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<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0"><?xmltex \makeatother\@nolinetrue\makeatletter?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">ACP</journal-id><journal-title-group>
    <journal-title>Atmospheric Chemistry and Physics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/acp-18-17029-2018</article-id><title-group><article-title>Application of a hygroscopicity tandem differential mobility analyzer for characterizing PM emissions in exhaust plumes from an aircraft engine burning conventional and alternative fuels</article-title><alt-title>Application of a hygroscopicity tandem differential mobility analyzer</alt-title>
      </title-group><?xmltex \runningtitle{Application of a hygroscopicity tandem differential mobility analyzer}?><?xmltex \runningauthor{M.~B.~Trueblood et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Trueblood</surname><given-names>Max B.</given-names></name>
          <email>trueblud@mst.edu</email>
        <ext-link>https://orcid.org/0000-0003-4483-2346</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff3">
          <name><surname>Lobo</surname><given-names>Prem</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0626-6646</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Hagen</surname><given-names>Donald E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Achterberg</surname><given-names>Steven C.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Liu</surname><given-names>Wenyan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Whitefield</surname><given-names>Philip D.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Center of Excellence for Aerospace Particulate Emissions Reduction Research, Missouri University <?xmltex \hack{\break}?> of Science and Technology, Rolla, MO, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Center for Research in Energy and Environment, Missouri University of Science <?xmltex \hack{\break}?> and Technology, Rolla, MO, USA</institution>
        </aff>
        <aff id="aff3"><label>a</label><institution>now at: Metrology Research Centre, National Research Council Canada, Ottawa, Ontario, Canada</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Max B. Trueblood (trueblud@mst.edu)</corresp></author-notes><pub-date><day>3</day><month>December</month><year>2018</year></pub-date>
      
      <volume>18</volume>
      <issue>23</issue>
      <fpage>17029</fpage><lpage>17045</lpage>
      <history>
        <date date-type="received"><day>21</day><month>May</month><year>2018</year></date>
           <date date-type="rev-request"><day>5</day><month>June</month><year>2018</year></date>
           <date date-type="rev-recd"><day>19</day><month>October</month><year>2018</year></date>
           <date date-type="accepted"><day>16</day><month>November</month><year>2018</year></date>
      </history>
      <permissions>
        
        
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018.html">This article is available from https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018.pdf</self-uri>
      <abstract>
    <p id="d1e143">In the last several decades, significant efforts have been directed toward
better understanding the gaseous and particulate matter (PM) emissions from
aircraft gas turbine engines. However, limited information is available on
the hygroscopic properties of aircraft engine PM emissions which play an
important role in the water absorption, airborne lifetime, obscuring effect,
and detrimental health effects of these particles. This paper reports the
description and detailed lab-based performance evaluation of a robust
hygroscopicity tandem differential
mobility analyzer (HTDMA) in terms of hygroscopic properties such as growth
factor (GF) and the hygroscopicity parameter (<inline-formula><mml:math id="M1" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>). The HTDMA system was
subsequently deployed during the Alternative Aviation Fuel
EXperiment (AAFEX) II field campaign to measure the hygroscopic properties of
aircraft engine PM emissions in the exhaust plumes from a CFM56-2C1 engine
burning several types of fuels. The fuels used were conventional JP-8,
tallow-based hydroprocessed esters and fatty acids (HEFA), Fischer–Tropsch,
a blend of HEFA and JP-8, and Fischer–Tropsch doped with tetrahydrothiophene
(an organosulfur compound). It was observed that GF and <inline-formula><mml:math id="M2" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> increased
with fuel sulfur content and engine thrust condition, and decreased with
increasing dry particle diameter. The highest GF and <inline-formula><mml:math id="M3" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values were
found in the smallest particles, typically those with diameters of 10 nm.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

      <?xmltex \hack{\newpage}?>
<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p id="d1e176">The increase in aviation related activities has led to concern about the
emissions from aircraft operations and their impact on local air quality
(Unal et al., 2005; Woody et al., 2011), global climate (Lee et al., 2009;
Brasseur et al., 2016), and public health (Levy et al., 2012; Brunelle-Yeung
et al., 2014). The primary products of conventional jet fuel combustion in
an aircraft engine are <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, unburned hydrocarbon (UHC),
CO, <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>, and soot
aerosol or soot particulate matter (PM). As the aircraft engine exhaust
plume expands, mixes with ambient air, and cools, volatile species present
in the gas phase at the engine exit plane undergo gas-to-particle
conversion and begin to condense onto existing soot particles and form new
particles (Onasch et al., 2009; Lobo et al., 2012; Timko et al., 2013). The
black carbon component of the PM is referred to as non-volatile particulate
matter (nvPM), while the volatile component consists of sulfates, nitrates,
and organic compounds (Onasch et al., 2009). The composition of the volatile
PM in the expanding aircraft engine exhaust plume varies greatly and
depends on a number of factors such as fuel composition, ambient
meteorological conditions, and plume age (Lobo et al., 2007, 2012, 2015a; Timko et al., 2013).</p>
      <p id="d1e225">The commercial aviation sector has been focused on developing and
implementing sustainable alternative jet fuels for use by airlines to
diversify fuel supplies and mitigate the impacts of aircraft engine
emissions. The American Society for<?pagebreak page17030?> Testing and Materials (ASTM) and other
fuel specification bodies have established a standard specification for the
manufacture of aviation turbine fuel consisting of conventional and
synthetic blending components under ASTM D7566 (ASTM International, 2016). The pure
alternative fuels have low to negligible amounts of aromatic, naphthalene,
and sulfur content when compared to conventional jet fuel. Studies have
shown that nvPM and sulfur oxide emissions are dramatically reduced during
alternative fuel combustion in aircraft engines (Timko et al., 2010; Lobo et
al., 2011, 2015b, 2016; Beyersdorf et al., 2014; Moore et al., 2015).
The nvPM at the engine exit plane is hydrophobic, but as
the nvPM evolves in the expanding plume, its aging results in enhanced
hydrophilicity (Weingartner et al., 1997; Zhang et al., 2008).</p>
      <p id="d1e228">Investigation of atmospheric pollution, and in particular atmospheric
visibility, has shown that aerosol optical properties are affected by size,
composition, and hygroscopic growth of particles (Tang et al., 1981;
Horvath, 1995; Kim et al., 2006; Meier et al., 2009). In urban environments,
emissions from vehicles including soot, sulfates, and nitrates have been
found to be the main contributors to visibility degradation (Ferron et al.,
2005; Kim et al., 2006).</p>
      <p id="d1e231">Hygroscopicity tandem differential
mobility analysis (HTDMA) systems have been widely used to measure the
hygroscopic growth properties of PM in the subsaturated regime in different
environments (Massling et al., 2007; Swietlicki et al., 2008; Park et al.,
2009b; Wu et al., 2013). HTDMA measurements of PM emissions from jet engine
combustors (Gysel et al., 2003; Popovicheva et al., 2008) have also been
performed. However, the application of a HTDMA system to measure the
hygroscopic properties of PM emissions in evolving aircraft engine exhaust
plumes from the combustion of different fuels has not been previously
performed.</p>
      <p id="d1e235">For field measurements, where ambient temperature and humidity cannot be
controlled, the HTDMA system must be fairly rugged, stable, and versatile.
The Missouri University of Science and Technology (MST) has developed a
HTDMA system to quantify the hygroscopic properties of PM emitted from
aircraft engines. The HTDMA system was automated to operate such that it
could determine the hygroscopic properties for an aerosol in approximately
45 s. This is critical when conducting aircraft engine emission tests
which can be quite expensive, and where the expanding exhaust plumes are
subject to perturbations in wind speed and wind direction. This paper
reports the results of lab-based experiments to evaluate the performance of
the MST HTDMA system and in-field measurements of PM emissions in exhaust
plumes from the combustion of conventional and alternative fuels in a
CFM56-2C1 engine during the Alternative Aviation Fuels EXperiment (AAFEX) II field campaign.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p id="d1e240">Schematic of the MST HTDMA system.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f01.png"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <title>Experimental method</title>
      <?pagebreak page17031?><p id="d1e255">The MST HTDMA system consists of two differential mobility analyzers (DMAs),
a humidifier (HUM), and a condensation particle counter (CPC),
similar to other systems (McMurry and Stolzenburg, 1989). Figure 1 presents the
schematic of the MST HTDMA system. The polydisperse aerosol was first
preconditioned by passing through an ice bath (IB-0) to remove excess
water vapor as much as reasonably possible and returning it to room temperature
with a saturation ratio of <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.15</mml:mn></mml:mrow></mml:math></inline-formula>. The aerosol was then
brought to charge equilibrium by passing it through a bipolar charger (BC),
which can contain 500 to 2000 <inline-formula><mml:math id="M9" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Ci of polonium-210 prior to entering
the first DMA (DMA1). The DMAs used in the HTDMA system were custom
designed and have been used in previous studies to classify aerosols based
on electrical mobility (Schmid, 2000). The DMAs were of cylindrical geometry
and had the following dimensions: effective inner length of 72.77 cm, a
sample flow annulus with an inner diameter of 5.07 cm, and an outer diameter
of 8.88 cm. The polydisperse aerosol flow rate (<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) was set to
3 L min<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and the sheath flow rate (<inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) was adjusted to
15 L min<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> using mass flow meters (Aalborg Instruments GFM 371) which were
calibrated periodically. In DMA1, the polydisperse aerosol was classified by
size, and monodisperse particles with a “dry” size (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) selected. The
excess flow in the DMA was recirculated as <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, after passing through a
second ice bath (IB-1) and a high-efficiency particulate air (HEPA) filter to further ensure that the sample
remained dry and had not prematurely deliquesced to a solution droplet. DMA1
was set at a fixed voltage, permitting the selection of a monodisperse
aerosol. The monodisperse sample flow (<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) out of DMA1 entered the
humidifier (HUM) section of the HTDMA system, where it is referred to as
the polydisperse flow, <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. The HUM brought the aerosol sample to a
controlled, precisely known saturation ratio (SR), typically 0.91 to 0.99,
which caused the particles to deliquesce to a new equilibrium “wet”
diameter (<inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). Valves V2 and V3 were used to direct the aerosol
flow <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> to either pass through HUM (wet mode) or to bypass it (dry mode).
Valves V4 and V5 were used to achieve the same function for the sheath air
flow (<inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). The third ice bath (IB-2) in the <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> loop removed the
water vapor from <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and minimized any unwanted vapors co-emitted from
the combustion process. The second DMA (DMA2) in conjunction with a CPC (TSI 3022)
measured <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The MST HTDMA system was designed to provide only
one SR condition and to hold that value regardless of variations in ambient
temperature and humidity or sampling duration. The water bath that encased
HUM/DMA2 was maintained at a fixed temperature by a refrigerated water
re-circulator that controlled the water temperature around the HUM/DMA2 to
<inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. This water passed alongside the <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> lines (not shown in figure). Thus, the dew point achieved in HUM was
well below room temperature. The water flow rate through the water bath
surrounding HUM/DMA2 was approximately 5 L min<inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e516">The SR values in flows <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> were brought to near unity at
16 <inline-formula><mml:math id="M31" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C by passing the aerosol through stainless-steel tubes lined
with wet cloth. The flow <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> passed through four such tubes
(11 mm ID <inline-formula><mml:math id="M33" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 762 mm L), thus having a total length of 3048 mm and
a residence time of 5.8 s. The flow <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> passed through eight similar tubes, thus having a total
length of 6096 mm and a residence time of 2.3 s. Theoretical studies have
shown that the lengths of wet-walled tubing should be sufficient to
bring the <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> to very near SR of 1 (Fitzgerald et al., 1981).
Just before entering DMA2, the SR of <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> was measured by a dew point
hygrometer (DPH) (Vaisala HMP247). The flow <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, in parallel with the
CPC, reduced the lag time (LT2) between when voltage was imposed on DMA2
and when particles selected by that voltage reached the CPC.</p>
      <p id="d1e645">During routine operation, to maximize the data acquisition frequency, the
HTDMA system was computer controlled by a LabVIEW program (LV). When the
program was initiated, it (1) set the desired voltage (HV1) in DMA1 causing
it to deliver dry particles of diameter <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, (2) waited long enough for
this monodisperse aerosol to travel from the outlet of DMA1 through the HUM
and into DMA2, (3) set the high voltage in DMA2 (HV2) to some fraction of
that in DMA1 (typically 0.1 <inline-formula><mml:math id="M40" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> HV1), and (4) caused HV2 to step through
104 increments such that the final value was a multiple of HV1 (typically
10 <inline-formula><mml:math id="M41" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> HV1). During the stepwise voltage increase of HV2 (the logarithm of the
voltage was linear with time.), LV recorded (at 1 Hz) values of HV1, HV2,
<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, P1, P2, SR, CPC
concentration, and elapsed time (d<inline-formula><mml:math id="M45" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>). The operator provided the general region (in time) where the peak in
CPC readings occurred as input, and LV fitted a quadratic function to the
CPC concentration time series. The quadratic function was differentiated and
the value of d<inline-formula><mml:math id="M46" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> at the maximum was obtained (d<inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). Based on
calibrations performed previously, LV computed the lag time (LT2) between
when a certain diameter of droplet was selected by DMA2 and when it arrived
at the CPC. This lag time has been found to be a function of <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. LV found the value of the high voltage on the central rod of DMA2
at that time. It then computed the wet diameter (<inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) of the solution
droplet (using the operating equation of the DMA2) and finally computed the
hygroscopic properties. LV was developed such that the hygroscopic
properties could be determined on more than one <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. LV changes the
particle diameter produced by DMA1 before the end of the voltage sweep on
DMA2. The new particle diameter selected did not arrive at DMA2 while the
current HV2 voltage sweep was running but did arrive immediately after that
sweep had been completed. DMA2 then immediately started the sweep on this
new wet diameter. Thus, the time taken to flush the tubing and the HUM is
minimized. This reduced the time for performing HV2 sweeps on 12 different
dry diameters to <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula> min.</p>
      <p id="d1e799">Periodically, experiments were performed where a challenge aerosol of a pure
inorganic salt (sodium chloride, NaCl, ammonium sulfate,
(<inline-formula><mml:math id="M53" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M54" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M55" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, potassium iodide, KI, or potassium chloride, KCl)
was used to validate/update the calibration of DPH (as described in Suda and
Peters, 2013). During an automated stepwise increase of HV2, the
diameters <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were precisely determined. The calculated saturation
ratios (SR-calc) were obtained from knowledge of the dry diameter <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
the wet diameter <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and the fact that the particles were a pure
chemical of known properties. The SR-calc values were computed and compared
to the value reported by the dew point hygrometer (SR-DPH). A calibration
for the DPH was thus obtained. Typically, a value of 0.85 to 0.99 is obtained for SR-calc.</p>
      <p id="d1e878">In the MST HTDMA system, the SR is measured in the growth region by
performing experiments (as recommended by Johnson et al., 2008). The SR is a
function of not only the water vapor–air mixing ratio but also a function
of gas temperature. Even though the mixing ratio will not change as <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>
travels from the region of the DPH to the middle of DMA2, the temperature
may, resulting in a potential change in SR. Thus, it is better to
self-calibrate the HTDMA system using this method. Furthermore, it is
generally known that reliable measurements of SR from commercial instruments
become very hard to obtain the closer one gets to SR of 1.</p>
      <p id="d1e895">All HTDMA systems described in the literature are designed to provide
precise values for the hygroscopic growth factor. Furthermore, almost all of
these systems have the<?pagebreak page17032?> ability to vary the SR, thus requiring separate
thermostating for the HUM and for DMA2 (Suda and Peters, 2013; Woods et al.,
2013; Shi et al., 2012; Fors et al., 2010; Park et al., 2009a; Massling et
al., 2011; Hu et al., 2010; Biskos et al., 2006; Lopez-Yglesias et al.,
2014). Others (Johnson et al., 2008; Cubison et al., 2005) utilize
controlled mixing of humid and dry air to achieve the desired humidity. Some
systems include water baths (Hennig et al., 2005; Weingartner et al., 2002),
temperature-controlled cabinets (Cocker et al., 2001), and passive, insulated
regions (Virkkula et al., 1999; Johnson et al., 2008).</p>
      <p id="d1e898">Although these designs offer very good precision and the ability to vary the SR,
they may not be well suited for field measurements, since most of them
involve two separate volumes that must have their temperatures maintained
very precisely. It is the temperature difference between these two volumes
that is the critically important parameter. The MST HTDMA system was
designed to be less susceptible to ambient temperature fluctuations. This
was achieved by encasing both the HUM and DMA2 in the same thermostated
container (volume <inline-formula><mml:math id="M61" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 14 L). Other systems have also immersed
DMA2 and the HUM in a water bath (Cubison et al., 2005; Hennig et al., 2005;
Weingartner et al., 2002) to minimize the temperature gradients. In the MST
HTDMA system, temperature drifts are not critical, since the temperature
difference between the HUM and the DMA2 (and the exposure time of the <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in HUM) is what determines the SR, and that remains
constant (zero temperature difference).</p>
      <p id="d1e936">Suda and Peters (2013) discussed the problem of
DMA offset, whereby the diameter as measured by DMA1 may be slightly
different from the diameter as measured by DMA2, even if they both sample
the same aerosol simultaneously. This situation was avoided in the MST
HTDMA system by performing a self-calibration. To accomplish this, an
inorganic challenge aerosol (e.g., (<inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M65" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)) was delivered
to DMA1, and LV directed DMA1 to deliver sample particles with a given
diameter <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The HUM was bypassed and LV initiated a voltage sweep on
DMA2, which yielded a diameter <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">wswp</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. This was repeated for a series
of <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values ranging from 10 to 160 nm, establishing a calibration curve
between <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">wswp</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, with <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> taken as the true diameter.
Within LV, this calibration was utilized to synchronize the two DMAs. Since
DMA1 was static during a voltage sweep and its <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> involves no error
from uncertainties in the lag time (LT2), DMA1 was chosen as the reference.</p>
</sec>
<sec id="Ch1.S3">
  <title>Hygroscopic properties</title>
<sec id="Ch1.S3.SS1">
  <title>Determining the saturation ratio</title>
      <p id="d1e1058">The SR can be calculated from Köhler theory
(Pruppacher and Klett, 1978). For hybrid particles that are composed of a
spherical, insoluble core of diameter <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> surrounded by a spherical
shell of soluble material, SR can be calculated from

                <disp-formula id="Ch1.E1" content-type="numbered"><mml:math id="M75" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>ln⁡</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">SR</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the diameter of the solution droplet. By expanding <inline-formula><mml:math id="M77" display="inline"><mml:mi>ln⁡</mml:mi></mml:math></inline-formula> (SR)
in a Taylor series and keeping only the first term in the expansion, an
error of less than 4.5 % is introduced. Thus, Eq. (1) can be approximated as

                <disp-formula id="Ch1.E2" content-type="numbered"><mml:math id="M78" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">SR</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>-</mml:mo></mml:mrow><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          <?xmltex \hack{\vspace*{-6mm}}?>

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M79" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>A</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>T</mml:mi><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>∼</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">3.12</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">nm</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:mrow><mml:mi>T</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">3.12</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi>T</mml:mi></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            <?xmltex \hack{\vspace*{-6mm}}?>

                <disp-formula id="Ch1.E4" content-type="numbered"><mml:math id="M80" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">4.297</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mi mathvariant="normal">mol</mml:mi></mml:mfrac></mml:mstyle></mml:mfenced><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">ν</mml:mi><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the molecular weight of water, <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the
surface tension of the solution–air interface (<inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.2</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> N m<inline-formula><mml:math id="M84" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>),
R is the universal gas constant [8.31 (N m K<inline-formula><mml:math id="M85" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> mol<inline-formula><mml:math id="M86" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)],
T is the absolute temperature, <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the density of water,
<inline-formula><mml:math id="M88" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula> is the number of ions into which the solute material disassociates,
<inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the mass of the dry (salt or solute) particle, <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the
osmotic coefficient of the solution droplet, and <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the molecular
weight of the solute.</p>
      <p id="d1e1528">For particles composed of a single, pure chemical species with no insoluble
core (<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>),

                <disp-formula id="Ch1.E5" content-type="numbered"><mml:math id="M93" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="normal">SR</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          and <inline-formula><mml:math id="M94" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M95" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> remain as defined above. The mass of the dry (salt or solute)
particle is given by

                <disp-formula id="Ch1.E6" content-type="numbered"><mml:math id="M96" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle></mml:mfenced><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          The osmotic coefficients for selected solute materials as a function of the
molality have been reported in the literature (Hamer and Wu, 1972;
Robinson and Stokes, 2002; Staples, 1981). We find that
<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be related to the square root of the molality (<inline-formula><mml:math id="M98" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula>) by a
sixth-order polynomial function. Hence, <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is dry and wet diameter
dependent, and this must be taken into account. The molality (<inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula>)
(number of moles of the solute/mass of solvent in kilograms) is given by

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M101" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="italic">ψ</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>n</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">solute</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">mass</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="normal">of</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="normal">solvent</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">kg</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle></mml:mfenced><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced><mml:msubsup><mml:mi>M</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mfenced close=")" open="("><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle></mml:mfenced><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E7"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M102" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> is the number of moles of the solute. Examples of how
<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is determined are provided in the Supplement.</p>
      <p id="d1e1875">Thus, a pure chemical of known properties can be used to self-calibrate the
HTDMA and verify SR.</p><?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page17033?><sec id="Ch1.S3.SS2">
  <?xmltex \opttitle{Determining the water activity factor, $a_{\mathrm{w}}$}?><title>Determining the water activity factor, <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></title>
      <p id="d1e1896">The Köhler theory (Pruppacher and Klett, 1978) describes how the
SR over an aqueous solution droplet is related to other
parameters characterizing the water droplet.

                <disp-formula id="Ch1.E8" content-type="numbered"><mml:math id="M105" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="normal">SR</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>⋅</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mo>⋅</mml:mo><mml:mi>T</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the activity of water in solution, and <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the
diameter of the droplet determined by the voltage sweep of DMA2/CPC. Thus,
<inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be calculated from Eq. (8).</p>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Determining the growth factor</title>
      <p id="d1e2009">The growth factor (GF) is the most commonly used parameter to describe the
hygroscopic properties of particles. It is defined as

                <disp-formula id="Ch1.E9" content-type="numbered"><mml:math id="M109" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="normal">GF</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the wet particle diameter and <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the dry particle
diameter. GF is a function of SR and provides a measure of the relative
change in size of the particle as a result of water absorption.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <?xmltex \opttitle{Determining the hygroscopicity parameter~($\kappa$)}?><title>Determining the hygroscopicity parameter (<inline-formula><mml:math id="M112" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>)</title>
      <p id="d1e2076">Petters and Kreidenweis (2007) proposed that a single parameter
representation for hygroscopicity was better to model complex,
multicomponent particle types such as atmospheric particles containing
insoluble components. The hygroscopicity parameter (<inline-formula><mml:math id="M113" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>) is defined
through its effect on the water activity of the solution by

                <disp-formula id="Ch1.E10" content-type="numbered"><mml:math id="M114" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="italic">κ</mml:mi><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">solute</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">solute</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume of the dry particulate matter and
<inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume of the water. It should be noted that
<inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">solute</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> also includes the volume of the insoluble core, if there
is one. For clarity, we note that

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M118" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E11"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">solute</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E12"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            The <inline-formula><mml:math id="M119" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>, calculated from Eq. (10), is an excellent choice when studying
ambient aerosols that derive from the agglomeration of particles from
multiple sources. It should be noted that <inline-formula><mml:math id="M120" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> can also be calculated
from the GF and <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> without determining the wet and dry volumes
(Holmgren et al., 2014).

                <disp-formula id="Ch1.E13" content-type="numbered"><mml:math id="M122" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="italic">κ</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msup><mml:mi mathvariant="normal">GF</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>/</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>

          Thus, for an aerosol of unknown composition, Eq. (8) is used to
compute <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, Eq. (9) to compute GF, and then Eq. (13) to compute <inline-formula><mml:math id="M124" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>. It should
also be noted that, for an aerosol of unknown composition, only Eqs. (8)–(13)
are used, and none of these require any prior knowledge of the physical
or chemical properties of the aerosol.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <title>MST HTDMA performance evaluation</title>
<sec id="Ch1.S4.SS1">
  <title>Performance evaluation using pure inorganic salts</title>
      <p id="d1e2337">The performance of the MST HTDMA system was evaluated by measuring GFs of
pure inorganic salts and comparing them to theory. The values of GF vs. <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
were measured and plotted for NaCl, (<inline-formula><mml:math id="M126" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M127" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M128" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, KI, and
KCl in Fig. 2. To obtain the theoretical GF, the SR-calc (Eqs. 3–5) for the
largest two or three dry particle diameters was computed and an average was
obtained. From this SR-calc, a non-linear equation solver was utilized to
compute the theoretical <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (using Eqs. 3–5) for the other sizes. The
GF could then be computed (Eq. 9). There is excellent agreement between the
measured growth factor and the value predicted from theory. It should also
be noted that the osmotic coefficient <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is quite different from
unity in several of the cases.</p>
      <p id="d1e2403">The dry diameter estimate (<inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) requires knowledge of the average
particle diameter actually exiting DMA1. A weighted average (neglecting
doubly charged particles) is given by

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M132" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">avg</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">SNN</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">TF</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">dlog</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>/</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E14"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">SNN</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">TF</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">dlog</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where SNN<inline-formula><mml:math id="M133" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula> is the differential size distribution entering the HTDMA
system (measured here by a Cambustion DMS500), <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the particle
diameter, <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the fraction of particles of diameter <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that
carry one elementary charge (Hagen and Alofs, 1983), TF<inline-formula><mml:math id="M137" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula> is the transfer
function of DMA1, and dlog<inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the differential in log<inline-formula><mml:math id="M139" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> between
adjacent data points in SNN<inline-formula><mml:math id="M140" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><caption><p id="d1e2615">Growth factor as a function of dry particle diameter (<inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)
for NaCl <bold>(a)</bold>, (<inline-formula><mml:math id="M142" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M143" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M144" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(b)</bold>,
KI <bold>(c)</bold>, and KCl <bold>(d)</bold>.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f02.png"/>

        </fig>

      <p id="d1e2678">The use of Eq. (14) rather than the DMA1 set point value for the average
particle diameter provided a more accurate <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> value for these pure
chemicals. The DMS500 reported the peak in SNN<inline-formula><mml:math id="M146" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula> at approximately 27 nm
for the nebulizer and the solutions of pure solute chemicals used. Since
SNN<inline-formula><mml:math id="M147" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were both monotonically increasing over the range
where TF<inline-formula><mml:math id="M149" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula> was non-zero, the <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">avg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was greater than the set point
diameter of DMA1. For example, when DMA1 was set to extract particles with
<inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">12.76</mml:mn></mml:mrow></mml:math></inline-formula> nm, the value of <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">avg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from Eq. (14) was found to be
13.49 nm, which resulted in a change to the GF from 2.33 to 2.22 (a 5 %
correction). This correction was taken into account for particle diameters
less than 20 nm. For particles diameters larger than 20 nm, the correction is
insignificant. This correction can be utilized for any diameter <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as
long as the SNN<inline-formula><mml:math id="M154" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula>, the <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and the TF<inline-formula><mml:math id="M156" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula> are known.</p>
      <?pagebreak page17034?><p id="d1e2810"><?xmltex \hack{\newpage}?>Most HTDMA systems for which data are reported in the literature are
designed to scan the SR (called humidigrams) and report (1) the GF for a
wide SR range (0.20 <inline-formula><mml:math id="M157" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> SR <inline-formula><mml:math id="M158" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1), and (2) the deliquescence
relative humidity, i.e., the SR at which the dry particles abruptly begin to
take on liquid water and grow to much larger solution droplets. The MST
HTDMA system was not designed to perform humidigrams. By inspection of
humidigrams in the literature and with knowledge of the SR that was recorded
in the MST HTDMA, the GF from these other systems can be estimated. Figure 2a–d
present the experimentally obtained GF as a function of <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for
various inorganic salts. The theoretical values along with those reported in
the literature from other systems are in good agreement with the GF determined by the MST HTDMA.</p>
      <p id="d1e2839">Figure 3 shows plots of <inline-formula><mml:math id="M160" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> vs. <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for the same four chemicals.
Also plotted are the ranges of <inline-formula><mml:math id="M162" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values for (<inline-formula><mml:math id="M163" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M164" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M165" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
and NaCl as reported by Petters and Kreidenweis (2007). There is good
agreement between the <inline-formula><mml:math id="M166" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values reported by the MST HTDMA system and
those from literature.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p id="d1e2907">Hygroscopicity parameter (<inline-formula><mml:math id="M167" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>) as a function of dry particle
diameter (<inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) for NaCl, (<inline-formula><mml:math id="M169" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M170" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M171" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
KI, and KCl.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f03.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <title>Residence time</title>
      <p id="d1e2970">Since the deliquescence technique is an equilibrium based methodology, the
closeness to equilibrium must be validated, especially for the larger
droplets (which grow more slowly). For such a test, the HTDMA system was
configured to select a dry diameter (<inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">17</mml:mn></mml:mrow></mml:math></inline-formula>, 30, or 51 nm)
of (<inline-formula><mml:math id="M173" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M174" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M175" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> aerosol. The wet diameter (<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) was
measured, allowing calculation of GF and SR-calc. This was repeated for a
series of <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values, which varied the residence time. The results are
shown in Fig. 4.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p id="d1e3045">GF <bold>(a)</bold> and SR-calc <bold>(b)</bold>
as a function of polydisperse flow rate <inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, with challenge
(<inline-formula><mml:math id="M179" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M180" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M181" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> aerosols of 17, 30, and 51 nm.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f04.png"/>

        </fig>

      <?pagebreak page17035?><p id="d1e3104"><?xmltex \hack{\newpage}?>From Fig. 4a and b, a small dependence of GF and SR-calc on <inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is
observed. Utilizing a small <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> would be best to achieve the highest SR
value. However, very small values of <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> result in very low
concentration delivered to the CPC. In field measurements where the sample
is diluted with ambient air, the concentration is already quite low, leading
to signal to noise issues. Alternatively, at large values of <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, the
peak is too broad. To avoid both of these extremes, the HTDMA system was
operated at <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3.0</mml:mn></mml:mrow></mml:math></inline-formula> L min<inline-formula><mml:math id="M187" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e3195">The HTDMA system, when deployed in the field, is primarily intended to
study particles with small <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values and small GFs. These particles
will probably not grow large enough to experience insufficient growth time
problems. However, it is good practice to periodically check the system and
the sample aerosol by choosing a large <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (30 nm or larger) to
determine if changes to <inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> result in a change to SR. If this is the
case, then it is better to maintain <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> at a lower value (2.0 L min<inline-formula><mml:math id="M192" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><caption><p id="d1e3263">SR as a function of elapsed time since last wetting for pure particles
of (<inline-formula><mml:math id="M193" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M194" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M195" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. The uncertainty in the SR (calculated)
is approximately 0.008.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f05.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS3">
  <title>Stability over long operating times</title>
      <p id="d1e3308">For field applications, the HTDMA system is required to maintain stable
operation for long periods of time. The HUM tubes are wetted at the
beginning of the day and need to be periodically re-wetted to maintain a
stable SR. The time after which the HUM tubes need to be re-wetted was
experimentally determined. Figure 5 displays the results of determining the
SR-calc by using particles of pure (<inline-formula><mml:math id="M196" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M197" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M198" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M199" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> in
Eq. 1) and measuring the wet diameter <inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, given that the dry diameter
set in DMA1 is held constant. Experiments were performed where the HUM tubes
were wet thoroughly, and then automated scans were conducted for several
hours with no further tube wetting. After the experimental measurements were
performed, the SR was calculated from Eq. (5). Figure 5 shows the measured SR
of the <inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">sh</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> as determined by DPH. It can be seen that the calculated
and the measured SR remained constant for a period of over 225 min
without having to re-wet the tubes.</p>
      <p id="d1e3381">When required, tube re-wetting was accomplished using a LabVIEW program which
acted through a relay board to energize a peristaltic pump and sequentially
opened 12 pinch valves for a short period (set by the operator),
allowing each tube to be re-wet in sequence. After re-wetting, valves at the
bottom of the 12 stainless-steel tubes were manually opened to allow excess
water to drain. During normal operations in the field, the HUM tubes were
re-wetted every 150 min.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p id="d1e3387">Selected fuel properties.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Property</oasis:entry>
         <oasis:entry colname="col2">Method</oasis:entry>
         <oasis:entry colname="col3">JP-8</oasis:entry>
         <oasis:entry colname="col4">HEFA</oasis:entry>
         <oasis:entry colname="col5">FT</oasis:entry>
         <oasis:entry colname="col6">HEFA-JP-8</oasis:entry>
         <oasis:entry colname="col7">FT plus THT</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">blend</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Density at 15 <inline-formula><mml:math id="M202" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (kg<inline-formula><mml:math id="M203" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">ASTM D4052</oasis:entry>
         <oasis:entry colname="col3">0.811</oasis:entry>
         <oasis:entry colname="col4">0.758</oasis:entry>
         <oasis:entry colname="col5">0.761</oasis:entry>
         <oasis:entry colname="col6">0.783</oasis:entry>
         <oasis:entry colname="col7">0.761</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Viscosity at <inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M205" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (mm<inline-formula><mml:math id="M206" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M207" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">ASTM D445</oasis:entry>
         <oasis:entry colname="col3">4.1</oasis:entry>
         <oasis:entry colname="col4">4.9</oasis:entry>
         <oasis:entry colname="col5">3.7</oasis:entry>
         <oasis:entry colname="col6">4.3</oasis:entry>
         <oasis:entry colname="col7">3.2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Distillation temperature (<inline-formula><mml:math id="M208" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">ASTM D86</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10 % recovered</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">168</oasis:entry>
         <oasis:entry colname="col4">175</oasis:entry>
         <oasis:entry colname="col5">164</oasis:entry>
         <oasis:entry colname="col6">166</oasis:entry>
         <oasis:entry colname="col7">164</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">End point</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">268</oasis:entry>
         <oasis:entry colname="col4">254</oasis:entry>
         <oasis:entry colname="col5">226</oasis:entry>
         <oasis:entry colname="col6">263</oasis:entry>
         <oasis:entry colname="col7">224</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Flash point (<inline-formula><mml:math id="M209" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">ASTM D93</oasis:entry>
         <oasis:entry colname="col3">46</oasis:entry>
         <oasis:entry colname="col4">52</oasis:entry>
         <oasis:entry colname="col5">43</oasis:entry>
         <oasis:entry colname="col6">46</oasis:entry>
         <oasis:entry colname="col7">43</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Net heat of combustion (MJ kg<inline-formula><mml:math id="M210" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">ASTM D4809</oasis:entry>
         <oasis:entry colname="col3">42.8</oasis:entry>
         <oasis:entry colname="col4">43.6</oasis:entry>
         <oasis:entry colname="col5">43.8</oasis:entry>
         <oasis:entry colname="col6">43.3</oasis:entry>
         <oasis:entry colname="col7">43.8</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Aromatics (% vol)</oasis:entry>
         <oasis:entry colname="col2">ASTM D1319</oasis:entry>
         <oasis:entry colname="col3">21.8</oasis:entry>
         <oasis:entry colname="col4">0.4</oasis:entry>
         <oasis:entry colname="col5">1.4</oasis:entry>
         <oasis:entry colname="col6">10.2</oasis:entry>
         <oasis:entry colname="col7">2.1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Naphthalene (% vol)</oasis:entry>
         <oasis:entry colname="col2">ASTM D1840</oasis:entry>
         <oasis:entry colname="col3">1.3</oasis:entry>
         <oasis:entry colname="col4">0</oasis:entry>
         <oasis:entry colname="col5">0</oasis:entry>
         <oasis:entry colname="col6">0.65</oasis:entry>
         <oasis:entry colname="col7">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Sulfur (ppm)</oasis:entry>
         <oasis:entry colname="col2">ASTM D2622</oasis:entry>
         <oasis:entry colname="col3">188</oasis:entry>
         <oasis:entry colname="col4">6</oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">276</oasis:entry>
         <oasis:entry colname="col7">1083</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Hydrogen content (% mass)</oasis:entry>
         <oasis:entry colname="col2">ASTM D3343</oasis:entry>
         <oasis:entry colname="col3">13.5</oasis:entry>
         <oasis:entry colname="col4">15.3</oasis:entry>
         <oasis:entry colname="col5">15</oasis:entry>
         <oasis:entry colname="col6">14.4</oasis:entry>
         <oasis:entry colname="col7">15</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Carbon content (% mass)</oasis:entry>
         <oasis:entry colname="col2">Calculated</oasis:entry>
         <oasis:entry colname="col3">86.5</oasis:entry>
         <oasis:entry colname="col4">84.7</oasis:entry>
         <oasis:entry colname="col5">85</oasis:entry>
         <oasis:entry colname="col6">85.6</oasis:entry>
         <oasis:entry colname="col7">85</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">H <inline-formula><mml:math id="M211" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> C ratio</oasis:entry>
         <oasis:entry colname="col2">Calculated</oasis:entry>
         <oasis:entry colname="col3">1.86</oasis:entry>
         <oasis:entry colname="col4">2.15</oasis:entry>
         <oasis:entry colname="col5">2.10</oasis:entry>
         <oasis:entry colname="col6">2.00</oasis:entry>
         <oasis:entry colname="col7">2.10</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S4.SS4">
  <title>Stability over varying ambient temperature conditions</title>
      <p id="d1e3884">The HTDMA must be able to operate under varying ambient temperature
conditions in the field. The stability of the HTDMA system was assessed
using pure (<inline-formula><mml:math id="M212" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)<inline-formula><mml:math id="M213" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula><inline-formula><mml:math id="M214" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> as the challenge aerosol. DMA1 was set
to extract dry particles of 30 nm. An automated voltage sweep with DMA2 was
performed every 2 min to determine <inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The SR-calc was computed
using Eq. (1), with <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>. At <inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> min (and 40 min), the ambient
conditions surrounding the HTDMA system were abruptly changed by blowing
cold air over the bottom of the HUM tubes (or not blowing cold air over the
bottom of the HUM), which is not as well thermally insulated as the rest of
the HTDMA system (Fig. 1). This experiment was repeated four times on four
different days. The SR-calc remained constant over the duration of any one
run as shown in Fig. 6. The average standard deviation in SR-calc divided by
the average SR-calc for that trial over all four trials (120 measurements)
was 0.0019, indicating that this system was insensitive to ambient temperature fluctuations.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><caption><p id="d1e3957">SR-calc and room temperature as a function of elapsed time.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f06.png"/>

        </fig>

<?xmltex \hack{\newpage}?>
</sec>
</sec>
<?pagebreak page17036?><sec id="Ch1.S5">
  <title>Field deployment during the AAFEX II campaign</title>
      <p id="d1e3975">The MST HTDMA system was deployed as part of the Alternative Aviation Fuels
EXperiment (AAFEX II) campaign conducted during 20 March–2 April 2011 at
the NASA Dryden Aircraft Operations Facility (DAOF), Palmdale, CA, USA. The
NASA DC-8 aircraft equipped with CFM56-2C1 engines was utilized as the
emissions source. The aircraft was parked in an open-air run-up facility
with no other aircraft or emission sources in the vicinity of the test site.
Detailed descriptions of the test site and experimental setup have been
previously reported (Timko et al., 2013; Moore et al., 2015). The main
objective of the campaign was to investigate the gaseous and PM emissions
characteristics of the CFM56-2C1 engine burning conventional and alternative
fuels as a function of engine thrust conditions at several sampling
locations in the exhaust plume. PM emissions data were acquired for a
typical cycle which consisted of the following engine thrust conditions:
4 %, 7 %, 30 %, 65 %, 85 %, and 100 % rated thrust. Two test
cycles were run for each fuel – one stepping up from 4 % to 100 % rated
thrust and the other stepping down from 100 % to 4 % rated thrust. Five
fuels were used during the campaign: (1) JP-8 (the military equivalent of
conventional Jet A/JetA-1), (2) tallow-based hydroprocessed esters and
fatty acids (HEFA), (3) coal-derived Sasol Fischer–Tropsch (FT), (4) a blend
of HEFA and JP-8, and (5) FT doped with tetrahydrothiophene (THT) to boost
the sulfur content of the fuel. A summary of selected fuel properties is
provided in Table 1. Chemical and physical analyses of the HEFA and FT fuels
have been reported elsewhere (Corporan et al., 2011).</p>
      <p id="d1e3978">The emissions from the CFM56-2C1 engine were measured at several distances
(1, 30, and 143 m) from the engine exit plane to study the
PM characteristics as the exhaust plume cooled and mixed with ambient air. Only
data acquired at the 143 m location are presented and discussed here to
investigate the hygroscopic properties of the evolving plume.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><caption><p id="d1e3983">Total (T) and non-volatile (NV) PM number-based emission index (EI<inline-formula><mml:math id="M218" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:math></inline-formula>)
size distributions for the various fuels at the 100 % engine thrust condition.</p></caption>
        <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f07.png"/>

      </fig>

      <p id="d1e4001">A 5.08 cm aluminum tube (<inline-formula><mml:math id="M219" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1.3</mml:mn></mml:mrow></mml:math></inline-formula> m above the concrete apron)
positioned downwind from engine no. 3 on the starboard side of the aircraft
was used to extract exhaust plume samples at the 143 m location. The exhaust
was transported through the tube to a small trailer approximately 18 m away
which housed the MST HTDMA system to measure hygroscopic properties. The
exhaust gas flow rate through the 0.052 m ID <inline-formula><mml:math id="M220" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 18 m L tubing was well over
100 L min<inline-formula><mml:math id="M221" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Also housed in the trailer was a Cambustion DMS500
(Reavell et al., 2002; Hagen et al., 2009) which measured the real-time
particle size distributions, and a LI-COR 840A nondispersive infrared (NDIR) detector that measured
exhaust <inline-formula><mml:math id="M222" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration. Ambient meteorological conditions such as
temperature, pressure, and relative humidity were also monitored and
recorded throughout the campaign. The exhaust samples at 4 % and 7 %
engine thrust conditions were impacted by the ambient conditions,
specifically, wind speed and wind direction. However, the <inline-formula><mml:math id="M223" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
measurements during the 7 % trust<?pagebreak page17037?> periods were approximately twice the
background level, indicating that the exhaust plume was being sampled.</p>
      <p id="d1e4056">The DMS500 measured total PM size distributions. The nvPM size distributions
were obtained by passing the sample through a thermal denuder. The thermal
denuder consisted of a coil of stainless-steel tubing (0.457 cm ID) housed
in a temperature-controlled aluminium box heated to 300 <inline-formula><mml:math id="M224" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C,
followed by a cooling section. It is similar in design to that used by Saleh
et al. (2011) and has been used in a previous study (Rye et al., 2012).
Laboratory evaluations have demonstrated that <inline-formula><mml:math id="M225" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> droplets of
diameter 10–100 nm are almost completely evaporated in the thermal denuder.</p>
      <p id="d1e4084">The total and nvPM number-based size distributions were converted to
number-based emission index (EI<inline-formula><mml:math id="M226" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:math></inline-formula>) distributions to account for varying
amounts of dilution for each plume, and are presented for selected fuels at
the 100 % thrust condition shown in Fig. 7. The total PM size
distributions are bimodal with a strong nucleation mode (<inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> nm)
and an accumulation mode. These observations are consistent with those
reported for PM emissions measured downwind of several different aircraft
engine types (Lobo et al., 2007, 2012, 2015a). The
enhancement of the nucleation mode in measurements made downwind of the
engine exit plane is due to gas-to-particle conversion in the exhaust plume
driven by fuel composition, ambient conditions, and degree of mixing. Timko
et al. (2013) found that the driving force for gas-to-particle conversion in
the expanding exhaust plume was the ratio of particle precursors (both
organic and sulfate) to soot.</p>
      <p id="d1e4106">The sulfur in the fuel is oxidized to <inline-formula><mml:math id="M228" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, a portion of which then
undergoes oxidation to <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and subsequently to sulfuric acid
(<inline-formula><mml:math id="M230" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) in the exhaust plume (Miake-Lye et al., 1998; Schumann et
al., 2002). The <inline-formula><mml:math id="M231" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> either homogenously nucleates to form pure
<inline-formula><mml:math id="M232" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> droplets or condenses onto existing soot particles to form
hybrid particles that have significant water-soluble components (Gysel et
al., 2003; Wyslouzil et al., 1994).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F8" specific-use="star"><caption><p id="d1e4181">GF and <inline-formula><mml:math id="M233" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> as a function of <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for particles generated
at different engine thrust conditions and different fuels.</p></caption>
        <?xmltex \igopts{width=298.753937pt}?><graphic xlink:href="https://acp.copernicus.org/articles/18/17029/2018/acp-18-17029-2018-f08.png"/>

      </fig>

      <?pagebreak page17039?><p id="d1e4208">The data acquired with the MST HTDMA system was used to calculate GF
and <inline-formula><mml:math id="M235" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> of these particles as a function of fuel type, engine thrust
condition, and dry particle diameter. The HTDMA was operated with a SR
of 0.91. Figure 8 shows GF and <inline-formula><mml:math id="M236" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> as a function of <inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for particles
generated at different engine thrust conditions and different fuels. The
uncertainty in GF was 9 % for particles with diameter <inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> nm and 3 %
for the larger diameters (26 nm). The uncertainty in <inline-formula><mml:math id="M239" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>
was 7 % and 2 % for particles with diameter <inline-formula><mml:math id="M240" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">26</mml:mn></mml:mrow></mml:math></inline-formula> nm, respectively.</p>
      <p id="d1e4275">Gysel et al. (2007) state that <inline-formula><mml:math id="M242" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is expected to retain water
at 5 %–10 % relative humidity, corresponding to a growth factor of <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1.15</mml:mn></mml:mrow></mml:math></inline-formula>,
and took this into account when calculating the mixed particle growth factor
in their data. This procedure was similarly followed for the current
dataset. Thus, the measured <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values were scaled by a factor of 0.869.</p>
      <p id="d1e4315">For a given engine thrust condition, both GF and <inline-formula><mml:math id="M245" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> increased with
increasing fuel sulfur content. GF and <inline-formula><mml:math id="M246" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> were also observed to be
dependent on particle diameter, with the highest GF and <inline-formula><mml:math id="M247" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> for
particles <inline-formula><mml:math id="M248" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10 nm, and decreasing for large particle
diameters. This increase in GF and <inline-formula><mml:math id="M249" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> corresponds to the nucleation
mode in the size distributions (Fig. 7), which was composed of particles or
droplets formed by the homogeneous nucleation of low equilibrium vapor
pressure species, such as <inline-formula><mml:math id="M250" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and other water-soluble organic
compounds. The GF and <inline-formula><mml:math id="M251" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> were also found to increase with increasing
engine thrust condition for a given <inline-formula><mml:math id="M252" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, with the largest values
observed at the 100 % engine thrust condition.</p>
      <p id="d1e4388">Gysel et al. (2003) reported GF of particles from a jet engine combustor
burning three different fuels with 50, 410, and 1270 ppm of sulfur
at two inlet temperature operating conditions: 566 and 766 K. These data
are in good agreement with the current study for very low sulfur (HEFA and FT)
fuels, conventional JP-8, and the sulfur-enhanced FT (FT plus THT), respectively.</p><?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <title>Conclusions</title>
      <p id="d1e4398">A robust, mobile HTDMA system has been developed for field measurements
that involve (1) particle sources that are very expensive to operate,
(2) exhaust plumes influenced by wind speed and direction, and (3) varying
meteorological conditions. The GF exhibited by particles of four inorganic
salts was studied and found to be in good agreement with theory and with
other experimental data reported in the literature. The fixed SR provided by
the HTDMA system during laboratory evaluation (typically <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.98</mml:mn></mml:mrow></mml:math></inline-formula>)
was found to be quite constant over long periods of time, even when
the ambient temperature varied considerably, making the MST HTDMA system
suitable for field experiments. The HTDMA was demonstrated to perform a
scan to determine GF and <inline-formula><mml:math id="M254" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> for one dry diameter in approximately 45 s.
It performed scans over as many as 12 dry diameters sequentially in
<inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula> min. The HTDMA system provided parameterization for
hygroscopic properties for aircraft engine exhaust plumes in terms of GF and
<inline-formula><mml:math id="M256" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> during the AAFEX II field campaign. It was observed that GF
and <inline-formula><mml:math id="M257" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> (1) increased with fuel sulfur content, (2) increased with
increasing engine thrust condition, and (3) decreased with increasing dry
particle diameter.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability">

      <p id="d1e4446">The data included in this paper can be obtained by contacting the authors.</p>
  </notes><?xmltex \hack{\clearpage}?><app-group>

<?pagebreak page17040?><app id="App1.Ch1.S1">
  <title>List of abbreviations</title><?xmltex \hack{\hsize\textwidth}?>
      <p id="d1e4459"><table-wrap id="Taba" position="anchor"><oasis:table><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">AAFEX</oasis:entry>
         <oasis:entry colname="col2">Alternative Aviation Fuels EXperiment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">ASTM</oasis:entry>
         <oasis:entry colname="col2">American Society for Testing and Materials</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">BC</oasis:entry>
         <oasis:entry colname="col2">Bipolar charger</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CPC</oasis:entry>
         <oasis:entry colname="col2">Condensation particle counter</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DPH</oasis:entry>
         <oasis:entry colname="col2">Dew point hygrometer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DMA</oasis:entry>
         <oasis:entry colname="col2">Differential mobility analyzer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DRH</oasis:entry>
         <oasis:entry colname="col2">Deliquescence relative humidity – the humidity at which the dry</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">particles abruptly take on water and become solution drops</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FT</oasis:entry>
         <oasis:entry colname="col2">Fischer–Tropsch</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">GF</oasis:entry>
         <oasis:entry colname="col2">Growth factor, <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">HTDMA</oasis:entry>
         <oasis:entry colname="col2">Hygroscopicity tandem differential mobility analyzer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">HEFA</oasis:entry>
         <oasis:entry colname="col2">Hydroprocessed esters and fatty acids</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">HUM</oasis:entry>
         <oasis:entry colname="col2">Humidifier</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">HV1, HV2</oasis:entry>
         <oasis:entry colname="col2">High voltage in DMA1 or DMA2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">IB</oasis:entry>
         <oasis:entry colname="col2">Ice bath</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">LV</oasis:entry>
         <oasis:entry colname="col2">LabVIEW program</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MST</oasis:entry>
         <oasis:entry colname="col2">Missouri University of Science and Technology</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">nvPM</oasis:entry>
         <oasis:entry colname="col2">Non-volatile particulate matter</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">PM</oasis:entry>
         <oasis:entry colname="col2">Particulate matter</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">R</oasis:entry>
         <oasis:entry colname="col2">Ideal gas law constant</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SR</oasis:entry>
         <oasis:entry colname="col2">Saturation ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SR-calc</oasis:entry>
         <oasis:entry colname="col2">Value of SR calculated from measured values of <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">when using a pure salt</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SR-DPH</oasis:entry>
         <oasis:entry colname="col2">Value of SR measured by the dew point hygrometer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">THT</oasis:entry>
         <oasis:entry colname="col2">Tetrahydrothiophene</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap></p><?xmltex \hack{\clearpage}?>
</app>

<?pagebreak page17041?><app id="App1.Ch1.S2">
  <title>List of symbols – symbol units' quantity</title>
      <p id="d1e4744"><table-wrap id="Tabb" position="anchor"><oasis:table><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">d<inline-formula><mml:math id="M261" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">s</oasis:entry>
         <oasis:entry colname="col3">elapsed time since a trial run began</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">d<inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">s</oasis:entry>
         <oasis:entry colname="col3">value of d<inline-formula><mml:math id="M263" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> when CPC reading is at its maximum</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M264" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">fraction of particles of diameter <inline-formula><mml:math id="M265" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that carry one elementary charge</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">LT2</oasis:entry>
         <oasis:entry colname="col2">s</oasis:entry>
         <oasis:entry colname="col3">lag time between when voltage is imposed on DMA2 and when the particles</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">selected by that voltage reach the CPC</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M266" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">g mol<inline-formula><mml:math id="M267" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">molecular weight of solute</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">g mol<inline-formula><mml:math id="M269" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">molecular weight of water</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M270" display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">g</oasis:entry>
         <oasis:entry colname="col3">mass of water-soluble portion of the dry particle</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">P1, P2</oasis:entry>
         <oasis:entry colname="col2">psia</oasis:entry>
         <oasis:entry colname="col3">pressure in <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> flow in either DMA1 or DMA2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">L min<inline-formula><mml:math id="M275" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">polydisperse aerosol gas flow rate, either for DMA1 or DMA2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M277" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">L min<inline-formula><mml:math id="M278" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">sheath gas flow rate, either for DMA1 or DMA2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M279" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M280" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">L min<inline-formula><mml:math id="M281" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">monodisperse aerosol gas flow rate, either for DMA1 or DMA2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M282" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">L min<inline-formula><mml:math id="M283" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">flow rate of dump gas in parallel with the CPC</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SNN<inline-formula><mml:math id="M284" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">differential size distribution entering the HTDMA system</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M285" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">K</oasis:entry>
         <oasis:entry colname="col3">absolute temperature</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TF<inline-formula><mml:math id="M286" display="inline"><mml:msub><mml:mi/><mml:mi>k</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">value of transfer function of DMA1 for <inline-formula><mml:math id="M287" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>th point in the series to determine <inline-formula><mml:math id="M288" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">avg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">avg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">nm</oasis:entry>
         <oasis:entry colname="col3">average particle diameter exiting the dry DMA, DMA1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">nm</oasis:entry>
         <oasis:entry colname="col3">set point diameter of DMA1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">nm</oasis:entry>
         <oasis:entry colname="col3">diameter of insoluble core in hybrid particle</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">nm</oasis:entry>
         <oasis:entry colname="col3">diameter of wet particle or solution droplet formed from dry particle after passing</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">through the HUM</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">wswp</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">nm</oasis:entry>
         <oasis:entry colname="col3">diameter of particles (solution drops) exiting DMA2 as measured by LV doing</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">an automated sweep</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">nm</oasis:entry>
         <oasis:entry colname="col3">the <inline-formula><mml:math id="M295" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>th particle diameter in the series to determine the <inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">avg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M297" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">mol kg<inline-formula><mml:math id="M298" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">molality of the solution droplet</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M299" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">number of ions into which the soluble salt disassociates</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">osmotic coefficient of the solution droplet</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M301" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">g cm<inline-formula><mml:math id="M302" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">density of soluble material in hybrid particle</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">g cm<inline-formula><mml:math id="M304" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">density of water</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">N m<inline-formula><mml:math id="M306" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">surface tension of water against air</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap></p><?xmltex \hack{\clearpage}?><supplementary-material position="anchor"><p id="d1e5568">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-18-17029-2018-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-18-17029-2018-supplement</inline-supplementary-material>.</p></supplementary-material>
</app>
  </app-group><notes notes-type="authorcontribution">

      <p id="d1e5579">MBT, PL, DEH, and PDW designed the study. MBT performed
the laboratory evaluations and field measurements. MBT and SCA developed the
LabVIEW code. MBT, PL, SCA, and WL analyzed the data. MBT, PL, and WL
prepared the figures. MBT and PL wrote the initial manuscript and subsequent
revisions with contributions from DEH, SCA, WL, and PDW.</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e5585">The authors declare that they have no conflict of
interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e5592">This work was partly funded by the US Federal Aviation Administration (FAA)
through the Partnership for AiR Transportation for Noise and Emissions
Reduction (PARTNER) – an FAA–NASA–Transport Canada–US DoD–US EPA sponsored
Center of Excellence Project 20 under grant no. 09-C-NE-MST amendment 003.
Any opinions, findings, and conclusions or recommendations expressed in this
paper are those of the authors and do not necessarily reflect the views of
the FAA. We thank the entire AAFEX II project team for their support during
the campaign. Otmar Schmid performed many early experiments to validate
the worthiness of this device and provided impetus for continued effort to
develop this instrument. We thank Veronica Villines Teat, Emitt Witt,
Christian Hurst, Nicholas Altese, Elizabeth Black, and Jonathon Sidwell for
their assistance in gathering some of the data. We are also grateful to
Markus Petters and Sonia Kreidenweis for their assistance with the <inline-formula><mml:math id="M307" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> calculations. <?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: Ari Laaksonen <?xmltex \hack{\newline}?>
Reviewed by: three anonymous referees</p></ack><ref-list>
    <title>References</title>

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    <!--<article-title-html>Application of a hygroscopicity tandem differential mobility analyzer for characterizing PM emissions in exhaust plumes from an aircraft engine burning conventional and alternative fuels</article-title-html>
<abstract-html><p>In the last several decades, significant efforts have been directed toward
better understanding the gaseous and particulate matter (PM) emissions from
aircraft gas turbine engines. However, limited information is available on
the hygroscopic properties of aircraft engine PM emissions which play an
important role in the water absorption, airborne lifetime, obscuring effect,
and detrimental health effects of these particles. This paper reports the
description and detailed lab-based performance evaluation of a robust
hygroscopicity tandem differential
mobility analyzer (HTDMA) in terms of hygroscopic properties such as growth
factor (GF) and the hygroscopicity parameter (<i>κ</i>). The HTDMA system was
subsequently deployed during the Alternative Aviation Fuel
EXperiment (AAFEX) II field campaign to measure the hygroscopic properties of
aircraft engine PM emissions in the exhaust plumes from a CFM56-2C1 engine
burning several types of fuels. The fuels used were conventional JP-8,
tallow-based hydroprocessed esters and fatty acids (HEFA), Fischer–Tropsch,
a blend of HEFA and JP-8, and Fischer–Tropsch doped with tetrahydrothiophene
(an organosulfur compound). It was observed that GF and <i>κ</i> increased
with fuel sulfur content and engine thrust condition, and decreased with
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