ABSTRACT
Two iPhone-sized differential mobility analyzers (DMAs) in the parallel-plate configuration (i.e., mini-plate DMAs) were designed and their performance was calibrated in this study in order to gain the instructive knowledge for the future mini-plate DMA design and to have a well-calibrated mini-plate DMA for the ultrafine particle (UFP) sensor network. The performance of mini-plate DMAs was calibrated using the tandem DMA (TDMA) technique. The experimental transfer functions of prototypes at different particle sizes and under various combinational conditions of aerosol and sheath flow rates were derived from the TDMA data. It is concluded that mini-plate DMAs performed reasonably well for UFP sizing. It was also found that the sizing resolution of mini-plate DMAs is closer to the aerosol-to-sheath flow rate ratio when the percentage of aerosol slit opening in length was increased (relative to the width of aerosol classification zone). A new concept of “effective sheath flow rate” was introduced to better interpret the experimental observation on the area and FWHM (full width at half maximum) data of measured DMA transfer functions. Based on the experimental data, we proposed a modified equation for mini-plate DMAs to better calculate the voltage required to size particles of a given electrical mobility.
Copyright © 2016 American Association for Aerosol Research
EDITOR:
1. Introduction
The requirement of continuous monitoring of spatial/surface distribution of fine and ultrafine particles (UFPs) under the budget constraint is in high demand for air quality monitoring and control in cities and in residential communities located in the close proximity to highways. It is because recent epidemiologic studies have shown UFPs are particularly relevant to pulmonary diseases, cancer, and mortality (Hoek et al. Citation2002; Peters et al. Citation2004; Delfino et al. Citation2005 Oberdörster et al. Citation2005; Bräuner et al. Citation2007; Shah et al. Citation2008; Li et al. Citation2010; Stewart et al. Citation2010). The increased asthma prevalence is also found to often occur in the areas with high UFP level in ambient air or high motor vehicle traffic density, and in residence community nearby freeways (Samet et al. Citation2000; Holguin Citation2008; Salam et al. Citation2008; Patel and Miller, Citation2009). The above monitoring task is best realized by the network built on UFP sensors. New applications can further be emerged once the UFP sensor network is made available. Examples of new applications include the traffic control in smart cities, early fire detection in buildings and hospitals, indoor air quality monitoring and control, protection of first responders under various emergency (e.g., house fire, chemical leak accidents, wild fire), worker protection in the facility producing and processing UFPs, vertical profiling of UFPs, better UFP exposure data collection in future epidemiologic study, and many others. Differential mobility analyzers (DMAs) have been applied to measure sub-micrometer-sized particles in aerosol community for years. Multiple cost-effective and compact UFP sizers based on the DMA technique are required to establish the aforementioned UFP sensor network.
Early development of particle-electrical-mobility-based instruments such as electrical aerosol analyzers (EAAs) and DMAs was primarily designed for scientific studies (Liu and Pui Citation1974, Citation1975; Knutson and Whitby Citation1975; Zhang et al. Citation1995; Russell et al. Citation1996; Chen et al. Citation1998; Santos et al. Citation2009). These EAA/DMA instruments typically have high particle sizing resolution (with their operation at high sheath flow rates) and sensitivity (with the use of CPCs, condensation particle counters, to detect the concentration of classified particles) for measuring particles in a wide size range. These EAAs/DMAs typically require large flow and power control sub-systems for their operation. They are in general bulky in overall package size, heavy in weight and expensive for the ownership, and not good candidates as the sensors in the UFP sensor network, especially under the budget constraint.
Compact DMAs have been developed to bridge the gap between scientific DMAs and those suitable for the UFP sensor network. Ranjan and Dhaniyala Citation(2007) designed a miniature electrical-mobility aerosol spectrometer (MEAS). Note that the numerical modeling of the prototype performance was published in 2007. The prototype however has low particle sizing resolution (because of only seven electrodes used for particle sizing). Qi et al. Citation(2008) developed a miniature disk-type aerosol precipitator for UFP sizing. No sheath flow was used in mini-disk precipitator, resulting in low sizing resolution. A mini-disk electrical aerosol classifier (mini-disk EAC) was further developed by Li et al. Citation(2009), providing better sizing resolution (because of its inclusion of sheath flow). The even-better sizing resolution can be achieved by a well-performed DMA.
Other small-sized DMAs (Brunelli et al. Citation2009; Mei et al. Citation2011; Fernández de la Mora and Kozlowski Citation2013; Mui et al. Citation2013), operating at high sheath flow rates, are developed for sizing ions and particles in the diameters less than 10 nm. Parallel-plate DMAs with very short particle classification lengths and operated at high sheath flow rates were also reported in literature for ion sizing and the integration with mass spectrometers (Rus et al. Citation2010; Larriba et al. Citation2011). These parallel-plate DMAs were again designed to realize their high sizing power for ions and macro-molecules. They typically operated at high sheath flow rates, requiring the use of large air movers and consuming much electric energy for the operation. Also note that, because of the integration with mass spectrometers, the aerosol outlets of these parallel-plate DMAs are much shorter in length compared to the aerosol inlet. The shape of the slit opening for aerosol inlet is also different from that of aerosol outlet. Again, these DMAs were designed for scientific studies.
Portable UFP particle sizers are available in the market. Examples include portable aerosol mobility spectrometer (PAMS, Kanomax, Osaka, Japan), Nanoscan 3910 (TSI Inc., Shoreview, MN, USA), Nano-ID PMC500 (Naneum, Canterbury, UK), and mini wide range aerosol spectrometer (Mini-WARS 1371, GRIMM, Ainring, Germany). PAMS, Nanoscan 3910, and Nano-ID PMC500 are DMA-typed particle sizers, while mini WRAS is precipitator-typed particle sizer. Their electrical mobility classifiers (either in DMA or precipitator type) may be small in size and could be made at low cost. Unfortunately, in the commercial package, these portable UFP sizers are considered large in size, heavy in weight, and expensive for the ownership (), not good candidates for the UFP sensor network, in which multiple units (i.e., at least 10 units for a small UFP sensor network) are required under the constraint of installation and operational budget.
Table 1. List of commercially available portable aerosol sizers (based on particle electric mobility technique).
We selected a DMA in parallel-plate configuration to develop a cost-effective, miniature particle sizer (with sensitive aerosol electrometers as the particle concentration detectors) for the UFP sensor network. These UFP sizers are estimated less than 0.8 kg in total weight and approximately 4′′ × 5′′ × 5′′ in the final package (including all the accessaries). The selection of plate DMAs is because of its simple design and easy machining (translating to low manufacture cost) as well as its easy maintenance. A similar DMA has been reported in the work of Steer et al. Citation(2014). However, the detail performance calibration of the DMA was not reported in the paper and the attempts making the contact with the vendor were not successful. It remains at large with respect to the particle sizing and transmission of the Steer's DMA. More important, the paper does not provide any instructive knowledge for the proper design of a plate DMA.
To obtain the instructive knowledge for future design of mini-plate DMAs and to have a well-calibrated plate DMA for the future UFP sensor network, two mini-plate DMAs were constructed and their detail performance was fully evaluated in this study. The effect of DMA geometry on the particle sizing performance of mini-plate DMAs can thus be investigated by calibrating the performance of two mini-plate DMAs having two different sets of key dimensions. Different from other plate DMAs reported in the literature, the studied DMAs have smaller spacing between two parallel plates, and the same opening slit lengths for aerosol inlet and outlet. More, the studied DMAs are also operated at the sheath flow rates (i.e., less than 3.0 lpm) much lower than those applied to existed ones. Please note that these prototype DMAs were designed for the use in the future UFP sensor network. Certain compromises in the DMA design were made to reduce the manufacture cost. They are thus not to replace/complete with the DMAs designed for scientific studies.
2. Design of mini-plate DMAs
shows the schematic diagram of prototype mini-plate DMAs (i.e., DMA-1). The section view of the prototype is given in and the top view in . Prototype DMAs consist of two metal plates installed in parallel and separated by a spacing of 1/16′ (i.e., the height of particle classification zone). Both polydisperse and classified aerosol flow channels were designed in the metal plates to minimize the electrostatic particle loss during the transport. Polydisperse aerosol flow was injected at the DMA top plate, passed through a triangular-shaped flow channel and then entered the particle classification zone from the entrance slit. The dimensions of slits for aerosol entrance and exit of the classification zone are 1 1/8′′ (in length) × 1/32′′ (in opening), which is 75% of the width of particle classification zone (i.e., 1 1/2′′). The reason for the shorter slit length as compared to the width of the classification zone is to keep the aerosol flow away from the side walls of DMAs for minimizing the wall effect. The classified aerosol channel built in the bottom metal plate was the same as that for the polydisperse aerosol flow. The distance between the aerosol entrance and exit slits was 2 1/16′′. A high DC voltage (positive/negative) was applied to the top electrode plate while the other was electrically grounded. A uniform electrical field was then established in the particle classification zone of mini-plate DMAs. For the safe operation, two metal plates were insulated in the Delrin enclosure. Particle-free sheath gas was directed into the DMAs from the left inlet, passed through screen-type flow laminarizer prior to reaching the particle classification region. The excess flow exited the DMA from the outlet located at the right-hand side of the prototypes. The prototype DMA-1 was designed to size particles with sizes up to 300 nm when operating at the sheath flow rate of 1.0 lpm. The overall size of this prototype mini-plate DMA was 4 7/8′′ in length, 2 7/16′′ in width, and 21/32′′ in height, which is comparable to the size of an iPhone 6.
Figure 1. Schematic diagram of studied mini-plate DMA: (a) the sectional view and (b) the top view.
To further reduce the device size and to investigate the geometry effect on the mini-plate DMA performance, the other mini-plate DMA (DMA-2) was also made. The overall size of DMA-2 is similar to that of an iPhone 5. The detail of dimensions of two studied mini-plate DMAs are given in . The classification length and width of DMA-2 are less than those of DMA-1 while the spacing between two plates is higher in DMA-2. The length of aerosol slit opening in DMA-2 is 50% the width of its classification region. The prototype mini-plate DMA-2 measures particles with sizes smaller than 200 nm at the sheath flow rate of 1.0 lpm.
Table 2. Key dimensions of two studied mini-plate DMAs, units: inch (mm).
3. Experimental setup and data reduction for mini-plate DMA performance evaluation
3.1. Experimental setup
The experimental setup to evaluate the performance of prototype mini-plate DMAs is shown in . Test NaCl nanoparticles were generated by DMA-classifying polydisperse particles generated from either a custom-made Collison atomizer or evaporation-condensation technique (Scheibel and Porstendorfer Citation1983; Li et al. Citation2009). Droplets produced by the atomizer were dried into solid particles by passing through a diffusion-type dryer with silicone gel as the desiccant. NaCl aerosol particles generated by the atomization technique had the peak electrical mobility sizes larger than 30 nm. The peak sizes of generated particles were varied by atomizing the NaCl solution at various concentrations. To produce particles with electrical mobility sizes smaller than 30 nm, NaCl powder (ACS reagent, ≥99.0%, Sigma-Aldrich) was placed in a ceramic boat (Al2O3, Coors Ceramics Co.), located in a high-temperature tube furnace (Lindberg/Blue M tube Furnace, HTF55322C, Thermo Scientific). The powder was evaporated when the furnace temperature was set in the range of 500–700°C. NaCl vapor was then carried by carrier gas (either nitrogen or compressed air), whose flow rates were controlled by a needle valve and a laminar flowmeter. At the exit of the furnace, the vapor-rich carrier gas was mixed with particle free air (as the quenching flow) at the room temperature to produce nanoparticles by nucleation and condensation processes. The mean sizes and concentration of generated particles could be varied by the furnace temperature and the ratio of vapor-rich and quenching flow.
Figure 2. Experimental setup for the performance evaluation of mini-plate DMAs.
Tandem DMA (TDMA) technique, in which two DMAs are operated in series, was applied in the performance evaluation (Rader and McMurry Citation1986; Fissan et al. Citation1996; Hummes et al. Citation1996; Chen et al. Citation2007). One of two calibrated DMAs (TSI Model 3081 and 3085) was used as the 1st DMA to classify monodisperse NaCl particles in selected sizes. Prior to the 1st DMA, polydisperse aerosol was passed through a Kr85 radioactive bipolar charger to impart a steady-state charge distribution on them (Knutson and Whitby Citation1975). The flow rate of polydisperse aerosol stream was monitored by a laminar flowmeter. The TSI DMAs were operated at the aerosol-to-sheath flow rate ratio of 1:10. The classified aerosol particles were directly delivered to the mini-plate DMA to be studied. For each mini-plate DMA under the study, 5–6 particles sizes were selected for the evaluation.
The classified aerosol flow rate of mini-plate DMAs was also monitored by a laminar flowmeter. Two laminar flowmeters and needle valves were applied to control the sheath and excess flows of mini-plate DMAs. To investigate the performance of mini-plate DMAs under various flow rate conditions (i.e., different aerosol-to-sheath flow rate ratios, different aerosol and sheath flow rates), aerosol and sheath flows were varied at rates less than 0.6 lpm and 6.0 lpm, respectively. A high-voltage power supply (Bertan Model 205B-10R) was used to apply a high DC voltage to the mini-plate DMA under investigation. The voltage on the 2nd DMA (i.e., mini-plate DMA) was varied within its possible voltage range while the 1st DMA was at a fixed voltage. The voltage needed to obtain the maximum downstream particle concentration of mini-plate DMA was considered as the central voltage for sizing particles of elected sizes. The particle number concentrations upstream (N1) and downstream (N2) of the mini-plate DMA were measured by the same ultrafine condensation particle counter (UCPC, TSI model 3776). A three-way valve was installed in front of the UCPC to switch the measurement between N1 and N2. The TDMA curve was obtained by normalizing the above two concentration readings as a function of the voltage applied on the 2nd DMA.
3.2. Deconvolution scheme for DMA transfer function
The experimental TDMA data are the result of convolution of the 1st and 2nd DMA transfer functions. A deconvolution scheme is required to obtain the real transfer function of mini plate DMAs. Since the 1st DMA (i.e., TSI DMAs) was different from the 2nd one (i.e., mini-plate DMAs) prior knowledge is required for the transfer function of the 1st DMA. Such prior knowledge can be obtained by conducting the TDMA experiment with two identical TSI DMAs. A piecewise-linear function deconvolution scheme was then applied to recover the true transfer function of mini-plate DMAs (Li et al. Citation2006). In this scheme, the transfer function curve is approximated by a series of linear functions in divided N subsections in the particle electrical mobility axis, resulting in (N + 1) unknowns to be solved. The convoluted TDMA data can be calculated from two such representative transfer functions of the 1st and 2nd DMA. A numerical optimization scheme was used to find best-fitted TDMA data to the experimental one in order to retrieve the unknowns. The same deconvolution scheme has been applied to obtain the real transfer function of nano-DMA (Li et al. Citation2006), multiple-stage DMA (MDMA; Chen et al. Citation2007), and cDMA (Mei et al. Citation2011). The sizing accuracy and sizing resolution could thus be investigated once the real transfer function of mini-plate DMAs was recovered.
4. Results and discussion
4.1. Sizing accuracy of mini-plate DMAs
For a properly functioning DMA, it is critical to be able to calculate the central electrical mobility of classified particles from the applied voltage and operational flow rates (given the known DMA dimensions). Since mini-plate DMAs are in the parallel-plate configuration, we first assumed that the central electrical mobility of classified particles could be predicted by the classical two-dimensional (2D) model. Equation Equation(1)[1] is derived from the model under the ideal condition in which the particle diffusion, flow expansion, wall effect, and particle loss are negligible.
[1] where
is central electrical mobility of classified particles; Qsh is the sheath flow rate; V is the voltage applied on the DMA; L is the effective particle classification length; W is the width of classification region; and h is the effective height of classification zone. The comparison of the experimental and calculated voltage for a given particle electrical mobility is shown in . The deviation between the experimental and calculated voltages at the given particle sizes is not negligible. It is further found that the voltage needed for classifying particles with a given electrical mobility varied when varying the aerosol and sheath flow rates. To more precisely calculate the voltage applied for sizing particles with the desired electrical mobility, we proposed to include the correction factor (η) in Equation Equation(1)
[1] to take into the consideration of the above observation:
Figure 3. Comparison of central voltage for particle sizing among experimental data, calculated data with and without correction: (a) for DMA-1 and (b) for DMA-2.
shows the correction factor, η, as a function of aerosol-to-sheath flow rate ratio (β). It is interesting to note that the relationship between η and β is quite linear for studied DMAs (i.e., DMA-1 and DMA-2). The correction factor decreases with the increase of aerosol-to-sheath flow rate ratio. Because of the narrow space between two parallel plates, high sheath flow is likely to confine the aerosol stream in the region closer to the inlet top plate when the aerosol flow remained constant. Higher voltage is thus required to classify particles when operated at a lower aerosol-to-sheath flow rate ratio. Due to the dimension difference for both studied DMAs, the correction factor, η(β), for DMA-1 is different from that for DMA-2. Note that the η value for DMA-1 is higher than that for DMA-2. The slope of η(β) for DMA-2 is about twice the slope of η(β) for DMA-1. A 3D modeling work may be required to investigate the above observation in detail.
Figure 4. Correction factor, η, as a function of aerosol-to-sheath flow rate ratio, β, for studied mini-plate DMAs.
As evidenced in , the reasonably good agreement between the calculated voltages based on the proposed Equation Equation(2)[2] and the experimental ones is achieved for both DMA-1 and DMA-2 operated at various aerosol and sheath flow rates. The ±2.5% for the voltage deviation for cases with DMA-1 and DMA-2 in might be attributed to the accuracy in the flow rate control and the possible 3D flow effect (e.g., the span-wise expansion of aerosol flow as it entered the classification zone).
4.2. Transfer function of mini-plate DMAs
The performance of a DMA is characterized by its transfer function, which can be deconvoluted from the TDMA data. shows the typical comparison between the experimental TDMA data and calculated curves via the piecewise linear deconvolution scheme for the cases of 100 nm particles and operating mini-plate DMAs at the aerosol and sheath flow rates of 0.3 and 3.0 lpm, respectively. The good agreement between two sets of data for each mini-plate DMA was obtained. shows the deconvoluted transfer functions of DMA-1 and DMA-2. The shape of both deconvoluted DMA transfer functions are nearly triangular (when the normalized electrical mobility is used as the abscissa), close to the shape of ideal DMA transfer function when the polydisperse aerosol and classified flow rates are set the same. It is because the particle diffusion effect can be neglected for particles with 100 nm in size under the operational flow condition. Minor difference in the maximal transmission probability of the transfer functions for two prototype mini-plate DMAs was observed. The maximal probability values for the transfer function are 0.93 and 0.99 for DMA-1 and DMA-2, respectively. The full widths at half the maximum (FWHM) are approximately 0.13 and 0.17 for DMA-1 and DMA-2, respectively. It indicates that DMA-1 has a better sizing resolution than DMA-2. It may be due to the fact that higher percentage in length of aerosol entrance slit is relative to the width of DMA particle classification zone in DMA-1 (i.e., 75%) than that in DMA-2 (i.e., 50%). For the reference, all the experimental transfer functions of mini-plate DMAs obtained in this study are included in the online supplemental information.
Figure 5. (a) Comparison of experimental and calculated TDMA curves for DMA-1 and DMA-2; (b) typical transfer functions of DMA-1 and DMA-2 for 100 nm particle size, obtained via the linear-piecewise function deconvolution scheme, when operated at the aerosol-to-sheath flow rate ratio of 0.1.
4.3 Performance of mini-plate DMA in various flow conditions
The area and full width at half maximum (FWHM) of the DMA transfer function are two important parameters for characterizing the performance of a DMA. The former indicates the particle penetration in the DMA at a fixed voltage and the later implies the sizing resolution. Moreover, the effect of particle diffusion can be easily observed via the maximal height of the DMA transfer function (i.e., the maximal probability for particles with the central electrical mobility to pass through the DMA). The transfer function of DMAs is also required in the data reduction scheme to better recover the size distribution of particles. To evaluate the performance of mini-plate DMAs, the TDMA experiments were conducted for the cases of particles with the sizes varied from 20 to 180 nm and operating DMAs at the aerosol flow rate of 0.3 lpm and sheath flow rates of 1.5, 3.0, and 6.0 lpm.
shows the area (a), height (b), and FWHM (c) of mini-plate DMA-1 transfer function as a function of particle size at three different sheath flow rates while keeping constant aerosol flow rate of 0.3 lpm. The area of the DMA transfer function is slightly reduced as the particle size decreases. It is concluded that the particle loss in DMA-1 was negligible for particles in sizes larger than 20 nm. For particles larger than 30 nm in size the area under the transfer function curves approaches to constant values of 0.278, 0.135, and 0.661 for the aerosol-to-sheath flow rate ratio of 0.2, 0.1, and 0.05, respectively. However, the particle diffusion effect in the DMA classification zone can be observed in . The height of transfer function (i.e., the maximal probability for particles having central electrical mobility to pass through a DMA) decreases with the particle size decreases. The transfer function height was also decreased when the aerosol-to-sheath flow rate ratio was decreased. The above observation implies that more particle loss was encountered in the cases of low aerosol-to-sheath flow rate ratios. The possible explanation for the above observation is that, under the consideration of narrow particle classification zone in studied DMAs, injected aerosol stream was moving in thinner layer adjacent to the top plate when operating at the lower aerosol-to-sheath flow rate ratios, resulting in more particle loss possibly due to the electrical image force and/or minor flow disturbance.
Figure 6. Comparison of the area (a), height (b), and FWHM (c) of the transfer function for mini-plate DMA-1 at various operational flow conditions. Also included in the figure are the experimental transfer function data of PAMS DMA presented in AAAR 2011 (Qi et al. Citation2011).
The sizing resolution of a DMA for a given particle size can be found from the FWHM of the DMA transfer function. gives the FWHM of transfer function of mini-plate DMA-1 as a function of particle size. The FWHMs at three test sheath flow rates follow the general trend that the FWHM value decreases and reaches a constant as the particle size increase. By the DMA theory (Knutson and Whitby Citation1975), the FWHM of a DMA transfer function for non-diffusive particles (in deal 2D case) can be predicted by[3] where
,
, and
are the flow rates of polydisperse aerosol, classified aerosol, sheath flow rate, and excess flow rate, respectively. Based on the operational flow conditions, the FWHM of a plate DMA under the ideal 2D assumption will be 0.05, 0.1, and 0.2 for the cases of sheath flow rate at 6.0, 3.0, and 1.5 lpm, respectively. As shown in , the experimental FWHMs of mini-plate DMA-1 are in general larger than the values calculated with the ideal 2D model, even for large particles. The same observation is shown in for the area of mini-plate DMA transfer function.
Note that the aerosol slits in the classification region of prototype mini-plate DMAs were not fully opened across the entire width of the flow channel (i.e., 75% for DMA-1 and 50% for DMA-2). The reason for such aerosol slit design is to eliminate the wall effect. In such slit design, certain percentage of sheath flow was used to keep the aerosol flow away from the side walls of DMAs. Equation Equation(3)[3] thus overestimates the sheath flow rate actually used for sheathing aerosol from the aerosol exit slit, resulting in lower values of FWHMs for mini-plate DMAs. Via the experimental data for sizing resolution, the FWHMs based on the ideal 2D case are approximately 72%–77% of the experimental data. To better interpret the measured FWHM values, we introduce the concept of “effective sheath flow rate.” We defined the “effective sheath flow rate” as the portion of total sheath flow rate underneath the aerosol entrance slit opening. Accordingly, the effective sheath flow rate for DMA-1 is 75% of total sheath flow rate. It is because the slit opening length is 75% of the classification zone width. Similarly, the effective sheath flow rate for DMA-2 is 50% of total sheath flow rates applied. The values for the area and FWHM of non-diffusive transfer function, based on the effective sheath flow rate, are also shown in a and c. Better agreement between the measured and predicted data is then achieved. A detail computational fluid dynamics (CFD) modeling will be also required to investigate the 3D flow effect on the sizing resolution of mini-plate DMAs, especially for smaller particle sizes.
Note that, in , we further included the area, height, and FWHM of measured transfer functions (at the particle sizes of 30, 200, and 300 nm) for PAMS DMA operated at the aerosol and sheath flow rates of 0.1 and 0.4 lpm, respectively (Qi et al. Citation2011). It is found that, for particles less than 200 nm in sizes, the performance of PAMS DMA noticeably deviates from that predicted by the DMA theory for non-diffusive particles with respect to the area (i.e., 0.25), height (i.e., 1.0), and FWHM (i.e., 0.25) of transfer function.
4.4. Geometry effect on performance of mini-plate DMAs
To investigate the effect of aerosol slit and plate-to-plate spacing on the particle sizing performance of mini-plate DMAs, TDMA experiment was also conducted on DMA-2 for particles with the sizes varied from 10 to 100 nm. gives the comparison of area (a), height (b), and FWHM (c) of the transfer functions of DMA-1 and DMA-2 when operated at the aerosol and sheath flow rates of 0.3 and 3.0 lpm, respectively. The increasing trend on the height of mini-plate DMA transfer function and the decreasing trend of FWHM with the increase of particle size are also observed herein.
Figure 7. Comparison of area (a), height (b), and FWHM (c) of mini-plate DMA-2 and DMA-2 at the aerosol and sheath flow rate of 0.3 and 3.0 lpm, respectively.
In , the area of transfer function for DMA-2 is close to 0.178 for particles larger than 60 nm. The area of DMA transfer function is noticeably decreased as the particle size decreases. Moreover, the area of transfer functions of DMA-2 is slightly larger than that of DMA-1 for all test particle sizes. It indicates a slightly better transmission efficiency of DMA-2 as compared to that of DMA-1. The larger area of the DMA-2 transfer function seems to imply that the shorter aerosol slit opening and larger plate-to-plate spacing of DMA-2 did minimize the particle loss due to the flow expansion and wall effect. The particle diffusion effect was more obviously observed in DMA-2, evidenced by the height of DMA transfer function given in as the function of particle size. The DMA height decreased when the particle size reduced. For particles larger than 20 nm, the difference on the height of transfer functions of DMA-1 and DMA-2 is negligible. For particles with sizes larger than 50 nm, the height of studied DMAs' transfer functions are both close to the value of 1.0, the ideal height of a DMA transfer function.
further evidences the observation on the particle diffusion effect. The sizing resolution of mini-plate DMA-2 is worse than DMA-1. The FWHM of mini-plate DMA-2 transfer function noticeably increases with the decrease of particle size as compared to that for the cases with DMA-1. It is possibly because of the higher plate-to-plate spacing and shorter aerosol slit in DMA-2, resulting in flow mismatching in the neighborhood of the aerosol entrance slit. The flow disturbance may enhance the particle dispersion in the DMA classification zone. For both mini-plate DMAs, the FWHM of transfer functions deviates much from the value of 0.1 estimated by the ideal 2D model. The FWHM of DMA-2 is in fact larger than that of DMA-1. It is probably because of the smaller opening in length of aerosol slit opening relative to the width of the classification zone.
5. Conclusion
The performance of miniature plate DMAs (i.e., mini-plate DMAs) was studied to gain the instructive knowledge for the future design of mini-plate DMAs and to have a well-calibrated mini-plate DMA for the future UFP sensor network. The TDMA technique was applied to evaluate the performance of mini-plate DMAs. Two prototype mini-plate DMAs (i.e., DMA-1 and DMA-2) were constructed. Mini-plate DMA-1 has the classification length of 52.4 mm, 75% aerosol slit opening in length (related to the width of the classification zone), and 2.11 mm in the plate-to-plate spacing, while the classification zone of mini-plate DMA-2 is 35.7 mm in length, 50% aerosol slit opening, and 3.2 mm in height. By design, the particle sizing range of DMA-2 is less than that of DMA-1 under the same sheath flow rate operation. Compared with cylindrical DMAs, mini-plate DMAs are cost effective and easy to make and maintain. They however require detail experimental calibration for their performance. The compact size of mini-plate DMAs make it suitable to incorporate in low-cost and compact ultrafine particle sizers.
For the sizing accuracy of mini-plate DMAs, a correction factor (η) was proposed to modify the equation derived from the 2D assumption in order to better determine the applied voltage for sizing particles with the selected electrical mobility. Because of the difference in the DMA dimensions, the correction factors for DMA-1 and DMA-2 are different. It is interesting to observe that the factor, η, is a linear function of aerosol-to-sheath flow rate ratio (β). To investigate the performance of mini-plate DMAs, a piecewise linear deconvolution scheme was applied in our study to recover the real transfer function of DMAs from the collected TDMA data. For both DMA-1 and DMA-2, the typical transfer functions are in the triangular shape for non-diffusive particles (i.e., particles in large sizes). The maximal height, area, and FWHM of DMA transfer function indicate the maximal transmission efficiency of particles with the central electrical mobility, transmission efficiency of DMA at a fixed DMA voltage, and the sizing resolution, respectively. The experimental transfer function of DMAs is also required in the data reduction schemes used to better recover the size distribution of particles.
In three studied cases (i.e., aerosol flow rate of 0.3 lpm; sheath flow rates of 1.5, 3.0, and 6.0 lpm), the height of transfer function of mini-plate DMAs increases as the particle size increases while the FWHM decreases. The better height of transfer function was found when DMAs were operated at a high aerosol-to-sheath flow rate ratio. The discrepancies between the FWHMs obtained in experiments and calculated by the 2D DMA model were obvious for all studied flow cases. It is possibly because the aerosol slits were not fully opened along the entire width of the classification zone. The higher percentage of opening in length (i.e., DMA-1) has the FWHM values closer to those calculated by the 2D model when compared to those for DMA-2. It should be noted that part of sheath flow was applied to keep the aerosol flow away from the side walls of DMAs, not for sheathing it from the aerosol exit slit. The effective sheath flow rate should be less than the total sheath flow rate used under the studied mini-plate DMA design. For plate DMAs having such aerosol slit design, the sizing resolution (i.e., FWHM) and accuracy cannot be simply estimated by the equations derived based on the ideal 2D assumption. The less percentage of slit opening in length (relative to the width of the classification zone) made it deviated more from the ideal 2D case in the sizing resolution. By introducing the new concept of “effective sheath flow rate,” better agreement between measured and predicted data on the transfer functions of studied DMAs was obtained.
Conflict of interests
Da-Ren Chen, one of the authors, holds the licensed IP, which is similar in name, but unrelated in configuration, to this project.
UAST_1149547_Supplementary_File.zip
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