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**Research article**
09 Aug 2018

**Research article** | 09 Aug 2018

Effects of temperature, pressure, and carrier gases

^{1}Graduate Institute of Environmental Engineering, National Taiwan University, Taipei, 10673, Taiwan^{2}Department of Occupational Safety and Health, China Medical University, Taichung, 40402, Taiwan^{3}Graduate Institute of Environmental Engineering, National Central University, Taoyuan, 32001, Taiwan

Abstract

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Effective density is a crucial parameter used to predict
the transport behaviour and fate of particles in the atmosphere, and to
measure instruments used ultimately in the human respiratory tract
(Ristimäki et al., 2002). The aerosol particle mass analyser (APM) was
first proposed by Ehara et al. (1996) and is used to determine the effective
density of aerosol particles. A compact design (Kanomax APM-3601) was
subsequently developed by Tajima et al. (2013). Recently, a growing number
of field studies have reported application of the APM, and experimental
schemes using the differential mobility analyser alongside the APM have been
adopted extensively. However, environmental conditions such as ambient
pressure and temperature vary with the experimental location, and this could
affect the performance of the APM. Gas viscosity and Cunningham slip factors
are parameters associated with temperature and pressure and are included in
the APM's classification performance parameter: *λ*. In this study,
the effects of temperature and pressure were analysed through theoretical
calculation, and the influence of varying carrier gas was experimentally
evaluated. The transfer function and APM operational region were further
calculated and discussed to examine their applicability. Based on the
theoretical analysis of the APM's operational region, the mass detection
limits are changed with the properties of carrier gases under a chosen
*λ* value. Moreover, the detection limit can be lowered when the
pressure is reduced, which implies that performance may be affected during
field study. In experimental evaluation, air, oxygen, and carbon dioxide
were selected to atomize aerosols in the laboratory with the aim of
evaluating the effect of gas viscosity on the APM's performance. Using
monodisperse polystyrene latex (PSL) spheres with nominal diameters of 50
and 100 nm, the classification performance of the APM was slightly varied
with carrier gases, while the classification accuracy was consistently
within 10 %.

How to cite

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How to cite.

Hsiao, T.-C., Young, L.-H., Tai, Y.-C., and Chang, P.-K.: Effects of temperature, pressure, and carrier gases on the performance of an aerosol particle mass analyser, Atmos. Meas. Tech., 11, 4617-4626, https://doi.org/10.5194/amt-11-4617-2018, 2018.

1 Introduction

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To determine the adverse health effects of inhalable particles, the lung
regional deposition fraction must be investigated (Chuang et al., 2016;
Haddrell et al., 2015). The lung regional deposition fraction is closely
associated with the density and morphology of submicron particles that can
be derived from their mass measurement (Broday and Rosenzweig, 2011;
Salma et al., 2002; Shi et al., 2015). Therefore, mass distribution and
particle density play pivotal roles in the study of associated health
effects. However, obtaining measurements of the morphology or density of
aerosol particles in the environment is not easy (Bau et al., 2014;
DeCarlo et al., 2004), and particles in an ambient environment are generally
irregular and nonspherical. In this regard, Liu et al. (2013)
demonstrated that the morphological parameter of a fractal soot particle,
namely the fractal dimension (*D*_{f}), could affect the particle's radiative
properties. In addition, according to theoretical calculations,
He et al. (2015) reported that aged soot
aggregates with partially encapsulated or externally attached structures
have weaker absorption properties than do fresh soot aggregates.

Nevertheless, theoretical simulations and experimental studies on the
effects of aerosols on human health and the atmosphere all require certain
assumptions regarding particle morphology or density to be made to enable
the conversion of number concentration to mass concentration or volume
concentration (Hand and Kreidenweis, 2002). To experimentally
retrieve the density of submicron-to-nanometre-sized particles, a
differential mobility analyser (DMA) system coupled with a low-pressure
impactor was developed to measure the aerodynamic sizes of particles of
known electric mobility size. By further assuming that the particles were
all spherical, the “effective” or “apparent” density was derived
(Kelly and McMurry, 1992; Schleicher et al., 1995; Skillas et al., 1998).
A similar system combining a scanning mobility particle sizer and electrical
low-pressure impactor in parallel was reported and applied to study diesel
particulate matter and ambient aerosols (Maricq et al., 2000; Ristimäki
et al., 2002; Symonds et al., 2007; Van Gulijk et al., 2004; Virtanen et al.,
2004). Furthermore, Ehara et al. (1996) developed the aerosol particle mass
analyser (APM), which is an aerosol instrument that classifies particle mass
by balancing the centrifugal force and electrostatic force. Based on an
identical classification mechanism but utilizing a different rotating scheme
to create centrifugal force, the Couette centrifugal particle mass analyser
is another commercially available instrument. With such advances in aerosol
instrumentation, McMurray et al. (2002) proposed using the APM to directly
measure the mass of monodispersed particles classified by a DMA (tandem
DMA–APM system) instead of using an impactor to probe the particle
aerodynamic size. This DMA–APM scheme is capable of revealing the density or
mass distribution of targeted aerosol particles in real time. Throughout the
past decades, this scheme has also been adopted extensively to determine the
*D*_{f} of aerosol aggregates
(Lall et al., 2008; McMurry et al., 2002; Park et al., 2003,
2004a, b; Scheckman et al., 2009) and atmospheric aerosols
(Kuwata and Kondo, 2009; Kuwata et al., 2011).

A growing number of APM experiments are being conducted in outdoor
environments in relation to the dual interest in human health and climate
change (Leskinen et al., 2014; Rissler et al., 2014). However, when
experiments are conducted in the field, environmental conditions such as
temperature (*T*) and pressure (*P*) vary spatially and temporally,
particularly at high-altitude sites. The viscosity $(\mathit{\mu}={\mathit{\mu}}_{r}\left(\frac{{T}_{r}+{S}_{u}}{T+{S}_{u}}\right){\left(\frac{T}{{T}_{r}}\right)}^{\mathrm{1.5}})$ and mean free path $(l=\frac{\mathit{\mu}}{P}\sqrt{\frac{\mathit{\pi}RT}{\mathrm{2}M}}={l}_{r}\left(\frac{{P}_{r}}{P}\right){\left(\frac{T}{{T}_{r}}\right)}^{\mathrm{2}}\left(\frac{{T}_{r}+{S}_{u}}{T+{S}_{u}}\right))$ of ambient air change
continuously (Kulkarni et al., 2011), thereby influencing the performance and
range of detection limits (classifiable region) for the APM. Therefore, in
this study, air, oxygen, and carbon dioxide were selected as carrier gases to
experimentally evaluate the effect of gas viscosity and the mean free path on
the performance of the APM, including the classifiable region and detection
limits. On the other hand, argon would be required as the carrier gas if the
APM were used as an aerosol particle classifier coupled with inductively
coupled plasma mass spectrometry (ICP-MS; in a similar manner to the
DMA–ICP-MS system) (Myojo et al., 2002). Therefore, the effects of changing
the carrier gas in the APM's transfer function require investigation. In this
regard, the experimental and simulated transfer functions for the APM
operated for various carrier gases were explored and are compared in this
paper. The results provide a valuable insight into the performance of the APM
when operated under various conditions.

2 Operational theory

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The APM was first proposed by Ehara et al. (1996), and a compact version was
recently developed by Tajima et al. (2013). The instrument consists of two
electrodes, namely coaxial and rotating cylindrical electrodes, between which
a narrow annular space is created for mass classification (classification
zone). When the APM is initialized, the inner and outer electrodes rotate at
the same speed (*ω*) to generate centrifugal force, and a high voltage
is applied to the inner electrode to create a “counter” electrostatic
force. The governing equations of particle movements in radial and axial
directions inside the classification zone are expressed as follows (Ehara et
al., 1996):

$$\begin{array}{}\text{(1)}& {\displaystyle}& {\displaystyle \frac{m}{\mathit{\tau}}}\cdot {\displaystyle \frac{\mathrm{d}r}{\mathrm{d}t}}=m\cdot r\cdot {\mathit{\omega}}^{\mathrm{2}}-{\displaystyle \frac{q\cdot V}{r\cdot \mathrm{ln}\left({r}_{o}/{r}_{i}\right)}}\phantom{\rule{0.125em}{0ex}}\text{(in\hspace{0.17em} a\hspace{0.17em} radial\hspace{0.17em} direction),}\text{(2)}& {\displaystyle}& {\displaystyle \frac{m}{\mathit{\tau}}}\left\{{\displaystyle \frac{\mathrm{d}z}{\mathrm{d}t}}-\mathit{\upsilon}\left(r\right)\right\}=\mathrm{0}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\text{(in\hspace{0.17em} an\hspace{0.17em} axial\hspace{0.17em} direction),}\text{(3)}& {\displaystyle}& {\displaystyle}\mathit{\tau}={\displaystyle \frac{{\mathit{\rho}}_{p}\cdot {d}_{p,m}^{\mathrm{2}}\cdot {C}_{\mathrm{c}}\left({d}_{p,m}\right)}{\mathrm{18}\mathit{\mu}}},\text{(4)}& {\displaystyle}& {\displaystyle}{S}_{\mathrm{c}}={\displaystyle \frac{m}{q}}={\displaystyle \frac{V}{{r}_{\mathrm{c}}^{\mathrm{2}}\cdot {\mathit{\omega}}^{\mathrm{2}}\cdot \mathrm{ln}\left({r}_{\mathrm{0}}/{r}_{i}\right)}}.\end{array}$$

Particles are then classified based on the balance between the centrifugal
force and counter electrostatic force, and only particles with a designated
mass-to-charge ratio (*S*) pass through the classification zone. The
mass-to-charge ratio for particles that remain in the central line
(*r*_{c}) within the classification zone is defined as the
“critical” *S* (*S*_{c}; Eq. (4). Based on this definition, the
classified particle mass (*m*), rotation speed (*ω*), and voltage
applied (*V*) are linearly correlated on a log scale, as shown in Eq. (5):

$$\begin{array}{ll}{\displaystyle}\mathrm{log}\left(m\right)& {\displaystyle}=\left[\mathrm{log}\left(q\right)-\mathrm{2}\mathrm{log}\left({r}_{\mathrm{c}}\right)-\mathrm{log}\left(\mathrm{ln}\left({r}_{\mathrm{0}}/{r}_{i}\right)\right)\right]\\ \text{(5)}& {\displaystyle}& {\displaystyle}+\mathrm{log}\left(V\right)-\mathrm{2}\mathrm{log}\left(\mathit{\omega}\right).\end{array}$$

Tajima et al. (2011, 2013) depicted the classifiable region for the APM by using a log–log mass-versus-rotation-speed plot. However, because of the physical limits of the operational voltage and rotation speed of the APM, a parallelogram of potential classifiable regions was reported.

The transfer function (Ω) is generally used to characterize the
classification performance of the DMA, and by defining the penetration
probability of particles under a designed condition, the transfer function is
employed to evaluate the performance of the APM. The nondiffusive transfer
function for the APM (Ω_{APM}) can be indexed by the
penetration at the *S*_{c} (*t*(*S*_{c})) and the resolution
parameter (Δ*S*) (Tajima et al., 2013); *t*(*S*_{c}) is the
maximum height of the transfer function, and Δ*S* can be estimated
theoretically as follows:

$$\begin{array}{}\text{(6)}& {\displaystyle}& {\displaystyle}t\left({S}_{\mathrm{c}}\right)=\mathrm{exp}\left(-{\mathit{\lambda}}_{\mathrm{c}}\right),\text{(7)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}S={\displaystyle \frac{{r}_{\mathrm{c}}}{\mathrm{4}\mathit{\delta}}}\mathrm{tanh}\left({\mathit{\lambda}}_{\mathrm{c}}/\phantom{{\mathit{\lambda}}_{\mathrm{c}}\mathrm{2}}\mathrm{2}\right).\end{array}$$

Both parameters are closely related to *λ*_{c}, which is the
major dimensionless performance parameter defined by Ehara et al. (1996) for
APM operation. The Ω_{APM} is a strong function of
*λ*_{c}:

$$\begin{array}{ll}{\displaystyle}{\mathit{\lambda}}_{\mathrm{c}}& {\displaystyle}={\displaystyle \frac{\mathrm{2}\mathit{\tau}\cdot {\mathit{\omega}}^{\mathrm{2}}\cdot L}{\overline{\mathit{\upsilon}}}}={\displaystyle \frac{\mathrm{2}\cdot \frac{{\mathit{\rho}}_{p}\cdot {d}_{p,m}^{\mathrm{2}}}{\mathrm{18}}\cdot {\mathit{\omega}}^{\mathrm{2}}\cdot L}{\left({Q}_{a}/\mathit{\pi}\left({r}_{o}^{\mathrm{2}}-{r}_{i}^{\mathrm{2}}\right)\right)}}\cdot {\displaystyle \frac{{C}_{\mathrm{c}}\left({d}_{p,m}\right)}{\mathit{\mu}}}\\ \text{(8)}& {\displaystyle}& {\displaystyle}={\displaystyle \frac{\mathrm{2}m\phantom{\rule{0.33em}{0ex}}\mathrm{3}{d}_{p,m}\cdot {\mathit{\omega}}^{\mathrm{2}}\cdot L}{\left({Q}_{a}/\left({r}_{o}^{\mathrm{2}}-{r}_{i}^{\mathrm{2}}\right)\right)}}\cdot {\displaystyle \frac{{C}_{\mathrm{c}}\left({d}_{p,m}\right)}{\mathit{\mu}}}.\end{array}$$

*λ*_{c} can be interpreted as the ratio of the timescale for
axial and radial particle movements in the classification zone. When the
value of *λ*_{c} is larger, the APM has a superior
classification resolution. Generally, the axial traversal timescale ($L/\phantom{L\overline{\mathit{\upsilon}}}\overline{\mathit{\upsilon}}$) is considered constant because
the aerosol flow rate is fixed when the instrument is operated. Thus, the
classification performance can be improved by decreasing the radial traversal
timescale ($\mathrm{1}/\phantom{\mathrm{12}\mathit{\tau}\cdot {\mathit{\omega}}^{\mathrm{2}}}\mathrm{2}\mathit{\tau}\cdot {\mathit{\omega}}^{\mathrm{2}}$). A shorter
radial traversal time enables easier removal of incompetent particles by
deposition onto the electrodes, which denotes lower penetration possibility
for particles with a mass-to-charge ratio other than *S*_{c}. In other
words, the transfer function is narrower, or Δ*S* is smaller, for a
larger value of *λ*_{c}, which suggests a higher classifying
resolution. However, the trade-off for operating the APM at a larger
*λ*_{c} is that the maximum penetration of the transfer function
(*t*(*S*_{c})) is lower. Tajima et al. (2011) recommended that the APM
be operated at a constant *λ*_{c} (with a fixed
Ω_{APM}) within the range of 0.25 to 0.5 when the aerosol flow
rate is 0.3 L min^{−1}.

For a constant value of *λ*_{c}, a unique curve in the log–log
mass-versus-rotation-speed plot can be determined iteratively through
Eq. (8), and this intercepts the APM classifiable region. This
constant-*λ*_{c} curve generally acts as the lower boundary for
the APM classifiable region. As observed in Eq. (8), *λ*_{c} is
a function of the APM rotation speed (*ω*) and depends on particle mass
and density with respect to relaxation time (*τ*). The value of *τ* is
closely related to gas viscosity (*μ*) and the Cunningham slip factor
(*C*_{c}). At a given *λ*_{c}, the *ω* for
classifying particles with a certain mass decreases with an increasing
*C*_{c}-to-*μ* ratio ($\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$). For air, oxygen,
argon, and carbon dioxide, limited variations in the values of
$\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$ are observed, and their constant-*λ*_{c} curves are closely clustered. By contrast, the long mean free
paths of low-molecular-weight gases such as hydrogen and helium can lead to a
relatively high $\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$. Consequently, when the APM is
operated with hydrogen and helium, the classifiable mass range needs to be
extended to a much lower detection limit without sacrificing the resolution
or modifying the APM hardware (Fig. 1). However, an implicit problem is that
the breakdown voltages of inert gases are generally approximately 1 order
of magnitude lower than that of air (Schmid et al., 2002) (values of
gas-specific parameters and the corresponding detection limits are listed in
Table 1).

The expression of $\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$ can be further rewritten to reveal the effects of temperature, pressure, and the carrier gas species as Eq. (9):

$$\begin{array}{ll}{\displaystyle \frac{{C}_{\mathrm{c}}\left({d}_{p}\right)}{\mathit{\mu}}}& {\displaystyle}={\displaystyle \frac{\mathrm{1}}{\mathit{\mu}}}+{\displaystyle \frac{\mathrm{2}l/\phantom{\mathrm{2}l{d}_{p}}{d}_{p}}{\mathit{\mu}}}\left[\mathit{\alpha}+\mathit{\beta}\cdot \mathrm{exp}\left({\displaystyle \frac{-\mathit{\gamma}}{\mathrm{2}l/\phantom{\mathrm{2}l{d}_{p}}{d}_{p}}}\right)\right]\\ {\displaystyle}& {\displaystyle}=\left({\displaystyle \frac{T+{S}_{u}}{{T}_{r}+{S}_{u}}}\right){\left({\displaystyle \frac{T}{{T}_{r}}}\right)}^{-\mathrm{1.5}}\cdot {\displaystyle \frac{\mathrm{1}}{{\mathit{\mu}}_{r}}}+\left({\displaystyle \frac{{P}_{r}}{P}}\right){\left({\displaystyle \frac{T}{{T}_{r}}}\right)}^{\mathrm{0.5}}\\ {\displaystyle}& {\displaystyle}\cdot {\displaystyle \frac{\mathrm{2}{l}_{r}/\phantom{\mathrm{2}{l}_{r}{d}_{p}}{d}_{p}}{{\mathit{\mu}}_{r}}}\left[\mathit{\alpha}+\mathit{\beta}\cdot \mathrm{exp}\left(\left({\displaystyle \frac{P}{{P}_{r}}}\right){\left({\displaystyle \frac{T}{{T}_{r}}}\right)}^{-\mathrm{2}}\left({\displaystyle \frac{T+{S}_{u}}{{T}_{r}+{S}_{u}}}\right)\right.\right.\\ \text{(9)}& {\displaystyle}& {\displaystyle}\left.\left.\cdot \left({\displaystyle \frac{-\mathit{\gamma}}{\mathrm{2}{l}_{r}/\phantom{\mathrm{2}{l}_{r}{d}_{p}}{d}_{p}}}\right)\right)\right],\end{array}$$

where *α*=1.142, *β*=0.558, and *γ*=0.999 (Allen and
Raabe, 1985). As shown in Fig. 2, compared to pressure,
$\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$ is somewhat invariant with temperature; when the
temperature changes from 273 to 318 K, the difference of
$\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$ for all gas species is less than 6 %. However,
the $\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$ for 100 nm particles increases by 42 %
when the air pressure decreases to 65 kPa (Fig. 3); therefore, when
operating the APM at high-altitude sites, the detection limits need to be
lowered or the resolution needs to be improved. By contrast, based on the
analytical predictions, Eq. (4) is unaffected by $\frac{{C}_{\mathrm{c}}}{\mathit{\mu}}$,
and the classification accuracy remains unchanged.

3 Experimental method

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Figure 4 depicts the experimental evaluation system. The particles were
generated by an aerosol atomizer (TSI, Model 3076) and dehumidified by two
desiccant dyers connected in series to remove excess water content. To
experimentally evaluate the classification accuracy, 50 and 100 nm
polystyrene latex (PSL) spheres certified by the National Institute of Standards
and Technology (Thermo Fisher Scientific, cat. no. 3050A and 3100A) were used
here. The mean diameters of the size distributions of the 50 and 100 nm PSL
given by the manufacturers are 46±2 and 100±3 nm,
respectively. These PSL
particles were classified using the DMA (TSI 3081) and then delivered to the
APM (Kanomax model II-3601) to determine particle mass. The overall aerosol
flow rate of the DMA–APM system was controlled by the downstream CPC
(condensation particle counter, TSI 3022A) and fixed at 0.3 L min^{−1}.
To optimize the size of the classification resolution, the sheath flow rate
of the DMA was set at 3.0 L min^{−1}. In addition to air, carbon dioxide
(CO_{2}) and oxygen (O_{2}) with purity levels of 99.99 %
were supplied as carrier gases. Before conducting measurements, the selected
gas was used to purge all apparatus for at least 5 min to ensure that no
residual contaminant gases remained, and the flow rates of the DMA's sheath
flow and aerosol flow were calibrated using a volumetric flow meter (Gilian
Gilibrator 2, Sensidyne, St. Petersburg, FL, USA). Because the DMA–APM was
used to investigate the effects of carrier gases on the APM's performance, it
was necessary to first study the sizing accuracy of the DMA for various
carrier gases. The results showed that the differences between the measured
modal diameters and nominal sizes of 50 and 100 nm certified PSL particles
were within 6 % for air, CO_{2}, and O_{2}. Therefore, no
significant effects of gas species on DMA sizing accuracy were observed,
which was consistent with the findings of Schmid et al. (2002).

The classifying accuracy of aerosol instruments under various conditions is
generally characterized by a normalized indicator relative to a known
reference (Karg et al., 1992; Marlow et al., 1976; Ogren, 1980; Schmid et
al., 2002). The normalized mass-to-charge ratio
$(\overline{S}=\frac{{S}_{\mathrm{gas}}}{{S}_{\mathrm{air}}})$ was used in the present
study to analyse the APM's performance at a constant rotation speed
(*ω*) and constant sizing resolution (*λ*) operation. For the
constant *λ* operation, *λ* values of 0.24 and 0.45 were chosen
for both 50 and 100 nm PSL spheres. The operation of DMA–APM is identical to
Kuwata and Kondo (2009) and Kuwata et al. (2011), in
which the DMA selects particles with +1 charge and predetermined mobility
diameters and then subjects them to the APM. Subsequently, the APM was set to
scan across a range of voltage (*V*), while the number concentration
(*C*_{N}) of the passing particles was measured by a CPC. The peak of
the *C*_{N}–*V* distribution was subsequently inspected to determine
the particle mass (*m*).

The APM's stepping *C*_{N}–*V* spectrum was converted to the transfer
function and compared with the simulated transfer function. The transfer function
is a kernel function used to theoretically evaluate the concentration of
downstream particles and is critical for evaluating the performance of the
APM (Ehara et al., 1996; Emery, 2005; Tajima et al., 2013). In the present
study, two computer programs, namely the TRANSFER program and SIM_APM
program (developed by the National Institute of Advanced Science and
Technology (AIST) of Japan) were utilized to theoretically evaluate the
operational performance of the APM (Tajima et al., 2011, 2013). The TRANSFER program calculated the theoretical APM transfer function
at a fixed rotation speed and voltage, and the SIM_APM program simulated
particle distribution at the APM outlet based on the known particle
distribution at the APM inlet (the size distribution was classified by the
front DMA). Both simulated results were compared with experimental APM
measurements.

4 Results and discussion

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For the case of constant *λ* operation, $\overline{S}$ is expressed as Eq. (10), where $\overline{S}$ is mainly a function of the voltage applied to the APM
(*V*), Cunningham slip correction factor (*C*_{c}), and gas viscosity
(*μ*):

$$\begin{array}{}\text{(10)}& {\displaystyle}\overline{S}={\displaystyle \frac{{S}_{\mathrm{gas}}}{{S}_{\mathrm{air}}}}={\displaystyle \frac{{V}_{\mathrm{gas}}}{{V}_{\mathrm{air}}}}{\displaystyle \frac{{C}_{\mathrm{c},\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\mathrm{gas}}/\phantom{{C}_{\mathrm{c},\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\mathrm{gas}}{\mathit{\mu}}_{\mathrm{gas}}}{\mathit{\mu}}_{\mathrm{gas}}}{{C}_{\mathrm{c},\mathrm{air}}/\phantom{{C}_{\mathrm{c},\mathrm{air}}{\mathit{\mu}}_{\mathrm{air}}}{\mathit{\mu}}_{\mathrm{air}}}}.\end{array}$$

To consider the various properties of the gas species, *ω* was adjusted
to enable *λ* to be fixed at approximately 0.24 and 0.45 for 50 nm
PSL particles, as shown in Table 2. The results revealed that particle mass
was generally underestimated for cases where CO_{2} was used as a
carrier gas. In particular, underestimation was 23–25 % for a 50 nm
PSL sphere. By contrast, when O_{2} was used as the carrier gas, an
overestimation of mass measurements was observed, with an error within 9 %.

^{a} The theoretical particle mass of a 50 nm PSL sphere is $\mathrm{6.87}\times {\mathrm{10}}^{-\mathrm{20}}$ kg
(assuming a density of 1050 Kg m^{−3}).
^{b} The theoretical particle mass of a 100 nm PSL sphere is
$\mathrm{5.50}\times {\mathrm{10}}^{-\mathrm{19}}$ kg (assuming a density of 1050 Kg m^{−3}).

As reported by Lall et al. (2009, 2008), the particle
concentration measured as a function of APM voltage is wider than the APM
transfer function even though the particle can be considered as
“monodisperse” in size. This is mainly due the spread in calibration
particle sizes or the transfer function of the DMA. To further eliminate the
spread propagated from DMA classification, the transfer function of the APM
was calculated using software developed by the AIST of Japan. The transfer
function predicted (hereafter referred to as “predicted
Ω_{APM}”) based on the known size distribution of the DMA
outlet (convoluted with the known size distribution classified by DMA) is
indicated by the blue line in Fig. 6, and the theoretical transfer function
(hereafter referred to as “theoretical Ω_{APM}”) at a fixed
optimal experimental peak voltage is indicated by a thinner green line.
Experimental data points are indicated by the dotted symbol in Fig. 6. It
should be noted that, according to the work done by Kuwata (2015), even when
the resolution of the DMA–APM system appears to be controlled by the APM,
the particle classification by the DMA–APM at a certain operating condition
still could be regulated by both DMA and APM.

The APM resolution defined as *s*_{c}∕Δ*s* is used as an indicator
to evaluate the classification performance. The resolution is recommended to
be between 0.5 and 1.2 when interpreted as Δ*s*∕*s*_{c} (Emery,
2005; Tajima et al., 2011). However, in this study, the values of
*s*_{c}∕Δ*s* for CO_{2} were 0.43 and 0.44 for 50 and
100 nm PSL spheres, respectively. Furthermore, the experimental optimal
voltage in the case of CO_{2} was consistently lower than the
theoretical voltage after convolution with the classified size distribution,
and in the case of O_{2} it was slightly higher than the theoretical voltage.
As shown in Table 1, the viscosity of CO_{2} was lower than that of
air, whereas the viscosity of O_{2} was higher than that of air. These
findings exhibit qualitative agreement with observations of under- or
overestimations of PSL spheres. Therefore, we suspect that the fluid field
in the APM classification zone is influenced by gas-specific properties such
as *μ* and *ρ*. A further numerical simulation of the flow field was
performed using COMSOL Multiphysics 4.3a. Using the flow velocity of air as a
reference, the velocity differences in an angular direction at the APM's
classification zone under various *ω* values are plotted in Fig. 7. The
velocity was generally lower in the classification zone of the APM when
CO_{2} was used as the carrier gas, and an increase in the distinct
differences between CO_{2} and air with an increase in the rotation
speed was observed. Therefore, a lower viscosity and higher gas density
likely intensify the shear force required to create rotating flow inside the
APM. Because of the lower rotating flow velocity, significant deviations were
observed in the measured results under normal conditions in the case of
CO_{2}; this phenomenon is intensified with higher values of *ω*
and is more significant for small particles, which are even more prone to
influence from the flow field.

According to Kuwata's theoretical analysis of transfer function and
resolution of the DMA–APM system, the common operation of constant *ω*
and varying *V* could not maintain the transfer function because of the range
of *d*_{p,m} passing the DMA (Kuwata, 2015). In such a case, the transfer
function may not be symmetric, and the transfer function is narrower for
larger *m* because of the dependence of *λ*_{c} on *m*. It was then
concluded that the operation of constant *V* and varying *ω*, on the
other hand, could better maintain the DMA–APM resolution because *m**ω*^{2} can be constant under constant *V*. However, this ideal operation
protocol is less employed for the DMA–APM system, mainly due to the practical
impediment of quickly and accurately scanning *ω* over a range.
Therefore, the common constant *ω* operation is investigated here.

As shown in Table 3, when determining the particle mass for 100 nm PSL
spheres, respective differences of −14 % and +6 % are observed when
CO_{2} and O_{2} are used as carrier gases in the APM. However,
in Eq. (4), *S*_{c} is independent of gas properties, and thus
*S*_{c} or the peak voltage of the *C*_{N}–*V* spectrum should
remain unchanged if identical values of *ω* are applied in the APM
for various carrier gases. The current experimental results demonstrate
that the classification ability of APM is dependent on the carrier gas and
influenced by gas viscosity. There could be changes in the flow field within
the APM when CO_{2} and O_{2} are used, and radial acceleration
may not be *r*_{c}*ω*^{2}, as used in Eq. (4). Therefore, to
determine the exact centrifugal force for *S*_{c}, further research is
required to investigate the velocity profile of particles in an angular
direction. In addition, when comparing air and O_{2}, a broader
*C*_{N}–*V* spectrum with weaker penetration was observed for
CO_{2}; this could be attributed to the higher diffusivity resulting
from the lower gas viscosity of CO_{2} (Stokes–Einstein equation:
$D={k}_{B}T/\phantom{{k}_{B}T\mathrm{3}\mathit{\pi}\mathit{\mu}{d}_{p}}\mathrm{3}\mathit{\pi}\mathit{\mu}{d}_{p})$. Based on the results,
on-site calibration of the APM's classification performance is strongly
recommended.

5 Conclusions

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In this study, the effects of temperature (“*T*” hereafter), pressure
(“*P*” hereafter), and gas viscosity (“*μ*” hereafter) on the
performance of the APM were evaluated analytically and experimentally. The
analytical results revealed that the APM's detection limit can be lowered
simply by increasing the *C*_{c} / *μ* ratio without modifying the
hardware of the APM or its classifying resolution. Under a constant *λ* and fixed *T* and *P*, the use of a low-molecular-weight carrier gas such
as H_{2} or He can lower the mass detection limit to approximately $<{\mathrm{10}}^{-\mathrm{2}}$ fg. Similarly, a reduction in operating *P* lowers the detection
limit or improves the resolution. Under these circumstances, the effects of
*T* on the APM's detection limit are relatively minor.

Our experimental results under constant *λ* or *ω* values reveal
that the use of a carrier gas other than air reduces accuracy. Specifically,
a carrier gas with a lower *μ* than air such as CO_{2} yields an
underestimation of mass, whereas one with a higher *μ* such as
O_{2} yields an overestimation. A subsequent flow field simulation
revealed variations in flow velocity in an angular direction at the APM's
inlet and outlet when air and other carrier gases were used. The flow
velocity decreased with *μ* but increased with *ω*. Thus, the
effects of *T* are expected to affect the APM's performance, and changes in
*μ*, density, and diffusivity in the carrier gas likely alter the radial
acceleration of flow in the APM; however, further research is recommended for
these aspects.

Data availability

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Data availability.

Data are available upon request by contacting the corresponding author.

Author contributions

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Author contributions.

TCH and LHY designed the research; YCT and PKC performed the research and analysed the data; and TCH, LHY and YCT wrote the paper.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The authors are grateful for the financial support provided by the National
Science Council, Taiwan (NSC102-2221-E-008-004-MY3). The manuscript was
edited by Wallace Academic Editing.

Edited by:
Mingjin Tang

Reviewed by: three anonymous referees

References

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