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Review Article

# Differential Mobility Particle Sizers for Nanoparticle CharacterizationOPEN ACCESS

[+] Author and Article Information
Jingjie Zhang

Department of Mechanical
and Nuclear Engineering,
Virginia Commonwealth University,
401 W Main Street,
Richmond, VA 23284
e-mail: jzhang4@vcu.edu

Daren Chen

Department of Mechanical
and Nuclear Engineering,
Virginia Commonwealth University,
401 W Main Street,
Richmond, VA 23284
e-mail: dchen3@vcu.edu

1Corresponding author.

Manuscript received April 5, 2014; final manuscript received July 14, 2014; published online August 19, 2014. Assoc. Editor: Hsiao-Ying Shadow Huang.

J. Nanotechnol. Eng. Med 5(2), 020801 (Aug 19, 2014) (9 pages) Paper No: NANO-14-1030; doi: 10.1115/1.4028040 History: Received April 05, 2014; Revised July 14, 2014

## Abstract

Differential mobility particle sizers (DMPSs) are instruments for online sizing gas-borne particles in submicrometer and nanometer diameter ranges. The aerosol charger, the differential mobility analyzer (DMA), and the particle concentration detector are three essential components in DMPSs. In the past four decades, the design of DMAs has evolved into a variety of modern versions to extend their sizing limits, especially in lower detectable size limits. The DMAs are now capable of classifying or sizing particles in the diameters down to 1.0 nm. This article gives a brief overview of state-of-the-art DMAs particularly designed for classifying particles with sizes down to sub-10 nm.

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## Introduction

Nanoparticles are defined as particles having one of the characteristic dimensions less than 100 nm and with unique mechanical, chemical, electrical, or even biological properties which would not be encountered in their bulk counterpart. In addition to their potential impact on the environment and public health, nanoparticles play important roles in diverse fields of applications. Example applications of nanoparticles have been reviewed from various perspectives [1-5]. Properties of nanoparticles are strongly dependent on their physical sizes. Nanoparticles typically with diameters less than 20–30 nm have shown unique crystallinity and enhanced interfacial properties/reactivity [6]. Technologies capable of characterizing particle sizes and classifying particles down to the nanometer range are thus in great demand for modern nanoparticle applications. For gas-borne particles in submicrometer and nanometer size ranges, DMPSs are now considered in aerosol and particle communities as primary tools to online characterize the size distribution of nanoparticles.

Basic components of a DMPS (shown in Fig. 1) consist of an aerosol charger to condition electrical charges on sampled particles to well-known charge distributions, a DMA to size/classify charged particles based on their electrical mobility, and a particle detector to measure the number/mass concentration of classified particles. By varying the voltage applied on the DMA and measuring the concentration of classified aerosol, the electrical mobility distribution of sampled particles after the charge conditioning can be directly measured by DMPSs. The size distribution of sampled particles can be consequently derived from the measured electrical mobility distribution (given the known charge distribution on particles). The voltage applied on DMA was originally varied step by step in the early days of the DMPS operation. The measuring cycle of early DMPSs was typically about 20 min. To reduce the measuring time, scanning mobility particle sizers, in which the voltage on DMAs is continuously varied, were developed [7]. With the scanning voltage operation, the measuring cycle of DMPSs has been reduced to 2 min or less.

Despite various designs, the fundamental configuration of a DMA remains similar. The configuration of a DMA typically has a pair of electrodes between which a DC electrical field is established by applying a high voltage on one electrode and electrically ground on the other. Two electrodes could be either two cylinders coaxially aligned in cylindrical DMAs or two parallel plates in planar DMAs. A typical cylindrical configuration of a DMA is shown in Fig. 2. The spacing between two electrodes is often named as the particle classification region, which is also used as the flow channel. Polydisperse aerosols, electrically charged by an aerosol charger, are introduced into the flow channel from the inlet designed on one electrode (i.e., polydisperse aerosol inlet). A particle-free sheath flow is also introduced into the flow channel from one channel end to keep the charged aerosol flow away from the other electrode. Prior to introducing into a DMA, particles are electrically charged to a well-defined charge distribution via an aerosol charger. In the presence of a fixed DC electric field, charged particles migrate across the sheath flow to reach the other electrode at the electric polarity opposite to that of particles. With both the polydisperse aerosol flow and sheath flow moving down the flow channel, particles with different electrical mobility arrive at various positions on the other electrode. An outlet (i.e., aerosol sampling outlet) is thus designed on the other electrode to extract classified aerosols from the flow channel. The remaining flow (i.e., excess flow) exits the classification region from the other end of the flow channel. Given fixed aerosol and sheath flow rates, classified particles with different central electrical mobility can be extracted from the aerosol sampling outlet by varying the intensity of applied DC electric field.

DMAs can be operated in two functional modes: classification and sizing. In both mode operations, the flow rates in DMAs are kept fixed. For particle classification, DMAs are operated at a constant electric field strength (i.e., the voltage applied on DMAs is fixed). For particle sizing, the electric field strength of DMAs is varied. Because of the operational principle, DMAs are required to work with an aerosol charger placing a well-defined charge distribution on particles prior to entering the DMAs. Radioactive sources, such as 85Kr, 241Am, and 210Po, and soft X-ray are common bipolar ion sources. For nanoparticles with reduced collision cross section between particles and ions, unipolar aerosol chargers, such as the one developed by Chen and Pui [8], are preferred. For measuring size distribution of particles, a detector/counter quantifying the number concentration of classified aerosols is further required at the downstream of a DMA. Condensation particle counters (CPCs) and aerosol Faraday cage electrometers are commonly used aerosol concentration detectors.

DMAs and electrical aerosol analyzers (EAA), the early generation of DMAs, have been applied for size distribution measurement and classification of submicron particles since the mid 1970s. DMAs were initially used to obtain relatively monodisperse particles for the calibration of aerosol instruments. They quickly played an important role in the measurement of particle size distributions once suitable aerosol concentration detectors were made available. Since then, DMAs have been routinely used in atmospheric aerosol characterization/monitoring and anthropogenic nanoparticle characterization. Combined with the electrospray technique, the applications of DMAs are extended to measuring macromolecules in colloidal/liquid systems [9]. The development of high-resolution and high transmission DMAs makes it possible to characterize sub-3 nm particles and ions, facilitating the investigation of ion-induced nucleation events and atmospheric aerosol formation. The coupling of a DMA in tandem with a mass spectrometer is used to analyze the particle mass [10,11]. Other tandem studies involving a DMA can be found in the review by Park et al. [12].

The history of ion measurements based on electrical mobility of ions dated back to the early 20th century when mobility of atmospheric ions was studied [13]. During the 1960s and 1970s, Particle Technology Laboratory, University of Minnesota, started a series of developments on electrical mobility based instruments. The development of the Whitby aerosol analyzer (WAA) marked a key step from the characterization of electrical mobility of atmospheric ions to the measurement of particle size distribution [14]. The EAA was the later version of WAA but with a substantially reduced size [15]. Both analyzers were commercialized by TSI Co., Ltd. (St. Paul, MN) and used in field studies. To further improve the size resolution of EAA, the cylindrical DMAs having two inlets (for polydisperse aerosol and sheath flows) and two outlets (for classified aerosol and excess flows) were a breakthrough in the apparatus design [16]. With the DMA theory later developed by Knutson and Whitby [17], DMAs have thus been widely accepted and applied in the aerosol community. In the past two decades, researchers have made much effort to explore new designs for improving the performance of DMAs, such as wider measurable particle size range, higher sizing resolution at DMA's lower size limit, better particle transmission efficiency, faster time response, and even better portability.

Major issues in the measurement of nanoparticles via the DMA technique are the particle diffusive loss and broadening of the transfer function due to the particle Brownian motion [18]. The transfer function of a DMA represents the apparatus performance for sizing particles (i.e., the sizing resolution and transmission efficiency). Strategically, the reduction of particle residence time in a DMA is required to minimize transfer function broadening and particle diffusion loss in a DMA. The particle residence time in a DMA can be shortened either by reducing its classification length or by increasing its sheath flow rate. In the work of Kousaka et al., a prototype TSI DMA with the reduced classification length of 11.11 cm (compared with the standard TSI DMA having the length of 44.44 cm) was evaluated to evidence the DMA performance improvement in sizing nanoparticles [18].

Reischl et al. designed a new cylindrical DMA, referred to as Vienna (or HAUKE) DMA, to lower DMA's sizing limit into the nanometer range [19,20]. This type of DMA (with a short particle classification length) was reported to have sufficient particle transmission for molecular ions measurement [20] and was also reported as the first DMA capable of operating at the sheath flow rate having the Reynolds number (Re) up to ∼2000 [21]. Based on the result of a four-DMA investigation (i.e., two TSI DMAs with the classification lengths of 44.44 cm and 11.11 cm; a HAUKE DMA and a RDMA) [22], a Nano-DMA numerically optimized for the particle size range of 3–150 nm was later developed and commercialized by TSI Inc. [23,24]. Taking a different design direction, a radial flow DMA, named as radial DMA (RDMA), was first developed by Pourprix and Daval [25] and Pourprix [26], and then by Zhang et al. [27,28] to classify particles from 3 nm to 200 nm. The design was recently refined by Brunelli et al. to extend the lower mobility particle size down to 1 nm (by significantly reducing the particle classification distance in RDMA) [29]. Note that RDMA was named by Pourprix as spectromètre de mobilité electrique circulaire (SMEC) when reported in European aerosol conferences.

To achieve high sizing resolution for molecular ions and particles with sizes below 3 nm, Fernández de la Mora and coworkers made the modification to Vienna DMAs. The modification enables to operate the DMAs at the flow rate with the Re number up to 5000 [30]. They continued working on various versions such as the isopotential DMA and its successor [31,32], as well as the Half-Mini DMA [33] which is operated at high sheath flow rates.

The other concern in applying DMAs for nanoparticle classification is on the low throughput. Using a DMA with multiple columns is one solution to scale up the throughput. The high cost tag on multiple-column DMA systems makes it financially difficult for ownership. A cost-effective cylindrical DMA was thus developed and evaluated by Mei et al. for the classification of macromolecules [34]. Recently, Hontañón and his coworkers developed high-aerosol flow DMAs (HF-DMAs) in both cylindrical and rectangular parallel-plate (or planar) configurations, aiming to enhance the throughput of classified nanoparticles [35-37]. The major advantages of planar DMAs are the ease of manufacture and low cost, compared with cylindrical ones. The portable DMA developed by Steer et al. is another example of the planar DMA [38].

Note that the effort has also been spent on the development of DMAs classifying large particles. To classify large particles, a long particle residence time in the DMA classification region is needed. The increase of particle residence time in a DMA can be achieved either by reducing the sheath flow rates or increasing the classification length. DMAs designed to size large particles usually have a long classification length ranging from 60 cm to 120 cm, and are operated at low sheath flow rates. The largest particle size measureable by a DMA (reported in the literature) is 10 μm, which is, however, not verified experimentally [39-43].

To further reduce the measuring cycle, multichannel DMAs have been developed and are commercially available for the measurement of time-varied aerosols. The design of multichannel DMAs includes a series of insulated metal ring sections which are stacked together as one of the DMA electrodes. Each metal section is connected to its own sensitive electrometer. When a constant electric field is applied in the classification region of the DMAs, charged particles separately deposit onto metal ring sections, depending on their electrical mobility. Consequently, electrical currents carried by particles deposited on metal rings are measured simultaneously, thus enabling the subsecond measurement of submicrometer particles. The drawbacks of multichannel DMAs are the low mobility sizing resolution due to the finite number of ring sections and the loss of the particle classification function. Multichannel DMAs in the cylindrical configuration were summarized in the review by Intra and Tippayawong [44].

Significant progress on the DMA development has been made in past decades for nanoparticle characterization. This paper focuses on the review of DMA design for the measurement and classification of nanoparticles. In the following sections, “Fundamental Principles of a DMA” and “DMA Design Evolution for Nanoparticle Characterization,” we will present the operational principle of DMAs, issues encountered in using DMAs for nanoparticle sizing, and various DMA designs to resolve these issues. Note that in this review we only focused on DMA works in which the prototypes were built and their performance was experimentally evaluated.

## Fundamental Principles of a DMA

###### Electrical Mobility and the Mobility Diameter.

A particle carrying i elementary units of charges in an electric field of intensity $E→$ will reach a steady migration velocity $v→$ when the forces acting on the particles by the flow and the electric field are balanced. For a spherical particle of diameter dp in the Stokes flow regime, the migration velocity of the particle under the influence of constant electrical field strength can be calculated in terms of the mechanical mobility of the particle, BDisplay Formula

(1)$v→=ieE→Cc3πηdp=ieBE→=ZE→$

The electrical mobility Z is then derived as Display Formula

(2)$Z=ieCc3πηdp$

where η is the gas viscosity. The electronic charge e is $1.602×10-19$ coulombs (C). Cc is the Cunningham slip correction coefficient for taking into account of noncontinuum flow effect when dp is comparable to or smaller than the mean free path of the carry gas, λ. Cc is typically given as Display Formula

(3)$Cc=1+2λdp(A1+A2e-A3dpλ)$

where A1 = 1.142, A2 = 0.558, and A3 = 0.500 [45].

By knowing the number of charges carried by particles, the size of the particles can be derived from the above equations when the electrical mobility of the particles is measured. The so-called mobility diameter dz of particles is defined by the relationship Z=ZM(dz).

###### DMA and the Transfer Function.

As shown in Fig. 2, given a fixed electric field applied on a DMA and operated at constant aerosol and sheath flow rates, particles with high electrical mobility will be deposited on the classification region before the sampling outlet and those with low electrical mobility will be either deposited on the classification section after the sampling outlet or exit the DMA via excess flow outlet. Only particles having electrical mobility in a specific narrow range can be extracted from the sampling outlet. Four flow rates are involved in the DMA operation, including the flow rates of the particle-free sheath flow, Qsh, the polydisperse aerosol flow, Qa, the classified aerosol (sampling) flow, Qs, and the excess flow, Qex. The flow rate control is one of the keys to operate a DMA.

Two basic configurations of DMAs (i.e., cylindrical and radial planar DMAs) are illustrated in Fig. 3. The characteristic mobility Z* of classified particles at given DMA flow rates and applied voltage, V, has been derived for DMAs in both the cylindrical and radial configurations

where, in Eq. (4), R1 and R2 are the radii of inner and outer cylinders and L is the characteristic classification length for cylindrical DMAs; and, in Eq. (5), R1 and R2 are the radii of DMA classification region (i.e., L=R2 − R1) and b is the spacing between two disks.

The probability that a particle with the mobility Z that enters the DMA classification region via the aerosol inlet and exits via the sampling outlet is usually expressed as the transfer function $Ω(Z,Z*)$. For the case of Qa=Qs and Qsh=Qex the nondiffusional transfer function of a DMA, derived by Knutson and Whitby [17], is in the triangular shape (shown in Fig. 4) with the 100% transmission efficiency at Z/Z*= 1.0 and a half-width of $ΔZ/Z*=(Qa+Qs)/(Qsh+Qe)=β$.

The mobility resolution R of a DMA can be defined as the ratio of Z* to the full width $ΔZfwhm$ at half the maximum transmission efficiency when the flows operated in the DMA are balanced (i.e., Qa=Qs and Qsh=Qex) and with the assumption that the effects of particle inertia and diffusion, and space and image charge are negligible [46]. It can also be defined equivalently as the ratio of the peak voltage V* to the full width at half the maximum, Vfwhm because the value of Z*V is fixed for given flow rates and DMA configuration [47]. The mobility resolution of a DMA is bounded by the ratio of flow rates, β. Display Formula

(6)$ℜnondiffusive=Z*ΔZfwhm=V*Vfwhm=β-1$

A high R value of a DMA is more desirable for high resolution measurements.

###### Particle Diffusion Effects On DMA Performance.

The broadened DMA transfer function due to the high diffusivity of nanoparticles was experimentally and numerically demonstrated in the work of Kousaka et al. [18,48]. The analytic diffusive transfer function of a cylindrical DMA (shown in Fig. 4) was nicely derived by Stolzenburg [49]. The Stolzenburg model was then validated using numerical modeling [23,50,51]. The theoretical limits to the resolution of a DMA were examined by Flagan using the Stolzenburg's analytical model [52]. The migration Peclét number is expressed as $Pemig=qVf/kT$, where q is the electrical charge carried by a particle, V is the applied DMA voltage, f is a factor to account for the nonuniformity of the DMA electric field, k is the Boltzmann constant, and T is the absolute temperature. The analysis shows that the diffusional degradation of the DMA resolution is a consequence of the DMA operation under the condition where the electrostatic potential energy of migrating particles is low relative to their thermal energy, kT. It is thus concluded that: (1) for ambient temperature and singly charged particles, the ideal DMA mobility resolution at any given classification voltage varies only slightly from one instrument to another; (2) a transitional voltage exists in any DMA measurement, below which the particle diffusion effects dominates; (3) in the particle diffusion dominated voltage range, the mobility resolution of a DMA is insensitive to the flow rate ratio and to details of instrument design; and (4) in the high voltage range where the mobility resolution of a DMA approaches the nondiffusive limit, the DMA performance is sensitive to the design or fabrication imperfections. The strategy for improving DMA performance for nanoparticle measurement is to operate the DMA at the voltage above the transitional value (i.e., at high Peclét number) when measuring the minimal particle sizes.

Rosell-Llompart et al. analyzed the effect of particle diffusion on the transfer function of cylindrical DMAs at a high Peclét number and concluded that the effect of particle diffusion on the DMA transfer function can be minimized under idealized conditions that the ratio of DMA classification length (L) to the width (Δ, i.e., the spacing of DMA classification channel) is near unity [21]. The same conclusion was reached in a simpler analysis on planar DMAs with the assumption of uniform flow in classification region [47]. Rosell-Llompart et al. evidenced the above prediction by comparing the performance of two Vienna type DMAs, one with the standard length and having the L/Δ ratio of 13.7, and the other with L/Δ = 2 [21]. Note that the L/Δ ratio of 2 or 1 has been used in a series of DMA designs for classification of nanoparticles down to 1 nm and macromolecules [47]. A high Peclét number corresponds to a strong electric field strength and/or a high Re number. For nonoptimal lengths of DMAs, the Re number of the sheath flow in DMAs must be increased to improve the mobility resolution R. However, the high Re number of a flow generally implies the better chance for the onset of flow instability and turbulence. It is thus wise to use DMAs with a short classification length for nanoparticle sizing and classification.

## DMA Design Evolution for Nanoparticle Characterization

This section provides a brief review of DMA design improvements for better characterization of nanoparticles in the past two decades.

###### Knutson and Whitby Mobility Analyzer.

The DMA was first developed by Liu and Pui [16], and was later described in detail by Knutson and Whitby [17] (shown in Fig. 3(a)). This DMA was an improved version of Hewitt's design [53] and was later commercialized by TSI (Model 3071 DMA). The DMA consists of two coaxially aligned cylinders (inner and outer ones) with two inlets and two outlets. Clean, filtered air enters the DMA through the central pipe at the top of the apparatus and flows downward through a mesh nylon screen which evenly distributes the flow into the annular classification region established by two cylinders. Polydisperse aerosol flow enters the DMA from two opposite aerosol inlets near the top of the outer cylinder and flows through a narrow annular flow channel adjacent to the outer cylinder. Polydisperse aerosol flow enters the classification region and meets the clean sheath flow at the exit of the annular flow channel. The aerosol sampling flow (a small percentage of total flow rate, i.e., the sum of polydisperse and sheath flow rates) is withdrawn out of the classification region via a circumferential slit opening near the bottom of inner cylinder and eventually exits the DMA from the sampling outlet pipe. The remaining flow is taken out of the analyzer from the main air outlet pipe. A high voltage is applied at the inner cylinder which is electrically insulated from the rest of the analyzer. With the voltage applied on the inner cylinder, charged particles with the polarity opposite to the applied voltage are drifted across the clean sheath flow toward the inner cylinder while the air flow carries particles moving downward. Particles with high electrical mobility deposit on the upper section of the aerosol sampling slit while those with low mobility either deposit in the lower section of the sampling outlet or are carried out by the main air flow (i.e., excess flow). Only particles within a narrow range of electrical mobility can reach the sampling slit, being extracted out by the sampling flow. The transfer function of this DMA was derived and verified using polystyrene latex particles of 0.79 μm. This analyzer can be either for the production of monodisperse aerosols or for measuring the size distributions of particles. The reported measurable size range of particles is from 0.005 μm to 1.0 μm [17].

It is found that the Brownian diffusion of particles in the DMA could not be negligible when sizing particles of diameters less than 100 nm. The loss of ultrafine particles in TSI DMAs (Model 3071, shown in Fig. 5) due to particle Brownian diffusion had been numerically and experimentally studied [18]. The results showed that the effect of particle Brownian diffusion increased with the decrease of particle size and flow rate of clean sheath air. The shape of the DMA transfer function became broadened in the electrical mobility base and reduced in the peak particle transmission when compared with that in the nondiffusive cases. In the same work, the authors further experimentally compared the performance of DMAs in the same configuration but with two different classification lengths (i.e., 44.44 and 11.11 cm), and the change of insulation material located next to the sampling slit (for insulating the high voltage applied on inner cylinder from the ground). The work concluded that the reduction of DMA classification length and the change of insulation material are effective to reduce the broadening of the transfer function and particle loss in the DMA.

Through the numerical model developed by Chen and Pui [23], Chen et al. [24] developed a Nano-DMA using the TSI-short DMA as the start point for optimization. Figure 6 shows the schematic diagram of the Nano-DMA. The Nano-DMA was primarily designed for particles in the size range of 3–50 nm (but can be extended to 150 nm by reducing the operational sheath flow rate). Polydisperse aerosol flow enters the DMA from the top inlet which is axially symmetric while the sheath flow enters the DMA from the base, flows to the top annular flow chamber, passes through a set of screens, and finally enters the classification region. The classification length of Nano-DMA is reduced to 5.0 cm. An optional aerosol passage is also included in the design, enabling the use of high polydisperse aerosol flow to further minimize the particle diffusion loss during the transport from the aerosol inlet to the classification entrance slit. The dimensions and shape of the aerosol entrance slit are designed and modeled aerodynamically to achieve optimal flow matching. Additionally, the base of the Nano-DMA is redesigned to reduce the loss of charged particles due to the surface charge effect. With these features, the transmission and resolution of nanoparticles are greatly improved for particles sized down to 3 nm. Recently the transfer function and penetration of Nano-DMA for 1–2 nm particles, which are beyond the design range, were studied [54]. With the aerosol/sheath flow ratio at 1:10 (1.5 lpm/15 lpm or 2 lpm/20 lpm), the transfer function of Nano-DMA was deteriorated for particles smaller than 2 nm in mobility size.

###### Vienna DMA and the Operation in Laminar Regime under High Reynolds Number.

Reischl and his coworkers at the University of Vienna developed a cylindrical DMA (often called as Vienna DMA) is shown in Fig. 7; Ref. [19]. The DMA was designed in two sets of dimensions (one for particles of 2–40 nm in size and the other for particles of 3–150 nm in size). The design of the Vienna DMA has a couple of new flow features: (1) tangentially introducing sheath flow and polydisperse aerosol flow into the DMA and (2) a bullet-shaped inner electrode to form a “trumpet” flow channel. The sheath air enters the DMA from the tangential inlet, passes through a flow screen located above the inner electrode, and accelerates as entering the classification region. The polydisperse aerosol flow tangentially enters the annular aerosol chamber and then the classification region via the aerosol entrance slit. No transfer function was shown in the original paper of Winklmyr et al. [19]. The diffusion broadening of the transfer function of the Vienna DMA was observed in the evaluation for particles in the size range 1–10 nm when compared with the theoretical prediction by the Stolzenburg's model [20]. The Vienna DMAs were embodied in the commercialized HAUKE DMA (Model 3/150). Controversial results [21,22] were reported by different research groups on the performance of this HAUKE 3/150 model. These reported results were explained (by Reischl) as the imperfection in numerous homemade Vienna DMAs [20].

Various modified Vienna DMAs had been reported in the literature. The theoretical analysis done by Rosell-Llompart et al. [21] suggested that the optimal L/Δ ratio to reduce the diffusion broadening of DMA transfer function is 1.0, where L is the aerosol classification path and Δ is the spacing between two electrodes [21]. To test the theoretical prediction, the authors made a Vienna DMA with a very short aerosol classification path by elevating the location of aerosol sampling slit in the inner electrode. The modified DMA has the axial distance between the polydisperse aerosol entrance slit and the sampling slit, L, of only 1.6 cm, resulting in an L/Δ ratio of 2.0. The authors also made an additional geometrical modification to the annular polydisperse aerosol chamber to minimize the potential swirling of polydisperse aerosol flow. This short Vienna DMA is the first one operated at the flow rate with the Re number up to almost 2000, achieving an improved sizing resolution in the whole measurable size range above 1 nm. The authors thus concluded that one promising direction to improve the DMA performance for particles less than 1 nm is to develop a DMA capable of operating at the flow rate with Re = 104 [21].

Since then, much effort has been made to modify the configuration of the Vienna DMA. De Juan and Fernández de la Mora managed to run the modified Vienna DMA at Re number up to 5000. In the above DMA, the classification length, L, was reduced to 1.27 cm [30]. To recirculate the excess flow back into the sheath air inlet, a flow laminarizer of one meter in length was used, resulting in the bulky size of the whole DMA system. The authors further suggested that a better sizing resolution might be reached by running a DMA at the flow rate of even higher Re numbers. However, the strategy of increasing the flow Reynolds numbers in DMAs by increasing sheath flow rates is limited by the pumping capacity. To overcome the limitation of the pumping capacity, the DMA designed by Rosser (shown in Fig. 8) had a special excess flow exhaust passage which enables the flow rates to approach 4000 l/min, compared with 800 l/min in the studies of Rosell-Llompart et al. [21,55]. The DMA classification length of Rosser's DMA, L, is 9.7 mm while keeping the same inner and outer electrode radii of 25 mm and 33 mm as those used in other Vienna DMAs. The 5 deg conical contraction was used as the sheath air entrance passage in order to further accelerate the flow and to delay the flow transition to turbulence at much higher Reynolds numbers. With all the above improvements, the authors managed to operate the DMA up to Re ∼ 62,000, although the sign of flow quality deterioration was evidenced at about Re = 20,000. The Rosser's DMA was the first one capable of good sizing resolution at 1 nm (in literature).

The aforementioned DMAs obtain the necessary sizing resolving power by the increase of sheath air flow rate, achieved by a free sheath flow entry, i.e., an open entrance. However, the open entrance for sheath air flow is not suitable for a DMA operated in tandem with carrier-gas-sensitive particle concentration detectors, such as CPCs and mass spectrometers. A Vienna type UDMA (shown in Fig. 9), based on the Vienna DMA, is specially designed for high-resolution mobility measurements for the particles size range between 1 nm and 5 nm, and optimized to work with a mass spectrometer [56]. For the high sizing resolution, the so called Vienna type UDMA features a very short DMA classification length of 6.5 mm, which is the optimal length with an L/Δ ratio close to unity. For the recirculation of sheath flow, the Vienna type UMDA has the “capped” design with the modification of sheath gas flow inlets. Instead of one, this DMA has four tangential sheath flow inlets at the top. To ensure the uniformity and reduce the flow swirling, the sheath flow passes through a stainless steel sponge located in the annular sheath flow chamber and a nylon screen prior to its entrance to the classification region. The polydisperse aerosol flow is tangentially introduced into the DMA. The Vienna type UDMA can operate at a stable sheath flow of approximately 700 l/min in a closed loop.

The most recent development based on Vienna DMA design is the so-called Half-Mini DMA [33]. Figure 10 shows the schematic diagram of the reported Half-Mini DMA. The Half-Mini DMA has a similar open sheath flow inlet and multilayer screens as those DMAs in the studies of Rosell-Llompart et al. and Rosser et al. [21,55]. Four DMAs with the flow channel spacing of either 2 or 3 mm, and several classification lengths have been tested using 1 nm particles. Short models with L/Δ = 2 consistently achieve a resolution above 40. Long models typically reach a resolution > 25–30.

###### RDMAs.

The radial configuration of DMAs was first proposed by Pourprix and his coworkers under the French name of SMEC and later developed by Zhang et al. under the name of RDMA for the measurement of ultrafine particles [25-28,57]. Figure 3(b) shows the schematic diagram of a RDMA. A RDMA has two parallel disks (i.e., top and bottom ones). Sheath air enters the RDMA tangentially into its annular flow chamber (located at the top disk), passes through a porous ring section to uniformly distribute sheath flow in the circumferential direction, and then flows to the classification region. The polydisperse aerosol flow is also introduced tangentially into the annular aerosol chamber and enters the classification region via the annular aerosol slit located on the bottom disk. Charged particles migrate from the bottom electrode to the top under the influence of uniform electric field between two parallel disks. Classified aerosol is then extracted through the sampling port on the center of the top disk. Excess flow exits through the outlet on the bottom disk. The reported RDMA can be used to measure particles with the size range of 3–200 nm.

RDMAs designed for measuring nanoparticles and ions (i.e., Nano-RDMA) has been recently developed [29]. Nano-RDMA is in the similar configuration as that reported by Zhang et al. [27,28]. The particle classification length of the Nano-RDMA has been reduced. By operating it at slightly higher sheath flow rates than that used in RDMAs, the Nano-RDMA is capable of classifying molecular ions with the mobility diameters in the range of 1–1.8 nm. Note that the above result is achieved by empirical corrections because of the nonuniformity in flow and electric fields, resulted from the very short classification region. The upper limit for particle size measurement was calculated at 13 nm. The sizing resolution for ions with the mobility diameter of 1.47 nm was approximated 7. Nano-RDMA has also been evaluated as the frontend separation device for mass spectrometric analysis of ions generated by an electrospray ionization source [58].

###### Drift DMA.

The other interesting variation of RDMA is the development of radial opposed migration ion and aerosol classifier (ROMIAC) [59]. The design of ROMIAC originates from the conceptual drift DMA proposed by Loscertales [60]. The Drift DMA originally proposed in cylindrical configuration includes the additional electrical field in the axial direction. The direction of axial electrical field is opposing that of sheath gas flow. With the addition of axial electric field the resultant electric field is tilted relative to the flow direction. The schematic diagram of a drift DMA is shown in Fig. 11. Based on the theoretical analysis, the sizing resolution of drift DMA in its most favorable configuration can be ultimately improved by six fold as compared to that of DMAs without axial electric field (operated at the same flow rate). The most favorable configuration of drift DMA is at the classification length of zero (when the polydisperse aerosol inlet and aerosol sampling outlet are placed opposed to each other) and when the strength of the axial electric field is three times as that of radial electric field. However, the construction of this cylindrical drift DMA is difficult and expensive. Flagan has thus proposed a variant of drift DMA (opposed migration aerosol classifier, OMAC) [61]. Instead of titling the direction of electric field relative to the flow direction, the OMAC tilts the flow direction relative to the direction of electric field. The implementation of OMAC in radial configuration results in the development of ROMIAC (shown in Fig. 12). Note that the ROMIAC further features the isopotential aerosol inlet and sampling outlet, which may potentially reduce the particle/ion loss due to the electrical charge-up of insulation used in typical DMAs. Similar ideas of tilting the flow direction were adopted by several other designs, such as the nanoparticle crossflow DMA (NCDMA) in a cylindrical configuration [62], and the crossflow ion analyzer [63]. No experimental data were published. The key feature shared in common among these designs is the introduction of a flow opposing the electric field. However, the stability of the laminar flow in the crossflow region is doubted. To simultaneously retain the laminar flow conditions, a periodic focusing DMA (PFDMA) was developed and evaluated [64]. This PFDMA came back to the idea of tilting the electric field opposing the sheath flow field. The authors did not present the design of the device but only explained the concept.

## Summary

DMPSs have been applied in aerosol and particle communities for characterizing the size distribution of gas-borne particles in the submicrometer and nanometer ranges. With the research interest of particle formation in the atmosphere and National initiate of Nanotechnology, much effort and resources have been recently focused on the development of mobility particle sizers to improve their performance in characterizing nanoparticles in the sub-10 nm range and ions. As a result, it is now possible to perform the characterization of nanoparticles down to sub-1 nm (mobility size) using electrical mobility particle sizers. In this review, we gave a brief introduction to the history of using electrical mobility techniques for aerosol measurements and applications. Basic operational principles and theory involved in the DMA development were also provided. The latest progress in the DMA development for the measurements of nanometer particles and molecular ions are finally reviewed in details.

Nomenclature
• Pe =

Peclét number

• Re =

Reynolds number

## References

Pui, D. Y. H., and Chen, D.-R., 1997, “Guest Editorial—Nanometer Particles: A New Frontier for Multidisciplinary Research,” J. Aerosol Sci., 28(4), pp. 539–555.
Kim, B. H., Hackett, M. J., Park, J., and Hyeon, T., 2014, “Synthesis, Characterization, and Application of Ultrasmall Nanoparticles,” Chem. Mater., 26(1), pp. 59–71.
Cheng, Y., Morshed, R. A., Auffinger, B., Tobias, A. L., and Lesniak, M. S., 2014, “Multifunctional Nanoparticles for Brain Tumors Imaging and Therapy,” Adv. Drug Del. Rev., 66, pp. 42–57.
Guo, D., Xie, G., and Luo, J., 2014, “Mechanical Properties of Nanoparticles: Basics and Applications,” J. Phys. D: Appl. Phys., 47(1), p. 013001.
Madl, A. K., Plummer, L. E., Carosino, C., and Pinkerton, K. E., 2014, “Nanoparticles, Lung Injury, and the Role of Oxidant Stress,” Annu. Rev. Physiol., 76, pp. 447–465. [PubMed]
Auffan, M., Rose, J., Bottero, J. Y., Lowry, G. V., Jolivet, J. P., and Wiesner, M. R., 2009, “Towards a Definition of Inorganic Nanoparticles From an Environmental, Health and Safety Perspective,” Nat. Nanotechnol., 4, pp. 634–641. [PubMed]
Wang, S. C., and Flagan, R. C., 1990, “Scanning Electrical Mobility Spectrometer,” Aerosol Sci. Technol., 13(2), pp. 230–240.
Chen, D.-R., and Pui, D. Y. H., 1999, “A High Efficiency, High Throughput Unipolar Aerosol Charger for Nanoparticles,” J. Nanopart. Res., 1(1), pp. 115–126.
Guha, S., Li, M., Tarlov, M. J., and Zachariah, M. R., 2012, “Electrospray–Differential Mobility Analysis of Bionanoparticles,” Trends Biotechnol., 30(5), pp. 291–300. [PubMed]
Hogan, C. J., Jr., and Fernández de la Mora, J., 2009, “Tandem Ion Mobility-Mass Spectrometry (IMS-MS) Study of Ion Evaporation From Ionic Liquid-Acetonitrile Nanodrops,” Phys. Chem. Chem. Phys., 11, pp. 8079–8090. [PubMed]
Fernández de la Mora, J., 2011, Ion Mobility Spectroscopy—Mass Spectrometry: Theory and Applications, Taylor and Francis, Oxford, UK, Chap. 5.
Park, K., Dutcher, D., Emery, M., Pagels, J., Sakurai, H., Scheckman, J., Qian, S., Stolzenburg, M. R., Wang, X., Yang, J., and McMurry, P. H., 2008, “Tandem Measurements of Aerosol Properties—A Review of Mobility Techniques With Extensions,” Aerosol Sci. Technol., 42(10), pp. 801–816.
Flagan, R. C., 1998, “History of Electrical Aerosol Measurements,” Aerosol Sci. Technol., 28(4), pp. 301–380.
Whitby, K. T., and Clark, W. E., 1966, “Electrical Aerosol Particle Counting and Size Distribution Measuring System for the 0.015 to 1 μ Size Range,” Tellus, 18(2–3), pp. 573–586.
Liu, B. Y. H., Whitby, K. T., and Pui, D. Y. H., 1974, “A Portable Electrical Analyzer for Size Distribution Measurement of Submicron Aerosols,” APCAJ, 24(11), pp. 1067–1072.
Liu, B. Y. H., and Pui, D. Y. H., 1974, “A Submicron Aerosol Standard and the Primary, Absolute Calibration of the Condensation Nucleus Counter,” J. Colloid Interface Sci., 47(1), pp. 155–171.
Knutson, E. O., and Whitby, K. T., 1975, “Aerosol Classification by Electric Mobility: Apparatus, Theory, and Applications,” J. Aerosol Sci.6(6), pp. 443–451.
Kousaka, Y., Okuyama, K., Adachi, M., and Mimura, T., 1986, “Effect of Brownian Diffusion on Electrical Classification of Ultrafine Aerosol Particles in Differential Mobility Analyzer,” J. Chem. Eng. Jpn., 19(5), pp. 401–407.
Winklmayr, W., Reischl, G. P., Lindner, A. O., and Berner, A., 1991, “A New Electromobility Spectrometer for the Measurement of Aerosol Size Distributions in the Size Range From 1 to 1000 nm,” J. Aerosol Sci., 22(3), pp. 289–296.
Reischl, G. P., Mäkelä, J. M., and Necid, J., 1997, “Performance of Vienna Type Differential Mobility Analyzer at 1.2–20 Nanometer,” Aerosol Sci. Technol., 27(6), pp. 651–672.
Rosell-Llompart, J., Loscertales, I. G., Bingham, D., and Fernández de la Mora, J., 1996, “Sizing Nanoparticles and Ions With a Short Differential Mobility Analyzer,” J. Aerosol Sci., 27(5), pp. 695–719.
Fissan, H., Hummes, D., Stratmann, F., Büscher, P., Neumann, S., Pui, D. Y. H., and Chen, D., 1996, “Experimental Comparison of Four Differential Mobility Analyzers for Nanometer Aerosol Measurements,” Aerosol Sci. Technol., 24(1), pp. 1–13.
Chen, D., and Pui, D. Y. H., 1997, “Numerical Modeling of the Performance of Differential Mobility Analyzers for Nanometer Aerosol Measurements,” J. Aerosol Sci., 28(6), pp. 985–1004.
Chen, D.-R., Pui, D. Y. H., Hummes, D., Fissan, H., Quant, F. R., and Sem, G. J., 1998, “Design and Evaluation of a Nanometer Aerosol Differential Mobility Analyzer (Nano-DMA),” J Aerosol Sci., 29(5–6), pp. 497–509.
Pourprix, M., and Daval, J., 1990, “Electrostatic Precipitation of Aerosol on Wafers, a New Mobility Spectrometer,” Aerosols: Science, Industry, Health and Environment: Proceedings of the Third International Aerosol Conference, S.Masuda, and K.Takahashi, Eds., Kyoto, Japan, Sept. 24–27, Pergamon Press, New York. Vol. 2.
Pourprix, M., 1994, “Selecteur de Particules Chargees, a Haute Sensibilite,” Brevet Francais, France Patent No. EP0685725 A1.
Zhang, S.-H., Akutsu, Y., Russell, L. M., Flagan, R. C., and Seinfeld, J. H., 1995, “Radial Differential Mobility Analyzer,” Aerosol Sci. Technol., 23(3), pp. 357–372.
Zhang, S.-H., and Flagan, R. C., 1996, “Resolution of the Radial Differential Mobility Analyzer for Ultrafine Particles,” J. Aerosol Sci., 27(8), pp. 1179–1200.
Brunelli, N. A., Flagan, R. C., and Giapis, K. P., 2009, “Radial Differential Mobility Analyzer for One Nanometer Particle Classification,” Aerosol Sci. Technol., 43(1), pp. 53–59.
De Juan, L., and Fernández de la Mora, J., 1998, “High Resolution Size Analysis of Nanoparticles and Ions: Running a Vienna DMA of Near Optimal Length at Reynolds Numbers up to 5000,” J. Aerosol Sci., 29(5–6), pp. 617–626.
Martinez-Lozano, P., and Fernández de la Mora, J., 2006, “Experimental Tests of a Nano-DMA With no Voltage Change Between Aerosol Inlet and Outlet Slits,” J. Aerosol Sci., 37(11), pp. 1629–1642.
Martinez-Lozano, P., and Labowsky, M., 2009, “An Experimental and Numerical Study of a Miniature High Resolution Isopotential DMA,” J. Aerosol Sci., 40(5), pp. 451–462.
Fernández de la Mora, J., and Kozlowski, J., 2013, “Hand-Held Differential Mobility Analyzers of High Resolution for 1–30 nm Particles: Design and Fabrication Considerations,” J. Aerosol Sci., 57, pp. 45–53.
Mei, F., Fu, H., and Chen, D.-R., 2011, “A Cost-Effective Differential Mobility Analyzer (cDMA) for Multiple DMA Column Applications,” J. Aerosol Sci., 42, pp. 462–473.
Santos, J. P., Hontañón, E., Ramiro, E., and Alonso, M., 2009, “Performance Evaluation of a High-Resolution Parallel-Plate Differential Mobility Analyzer,” Atmos. Chem. Phys., 9, pp. 2419–2429.
Hontañón, E., and Kruis, F. E., 2009, “A Differential Mobility Analyzer (DMA) for Size Selection of Nanoparticles at High Flow Rates,” Aerosol Sci. Technol., 43(1), pp. 25–37.
Hontañón, E., Rouenhoff, M., Azabal, A., Ramiro, E., and Kruis, F. E., 2014, “Assessment of a Cylindrical and a Rectangular Plate Differential Mobility Analyzer for Size Fractionation of Nanoparticles at High-Aerosol Flow Rates,” Aerosol Sci. Technol., 48(3), pp. 333–339.
Steer, B., Gorbunov, B., Muir, R., Ghimire, A., and Rowles, J., 2014, “Portable Planar DMA: Development and Tests,” Aerosol Sci. Technol., 48(3), pp. 251–260.
Myojo, T., Ikawa, S., Sakae, H., and Kohyama, N., 2001, “A New Long DMA and Its Performance for Size-Measurement of 1 μm Polystyrene Latex Particles,” J. Air Clean. Contam. Control, 39, pp. 168–175 (in Japanese).
Myojo, T., Ehara, K., Koyama, H., and Okuyama, K., 2004, “Size Measurement of Polystyrene Latex Particles Larger Than 1 Micrometer Using a Long Differential Mobility Analyzer,” Aerosol Sci. Technol., 38(12), pp. 1178–1184.
Uin, J., Tamm, E., and Mirme, A., 2011, “Very Long DMA for the Generation of the Calibration Aerosols in Particle Diameter Range up to 10 μm by Electrical Separation,” Aerosol Air Qual. Res., 11, pp. 531–538.
Raddatz, M., Wiedensohler, A., Wex, H., and Stratmann, F., 2013, “Size Selection of Sub- and Super-Micron Clay Mineral Kaolinite Particles Using a Custom-Built Maxi-DMA,” Nucleation and Atmospheric Aerosols: 19th International Conference, AIP Conf. Proc., Fort Collins, CO, June 23–28, Vol 1527, pp. 457–460.
Rosch, M., Pfeifer, S., Wiedensohler, A., and Stratmann, F., 2014, “Selection of Quasi-Monodisperse Super-Micron Aerosol Particles,” EGU General Assembly, Geophysical Research Abstracts, 16, Paper No. EGU2014-4957.
Intra, P., and Tippayawong, N., 2008, “An Overview of Differential Mobility Analyzers for Size Classification of Nanometer-Sized Aerosol Particles,” Songklanakarin J. Sci. Technol., 30(2), pp. 243–256.
Allen, M., and Raabe, O., 1985, “Slip Correction Measurements of Spherical Solid Aerosol Particles in an Improved Millikan Apparatus,” Aerosol Sci. Technol., 4(3), pp. 269–286.
Flagan, R. C., 2011, Aerosol Measurement: Principles, Techniques, and Applications, 3rd ed., Wiley, Hoboken, NJ, Chap. 15.
Fernández de la Mora, J., 2011, Aerosol Measurements: Principles, Techniques, and Applications, 3rd ed. Wiley, Hoboken, NJ, Chap. 32.
Kousaka, Y., Okuyama, K., and Adachi, M., 1985, “Determination of the Size Distribution of Ultrafine Aerosol Particles Using a Differential Mobility Analyzer,” Aerosol Sci. Technol., 4(2), pp. 209–225.
Stolzenburg, M. R., 1988, “An Ultrafine Aerosol Size Distribution Measuring System,” Ph.D. thesis, University of Minnesota, Minneapolis, MN.
Hagwood, C., 1999, “The DMA Transfer Function With Brownian Motion a Trajectory/Monte-Carlo Approach,” Aerosol Sci. Technol., 30(1), pp. 40–61.
Mamakos, A., Ntziachristos, L., and Samaras, Z., 2007, “Diffusion Broadening of DMA Transfer Functions. Numerical Validation of Stolzenburg Model,” J. Aerosol Sci., 38(7), pp. 747–763.
Flagan, R. C., 1999, “On Differential Mobility Analyzer Resolution,” Aerosol Sci. Technol., 30(6), pp. 556–570.
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Rosser, S., and Fernández de la Mora., 2005, “Vienna-Type DMA of High Resolution and High Flow Rate,” Aerosol Sci. Technol., 39(12), pp. 1191–1200.
Steiner, G., Attoui, M., Wimmer, D., and Reischl, G. P., 2010, “A Medium Flow, High-Resolution Vienna DMA Running in Recirculating Mode,” Aerosol Sci. Technol., 44(4), pp. 308–315.
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Mui, W., Thomas, D. A., Downard, A. J., Beauchamp, J. L., Seinfeld, J. H., and Flagan, R. C., 2013, “Ion Mobility-Mass Spectrometry With a Radial Opposed Migration Ion and Aerosol Classifier (ROMIAC),” Anal. Chem., 85(13), pp. 6319–6326. [PubMed]
Loscertales, I. G., 1998, “Drift Differential Mobility Analyzer,” J. Aerosol Sci., 29(9), pp. 1117–1139.
Flagan, R. C., 2004, “Opposed Migration Aerosol Classifier (OMAC),” Aerosol Sci. Technol., 38(9), pp. 890–899.
Song, D. K., and Dhaniyala, S., 2007, “Nanoparticle Cross-Flow Differential Mobility Analyzer (NCDMA): Theory and Design,” J. Aerosol Sci., 38, pp. 964–979.
Rockwood, A. L., Lee, E. D., Agbonkonkon, N., and Lee, M. L., 2007, “Cross-Flow Ion Mobility Analyzer,” U.S. Patent No. 7199362 B2.
Gillig, K. J., and Chen, C.-H., 2014, “Increasing the Performance of Portable Ion Mobility Analyzers: Development of the Periodic Focusing Differential Mobility Analyzer (PFDMA),” Mass Spectrom., 3(S0032), 1–5.
View article in PDF format.

## References

Pui, D. Y. H., and Chen, D.-R., 1997, “Guest Editorial—Nanometer Particles: A New Frontier for Multidisciplinary Research,” J. Aerosol Sci., 28(4), pp. 539–555.
Kim, B. H., Hackett, M. J., Park, J., and Hyeon, T., 2014, “Synthesis, Characterization, and Application of Ultrasmall Nanoparticles,” Chem. Mater., 26(1), pp. 59–71.
Cheng, Y., Morshed, R. A., Auffinger, B., Tobias, A. L., and Lesniak, M. S., 2014, “Multifunctional Nanoparticles for Brain Tumors Imaging and Therapy,” Adv. Drug Del. Rev., 66, pp. 42–57.
Guo, D., Xie, G., and Luo, J., 2014, “Mechanical Properties of Nanoparticles: Basics and Applications,” J. Phys. D: Appl. Phys., 47(1), p. 013001.
Madl, A. K., Plummer, L. E., Carosino, C., and Pinkerton, K. E., 2014, “Nanoparticles, Lung Injury, and the Role of Oxidant Stress,” Annu. Rev. Physiol., 76, pp. 447–465. [PubMed]
Auffan, M., Rose, J., Bottero, J. Y., Lowry, G. V., Jolivet, J. P., and Wiesner, M. R., 2009, “Towards a Definition of Inorganic Nanoparticles From an Environmental, Health and Safety Perspective,” Nat. Nanotechnol., 4, pp. 634–641. [PubMed]
Wang, S. C., and Flagan, R. C., 1990, “Scanning Electrical Mobility Spectrometer,” Aerosol Sci. Technol., 13(2), pp. 230–240.
Chen, D.-R., and Pui, D. Y. H., 1999, “A High Efficiency, High Throughput Unipolar Aerosol Charger for Nanoparticles,” J. Nanopart. Res., 1(1), pp. 115–126.
Guha, S., Li, M., Tarlov, M. J., and Zachariah, M. R., 2012, “Electrospray–Differential Mobility Analysis of Bionanoparticles,” Trends Biotechnol., 30(5), pp. 291–300. [PubMed]
Hogan, C. J., Jr., and Fernández de la Mora, J., 2009, “Tandem Ion Mobility-Mass Spectrometry (IMS-MS) Study of Ion Evaporation From Ionic Liquid-Acetonitrile Nanodrops,” Phys. Chem. Chem. Phys., 11, pp. 8079–8090. [PubMed]
Fernández de la Mora, J., 2011, Ion Mobility Spectroscopy—Mass Spectrometry: Theory and Applications, Taylor and Francis, Oxford, UK, Chap. 5.
Park, K., Dutcher, D., Emery, M., Pagels, J., Sakurai, H., Scheckman, J., Qian, S., Stolzenburg, M. R., Wang, X., Yang, J., and McMurry, P. H., 2008, “Tandem Measurements of Aerosol Properties—A Review of Mobility Techniques With Extensions,” Aerosol Sci. Technol., 42(10), pp. 801–816.
Flagan, R. C., 1998, “History of Electrical Aerosol Measurements,” Aerosol Sci. Technol., 28(4), pp. 301–380.
Whitby, K. T., and Clark, W. E., 1966, “Electrical Aerosol Particle Counting and Size Distribution Measuring System for the 0.015 to 1 μ Size Range,” Tellus, 18(2–3), pp. 573–586.
Liu, B. Y. H., Whitby, K. T., and Pui, D. Y. H., 1974, “A Portable Electrical Analyzer for Size Distribution Measurement of Submicron Aerosols,” APCAJ, 24(11), pp. 1067–1072.
Liu, B. Y. H., and Pui, D. Y. H., 1974, “A Submicron Aerosol Standard and the Primary, Absolute Calibration of the Condensation Nucleus Counter,” J. Colloid Interface Sci., 47(1), pp. 155–171.
Knutson, E. O., and Whitby, K. T., 1975, “Aerosol Classification by Electric Mobility: Apparatus, Theory, and Applications,” J. Aerosol Sci.6(6), pp. 443–451.
Kousaka, Y., Okuyama, K., Adachi, M., and Mimura, T., 1986, “Effect of Brownian Diffusion on Electrical Classification of Ultrafine Aerosol Particles in Differential Mobility Analyzer,” J. Chem. Eng. Jpn., 19(5), pp. 401–407.
Winklmayr, W., Reischl, G. P., Lindner, A. O., and Berner, A., 1991, “A New Electromobility Spectrometer for the Measurement of Aerosol Size Distributions in the Size Range From 1 to 1000 nm,” J. Aerosol Sci., 22(3), pp. 289–296.
Reischl, G. P., Mäkelä, J. M., and Necid, J., 1997, “Performance of Vienna Type Differential Mobility Analyzer at 1.2–20 Nanometer,” Aerosol Sci. Technol., 27(6), pp. 651–672.
Rosell-Llompart, J., Loscertales, I. G., Bingham, D., and Fernández de la Mora, J., 1996, “Sizing Nanoparticles and Ions With a Short Differential Mobility Analyzer,” J. Aerosol Sci., 27(5), pp. 695–719.
Fissan, H., Hummes, D., Stratmann, F., Büscher, P., Neumann, S., Pui, D. Y. H., and Chen, D., 1996, “Experimental Comparison of Four Differential Mobility Analyzers for Nanometer Aerosol Measurements,” Aerosol Sci. Technol., 24(1), pp. 1–13.
Chen, D., and Pui, D. Y. H., 1997, “Numerical Modeling of the Performance of Differential Mobility Analyzers for Nanometer Aerosol Measurements,” J. Aerosol Sci., 28(6), pp. 985–1004.
Chen, D.-R., Pui, D. Y. H., Hummes, D., Fissan, H., Quant, F. R., and Sem, G. J., 1998, “Design and Evaluation of a Nanometer Aerosol Differential Mobility Analyzer (Nano-DMA),” J Aerosol Sci., 29(5–6), pp. 497–509.
Pourprix, M., and Daval, J., 1990, “Electrostatic Precipitation of Aerosol on Wafers, a New Mobility Spectrometer,” Aerosols: Science, Industry, Health and Environment: Proceedings of the Third International Aerosol Conference, S.Masuda, and K.Takahashi, Eds., Kyoto, Japan, Sept. 24–27, Pergamon Press, New York. Vol. 2.
Pourprix, M., 1994, “Selecteur de Particules Chargees, a Haute Sensibilite,” Brevet Francais, France Patent No. EP0685725 A1.
Zhang, S.-H., Akutsu, Y., Russell, L. M., Flagan, R. C., and Seinfeld, J. H., 1995, “Radial Differential Mobility Analyzer,” Aerosol Sci. Technol., 23(3), pp. 357–372.
Zhang, S.-H., and Flagan, R. C., 1996, “Resolution of the Radial Differential Mobility Analyzer for Ultrafine Particles,” J. Aerosol Sci., 27(8), pp. 1179–1200.
Brunelli, N. A., Flagan, R. C., and Giapis, K. P., 2009, “Radial Differential Mobility Analyzer for One Nanometer Particle Classification,” Aerosol Sci. Technol., 43(1), pp. 53–59.
De Juan, L., and Fernández de la Mora, J., 1998, “High Resolution Size Analysis of Nanoparticles and Ions: Running a Vienna DMA of Near Optimal Length at Reynolds Numbers up to 5000,” J. Aerosol Sci., 29(5–6), pp. 617–626.
Martinez-Lozano, P., and Fernández de la Mora, J., 2006, “Experimental Tests of a Nano-DMA With no Voltage Change Between Aerosol Inlet and Outlet Slits,” J. Aerosol Sci., 37(11), pp. 1629–1642.
Martinez-Lozano, P., and Labowsky, M., 2009, “An Experimental and Numerical Study of a Miniature High Resolution Isopotential DMA,” J. Aerosol Sci., 40(5), pp. 451–462.
Fernández de la Mora, J., and Kozlowski, J., 2013, “Hand-Held Differential Mobility Analyzers of High Resolution for 1–30 nm Particles: Design and Fabrication Considerations,” J. Aerosol Sci., 57, pp. 45–53.
Mei, F., Fu, H., and Chen, D.-R., 2011, “A Cost-Effective Differential Mobility Analyzer (cDMA) for Multiple DMA Column Applications,” J. Aerosol Sci., 42, pp. 462–473.
Santos, J. P., Hontañón, E., Ramiro, E., and Alonso, M., 2009, “Performance Evaluation of a High-Resolution Parallel-Plate Differential Mobility Analyzer,” Atmos. Chem. Phys., 9, pp. 2419–2429.
Hontañón, E., and Kruis, F. E., 2009, “A Differential Mobility Analyzer (DMA) for Size Selection of Nanoparticles at High Flow Rates,” Aerosol Sci. Technol., 43(1), pp. 25–37.
Hontañón, E., Rouenhoff, M., Azabal, A., Ramiro, E., and Kruis, F. E., 2014, “Assessment of a Cylindrical and a Rectangular Plate Differential Mobility Analyzer for Size Fractionation of Nanoparticles at High-Aerosol Flow Rates,” Aerosol Sci. Technol., 48(3), pp. 333–339.
Steer, B., Gorbunov, B., Muir, R., Ghimire, A., and Rowles, J., 2014, “Portable Planar DMA: Development and Tests,” Aerosol Sci. Technol., 48(3), pp. 251–260.
Myojo, T., Ikawa, S., Sakae, H., and Kohyama, N., 2001, “A New Long DMA and Its Performance for Size-Measurement of 1 μm Polystyrene Latex Particles,” J. Air Clean. Contam. Control, 39, pp. 168–175 (in Japanese).
Myojo, T., Ehara, K., Koyama, H., and Okuyama, K., 2004, “Size Measurement of Polystyrene Latex Particles Larger Than 1 Micrometer Using a Long Differential Mobility Analyzer,” Aerosol Sci. Technol., 38(12), pp. 1178–1184.
Uin, J., Tamm, E., and Mirme, A., 2011, “Very Long DMA for the Generation of the Calibration Aerosols in Particle Diameter Range up to 10 μm by Electrical Separation,” Aerosol Air Qual. Res., 11, pp. 531–538.
Raddatz, M., Wiedensohler, A., Wex, H., and Stratmann, F., 2013, “Size Selection of Sub- and Super-Micron Clay Mineral Kaolinite Particles Using a Custom-Built Maxi-DMA,” Nucleation and Atmospheric Aerosols: 19th International Conference, AIP Conf. Proc., Fort Collins, CO, June 23–28, Vol 1527, pp. 457–460.
Rosch, M., Pfeifer, S., Wiedensohler, A., and Stratmann, F., 2014, “Selection of Quasi-Monodisperse Super-Micron Aerosol Particles,” EGU General Assembly, Geophysical Research Abstracts, 16, Paper No. EGU2014-4957.
Intra, P., and Tippayawong, N., 2008, “An Overview of Differential Mobility Analyzers for Size Classification of Nanometer-Sized Aerosol Particles,” Songklanakarin J. Sci. Technol., 30(2), pp. 243–256.
Allen, M., and Raabe, O., 1985, “Slip Correction Measurements of Spherical Solid Aerosol Particles in an Improved Millikan Apparatus,” Aerosol Sci. Technol., 4(3), pp. 269–286.
Flagan, R. C., 2011, Aerosol Measurement: Principles, Techniques, and Applications, 3rd ed., Wiley, Hoboken, NJ, Chap. 15.
Fernández de la Mora, J., 2011, Aerosol Measurements: Principles, Techniques, and Applications, 3rd ed. Wiley, Hoboken, NJ, Chap. 32.
Kousaka, Y., Okuyama, K., and Adachi, M., 1985, “Determination of the Size Distribution of Ultrafine Aerosol Particles Using a Differential Mobility Analyzer,” Aerosol Sci. Technol., 4(2), pp. 209–225.
Stolzenburg, M. R., 1988, “An Ultrafine Aerosol Size Distribution Measuring System,” Ph.D. thesis, University of Minnesota, Minneapolis, MN.
Hagwood, C., 1999, “The DMA Transfer Function With Brownian Motion a Trajectory/Monte-Carlo Approach,” Aerosol Sci. Technol., 30(1), pp. 40–61.
Mamakos, A., Ntziachristos, L., and Samaras, Z., 2007, “Diffusion Broadening of DMA Transfer Functions. Numerical Validation of Stolzenburg Model,” J. Aerosol Sci., 38(7), pp. 747–763.
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## Figures

Fig. 1

Fundamental configuration of a DMPS

Fig. 2

Principle of operation of the DMA

Fig. 3

Schematic diagram of (a) cylindrical DMA by Knutson and Whitby [17] and (b) RDMA

Fig. 4

Transfer function of the DMA (a) nondiffusion, ideal transfer function and (b) diffusion broadening of the ideal transfer function

Fig. 5

Schematic diagram of the TSI DMA (Model 3071)

Fig. 6

Schematic diagram of the Nano-DMA developed by Chen et al. [24]

Fig. 7

Schematic diagram of the Vienna type DMA developed by Reischl and coworkers [19]

Fig. 8

Schematic diagram of the Rosser DMA—a variant of the Vienna DMA [55]

Fig. 9

Schematic diagram of the Vienna type UDMA—a variant of the Vienna DMA [56]

Fig. 10

Schematic diagram of the Half-Mini DMA developed by Fernández de la Mora and Kozlowski [33]

Fig. 11

Illustration of the principle of the 2D drift DMA [60]

Fig. 12

Cross-sectional view of functional region of the ROMIAC [59]

## Discussions

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