Measurement of aerosol size distribution is critical for understanding the impact of aerosols on human health and the global climate. Electrical mobility techniques have been widely used for size measurement of ultrafine aerosol, nanoparticles, and submicrometer aerosols due to their unique advantages over inertial or optical techniques. The differential mobility analyzers (DMA) have served a critical role in aerosol science, allowing separation of particles based on their electrical mobility. Since their initial development (Knutson and Whitby 1975; Liu and Pui 1975), DMAs have been extensively used for producing calibration aerosol and size classification and measurement. Several different designs of DMAs have been developed to overcome certain limitations of earlier designs, such as the Vienna type (Winklmayr et al. 1991), the French radial type (Fissan et al. 1998; Mesbah 1994), the Caltech radial type (Brunelli et al. 2009; Zhang et al. 1995), and the nanoDMA (Chen et al. 1998). Some other designs have also been developed to target specific size distribution measurement applications (Birmili et al. 1999; Li et al. 2009; Mei et al. 2011; Qi and Kulkarni 2012).

Growing concerns over inhalation exposure to nanoparticles have prompted development of compact instruments to characterize personal exposures in industrial atmospheres. In turn, such compact, portable instruments require design of smaller and efficient DMAs (Li et al. 2009; Qi and Kulkarni 2012). Most mobility spectrometers in use today employ DMAs that were not designed for dedicated stepping or scanning mobility measurements. For example, the Knutson and Whitby design (Knutson and Whitby 1975), originally designed to produce calibration aerosol at large sample flow rates has been adopted for scanning mobility size spectrometers with little modifications. Compact design of mobility spectrometers requires that the DMA samples only as much flow as that analyzed in the sensing volume of the downstream condensation particle counter (CPC). This allows optimizing the DMA size with respect to operational and measurement characteristics of the overall mobility spectrometers.

In this paper, we describe the design of a miniature DMA (mDMA) that addresses some of the drawbacks discussed above. The mDMA was designed specifically for use in hand-held spectrometers to classify the submicrometer size range at low to moderate size resolution, and with penetration efficiencies comparable to those of the Knutson-Whitby DMA. This was accomplished by using a small sample flow rate in the mDMA that matched the aerosol flow rate in the downstream CPC. The transfer function, mobility resolution, and transmission efficiencies of the DMA were experimentally measured for submicrometer aerosol. The results of these measurements are presented and discussed.

The cross-sectional view of the mDMA is shown in Figure 1. It has a cylindrical configuration with an outer cylindrical electrode (E) having an inner diameter (d_o) of 2.54 cm (1.0 inch), and an inner rod (D) with an outer diameter (d_i) of 1.778 cm (0.7 inch). The outer and inner electrodes are concentrically aligned with each other and the space between them forms the classification zone of the mDMA. A large part of the inner electrode rod is hollowed to reduce its weight. Sampled aerosol enters at the center of inlet (A) and subsequently splits into six small channels (diameter of 0.794 mm or 1/32 inch) evenly spaced along the circumference of the flow splitter (B). After passing through the annular chamber between the flow splitter and the top expanded portion of outer cylindrical electrode, the aerosol enters the classification zone through a narrow annular slit located on the outer electrode. Clean sheath flow enters the DMA through a channel in the side of the inlet and flows through 12 holes (diameter of 1.588 mm or 1/16 inch) on the flow splitter. These 12 holes were evenly spaced and staggered with the six channels for the aerosol flow. The sheath flow then enters the classification zone after passing through a flow laminarizer (C), which has 230 evenly distributed small holes (diameter of 0.508 mm or 0.02 inch) to help distribute and create a laminar sheath flow. The sheath flow exiting the flow laminarizer travels 5.588 mm before entering the classification zone of the DMA, which allows uniform circumferential flow distribution obtained at the design aerosol and sheath flow rates. This was qualitatively confirmed with flow visualization using smoke, which revealed uniformly distributed (azimuthally) laminar flow (see Figure S1 in SI). The flow laminarizer is made of Delrin^® and it also serves as an electrical insulator between the flow splitter and the inner rod. The classification zone has a length of 2.54 cm (1.0 inch). The classified aerosol exits the classification zone by entering the flow channels in the inner rod, and subsequently exits the DMA from the center of the outlet (G) part. The aerosol exit flow channels located in the inner rod oriented at an angle of 60° with respect to the longitudinal axis of the central electrode. The detailed configuration of these channels is shown in Figure S2 in SI. Excess flow exits the mDMA from two opposite outlet ports on G after passing through 48 small holes (diameter of 0.794 mm or 1/32 inch) on the outlet insulator (F). Outlet insulator is made of Delrin^® and also serves as an electrical insulator. The 48 holes on the outlet insulator and the symmetrically placed outlet ports are designed to help ensure uniform flow in the classification zone.

For a DMA operated under a fixed sheath flow rate, the largest classifiable particle diameter depends on the highest voltage that can be applied on the central electrode of the DMA at a given sheath flow. This voltage limit is normally set to avoid sparking caused by electrical breakdown of gas at high electrical field strength. For a DMA of cylindrical configuration, the highest electrical field strength is at the surface of the central electrode, and the breakdown strength (E_b, unit in KV/cm) can be calculated by Equation (1) (White 1963): (1)Eb=30+12.7di−0.5 where, d_i (in cm) is the outer diameter of the central electrode. Using Equation (1), the breakdown strength of the electrical field for the mDMA was found to be 39.5 KV/cm, which is higher than that of the TSI 3081 and 3085 DMAs (39.3 KV/cm).. In practice, the breakdown strength could be much lower than the value calculated from Equation (1), mainly due to the intensified electrical field at the edges of the aerosol entrance and exit slits, the imperfections in electrode alignment or surface finish during fabrication, or the presence of excess moisture or volatile species in the sampled aerosol. Most commercial DMAs are designed not to exceed a maximum electrical field strength (E_max) of approximately 15 KV/cm. Using this same limit, the maximum allowable voltage for the mDMA would be 4.8 KV. However, we have been able to operate the mDMA safely at higher voltages up to 6.3 KV (corresponding to E_max of 20 KV/cm). The smallest classifiable electrical mobility can then be calculated by, (2)Zp,min*=QshπLdiEmax where, Q_sh is the sheath flow rate, and L is the length of the classification zone. The largest measurable particle diameter for the mDMA can then be derived using the smallest classifiable electrical mobility for singly charged particles. Figure 2 shows the largest classifiable size (left y-axis) and the theoretical mobility resolution (right y-axis, defined and discussed in Section 4.5) as a function of sheath flow in the DMA.

As shown in Figure 2, with an E_max of 20 KV/cm for the mDMA (a factor of ~2 lower than the value used above of 39.5KV/cm), the largest classifiable particle diameter is 921 nm and 515 nm at 0.2 L/min and 0.4 L/min sheath flow rate, respectively. Although the lower sheath flow rate leads to a larger upper size limit of the DMA, it results in a lower mobility resolution of the DMA if the aerosol flow rate remains the same. For a DMA operating in a closed-loop sheath flow, its theoretical mobility resolution for non-diffusive particles is a function of the ratio of its sheath flow rate to its aerosol flow rate, and it is also plotted in Figure 2 for the mDMA operating at a 0.05 L/min aerosol flow rate. Considering both the upper size limit and mobility resolution, the mDMA was designed and evaluated at 0.2 L/min and 0.4 L/min sheath flow rates with a fixed aerosol flow rate of 0.05 L/min in this study. At these operating flow rates, the mDMA covers a large size range below 1 µm and provides a reasonable mobility resolution for personal exposure monitoring and mobile measurement applications.

Overall, the parts in the mDMA can be fabricated at reasonably low cost and they are easy to assemble. The design also allows fabrication of the DMA using additive manufacturing techniques.

Tandem DMA (TDMA) measurements have been widely used to experimentally obtain the transfer function of a DMA (Stolzenburg 1988; Stolzenburg and McMurry 2008), which characterizes accuracy, precision, and transmission efficiency of the DMA. Ideally, two identical DMA units must be used in the TDMA measurements. A classifying first DMA with a known transfer function has also been used to measure the unknown transfer function of the second DMA (Birmili et al. 1997; Li et al. 2006; Stolzenburg 1988; Stolzenburg and McMurry 2008; Stratmann et al. 1997). In our experimental setup, using two identical mDMAs presented several challenges in maintaining a reliable flow scheme over extended period of time. This was mainly due to significantly low aerosol flow rate (0.05 L/min) in the mDMA. Therefore, we used the first classifying DMA with a known transfer function to probe the transfer function of the test mDMA. The first DMA was operated at a much higher mobility resolution (compared to that of mDMA) to minimize measurement uncertainties.

The experimental setup for TDMA measurements is shown in Figure 3. Both silver nanoparticles (smaller than 50 nm in diameter) and ammonium sulfate particles (50 nm and larger) were used in the experiment. For silver nanoparticles, the test aerosol was produced using a tube furnace as an evaporation-condensation particle generator. A pneumatic atomizer (Model 3076; TSI Inc., Shoreview MN) was used to atomize an aqueous solution of ammonium sulfate to produce the ammonium sulfate test particles after passing the aerosol through a diffusion dryer. The concentration of the aqueous solution of ammonium sulfate was controlled so that the geometric mean diameter of the polydisperse aerosol generated from the atomizer was below 50 nm. This was to minimize the effect of multiply charged particles on the TDMA test. Test aerosols from different aerosol generators were subsequently charge-conditioned using a Kr⁸⁵ neutralizer and then classified in the 1^st DMA (Model 3081 for 200 nm particles and 3085 for particles of the other sizes; TSI Inc., Shoreview MN; operating at a 20:1 sheath-to-aerosol flow ratio) to provide monodisperse test particles. An Electrostatic Classifier (Model 3080; TSI Inc., Shoreview MN) controlled the sheath flow rate and voltage for the 1^st DMA. An Ultrafine Condensation Particle Counter (UCPC, Model 3025A, TSI Inc., Shoreview MN) continuously monitored the concentration of particles exiting the 1^st DMA at a flow rate of 0.3 L/min. The rest of the size-classified aerosol then entered a three-way valve at a flow rate of 0.05 L/min so that the concentration of particles upstream and downstream of the mDMA was measured by switching the three-way valve and directing the aerosol to a CPC. The particle loss in the two flow paths downstream of the three-way valve was measured and found to be identical. The CPC (Kanomax USA Inc., Andover, NJ) was specifically designed to operate at 0.05 L/min, which had a counting efficiency of 50% at 10 nm (Qi et al. 2011). As mentioned earlier, the mDMA was evaluated at an aerosol sampling flow rate of 0.05 L/min and sheath flow rates of 0.2 L/min and 0.4 L/min. The sheath flow for the mDMA was operated in a closed loop, and it was controlled and monitored by a modified electrostatic classifier set up (Model 3080, TSI Inc.).

When conducting the TDMA measurements, the first DMA was operated at a fixed sheath flow rate and its electrode voltage was set to correspond to desired test particle diameter. Two DC power supplies stepped through the entire voltage range for the mDMA under test. For improved accuracy, a DC power supply (Model GPR-30H10D, Good Will Instrument Co., Ltd, New Taipei City, Taiwan) applied a voltage between 0 to 300 V. This applied voltage was simultaneously monitored by using a multimeter (Fluke 111 True RMS; Fluke Corporation, Everett WA). A high-voltage power supply (Bertan Model 206B-10R, Spellman High Voltage Electronics Corporation, Hauppauge NY) provided the voltage above 300 V. This voltage was monitored using the multimeter through a HV probe (Model Fluke 80K-6; Fluke Corporation, Everett WA). Stepping through a series of voltages, an experimental TDMA curve was obtained by normalizing the particle concentrations measured by the same CPC downstream (N₂) and upstream (N₁) of the mDMA at a given voltage. Identical lengths of tubing (and the flow rate) established the flow paths for the measurement of N₁ and N₂, such that particle losses in the transport tubing (without the DMA) of both flow paths were identical and did not introduce error in the measurement of N₂/N₁. The particle concentration downstream of the first DMA was monitored using the UCPC during the TDMA measurements to account for any concentration fluctuation of the test aerosol during the measurement of N₁ and N₂ (N_3,1 and N_3,2 corresponding to N₁ and N₂, respectively).

The mDMA was designed to classify submicron particles for personal exposure monitoring and mobile measurements. The design specifically addresses the need to use very low aerosol sample flow rates needed to achieve particle size classification over a wide submicrometer size range in a compact instrument. The design allows fabrication of a low-cost, compact DMA that is easy to assemble. The performance of the mDMA was characterized using a tandem DMA (TDMA) technique operated at an aerosol flow rate of 0.05 L/min and a sheath flow rate of 0.2 L/min or 0.4 L/min. The transfer function of the mDMA was described using Stolzenburg’s model. The experimentally measured transfer function shows good agreement with the theoretical values derived using Stolzenburg’s model of the transfer function. The transmission efficiency is adequate and comparable to other DMA designs for particles in the range 10–1000 nm. The mobility resolution is comparable to that of the TSI 3085 nanoDMA at the same aerosol flow rates. The design features and performance make the mDMA suitable for compact field portable mobility size spectrometers for submicrometer aerosol measurement.