Introduction
The interplay between aerosol particles and water droplets in the atmosphere,
especially in clouds, influences both aerosol and cloud properties. The major
uncertainty in our understanding of climate arises from this interplay: the
ability of an aerosol to affect cloud formation and, consequently, alter the
global radiative balance (IPCC, 2007). When an aerosol particle comes in
contact with a water droplet, the interaction can result in a collision
followed by coalescence of the two. This process is known as “collection”
or “coagulation”. The collection process is considered an important
mechanism that can “scavenge”, and thereby remove, aerosol particles from
the atmosphere (Starr and Mason, 1966; Owe Berg et al., 1970; Hampl and
Kerker, 1972; Pranesha and Kamra, 1996). Collection can also affect cloud
dynamics, the precipitation process and cloud lifetime, and thereby change
the global radiation budget (Rasch et al., 2000; Croft et al., 2009).
Mechanisms that affect the collection process of aerosol particles
by water droplets. The mechanisms, from left to right, are Brownian
diffusion, inertial impaction, interception, electro-scavenging and phoresis.
Td and ρd are the temperature and water molecule
density at the droplet surface, while Ta and ρa are
the ambient temperature and water molecule density. See text for additional
description. Figure based on Ladino (2011).
In supercooled clouds, where droplets are present at temperatures below
0 ∘C, the collection process can have an effect on precipitation
when the contacting aerosol initiates ice nucleation. The result is the
creation of an ice crystal, a process known as “contact nucleation” (Vali,
1996). Contact can influence cloud lifetime and precipitation formation in
mixed-phase clouds, which will also affect the global radiation budget. In
order to understand the contact freezing process, it is important to
determine the efficiencies at which the aerosol particles collide with a
liquid droplet within a cloud.
Collection efficiency (CE) is the ability of a droplet to coagulate with the
aerosol particles within the volume swept out as it falls. Several mechanisms
and forces can affect the collection process. These include inertial
impaction, Brownian diffusion, interception, electrical and other phoretic
forces (see Fig. 1). Inertial impaction is defined as the impaction of
particles that have sufficient inertia that they do not follow their original
streamline around the droplet but instead travel close enough to the surface
to result in a collision. Brownian diffusion refers to the movement of the
particle due to collisions with air molecules. In this context it results in
a “random walk” into the droplet surface. Interception is the impaction of
particles that follow a streamline that approaches the droplet within a
distance equivalent to the particle radius. Electrical forces, also commonly
termed electro-scavenging or electrophoresis, occur when opposite electrical
charges are present on the droplet and the particle, resulting in an
attraction between the two. Other phoretic forces occur when a droplet
evaporates or grows. These phoretic forces include thermophoresis and
diffusiophoresis. Thermophoresis takes place when there is a temperature
gradient between a droplet and its surroundings. When a droplet evaporates,
its surface can become colder and aerosols will be drawn towards it.
Diffusiophoresis, a counterforce to thermophoresis, occurs when there is a
concentration gradient in water vapor, as is the case near an evaporating
droplet. Higher water vapor concentration surrounding the droplet “pushes”
particles outward. A review of the phoretic forces can be found in Pruppacher
and Klett (1997).
The mechanisms described above are dependent on the size of the aerosol
particle being collected. Whereas for large particles
(radius > 1 µm) inertial effects dominate the collection
process, small particle (radius < 0.1 µm) motion is dominated
by Brownian diffusion and electro-scavenging (Wang and Pruppacher, 1977),
where the effects of the latter are higher (Tinsley et al., 2001). Phoretic
forces have a larger impact on particles in the intermediate size range (Wang
and Pruppacher, 1977). This intermediate range, 0.1–1 µm, is
normally termed the “Greenfield gap”, and coincides with an observed
minimum in CE (Greenfield, 1957). The particle radius of the Greenfield gap
has also been observed to vary with the collecting droplet size (Tinsley et
al., 2001).
Many factors, besides particle size, have been observed to affect CE (Byrne
and Jennings, 1993). These include particle density (Chate and Kamra, 1997),
turbulence (Grover and Pruppacher, 1985) and relative humidity (RH). Lower RH has been observed
to correlate with higher CE values, apparently due to phoretic forces (Grover
et al., 1977; Tinsley et al., 2001). Droplet size can impact CE, where lower
values correlate with larger droplets (Lai et al., 1978; Pranesha and Kamra,
1996). Higher charge also correlates with higher CE, indicative of greater
electrical force (Beard, 1974; Wang and Pruppacher, 1977; Lai et al., 1978;
Barlow and Latham, 1983; Pranesha and Kamra, 1997a, b; Tinsley et al., 2000).
It should be noted that the number of elementary charges used in previous
work was often motivated by atmospheric observations: a few tens to hundreds
of elementary charges for altostratus and stratocumulus clouds (Phillips and
Kinzer, 1958; Beard et al., 2004) and hundreds to thousands of elementary
charges in cumulonimbus clouds (Thomson and Iribarne, 1978; Marshall and
Winn, 1982).
Experimental results from previous studies of CE.
Reference
Droplet radius (µm)
Aerosol radius (µm)
Aerosol type
Aerosol concentration (cm-3)
RH
Starr and Mason (1966)
100–1000
2.25, 2.5, 6.4
Spores, various
Not given
Not given
Owe Berg et al. (1970)
1210–1305
7.5–15
PSL
Not given
Not given
Hampl et al. (1971)
710–2540
0.2–0.5
AgCl
Not given
Not given
Hampl and Kerker (1972)
2540
53–2000
AgCl
Not given
Not given
Beard (1974)
200–425
0.35–0.44
In(C5H7O2)3
5 × 104
97–99
Kerker and Hampl (1974)
940–2540
0.15–0.6
AgCl
Not given
Not given
Wang and Pruppacher (1977)
150–2500
0.25 ± 0.03
In(C5H7O2)3
1017–1018
23 ± 2
Lai et al. (1978)
620, 820, 980
0.15–0.45
AgCl
Not given
Not given
Leong et al. (1982)
56–93
0.58–3.2
MnO4P2
Not given
∼ 30
Barlow and Latham (1983)
270–600
0.2–1
Not given
> 1000
50–70
Deshler (1985)
1200–1300
0.03, 0.06, 0.13
Not given
2 × 104–1.4 × 105
60–97
Byrne and Jennings (1993)
400–550
0.35–0.88
Not given
Not given
50–80
Pranesha and Kamra (1993)
1800, 2100, 2400
0.95, 1.9, 3.2
NaCl
Not given
Not given
Pranesha and Kamra (1996)
1800, 2100, 2400
0.95, 1.9, 3.2
NaCl
Not given
35–50
Pranesha and Kamra (1997a)
1800, 2100, 2400
0.95, 1.9, 3.2
NaCl
Not given
35–50
Chate and Kamra (1997)
1800, 2100, 2400
1.5, 2 , 3
MgSO4 & MnCl2
Not given
35–50
Vohl et al. (2001)
346, 1680, 2880
0.16–0.24
In(C5H7O2)3
Not given
40
Ladino et al. (2011), Ladino (2011)
12.8, 15, 18.2, 20
0.05–0.33
LiBO2
2 × 103
88 ± 2
Prodi et al. (2014)
240–1075
0.2–1
NaCl
Not given
< 100
To date, there have been numerous experimental and theoretical studies of the
collection process (Beard, 1974; Grover et al., 1977; Pranesha and Kamra,
1996; Park et al., 2005; Tinsley et al., 2006). Most of the experimental
studies have focused on drizzle and raindrop sizes (Hampl and Kerker, 1972;
Deshler, 1985; Pranesha and Kamra, 1997a, b), while few have used smaller
cloud droplets (Ladino et al., 2011). A list of these studies is provided in
Table 1. Note that only a few of the experiments reported aerosol
concentrations and none mentioned whether different concentrations were
compared.
Previous studies have relied on bulk collection of coagulated droplets
followed by offline analysis to assess CE (Hampl et al., 1971; Deshler,
1985; Pranesha and Kamra, 1993; Chate and Kamra, 1997). Offline analytical
instruments include mass spectrometry (Ladino et al., 2011), atomic
absorption spectroscopy (Barlow and Latham, 1983; Pranesha and Kamra, 1996),
fluorescence spectrometry (Byrne and Jennings, 1993) and neutron activation
analysis (Beard, 1974). The efficiency determined from bulk collection of
droplet results in a signal-to-noise issue where minimal collection events
can fall below instrumental detection limits. The inability to determine
multiple collection events by single droplets is another possible source of
error. To our knowledge, no previous study allowed for determination of
collection on a single-droplet basis with atmospherically relevant
conditions of droplet size, droplet charge and flow, which are a key to
many cloud processes, including contact nucleation. Another limitation of
these bulk analytical methods lies in the aerosol type. Since each technique
relies on certain property of the aerosol particles (such as fluorescence,
radioactivity or atomic absorption), these experiments were restricted to a
specific particle type exhibiting that property. These constraints often
limit the atmospheric applicability of the results.
Theoretical calculations of CE in a cloud environment have been the subject
of many studies, driven by the necessity to explain aspects of both warm and
cold precipitations. An experimental validation of the theoretical knowledge
related to CE, particularly for droplet–aerosol collisions, is difficult and
far from complete (Ladino, 2011). According to Santachiara et al. (2012),
significant discrepancies between theoretical and experimental studies have
been found for sub-micrometer particles in the “Greenfield gap”, and the
measured values can be 1 to 2 orders of magnitude higher than predicted.
According to Wang et al. (2010), this disagreement could be because some
physical processes considered in theoretical models are neglected, difficult
to represent or hard to control in experimental studies.
The goal of this study was to determine the CE of sub-micrometer aerosol
particles by cloud droplets. This study was conducted on a single-droplet
basis with sensitivity to one or more collection events.
Experimental methods
Experimental setup
The CE experiments were performed in the new Massachusetts Institute of
Technology Collection Efficiency Chamber (MIT-CEC). A schematic of the system
is shown in Fig. 2. Aerosol particles and droplets were generated and
separately passed into the MIT-CEC chamber, where they could fall, in a
0.48 L m-1 flow, and interact in the laminar flow environment of the
chamber. Condensed-phase water was removed in dryers after the chamber, and
the flow containing aerosol particles and droplet residuals was directed to
the Particle Analysis by Laser Mass Spectrometry (PALMS) instrument for
single-particle analysis.
Experimental setup. DGN denotes the droplet generation and neutralizer unit.
Additional description is provided in the text.
Polystyrene latex (PSL) spheres with radius 0.025, 0.125, 0.25 and
0.475 µm were used in the experiments. PSL spheres were wet generated
using a Brechtel Manufacturing Inc. (BMI, Hayward, CA) model 9203 aerosol
generation system. Condensed-phase water was removed by in-line dryers. Large
particle (diameter < 0.35 µm) and residual concentrations were
measured by an optical particle sizer (OPS; TSI Inc., Shoreview, MN, model
3330). Particles below diameter of 0.35 µm were measured using a
scanning mobility particle sizer (SMPS) consisting of a differential mobility
analyzer (DMA; BMI Inc., model 2002) and a condensation particle counter
(CPC; BMI Inc., MCPC model 1710).
Similar concentrations were observed in the overlapping sensitivity region of
both instruments. Two aerosol concentrations were used in the experiments: 50
and 100 cm-3. Particle losses were calculated by measuring the particle
concentration at the entrance and at the bottom of the chamber (i.e., before
PALMS). Particle losses were 14 ± 10 %.
After the particles were generated, but before they entered the chamber, the
particle flow either passed directly over an RH sensor (Omega EE08) in a
low-RH experiment or through a humidifier and then over the RH sensor in a
high-RH experiment. The humidifier, a glass container with a volume of 9 L containing Milli-Q 18.2 MΩ cm water, was used to increase the RH of the airflow to 88 ± 3 %. Two additional RH sensors were
placed at the chamber top and bottom to monitor the temperatures and RH
profiles. Valves were placed in line to either block or admit particles
depending on the experimental phase described in the following paragraphs.
The overall length of the MIT-CEC is 160 cm. The chamber was constructed of
glass with stainless steel and aluminum ports for connections to the dryers,
aerosol and droplet inputs. The upper part of the chamber, termed the droplet
generator and neutralizer (DGN) unit, is a 21 cm long, 5 cm diameter
stainless steel cylinder. This section contains a commercial droplet
generator, a charge neutralizer, and ports for aerosol injection. A mesh grid
is used to straighten the particle flow. Droplets are injected vertically
downward through a tube to avoid contact with the aerosol particles until the
lower portion of the DGN. A neutralizer, containing two polonium-210 strips
(0.64 cm thickness and 15 cm long), is placed in the lower part of the DGN.
The lower part of the DGN is connected directly to the main chamber, a
single-jacketed glass column with an inner diameter of 5 cm. The length of
the jacketed area is 140 cm. An aluminum cone reducer, 4 cm in length, is
attached to the bottom of the main chamber in order to focus the flow into a
variable length dryer used for condensed-phase water removal prior to
analysis with PALMS.
A Microdrop Technologies dispenser system (Microdrop Technologies,
Norderstedt, Germany, model MD-K-130) was used to generate droplets. This
droplet generator (DG), based on piezo-driven inkjet printing technology,
generates droplets with an average radius of 21.6 ± 0.8 µm. A
Microdrop CCD camera (model MD-O-538-85) and imaging system, with a total
magnification of 120×, was used to determine droplet size on a daily
basis before the generator was set atop the chamber. The size differed
slightly for the low- and high-RH experiments, 21.9 and 21.4 µm,
respectively. Due to the position of the camera, droplet size could not be
monitored during an experiment or within the chamber. Droplet size was,
however, measured before and after the experiment, and the size was constant
within the quoted uncertainty. Droplet size during experiments was also
verified by the residual size after the droplets evaporated. Droplets were
generated at 30 Hz. This is a frequency much lower than previously used in
other experimental works using cloud droplets (e.g., 1000 Hz in Ladino et
al., 2011) where analysis was performed on a bulk basis. This rate yielded
both a collection signal with PALMS and minimized possible droplet-droplet
collisions inside the chamber.
As mentioned in the previous section, droplet and aerosol charge affect
electro-scavenging forces and can therefore impact the collection rate. To
determine the droplet charge, we utilized an electrometer (Liu and Pui, 1974)
which was connected to the DG. Using the electrometer, we determined that
∼ 104 elementary charges are imparted to each droplet upon
production from the generator. The neutralizer reduces this charge to
400 ± 400 elementary charges. Aerosol charge distribution was assumed
to be a Boltzmann distribution after neutralization where the most common
charge state other than neutral is a single charge (Wiedensohler, 1988;
Hinds, 1999).
The droplets were produced from a dilute ammonium sulfate
((NH4)2SO4; hereafter AS) solution, 0.08 g L-1. Dilute AS
was used due to its atmospheric relevance as a condensation nucleus and in
order to provide a chemically distinct signature for detection of droplet
residuals with PALMS. Based on the original droplet size and solution
concentration, and as verified by PALMS sizing, a single effloresced residual
was 0.75 µm radius.
Mass spectra of a PSL particle (a), an evaporated droplet
composed of dilute AS, termed a droplet residual (b), and a coagulated
and evaporated droplet that contained both a PSL particle and residual AS (c).
The PALMS instrument determines size and chemical composition of a
single-particle basis. A detailed description of the PALMS instrument has
been published previously (Murphy and Thomson, 1995; Cziczo et al., 2006). In
brief, particles enter an aerodynamic inlet, which focuses the particle
stream. The particles then pass through two 532 nm Nd:YAG laser beams, yielding scattering signals that are used to trigger an excimer laser beam (193 nm). The time difference between the two scattering signals provides an
aerodynamic size of the particle (Cziczo et al., 2006). The excimer laser
ablates and ionizes the particle. The ions from each detected particle are
ejected into a reflectron mass spectrometer and detected on a micro-channel
plate (MCP), thus providing a mass spectrum of the particle.
Data analysis
Droplet residuals, PSL particles and coagulated droplets had distinct sizes
and mass spectrum (Fig. 3). In positive ion mode, PSL particles had distinct
signatures of their carbon chains at mass-to-charge ratio
(m/z) 12
(C1), 24 (C2), 36 (C3) and 48 (C4); in many cases the
carbons were associated with hydrogen. Droplet residuals had a signature at
m/z 18 (NH4) and 30 (NO). It should be noted that the PSL spheres did not
contain the droplet signature, nor did the droplets contain a PSL signature.
Coagulated droplets, on the other hand, exhibited mass spectra with
signatures from both the droplet residuals and the PSL particles (Fig. 3c).
In order to determine the presence or absence of a collection event, a
coagulation index (CI) was developed:
CI=carbonsignalammoniumsulfatesignal.
Each experiment started by passing only droplets through the chamber. This
allowed for a reference case of maximum CI without collection based on
> 1000 droplets analyzed. After the reference spectra were obtained,
aerosol particles were added to the chamber by opening the in-line valves.
Each collection experiment contained at least 1000 analyzed droplets with a
CI value greater than the baseline obtained from the droplet-only phase. CI
for each droplet during a typical experiment is plotted in Fig. 4. The
leftmost data comprise the baseline CI, in this case for > 2500 droplets. The
collection experiment is on the right where five collection events were
observed. Using these data, an experimental collection ratio (ECR) was
calculated:
ECR=numberofdropletsthatcoagulatedtotalnumberofdroplets.
For this experiment, 5 out of the 1189 droplets experienced collection,
yielding an ECR of 4.2 × 10-3. It should be noted that an
experiment of PSL with AS residual (from the evaporated droplet) was
performed. Several thousand spectra were examined with PALMS but no
collection event was observed.
A CE value, normalized by the number of particles contained within the
volume swept out by a falling droplet, was also calculated. This calculation
takes into account a droplet's cross section, the aerosol concentration, and
the effective interaction length of the chamber so that comparisons can be
drawn between these data and previous experiments:
CE=ECRπ(Rd+Ra)2LAc,
where Rd is the droplet radius; Ra is the aerosol radius;
Ac is the aerosol number concentration and L is the effective
interaction length of the chamber; which defined as
L=Vd⋅lVd+Va,
where Vd and Va are the droplet terminal (settling)
velocity and the velocity of the air carrying the particles, respectively,
and l is the length of the chamber before the droplets evaporate.
Theoretical CE models
Previous studies have theoretically determined the CE between droplets and
aerosol particles (Slinn and Shen, 1970; Beard, 1974; Grover et al., 1977;
Davenport and Peters, 1978; Wang et al., 1978; Park et al., 2005; Tinsley et
al., 2000, 2006; Chate, 2005; Andronache et al., 2006; Feng, 2007; Croft et
al., 2009; Tinsley, 2010; Wang et al., 2010; Tinsley and Leddon, 2013). In
order to understand our experimental data, we compare them to a theoretical
treatment of CE. This treatment includes Brownian diffusion, interception,
inertial impaction, thermophoresis, diffusiophoresis and electro-scavenging.
The total CE is the sum of these processes. The CE due to Brownian diffusion,
interception and inertial impaction are based on Park et al. (2005), which
expands on Jung and Lee (1998). Thermophoresis, diffusiophoresis and
electro-scavenging are based on Wang et al. (2010), which expands on
Andronache et al. (2006) and Davenport and Peters (1978). The efficiencies
used here are
EBdiff=2π34Pe2/31-∝3μwμa+41-65∝1/3+15∝2+μwμa1-95∝1/3+15∝2+∝1/3,
Eint=1-∝1-65∝1/3+15∝2+μwμa1-95∝1/3+15∝2+∝Da/Dd1+Da/Dd+12Da/Dd1+Da/Dd23μwμa+4,Eimp=StkStk+0.352,
Eth=42CcKa+5λDdKpKa5P1+6λDd2Ka+Kp+10λDdKp2+0.6Re1/2Pr1/3Ta-TdDdVd,
Definition of acronyms and relevant units.
Parameter
Definitions
Units
Cc
Cunningham slip correction factor
[–]
CE
Collection efficiency
[–]
Da
Aerosol particle diameter
[m]
Dd
Droplet diameter
[m]
Dw
Diffusivity of water vapor
[m2 s-1]
EBdiff
Brownian diffusion efficiency
[–]
ECR
Experimental collection ratio
[–]
Eec
Electric charge efficiency
[–]
Edf
Diffusiophoresis efficiency
[–]
Eimp
Inertial impaction efficiency
[–]
Eint
Interception efficiency
[–]
Eth
Thermophoresis efficiency
[–]
Ka
Thermal conductivity of moist air
[kg m s-3 K-1]
Kp
Thermal conductivity of particles
[kg m s-3 K-1]
Ma
Molecular weight of air
[kg mol-1]
kec
K constant for Eec calculations equal to 9 × 109
[nm2 C-2]
Mw
Molecular weight of water
[kg mol-1]
P
Atmospheric pressure
[Pa]
Pe
Peclet number
[–]
Pr
Prandtl number of air
[–]
qr
Mean charge on aerosol particles
[Coulomb, C]
Qr
Mean charge on droplets
[Coulomb, C]
Ra
Aerosol radius
[m]
Rd
Droplet radius
[m]
Re
Reynolds number
[–]
Stk
Stokes number
[–]
Ta
Temperature of air
[K]
Td
Temperature at droplet surface
[K]
Vd
Droplet terminal velocity
[m s-1]
μw
Water viscosity
[kg m-1 s-1]
μa
Air viscosity
[kg m-1 s-1]
ρa
Water vapor of water at air temperature
[Pa]
ρd
Water vapor of water temperature at droplet surface
[Pa]
λ
Mean free-path length of air molecules
[m]
∝
Packing density of drops
[m3]
Edf=4TaDwPMwMa1/22+0.6Re1/2Pr1/3ρa-ρdTa-TdDdVd,
Eec=16CckecQrqr3πμaDp2DaVd,
where EBdiff, Eint, Eimp, Eth,
Edf and Ees are Brownian diffusion, interception,
inertial impaction, thermophoresis, diffusiophoresis and electro-scavenging
efficiencies, respectively. A full definition of all variables is provided in
Table 2. These theoretical models include the known forces that affect CE
values and which were measured or constrained by data in the experimental
measurements presented here. It should be noted that, although these
theoretical models were developed for large droplets, they have been used to
calculate CE for sizes relevant to this work (Ladino, 2011).
Particle size and concentration, RH, droplet size and total
analyzed and experimental collection ratio (ECR; see text for details) for
this study.
Experiment
Particle
Particle
RH
Droplet
Total
ECR
radius
concentration
(%)
radius
number of
(µm)
(cm-3)
(µm)
droplets
1
0.025 ± 0.005
48 ± 3
11
20.0 ± 2.2
1966
2.4 × 10-3
2
0.025 ± 0.005
96 ± 8
11
20.0 ± 2.2
2578
8.6 × 10-3
3
0.025 ± 0.005
56 ± 13
85 ± 1
22.2 ± 2.2
3778
1.5 × 10-3
4
0.025 ± 0.005
100 ± 6
83
22.2 ± 2.2
2446
1.6 × 10-3
5
0.125 ± 0.01
49 ± 5
13 ± 2
22.2 ± 2.2
1923
2.0 × 10-3
6
0.125 ± 0.01
88 ± 20
15 ± 1
22.2 ± 2.2
2025
4.9 × 10-3
7
0.125 ± 0.01
50 ± 3
87
22.2 ± 2.2
4598
2.6 × 10-3
8
0.125 ± 0.01
102 ± 9
88
22.2 ± 2.2
2831
2.5 × 10-3
9
0.25 ± 0.02
49 ± 2
17 ± 1
21.7 ± 0.8
1039
6.5 × 10-4
10
0.25 ± 0.02
92 ± 4
16 ± 1
21.7 ± 0.8
3282
1.9 × 10-3
11
0.25 ± 0.02
51 ± 2
94 ± 3
22.2 ± 2.9
1530
9.6 × 10-4
12
0.25 ± 0.02
101 ± 18
90 ± 3
22.2 ± 2.9
1554
3.0 × 10-3
13
0.475 ± 0.02
52 ± 3
17
21.7 ± 0.8
1050
1.4 × 10-3
14
0.475 ± 0.02
98 ± 11
20 ± 3
21.7 ± 0.8
1232
2.9 × 10-3
15
0.475 ± 0.02
48 ± 10
87 ± 2
20.9 ± 0.9
1473
1.9 × 10-3
16
0.475 ± 0.02
99 ± 16
88 ± 1
20.9 ± 0.9
1049
4.9 × 10-3
Result and discussion
A total of 16 collection experiments were performed. The collection
experiments were for four different aerosol sizes (with radius 0.025, 0.125,
0.25 and 0.475 µm), each at two different concentrations (50 and
100 cm-3) and two different RH conditions (15 ± 3 and
88 ± 3 %). A full description of the experiments is summarized in
Table 3. All experiments were conducted at room temperature
(22.5 ± 1.3 ∘C). Droplet radius was
21.6 ± 0.8 µm. Terminal (settling) velocity was calculated
based on the experimental temperature and droplet size. The terminal velocity
varied from 4.7 to 5.8 cm s-1. Total droplet evaporation time (i.e.,
residence in the generator section and experimental chamber) was calculated
based on the average droplet size and the RH condition: 2.1 and 16.6 s for
the low- and high-RH cases, respectively. The droplets' residence time in the
chamber was 0.7 and 6.1 s, for the low- and high-RH cases, respectively.
Calculations of Reynolds numbers were performed using the experimental
conditions and chamber geometry. Reynolds numbers from 0.12 to 0.16 were
calculated and, based on this, we assume the aerosol particles and droplets
interact in flow conditions close to laminar throughout the chamber.
Each collection experiment incorporated between 1039 and 4598 droplets. The
droplets that coagulated were identified based on their CI as described in
Sect. 2.2. ECRs were based on the ratio between the number of coagulated
droplets to the total number of droplets per experiment and these values
varied from 6.5 × 10-4 to 8.6 × 10-3 for the low-RH experiments and from 9.6 × 10-4 to 4.9 × 10-3
for the high-RH experiments. The ECR was higher for the higher aerosol
concentration experiments for most particles sizes; this is consistent with
higher aerosol concentration increasing the chances for particles to
coagulate with droplets.
Coagulation index (CI), the ratio of PSL (aerosol) to AS (droplet
residual) signal in a mass spectrum, for a typical experiment. In this
experiment the RH was 15 %, droplet radius was 20 µm, and PSL
particles were 0.125 µm radius with a concentration of
100 cm-3. The x axis represents the sequential analysis of single
droplet residuals over the course of the experiment. Particles which exceed
the ratio found when only droplets are analyzed (dashed line; the “droplets
only” data acquired at the start of each experiment) are considered
collection events. There are five collection events during this experimental
period.
CE value was calculated for each experiment, based on the average droplet
size measured from each experiment and when similar RH, aerosol size and
concentration conditions were used. CE values, normalized to aerosol
concentration and time, ranged from 2.0 × 10-1 to 1.6 for the
low-RH experiments and from 1.5 × 10-2 to
9.0 × 10-2 for the high-RH experiments (see Fig. 5). These
values are in a similar range to that found by previous works (Wang and
Pruppacher, 1977; Lai et al., 1978). As shown in Fig. 5, no significant
difference in CE values between the two aerosol concentrations (50 and
100 cm-3) was observed. Most previous experiments did not specify what
aerosol concentration were used during their collection experiments (Hampl et
al., 1971; Lai et al., 1978; Prodi et al., 2014). Those that did specify had a
higher aerosol concentration, in most cases above atmospheric relevance
except within polluted boundary layers (above 1000 cm-3; Beard, 1974;
Wang and Pruppacher, 1977; Barlow and Latham, 1983; Deshler, 1985; Ladino et
al., 2011). The use of these high aerosol concentrations was likely due to
the limitation of bulk analysis methods, as discussed in the Introduction,
which required a high concentration for adequate signal.
CE calculated as a function of particle radius. Shapes represent
different aerosol concentrations. CE error bars are based on droplet size,
aerosol size and aerosol number concentration measured from each experiment
as described in Eq. (3). (a) Low-RH experiments.
(b) High-RH experiments.
It has been shown theoretically by Wang et al. (1978), Grover and
Pruppacher (1985) and Ladino et al. (2011), and experimentally by Grover et
al. (1977), that CE increases with decreasing RH. This is because a lower RH
leads to an increase in the evaporation rate of the droplet, which
strengthens the phoretic forces. Two RH conditions were measured in this
experimental work: low (15 ± 3 %) and high (88 ± 3 %).
Consistent with these previous works, we find a higher CE values for the low-RH experiments, by as much as 1 order of magnitude, when compared to
otherwise similar high-RH experiments.
In previous experimental studies of collection, many considered
significantly larger droplets (of drizzle or rain size; Leong et al., 1982;
Pranesha and Kamra, 1993; Chate and Kamra, 1997) and particle sizes
(super-micrometer; Owe Berg et al., 1970; Hampl and Kerker, 1972). For these
reasons, we do not believe a direct comparison to our data is valid. This
lack of comparison holds for other studies using aerosol in a similar size
range but with much larger droplets (Hampl et al., 1971; Deshler, 1985; Vohl
et al., 2001). The droplets used in the current work were significantly
smaller, > 15 times, than those used in the aforementioned experiments.
Those studies reported lower CE values than measured here, in some cases by
an order of magnitude. It has been shown in previous experimental and
theoretical studies that the CE decreases with increasing droplet size
(Davenport and Peters, 1978; Wang et al., 1978; Leong et al., 1982; Pranesha
and Kamra, 1993). It is likely that some of the differences in CE are also a
result of different experimental conditions, such as droplets and/or particle
charge.
Comparison of CE from this study to previous experimental work.
(a) Low-RH experiments. (b) High-RH experiments. Shapes
(squares and triangles) represent different aerosol concentrations. Diamond
shapes represent previous experimental work. Black diamonds are from
Ladino et al. (2011), with RH 88 ± 2 %, aerosol concentration
2000 cm-3 and droplet size of 12.8–20.0 µm. Brown diamonds
are from Wang and Pruppacher (1977), with RH of 23 ± 2 %,
aerosol concentration of about 1017 cm-3 and droplet size of
170–340 µm. Pink diamonds are from Lai et al. (1978), with 620 µm droplets and no information regarding the RH or aerosol concentration.
Two experimental studies, Wang and Pruppacher (1977) and Lai et al. (1978),
are roughly similar to our study, and both exhibit CE values slightly lower
than the values from our measurements. A comparison is provided in Fig. 6.
The differences in CE values could be a result of the different experimental
conditions. For example, Wang and Pruppacher (1977) and Lai et al. (1978)
used somewhat larger droplets (of 170–340 and 620 µm,
respectively), with higher charges than those used in the current work,
5 × 105–7.1 × 106 elementary charges in Wang and
Pruppacher (1977) and 6.6 × 108–1.9 × 109
elementary charges in Lai et al. (1978). The larger droplets and higher
droplet charges used by Wang and Pruppacher (1977) and by Lai et al. (1978)
could explain the differences between these works and ours, as will be
discussed further in subsequent sections. Lai et al. (1978) did not mention
the aerosol concentrations or RH conditions used in their work. Wang and
Pruppacher (1977) used an RH condition similar to the low RH used in this
study but with higher aerosol concentrations. It is expected that a higher
aerosol concentration will increase the chance of collision between particles
and droplets, which will increase the value of the ECR, but will not affect CE,
which is normalized.
Theoretical CE and the individual contribution of each force.
Calculation details are provided in the text. Experimental conditions of 400
elementary charges per droplet and one elementary charge per particle are
used for a variable aerosol size, a droplet radius of 21.6 µm, an RH
of 50 % and room temperature.
CE values for 50 % RH and 400 elementary charges per droplets
with different particles elementary charge for a droplet radius of
21.6 µm and room temperature.
Comparison of CE experimentally determined in this study (points)
with theoretical calculations (lines) where the charge number is elementary
charge units per droplet (i.e., the lines span the range of measured droplet
charge) and particles are singly charged.
CE as a function of particle radius at low and high RH (a and
b, respectively). CE experimentally determined in this study (points) with
theoretical calculations (lines). The lines represent calculation with
different droplet sizes: the measured droplet size (brown), droplets with
half the volume (green) and 5 µm droplets (black). See text for
details.
CE as a function of particle radius under high-RH conditions. CE
experimentally determined in this study (points) with theoretical
calculations (lines), where the charge number is in elementary charge units
per droplet. Black lines are for CE of 200 µm droplet size and red
for 20 µm droplet size.
The most similar experimental conditions to ours are those of Ladino et
al. (2011). Ladino et al. (2011) used similar droplet (radius of
12.8–20 µm) and particle sizes (radius of
0.05–0.33 µm). Experiments were conducted under RH conditions similar
to our high-RH experiments (88 ± 2 %). Although most of the
experimental conditions were similar, there are noteworthy differences
between the CE values of Ladino et al. and those measured in this study,
which are lower overall (Fig. 6). The main difference between the two studies
is the droplet charge, which has a stronger impact on the electro-scavenging
force. Ladino et al. (2011) used droplets with high charges,
5 × 104 elementary charges per droplet (Claudia Marcolli,
personal communication, 2014), which are 2 orders of magnitude higher than
the one used in this study. The higher droplet charge explains the higher CE
values compared to those determined in this study.
In order to compare our experimental work with theoretical studies, a set of
calculations combining six different forces, as described in Sect. 2.3, was
conducted. Examples of theoretical forces and CE are given in Fig. 7. The
properties used in these calculations included an air temperature of
22.5 ∘C, a pressure of 981 mbar, RH of 50 %, PSL particles with a
density of 1000 kg m-3 of different sizes matching the experiments, a
thermal conductivity of 0.1 kg m s-3 K-1 (Romay et al., 1998),
and a constant droplet radius of 21.6 µm. Droplets were assumed to
have 400 elementary charges, the average value determined by the electrometer
experiments (see Sect. 2.1). These calculations were made for charged
particles that contained one elementary charge per particle. Most particles
in a Boltzmann distribution contain no charges and will therefore not be
affected by electro-scavenging forces. The most common charge state other
than neutral is a single charge, about 10 % of particles, and this forms
the basis of our calculation (Hinds, 1999). This is further supported by a
decreasing effect of multiple charges when considering the effect on CE
(Fig. 8).
As can be seen in Fig. 7, the total CE varies for different particle sizes.
The contribution of Brownian diffusion decreases rapidly as particle size
increases, while the contribution of inertial impaction increases rapidly as
particle size increases. Interception forces also increase as particle size
increases, but the effect is smaller than that of inertial impaction. The
contribution of diffusiophoresis is smaller than that of thermophoresis for
particles below 0.05 µm. The Greenfield gap is evident in this figure as the local minimum between the diffusion- and impaction-dominated regimes. This corresponds
to a minimum at a particle size of 0.15 µm. In Fig. 7,
electro-scavenging have a significant impact on the curves. Previous work by
Wang et al. (1978), Byrne and Jennings (1993) and Tinsley et al. (2000) shows
the presence of charge on droplets and aerosol can increase the CE throughout
the Greenfield gap. Moreover, as described by Tinsley et al. (2001), the
electrical effect is more important for smaller particle sizes
(< 0.1 µm) than Brownian diffusion. This could explain why the
Greenfield gap is highly pronounced in the data in Fig. 6, while it is more
pronounced in the data of Lai et al. (1978) and Ladino et al. (2011).
In order to directly compare theoretical and measured CE, two cases were
calculated: (1) droplet radius 21.4 µm and low RH and
(2) 21.9 µm and high RH. In both calculations the range of values determined in the electrometer experiments, i.e., 0, 400 and 800 elementary charges per droplet, was used. The result of this comparison is shown in Fig. 9, where the
points represent the experimental work and the lines represent the
theoretical CE. Overall, the experimental work presents higher CE values
compared to the theoretical CE. Differences between theoretical and measured
CE may be considered a result of conditions not modeled theoretically or
difficult to constrain experimentally. Possibilities include rare multiply
charged particles, aerosol droplet electric interactions that are not fully
considered (such as the induced dipole force), the evaporation rate of the
droplets, variable terminal settling velocity due to changes in droplet size,
and the presence of solute in the droplets.
As noted earlier, the droplets evaporated completely while in the chamber
in both RH conditions. Since droplet size could not be determined precisely at
the moment when collection occurred in the chamber, calculations of
theoretical CE were performed for three relevant droplet sizes. The first
was the original droplet size as measured from the droplet generator (21.4
and 21.9 µm, for low- and high-RH conditions, respectively) for the
full droplet lifetime. The second was the droplet size with half the volume of the
original droplet (radius of 17 and 17.4 µm, for low- and high-RH
conditions, respectively) over the full lifetime. For the third, an extreme
case was considered: droplets with a radius of 5 µm for the full
droplet lifetime. The results of these calculations are presented in Fig. 10.
Overall, as droplet size decreases, CE values increase. In the extreme
5 µm case, CE values increases by more than an order of magnitude.
For the low-RH case the best agreement is with the 5 µm case, which
logically follows from the rapid evaporation of these droplets. In the high-RH case the experimental CE values fall nearest the half-volume case, which
again logically follows since these droplets more slowly evaporate.
It is known that droplets carrying higher electric charge have higher CE
(Barlow and Latham, 1983; Byrne and Jennings, 1993; Pranesha and Kamra,
1997a, b; Tinsley and Leddon, 2013; Tinsley et al., 2000; Tinsley, 2010), and
this is consistent with our data in Fig. 9. Droplet size also affects CE,
where smaller droplets have higher CE values (Lai et al., 1978; Pranesha and
Kamra, 1996). Figure 11 shows a calculation of CE based on different droplet
charges and sizes. Two droplet sizes were used: 20 µm, which is
similar to the size used in this study and by Ladino et al. (2011), and
200 µm, which is the size used by Wang and Pruppacher (1977). Three
different droplet charges were considered: 400 elementary charges, as used in
this study; 5 × 104 elementary charges, as used by Ladino et
al. (2011); and 5 × 105 elementary charges, the lower limit of
charges used by Wang and Pruppacher (1977). As shown in Fig. 11, CE values
increase as droplet charge increases. Droplet size and charge conditions can
counteract each other in the case of larger droplets (lower CE) with higher
charge (higher CE). We suggest this may explain the agreement found between
the CE values measured in this study and those of Wang and Pruppacher (1977)
and the disagreement between our values and those of Ladino et al. (2011). It
should be noted that the experimental CE values fall within the region of the
20 µm case. The CE values of the small particles
(< 0.1 µm) match the theoretical CE, while for larger particles
(> 0.1 µm) they are slightly higher. These differences could be
a result of some conditions not modeled theoretically or conditions difficult
to constrain experimentally, as discussed above.