates was used to invert the electrometer data to obtain particle size distributions for different test cases using the L-curve inversion routine. The size distributions obtained with MEAS for 0% and 20% load conditions are compared with those obtained with an SMPS system (Fig. 11). The electrometer noise is seen to influence the zeroth order inversion, resulting in a noisy size distribution that is largely consistent with the SMPS measurements. This suggests that the calculated transfer functions accurately represent particle capture characteristics in the MEAS classifier section. With the L-curve optimized inversion routine a smooth size distribution curve is obtained and this compares well with the size distribution obtained with the SMPS. Thus, the inversion algorithm is effective for the overlapping MEAS transfer functions. The test results suggest that the MEAS instrument can be field-deployed for measurements such as diesel emission characterization. 10. Size distribution measurement with different collection plates and injection channels Size distribution measurements were also made using constant flowrate and a set of collection electrodes for the second and third injection channels in the MEAS. For this experiment, a spark generator (Palas GFG 1000) is used to generate carbon particles in a ultrafine size range and upstream size distributions are monitored with an FMPS system (Fig. 6). An electrometer, Keithley sourcemeter (Model 6430), is connected to one collection electrode at a time and the resultant signals are converted to a particle size distribution. The electrometer response corresponding to the collected particle numbers was obtained from a difference between the electrometer signal with and without particles in flow. The background signal (i.e., without particles) was obtained by switching the aerosol flow to pass through the filter. The electrometer signal was recorded at 1 Hz over a 2 min interval and the median value recorded. An average of three statistical medians for each of the seven collection plates was used with the regularization routine and the MEAS theoretical transfer functions to calculate the MEAS-measured size distribution. In these tests, the confidence interval for the measured electrometer signal for the different collection plates was found to be in the same range as characterized previously (Fig. 7). To achieve the low-noise data, an updated MEAS unit was designed and built with a shielded housing and isolated triax connectors in contact with the collection electrodes. Experiments with the new MEAS unit show that the measured electrometer signal differs from the theoretical electrometer signal by a factor of 0.85, possibly due to 3D effects that are not considered in theory. A comparison of the MEAS size distribution measurement with FMPS size distribution measurement with the electrometer signals from the seven collection plates is shown in Fig. 12. Considering the scaling factor of 0.85 the size distributions are seen to match well, thus validating the transfer function calculations of the different collection plates for varying injection locations. 11. Limitations The minimum particle concentration detected on the collection plates depends on the RMS noise of the electrometer used. Typically, lab-built electrometers have noise in the range of 1–5 fA. The minimum electrometer signal should exceed the noise. The minimum particle concentration required for detection as a function of particle diameter is theoretically calculated and shown in Fig. 13. For these calculations, it is assumed that the particles are charged using a bipolar diffusion charger and that the charge distribution is Boltzmann. The calculations suggest that for uniform size distribution (i.e., dN/dDp constant for all particle diameters, Dp ), a total concentration of 1.5E4 cm−3 is required at 1 LPM to obtain an electrometer signal in the range of 1–2.4 fA on the different collection plates. The minimum
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Fig. 12. Comparison of size distribution measurements made using MEAS and FMPS.
Fig. 13. The minimum concentration for detection with MEAS for electrometer noise levels of 1 and 5 fA and flowrates of 0.5, 1, and 2 LPM.
particle concentration required for detection is a function of average collected particle diameter, charging technique, collection plate transfer function, and flowrate through the instrument. This result provides a basis to determine the conditions under which MEAS operation is possible. The minimum detectable concentration can be further reduced by using a unipolar diffusion charger (Biskos et al., 2005a, 2005b; Büscher, Schmidt-Ott, & Wiedensohler, 1994) which produces larger fraction of charged particles. Also, to minimize pressure drop through the instrument, no impactor is used upstream of the MEAS. Thus, for size distributions with significantly large particles, multiple charging effects will result in significant error in size distribution measurements.
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12. Conclusions A miniature electrical-mobility aerosol spectrometer (MEAS) design was recently introduced. This paper describes a prototype MEAS instrument and its performance. The ESP and classifier sections were tested individually and the measurements were seen to match the MEAS theoretical model. Under laboratory and field conditions, MEAS size distribution measurements are seen to closely match measurements with commercial sizing instruments. The instrument detection limits are dependent on electrometer characteristics and instrument dimensions. Our results suggest that a compact-sized MEAS can be deployed for personal and large-scale monitoring under conditions of moderately high particle loading. Acknowledgments The authors would like to thank New York Energy Research and Development Authority (NYSERDA) for funding this project (Contract number 7652). The help of Brian Frank, Thomas Lanni, and the New York State Department of Environmental Conservation (NYSDEC) staff with measurements at the diesel generator testing facility is gratefully acknowledged. A special thanks goes to Clarkson University machine shop technician Ted Ritzko for the help in building the MEAS prototypes. References Agarwal, J. K., & Sem, G. J. (1980). Continuous flow, single-particle-counting condensation nucleus counter. Journal of Aerosol Science, 11, 343–357. Bashurova, V. S., Koutzenogil, K. P., Pusep, A. Y., & Shokhirev, M. V. (1991). Determination of atmospheric aerosol size distribution function from screen diffusion battery data. Mathematical aspects. Journal of Aerosol Science, 22, 373–388. Biskos, G., Reavell, K., & Collings, N. (2005a). Description and theoretical analysis of a differential mobility spectrometer. Aerosol Science and Technology, 39, 527–541. Biskos, G., Reavell, K., & Collings, N. (2005b). Unipolar diffusion charging of aerosol particles in the transition regime. Journal of Aerosol Science, 36, 247–265. Busigin, A., Vooren, W., & Phillips, C. R. (1980). A technique for calculation of aerosol particle size distributions from indirect measurements. Journal of Aerosol Science, 11, 359–366. Büscher, P., Schmidt-Ott, A., & Wiedensohler, A. (1994). Performance of a unipolar ‘squarewave’ diffusion charger with variable Nt-product. Journal of Aerosol Science, 25, 651–663. Cooper, D. W., & Spielman, L. A. (1976). Data inversion using nonlinear programming with physical constraints: Aerosol size distribution measurement by impactors. Atmospheric Environment, 10, 723–729. Hansen, P. C. (1992). Analysis of discrete ill-posed problems by means of the L-curve. Society for Industrial and Applied Mathematics Review, 34, 561–580. Hansen, P. C., & O’Leary, D. P. (1993). The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal of Scientific Computing, 14, 1487–1503. Hinds, W. C. (1999). Aerosol technology: Properties, behavior and measurement of airborne particles. 2nd ed., New York: Wiley. Kandlikar, M., & Ramachandran, G. (1999). Inverse methods for analysing aerosol spectrometer measurements: A critical review. Journal of Aerosol Science, 30, 413–437. Knutson, E. O., & Whitby, K. T. (1975). Aerosol classification by electric mobility: Apparatus, theory, and applications. Journal of Aerosol Science, 6, 443–451. Lesnic, D., Elliot, L., & Ingham, D. B. (1996). A numerical analysis of the data inversion of particle sizing instruments. Journal of Aerosol Science, 27, 1063–1082. Lloyd, J. J., Taylor, C. J., Lawson, R. S., & Shields, R. A. (1997). The use of the L-curve method in the inversion of diffusion battery data. Journal of Aerosol Science, 28, 1251–1264. Phillips, D. L. (1962). A technique for the numerical solution of certain integral equations of the first kind. Journal of the Association for Computing Machinery, 9, 84–97. Ranjan, M., & Dhaniyala, S. (2007). A new miniature electrical spectrometer: Theory and design. Journal of Aerosol Science, 39, 950–963. Talukdar, S., & Swihart, M. (2003). An improved data inversion program for obtaining aerosol size distributions from scanning differential mobility analyzer data. Aerosol Science and Technology, 37, 145–161. Tammet, H., Mirme, A., & Tamm, E. (2002). Electrical aerosol spectrometer of Tartu University. Atmospheric Research, 62, 315–324. Wahba, G. (1990). Spline models for observational data. Philadelphia, PA: Society for Industrial and Applied Mathematics. Wolfenbarger, J. K., & Seinfeld, J. H. (1990). Inversion of aerosol size distribution data. Journal of Aerosol Science, 21, 227–247. Wolfenbarger, W. L., & Seinfeld, J. H. (1991). Regularized solutions to the aerosol data inversion problem. SIAM Journal on Scientific and Statistical Computing, 12, 342–361.
A new miniature electrical aerosol spectrometer (MEAS): Experimental characterization Manish Ranjan, Suresh Dhaniyala∗ Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA Received 12 September 2007; received in revised form 8 April 2008; accepted 9 April 2008
Abstract Design and theory of a new compact ultrafine particle sizing instrument, called the miniature electrical-mobility aerosol spectrometer (MEAS), was recently introduced [Ranjan, M., & Dhaniyala, S. (2007). A new miniature electrical spectrometer: Theory and design. Journal of Aerosol Science, 39, 950–963]. In the MEAS, electrostatic precipitation technique is used for both generation of sheath flow and classification of particles based on their electrical mobility. An electrometer-array, connected to the collection electrodes in the classifier section, is used to measure the number of particles collected in the different mobility channels, and these data are inverted using MEAS transfer functions to obtain particle number size distributions. Design of a prototype MEAS and the experimental approach to validate the performance of the individual components of the instrument are presented. Particle size distributions obtained from MEAS measurements compare well with those obtained using a scanning mobility particle sizer (SMPS; TSI 3936), validating theoretical calculations of instrument transfer functions. The operational limits of MEAS are determined from the calculation of error in the inverted size distribution as a function of total particle concentration. This analysis suggests that the designed MEAS can be used for applications such as personal and ambient monitoring under conditions of moderate to high particle concentrations. 䉷 2008 Elsevier Ltd. All rights reserved. Keywords: Electrical mobility; DMA; MEAS; Miniature; Compact; Aerosol instrument; Electrometer; Size distribution; Experiments; Personal sampler
1. Introduction A compact real-time size distribution measurement instrument is essential to study spatial and temporal variation of particle concentration in the ambient atmosphere and our microenvironment. Commonly used electrical-mobilitybased particle characterization instruments include scanning mobility particle sizer (SMPS; TSI Inc.), electrical aerosol spectrometer (EAS; Tammet, Mirme, & Tamm, 2002), and differential mobility spectrometer (DMS; Biskos, Reavell, & Collings, 2005a). SMPS uses a differential mobility analyzer (DMA; Knutson & Whitby, 1975) to classify particles based on electrical mobility and a condensation particle counter (CPC; Agarwal & Sem, 1980) or a Faraday cup electrometer to count them. The EAS and DMS use inside-out classification columns with a set of electrometers for sub-second particle size distribution measurements. These instruments are most suitable for site-specific, highresolution particle size distributions, but these instruments are large in size, expensive, and complicated to use due to ∗ Corresponding author. Tel.: +1 315 268 6586; fax: +1 315 268 6695.
E-mail address: [email protected] (S. Dhaniyala). 0021-8502/$ - see front matter 䉷 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2008.04.005
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Fig. 1. A schematic diagram of the MEAS instrument illustrating the injection of particles from one ESP channel (E3) and the subsequent electrical-mobility-based classification of particles in the classifier section.
multiple flow controls and several size classification channels. There is an immediate need for a compact, portable, inexpensive, and easy to deploy instrument which can measure the real-time size distribution with reasonable accuracy. Recently, design of a new compact electrical-mobility-classification instrument, called the miniature electricalmobility aerosol spectrometer (MEAS; Ranjan & Dhaniyala, 2007), was introduced (Fig. 1). MEAS consists of three major parts: inlet, electrostatic precipitator (ESP), and classifier sections (Fig. 1). For sizing with MEAS, particles are charged upstream of the instrument with a bipolar or a unipolar charger and enter the instrument through the inlet section. The inlet section is designed to ensure a uniform spatial distribution of particle concentration over the ESP entrance cross-section. The ESP section consists of a series of narrow channels maintained at desired electric potential differences. As particles move through the ESP section, they are electrostatically filtered from all channels, except one, the injection channel. Particles and flow traversing through the selected injection channel into the classifier region form the aerosol flow, while the rest of the flow acts as sheath flow. In the classifier section, an electric potential difference is maintained to classify the injected particles based on their electrical mobility. Collection electrodes in the classifier section are connected to electrometers and the signals obtained from the collection of charged particles are used to determine the size distribution of the sampled particles, considering the transfer function of the collection plates. The MEAS design is advantageous over other existing electrical-mobility measurement instruments, as it requires control of only one flow. The relatively open MEAS geometry results in a low-pressure-drop instrument and the option of varying the injection channel permits measurements over a broad range of particle sizes. The compact and simple design of the MEAS makes it inexpensive to manufacture. The rectangular geometry permits easy scaling of MEAS dimensions to optimize its response based on sampling conditions. 2. Design description A prototype MEAS (Fig. 2) was fabricated for experimental validation of theoretical predictions. The MEAS inlet section is designed to transition flow from the circular entrance to the rectangular cross-section of the ESP section. To minimize flow recirculation regions, the cross-section of the inlet section gradually changes from a circle to a rectangle with an expansion angle of ∼18◦ over a length of 10 cm. While an optimal expansion angle would be ∼7◦ , to keep the inlet section short a larger expansion angle is chosen with additional pressure drop generated by placing a wire mesh in the center of the inlet section length. To minimize the particle loss within the instrument due to charge effects, the MEAS inlet and outlet were both cast out of aluminum. In the prototype MEAS, the ESP section is designed with five parallel electropolished stainless steel plates that are 2 cm long, 5 cm wide, 0.7 mm thick, and spaced 2 mm apart. An ultraminiature voltage amplifier (EMCO Model Q40-5) is used to set the voltage on the ESP plates. The ESP plate voltages are chosen such that charged particles are electrostatically filtered through all the ESP channels except one selected injection channel. For typical operation, the potential difference in the ESP channels must be below the breakdown limit, while resulting in the capture of all charged particles of measurement interest. The potentials on the individual ESP plates are maintained using a single high-voltage source via a distributor setup. For handling safety, the ESP and classifier sections are housed in an external insulated unit made of Delrin䉸 . The classifier section of the MEAS consists of a set of seven collection plates, spaced 1 mm apart, located across a classifier plate maintained at high voltage. Electropolished stainless steel rectangular plates of 1 cm length, 5 cm width, and 0.7 mm thickness are used as collection plates.
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Fig. 2. The MEAS prototype that was built and tested.
The MEAS particle capture characteristics are complicated by the non-uniform nature of the electric and flow fields in the classifier section. The details of the calculation of the electric and flow fields in the MEAS are provided in Ranjan and Dhaniyala (2007) and only a brief overview is given here. The classifier section flow field at the vicinity of the ESP section exit must be accurately modeled for accurate particle trajectory calculations. For this, the assumed parabolic velocity profiles in the individual ESP channels are combined using a Heaviside step function to represent the classifier section velocity profile near the ESP exit. In the rest of the classifier section a single parabolic velocity profile over the entire channel is assumed. For the non-uniform electric potential field in the MEAS classifier section, space charge effects are neglected and the Laplace equation is solved with appropriate boundary conditions. The resultant electric flux () and stream () functions in the classifier section are then analytically calculated and contours of + Zp are used to determine particle trajectories in the MEAS instrument. The instrument transfer functions were calculated as the fraction of charged aerosol particles entering the ESP injection channel that are captured on the collection plate. With known transfer functions, appropriate data inversion routines can be used to determine size distribution of the sample aerosol from the electrometer signals. In addition to the theoretical modeling, the MEAS performance is also obtained from computational fluid dynamics (CFD) simulations using the software FLUENT (FLUENT Inc., NH). A user-defined function (UDF) code is used to accurately account for slip correction and the effect of electric field on particle trajectories in the instrument (Ranjan & Dhaniyala, 2007). The numerically calculated transfer functions are seen to compare well with theoretical predictions. 3. MEAS performance validation Validation of theoretical and numerical predictions of MEAS performance requires a number of different experiments. In the first test, the overall collection efficiency of the classifier section is measured. For this test, all ESP plates are grounded, thus permitting the injection of charged particles from all ESP channels into the classifier section. The total collection efficiency can be determined from measurement of particle concentrations upstream and downstream of the instrument and compared with the theoretically predicted collection efficiency. In the second test, the ESP plate voltages are set such that particles are injected through one channel and corresponding classifier section collection efficiencies are experimentally obtained. In the third test, electrometers are connected to collection plates and the response is measured for varying flowrates and injection channels. Particle size distributions measured with MEAS in this test are compared with measurements with commercial instruments.
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4. Performance evaluation of the MEAS classifier section The experimental setup used for testing the performance of the classifier section is shown in Fig. 3. The combination of a particle source (nebulizer; NaCl in H2 O), compressed air (∼50 psi) dried with silica gel, and a long column DMA (TSI Model 3071, aerosol flowrate—0.9 LPM and sheath flowrate—10 LPM, recirculated) was used to generate particles over a narrow range of electrical mobilities. The aerosol flow from the nebulizer was sent to a chamber (volume—10 L) to dampen out fluctuations in the generated aerosol size distributions. Particle size distributions downstream of the chamber were continuously monitored using a fast mobility particle spectrometer (FMPS; TSI 3091) and were observed to be largely uniform over a 2-h interval (total concentration mean: 7.93E4 cm−3 , upper 95% confidence interval: 7.99E4 cm−3 , lower 95% confidence interval: 7.88E4 cm−3 , geometric mean: 124 nm, geometric standard deviation: 1.54). Downstream of the DMA, charged monodisperse particles were passed through the MEAS. Particle concentrations upstream and downstream of the MEAS were measured using two CPCs (TSI CPCs 3025 and 3786) to calculate the MEAS collection efficiency as a function of the classifier plate voltage. With two particle counters, temporal variations in monodisperse particle concentrations can be accounted for in the collection efficiency calculation. For efficiency measurements, the classifier plate voltages were varied over 4-min intervals and particle counts were recorded at 1 Hz on a computer. For MEAS operation with grounded classifier and ESP plates (i.e., no controlled particle collection in MEAS), a slight discrepancy was observed between the upstream and downstream CPCs. The average of the median values of the ratio of particle concentrations measured by the upstream (CPC 3025; ref ) and the downstream (CPC 3786; C ref ) counters was found to be 1.1 with the standard deviation of 0.035 for Cup down two tested particle diameters (136 and 164 nm). This constant factor is due to the combination of small difference in the detection efficiencies of the two CPCs, particle loss within the MEAS, and slight noise in the voltage source. This factor is accounted for in all subsequent collection efficiency measurements. A comparison of the experimentally measured collection efficiency with the theoretical predictions of the classifier section collection efficiency is shown in Fig. 4 for the two test sizes. The error bars in the plot represent the standard deviation of the collection efficiency calculated using the uncertainty propagation method. The parameter Vte Ac /Q is used for the comparison tests, where Vte is the electrostatic terminal velocity (Hinds, 1999), Ac is the collection area of the entire classification section, and Q is the flowrate through the instrument. This parameter represents the collection efficiency for a uniform electric field and plug flow condition. The experimental results are seen to compare well with the numerical and theoretical predictions. At zero classifier voltage, small collection efficiency is observed, possibly because of particle loss due to exposure to the Delrin䉸 housing over a small area. The overall result of this test validates the performance of the classifier section without considering the ESP voltages.
Fig. 3. Schematic diagram of the experimental setup used for testing the individual components of MEAS.
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Fig. 4. Comparison between theoretical and experimental collection efficiencies of the classifier section with the grounded ESP section using 136 and 164 nm test particles.
5. MEAS collection efficiency evaluation In the next test, the collection characteristics of the classifier section with the ESP operated to permit injection through one channel are evaluated. Particles are injected through the third injection channel and the penetration through the classifier section is measured as a function of applied potential difference. The experimental setup shown in Fig. 3 is again used for these experiments. Particles of 134 nm diameter are selected to be output from the DMA. The MEAS classifier section voltage is varied and the collection efficiency of the classifier section is measured as before. A comparison of measured MEAS particle penetrations and theoretical predictions is shown in Fig. 5. The experimental penetration through the third injection channel was found to be 16.4%, while the ESP penetration in the theoretical calculation was assumed to be 16.6%. The theoretical collection efficiencies are seen to largely match experimental data and the error bars are calculated as explained in the previous section. A slight difference between theory and experiments for collection efficiency in the presence of ESP plate voltages is likely due to simplifications made in the calculation of non-uniform electric and flow fields in the classifier section.
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Fig. 5. Comparison between theoretical and experimental collection efficiencies with 350 V on the ESP section and 135 nm particles are passed through the third injection channel of the ESP section. Theoretical ESP penetration is 16.67% ( 16 th) and experimental penetration was measured to be 16.4%.
6. Measurement and comparison of particle size distribution by MEAS To test the performance of the integrated MEAS instrument, the transfer function of the different collection stages must be experimentally determined and compared with theoretically predicted results. Direct transfer function measurements are very difficult for electrometer-based instruments due to the difficulty of generating charged particles over a narrow size range at concentrations that are high enough for electrometer detection but lower than the upper limit of an upstream counter. Moreover, electrostatic capture of charged particles for sheath flow generation in the ESP channels of MEAS reduces the charged aerosol concentration available for detection to 16 th of the entrance concentration. Validation of MEAS transfer function calculation is, therefore, made by comparing size distributions determined from measured MEAS electrometer signals with those obtained from other instruments. Due to the availability of only one electrometer, the size distribution measurements were made by varying one of the instrument parameters controlling the collected mobility range. In the MEAS, the detected mobility range depends on the classifier plate voltage, the operating flowrate, the choice of collection plate number, and the selection of injection channel. Changing the classifier plate voltage was observed to result in electrometer noise as the classifier channel acts as a large capacitor with a certain time constant. This also slows the electrometer response time. Size distribution measurements obtained by varying the ESP injection channel and the collection plate will be limited by the number of ESP channels and collection plates. Also, changing ESP voltages increases electrometer noise. For measurements with a single electrometer, varying the flowrate is most suitable. For measurements of particles in the ultrafine size range, flowrates were stepped up gradually over a range of 0.1–5 LPM. For this operating range, the flow in the instrument is laminar and uniform throughout the instrument. Size distribution measurements were performed by different combinations of flowrates, injection channel, and collection plates. Initial experiments with the electrometer were to test the linearity of the signal response to upstream particle concentration. The experimental setup used for this test is shown in Fig. 6. The electrometer (Keithley sourcemeter, Model 6430) was connected to the seventh collection plate from the ESP channel side. The ESP plates were set to 500 V with the injection channel chosen as the fourth channel above the collection plates. The classifier plate was set to 450 V and flowrate through the instrument was 1 LPM. Particle size distribution upstream of the MEAS was monitored with an FMPS system and the MEAS electrometer signal was recorded at 1 Hz. The upstream particle concentrations were varied and the expected number of particles captured on the seventh collection plate was calculated by convolving the theoretical transfer function (Ranjan & Dhaniyala, 2007) with the FMPS particle size distribution. A comparison of the expected concentration and the measured electrometer signal is shown in Fig. 7. The fluctuation in the FMPS size distribution measurement has been accounted in the expected particle concentration calculation. Upper and lower
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Fig. 6. Experimental setup used for the tests of electrometer signal variation and measurements of size distributions with MEAS.
Fig. 7. Comparison of raw electrometer signal with expected particle concentration on the collection plate.
95% confidence interval limits for the FMPS size distribution are used for error calculation in the expected particle concentration. Electrometer signal was recorded every second and the 95% upper and lower confidence intervals for the 30 s steady-state electrometer signal are also shown in Fig. 7. Excellent error values are attributed to the highly stable nature of the aerosol flow through the chamber outlet and the highly stable signal measured by the sourcemeter (Keithley, 6430 with preamp) operated at slow speed (10 plc) with three stage internal filtering system. As expected, the electrometer signal varied linearly with the change in upstream particle concentration. This test provides a validation of the consistency of the electrometer signal response to captured particle concentrations. 7. Size distribution measurement with flowrate variation For size distribution measurements, the flowrate through the instrument was stepped from 0.25 to 1.5 LPM. The classifier and the ESP voltages were set to 500 and 700 V, respectively. An experimental setup similar to that shown in Fig. 8 is used for this test. The flowrate through the instrument was controlled by an adjustable valve placed downstream of the instrument. The electrometer data were continuously acquired via an RS232 port using a LabView code.
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Fig. 8. Experimental setup used for size distribution measurements with MEAS.
Fig. 9. Particle size distribution comparison of MEAS and SMPS using laboratory-generated aerosol.
To calculate particle size distributions, the discretized linear inversion equations are solved with a first order inversion routine considering the theoretical instrument transfer functions. A large upstream particle concentration was used to reduce the effect of electrometer noise on the signal and the flowrates were chosen to ensure minimal overlapping of transfer functions. This facilitates easy size distribution calculation using first order direct inversion. Size distribution measurements with MEAS are seen to compare well with those made using an SMPS (Fig. 9). The large concentrations used in this test ensured sufficient electrometer signal strengths in the range of 30–400 fA. Highly stable flow measurement device (Alicat Scientific, Model MC-20SLPM) and minimal electrometer fluctuation cause negligibly small variation in the measured size distribution. A more stringent test of MEAS performance requires measurements with lower particle concentrations and at higher resolution. Increasing the number of measurement channels results in overlapping of transfer functions and complicating data inversion. For such data sets, advanced data inversion techniques are required and our approach is outlined below.
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8. Data inversion methodology The electrometer response is related to the upstream size distribution and the instrument transfer function as follows: ∞ ∞ (nf (n, Dp )i (n, Dp )) d log Dp , (1) N (log Dp ) Ei = Qe 0
n=1
where Ei is the ith channel electrometer current, N is the particle size distribution entering the instrument, n is the number of elementary charges on the particle, e is the charge on an electron, f is the particle charge distribution, i is the MEAS transfer function, and Dp is the particle diameter. This equation is commonly referred to as the Fredholm integral equation of the first kind and its inversion is an ill-posed problem that is further complicated by overlapping set of transfer functions (Ranjan & Dhaniyala, 2007). Data inversion for an ill-posed system of equations is discussed by Talukdar and Swihart (2003), Kandlikar and Ramachandran (1999), Lesnic, Elliot, and Ingham (1996), Wolfenbarger and Seinfeld (1990), Busigin, Vooren, and Phillips (1980), and Cooper and Spielman (1976) among others. The ill-posed inversion equation is commonly solved with a regularization technique to obtain a best estimate of the size distribution (Bashurova, Koutzenogil, Pusep, & Shokhirev, 1991; Lloyd, Taylor, Lawson, & Shields, 1997; Phillips, 1962; Talukdar & Swihart, 2003; Wolfenbarger & Seinfeld, 1990, 1991). A regularization technique balances the accuracy of inversion result with the smoothness of the solution using a regularization parameter. One efficient method to determine the regularization parameter is the L-curve optimization technique (Hansen & O’Leary, 1993) used for inversion of DMA data (Hansen, 1992; Talukdar & Swihart, 2003; Wahba, 1990; Wolfenbarger & Seinfeld, 1991). An inversion routine based on the L-curve regularization technique is developed for size distribution calculation with the MEAS. In the L-curve technique, the optimal value of the regularization parameter is obtained by a maximum curvature approach (Hansen, 1992). To test the performance of the MEAS inversion routine, the theoretical MEAS transfer functions are convolved with an assumed size distribution to calculate the expected electrometer signal (Ei ) in terms of total particle concentration. To account for signal errors, we consider two types of noise: a Poisson-type pois counting noise (Ei ) inherent with the expected particle concentration on the collection electrodes and a Gaussian spectrum (Ei εi ) with mean zero and standard deviation of (Ei ) to account for the electrometer noise. For inversion tests, the expected electrometer signal is obtained as follows: noisy
Ei
pois
= Ei
+ E i εi ,
i = 1, N ,
(2)
noisy
where Ei is the electrometer current with noise in channel i. To estimate the accuracy of inversion for different starting size distributions, the difference between the inverted and actual distributions is represented as percentage area error, area , calculated as follows: ⎤ ⎡ Df |N − N | dD p inv D ⎦ ∗ 100, (3) area = ⎣ i D f Di N dDp where Ninv is the inverted size distribution. The percentage area error as a function of total particle concentration for a lognormal distribution [ = 70 nm, g = 1.35] is shown in Fig. 10. As expected, the area error reduces with increasing total concentration. This analysis provides an estimate of the operating limits of the fabricated MEAS. Similar analysis can be extended to determine the dimensions and the operating conditions of an MEAS design for a desired minimum concentration detection limit. 9. Field testing To test the performance of the instrument for low particle concentrations and in field conditions, the MEAS was tested at the mobile emissions test facility at the New York State Department of Environmental Conservation (NYSDEC), Albany, NY. An experimental setup similar to that shown in Fig. 8 is used. A diesel generator (Genset), with a dilution flow of 1:150 and operating at different load conditions was used as a source of particles. A bipolar neutralizer (Kr85 ) was used as a particle charger. An electrometer (Keithley sourcemeter, Model 6430) was connected to the third collection
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Fig. 10. Percentage area error after inversion as a function of total particle number concentration.
Fig. 11. Comparison of MEAS and SMPS measurements of particle size distributions from a diesel generator.
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plate from the ESP channel side. The ESP and classifier plate voltages were set to 200 and 500 V, respectively. Particles were injected from the third ESP injection channel. A valve was used downstream of MEAS to change the flowrate through the instrument. Since the detected electrometer signals were low (0.1–1.5 fA) and in the same order of magnitude as RMS noise of the electrometer (0.1–0.2 fA), the background signals were obtained for all flowrate conditions. The signal due to particle collection was obtained as the difference of the measured and background signals. Flowrates were selected such that the transfer function can span the size range of the aerosol distribution. The size bins for the inversion were selected to be the median diameter for the transfer functions except the extreme points which are the maximum and minimum mobilities collected for the minimum and maximum flowrates, respectively. The linearized inversion equation, considering only singly charged particles, equates the electrometer signal with the product of a coefficient matrix and the discrete size distribution. Elements of the coefficient matrix represent the area under the transfer function in various size bins. The theoretical MEAS transfer function, including the 16 th ESP penetration factor, for the various test flowrates was used to invert the electrometer data to obtain particle size distributions for different test cases using the L-curve inversion routine. The size distributions obtained with MEAS for 0% and 20% load conditions are compared with those obtained with an SMPS system (Fig. 11). The electrometer noise is seen to influence the zeroth order inversion, resulting in a noisy size distribution that is largely consistent with the SMPS measurements. This suggests that the calculated transfer functions accurately represent particle capture characteristics in the MEAS classifier section. With the L-curve optimized inversion routine a smooth size distribution curve is obtained and this compares well with the size distribution obtained with the SMPS. Thus, the inversion algorithm is effective for the overlapping MEAS transfer functions. The test results suggest that the MEAS instrument can be field-deployed for measurements such as diesel emission characterization. 10. Size distribution measurement with different collection plates and injection channels Size distribution measurements were also made using constant flowrate and a set of collection electrodes for the second and third injection channels in the MEAS. For this experiment, a spark generator (Palas GFG 1000) is used to generate carbon particles in a ultrafine size range and upstream size distributions are monitored with an FMPS system (Fig. 6). An electrometer, Keithley sourcemeter (Model 6430), is connected to one collection electrode at a time and the resultant signals are converted to a particle size distribution. The electrometer response corresponding to the collected particle numbers was obtained from a difference between the electrometer signal with and without particles in flow. The background signal (i.e., without particles) was obtained by switching the aerosol flow to pass through the filter. The electrometer signal was recorded at 1 Hz over a 2 min interval and the median value recorded. An average of three statistical medians for each of the seven collection plates was used with the regularization routine and the MEAS theoretical transfer functions to calculate the MEAS-measured size distribution. In these tests, the confidence interval for the measured electrometer signal for the different collection plates was found to be in the same range as characterized previously (Fig. 7). To achieve the low-noise data, an updated MEAS unit was designed and built with a shielded housing and isolated triax connectors in contact with the collection electrodes. Experiments with the new MEAS unit show that the measured electrometer signal differs from the theoretical electrometer signal by a factor of 0.85, possibly due to 3D effects that are not considered in theory. A comparison of the MEAS size distribution measurement with FMPS size distribution measurement with the electrometer signals from the seven collection plates is shown in Fig. 12. Considering the scaling factor of 0.85 the size distributions are seen to match well, thus validating the transfer function calculations of the different collection plates for varying injection locations. 11. Limitations The minimum particle concentration detected on the collection plates depends on the RMS noise of the electrometer used. Typically, lab-built electrometers have noise in the range of 1–5 fA. The minimum electrometer signal should exceed the noise. The minimum particle concentration required for detection as a function of particle diameter is theoretically calculated and shown in Fig. 13. For these calculations, it is assumed that the particles are charged using a bipolar diffusion charger and that the charge distribution is Boltzmann. The calculations suggest that for uniform size distribution (i.e., dN/dDp constant for all particle diameters, Dp ), a total concentration of 1.5E4 cm−3 is required at 1 LPM to obtain an electrometer signal in the range of 1–2.4 fA on the different collection plates. The minimum
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Fig. 12. Comparison of size distribution measurements made using MEAS and FMPS.
Fig. 13. The minimum concentration for detection with MEAS for electrometer noise levels of 1 and 5 fA and flowrates of 0.5, 1, and 2 LPM.
particle concentration required for detection is a function of average collected particle diameter, charging technique, collection plate transfer function, and flowrate through the instrument. This result provides a basis to determine the conditions under which MEAS operation is possible. The minimum detectable concentration can be further reduced by using a unipolar diffusion charger (Biskos et al., 2005a, 2005b; Büscher, Schmidt-Ott, & Wiedensohler, 1994) which produces larger fraction of charged particles. Also, to minimize pressure drop through the instrument, no impactor is used upstream of the MEAS. Thus, for size distributions with significantly large particles, multiple charging effects will result in significant error in size distribution measurements.
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12. Conclusions A miniature electrical-mobility aerosol spectrometer (MEAS) design was recently introduced. This paper describes a prototype MEAS instrument and its performance. The ESP and classifier sections were tested individually and the measurements were seen to match the MEAS theoretical model. Under laboratory and field conditions, MEAS size distribution measurements are seen to closely match measurements with commercial sizing instruments. The instrument detection limits are dependent on electrometer characteristics and instrument dimensions. Our results suggest that a compact-sized MEAS can be deployed for personal and large-scale monitoring under conditions of moderately high particle loading. Acknowledgments The authors would like to thank New York Energy Research and Development Authority (NYSERDA) for funding this project (Contract number 7652). The help of Brian Frank, Thomas Lanni, and the New York State Department of Environmental Conservation (NYSDEC) staff with measurements at the diesel generator testing facility is gratefully acknowledged. A special thanks goes to Clarkson University machine shop technician Ted Ritzko for the help in building the MEAS prototypes. References Agarwal, J. K., & Sem, G. J. (1980). Continuous flow, single-particle-counting condensation nucleus counter. Journal of Aerosol Science, 11, 343–357. Bashurova, V. S., Koutzenogil, K. P., Pusep, A. Y., & Shokhirev, M. V. (1991). Determination of atmospheric aerosol size distribution function from screen diffusion battery data. Mathematical aspects. Journal of Aerosol Science, 22, 373–388. Biskos, G., Reavell, K., & Collings, N. (2005a). Description and theoretical analysis of a differential mobility spectrometer. Aerosol Science and Technology, 39, 527–541. Biskos, G., Reavell, K., & Collings, N. (2005b). Unipolar diffusion charging of aerosol particles in the transition regime. Journal of Aerosol Science, 36, 247–265. Busigin, A., Vooren, W., & Phillips, C. R. (1980). A technique for calculation of aerosol particle size distributions from indirect measurements. Journal of Aerosol Science, 11, 359–366. Büscher, P., Schmidt-Ott, A., & Wiedensohler, A. (1994). Performance of a unipolar ‘squarewave’ diffusion charger with variable Nt-product. Journal of Aerosol Science, 25, 651–663. Cooper, D. W., & Spielman, L. A. (1976). Data inversion using nonlinear programming with physical constraints: Aerosol size distribution measurement by impactors. Atmospheric Environment, 10, 723–729. Hansen, P. C. (1992). Analysis of discrete ill-posed problems by means of the L-curve. Society for Industrial and Applied Mathematics Review, 34, 561–580. Hansen, P. C., & O’Leary, D. P. (1993). The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal of Scientific Computing, 14, 1487–1503. Hinds, W. C. (1999). Aerosol technology: Properties, behavior and measurement of airborne particles. 2nd ed., New York: Wiley. Kandlikar, M., & Ramachandran, G. (1999). Inverse methods for analysing aerosol spectrometer measurements: A critical review. Journal of Aerosol Science, 30, 413–437. Knutson, E. O., & Whitby, K. T. (1975). Aerosol classification by electric mobility: Apparatus, theory, and applications. Journal of Aerosol Science, 6, 443–451. Lesnic, D., Elliot, L., & Ingham, D. B. (1996). A numerical analysis of the data inversion of particle sizing instruments. Journal of Aerosol Science, 27, 1063–1082. Lloyd, J. J., Taylor, C. J., Lawson, R. S., & Shields, R. A. (1997). The use of the L-curve method in the inversion of diffusion battery data. Journal of Aerosol Science, 28, 1251–1264. Phillips, D. L. (1962). A technique for the numerical solution of certain integral equations of the first kind. Journal of the Association for Computing Machinery, 9, 84–97. Ranjan, M., & Dhaniyala, S. (2007). A new miniature electrical spectrometer: Theory and design. Journal of Aerosol Science, 39, 950–963. Talukdar, S., & Swihart, M. (2003). An improved data inversion program for obtaining aerosol size distributions from scanning differential mobility analyzer data. Aerosol Science and Technology, 37, 145–161. Tammet, H., Mirme, A., & Tamm, E. (2002). Electrical aerosol spectrometer of Tartu University. Atmospheric Research, 62, 315–324. Wahba, G. (1990). Spline models for observational data. Philadelphia, PA: Society for Industrial and Applied Mathematics. Wolfenbarger, J. K., & Seinfeld, J. H. (1990). Inversion of aerosol size distribution data. Journal of Aerosol Science, 21, 227–247. Wolfenbarger, W. L., & Seinfeld, J. H. (1991). Regularized solutions to the aerosol data inversion problem. SIAM Journal on Scientific and Statistical Computing, 12, 342–361.