ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-4159-2017Experimental evidence of the rear capture of aerosol particles by
raindropsLemaitrePascalpascal.lemaitre@irsn.frQuerelArnaudMonierMarieMenardThibaultPorcheronEmmanuelFlossmannAndrea I.https://orcid.org/0000-0002-4484-6425Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SCA, LPMA, Gif-sur-Yvette, FranceInstitut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-CRI, SESUC, BMCA, Fontenay-aux-Roses, FranceClermont Université, Université Blaise Pascal, Laboratoire de Météorologie Physique, Clermont-Ferrand, FranceCNRS, INSU, UMR6016, LaMP, Aubière, FranceCNRS UMR6614, CORIA Rouen, Site Universitaire du Madrillet, Saint-Étienne-du-Rouvray, Francecurrently at: Strathom Energie, Paris, FrancePascal Lemaitre (pascal.lemaitre@irsn.fr)28March2017176415941761December20165January20174March20177March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/17/4159/2017/acp-17-4159-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/4159/2017/acp-17-4159-2017.pdf
This article presents new measurements of the efficiency
with which aerosol particles of accumulation mode size are collected by a
1.25 mm sized raindrop. These laboratory measurements provide the link to
reconcile the scavenging coefficients obtained from theoretical approaches
with those from experimental studies. We provide here experimental proof of
the rear capture mechanism in the flow around drops, which has a fundamental
effect on submicroscopic particles. These experiments thus confirm the
efficiencies theoretically simulated by Beard (1974). Finally, we propose a
semi-analytical expression to take into account this essential mechanism to
calculate the collection efficiency for drops within the rain size range.
Introduction
Aerosol particles are important components of the atmosphere. They
contribute significantly to the Earth's energy budget by interacting with
solar radiation directly as well as indirectly by serving as precursors to
cloud formation (cloud condensation nuclei – CCN) which also will interact
with this radiation (Twomey, 1974). Furthermore, the physical properties of
these particles in suspension within the atmosphere (size, concentration,
affinity for water, etc.) are essential parameters for characterising air
quality. For these reasons, the scientific community has actively studied
the physics of atmospheric aerosol particles.
There are several aerosol particles origins. The primary natural sources are sea
spray, wind-driven dust, volcanic eruptions and human activities. The
secondary sources are associated with the gas-to-particle conversion of
certain gases present in the atmosphere. The size of these particles greatly
varies and ranges from 1 nm to several hundred microns. Particles
of anthropogenic origin represent an increasingly large proportion of
aerosol particles in the atmosphere (Charlson et al., 1992; Wang
et al., 2014). Among all anthropogenic pollutants, radioactive
releases from a nuclear accident are of high risk for both humans and
the environment. Just like all other particles, once emitted, radioactive
particles undergo physical processes that drastically change their size
distribution during their transport in the atmosphere. Ultrafine particles
are very sensitive to Brownian diffusion and grow by coagulation. Large
particles settle on the ground due to gravity. Hence, there is a particle
size range that has no efficient removal process and a very long
atmospheric residence time. This size range is referred to as the
accumulation mode (Whitby, 1973) and comprises particles with a diameter
between 0.1 and 2 µm. These particles can remain in the
upper troposphere for several months (Jaenicke, 1988) and can be transported
over long distances, crossing oceans and continents (Pruppacher et al., 1998).
The accumulation of particles within this size range is essentially limited
by two atmospheric processes: in-cloud scavenging (rainout) and below-cloud
scavenging (washout) during rainfall events. Thus, in the event of a nuclear
accident with a release of radioactive aerosol particles, it is essential to
correctly model both of these mechanisms in order to predict their number
concentration within the troposphere as well as the ground contamination.
This study focuses on the below-cloud scavenging of aerosol particles by
rain with a microphysical approach. We aim to measure, in a laboratory setting, the
collection efficiency of the aerosol particles constituting the accumulation
mode, by drops of a size representative of rain. Recent measurements with 2 mm drops (Quérel et al., 2014b) have shown that, for
submicron particles, the collection efficiency increases very rapidly when
the size of the particles is reduced. The Slinn (1977) model does not
reproduce this increase in efficiency, leading to errors of several orders
of magnitude for the collection efficiency. We impute this discrepancy to
the key hypothesis of the Slinn model which assumes Stokes flow conditions
around the drop. Yet, since the Reynolds number of a 2 mm drop at its
terminal velocity is approximately 800, this assumption of Stokes flow is
unjustified. This model nonetheless remains the most common in the
literature mainly because it is easy to use.
Quérel et al. (2014b) showed that the Beard (1974) model was
the only one to predict this increase in the collection efficiency for
submicron aerosol particles. However, direct measurements in the drop size
range simulated by Beard (1974) could not be performed; the only comparison
results from a linear extrapolation of theoretical computations to the
measured size range. These efficiencies compared reasonably well even for
aerosol particles in the submicron range. But the linear extrapolation is
not completely satisfactory for an experimental validation of this model.
This article provides experimental evidence of the robustness of
Beard's simulation for the raindrop sizes under investigation in his paper,
i.e. for diameters between 0.28 and 1.25 mm.
Our paper is divided into three sections. First, we present a theoretical
description of aerosol scavenging by rain. We then present our experimental
setup and the associated experimental results. Finally, we compare our
measurement results with the outcomes of the models of Beard (1974) and
Slinn (1977) in order to propose a semi-empirical correlation for
calculating the elementary collection efficiency associated with rear
capture.
Theoretical description of washout
At mesoscale, the scavenging of aerosol particles by rain is described by
the scavenging coefficient λ. This
parameter is defined as the fraction of particles of diameter dap
captured by the raindrops per unit of time (Eq. 1). In this equation,
C(dap) is the concentration of aerosol particles of diameter dap
in suspension in air per unit of volume.
dC(dap)C(dap)=-λraindapdt
This parameter is essential for predicting air quality (Chate, 2005) and
ground contamination following a nuclear accident with release of
radionuclides into the environment (Groëll et al., 2014; Quérel et
al., 2015). There are several approaches for determining this parameter. It
can either be determined theoretically by solving Eq. (2) (Flossmann,
1986; Mircea and Stefan, 1998; Mircea et al., 2000) or measured in the environment by
monitoring the variation of particulate concentration in the atmosphere
during precipitation (Volken and Schumann, 1993; Laakso et al., 2003;
Chate, 2005; Depuydt, 2013).
λraindap,Ddrop is defined by
λraindap,Ddrop=∫Ddrop=0∞πDdrop24⋅U∞DdropEdapDdrop,RHNDdropdDdrop,
where Ddrop is the drop diameter, U∞Ddrop is the terminal fall velocity, NDdropdDdrop
is the number concentration of drops with a diameter between
Ddrop and Ddrop+dDdrop during the rainfall
event, and Edap,Ddrop,RH is the collection efficiency for
a given drop size, particle size (dap) and relative humidity
(RH).
Unfortunately, these two approaches yield λrain values that
differ by several orders of magnitude, in particular for submicron particles
(Laakso et al., 2003). It is clear, when we examine Eqs. (1)
and (2), that each of the two methods has advantages and significant
limitations, which are also highlighted by the authors. The main limitation
for measurement of the scavenging coefficient in the environment remains the
assumption that the change in concentration is exclusively related to
collection by the drops. Even if the rainfall events are methodically
selected, it is difficult to completely neglect advection, turbulent
transport, coagulation and the influence of the hygroscopic behaviour of
particle (Flossmann, 1991). For example, Quérel et al. (2014a) have
recently shown that, during convective episodes, downdraft was
the main cause of the reduction in particulate concentration, well before
collection by the drops.
For the theoretical approach, the main limitation is the requirement to know
the collection efficiency (Eq. 3). This microphysical parameter is
defined as the ratio between the effective collection area (in other words,
the cross-sectional area inside which the particle trajectory is intercepted
by the drop) and the cross-sectional area of the drop. It is equivalent to
defining the ratio of the mass of particles (of a given diameter) collected
by the drop over the mass of particles (of the same diameter) within the
volume swept by a sphere of equivalent volume (Eq. 3).
Edap,Ddrop,RH=mAP,collecteddAPmAP,sweptdAP
To compute this efficiency, one has to describe and model all the processes
involved in the collection of particles by falling raindrops. Several
mechanisms are usually considered, which are summarised hereafter; however,
a more exhaustive review can be found in the literature (Pruppacher
et al., 1998; Chate, 2005; Ladino et al., 2013;
Ardon-Dryer et al., 2015). The three main mechanisms leading to
this collection are Brownian motion, inertial impaction and interception.
Small particles, with a radius on the order of the mean free path of the air
molecules or smaller, are very sensitive to the collision of air molecules.
Therefore, they shall deviate from streamlines due to Brownian motion. For
large particles, with a diameter greater than 1 µm, their inertia
prevents them from following the streamlines of the flow and they impact the
drop on its leading edge. Aerosol particles with a diameter smaller than 1 µm and much larger than the mean free path of the air molecules
follow the streamlines of the flow around the drop. They might nevertheless
enter in contact with the drop when the streamlines approach the drop at a
distance smaller than the radius of the aerosol particle. For particles with
diameter between 0.2 and 1 µm, there is a minimum
collection efficiency called the “Greenfield gap” (Greenfield, 1957). For
these particles, none of the three described mechanisms are efficient for
collection. It is expected that phoretic forces would be the most efficient
mechanisms. To be thorough, secondary mechanisms for collision are also
described here. Thermophoresis and diffusiophoresis are, respectively, linked
to thermal and water vapour gradients. The side of a particle exposed to
warmer air is impacted by molecules with higher kinetic energy than
molecules impacting the colder side. As a result, thermophoresis results in
a force whose direction is the opposite of the thermal gradient. Similarly,
particles exposed to a water vapour gradient are exposed to molecular
collisions with a dissymmetric kinetic energy since water vapour molecules
are lighter than air molecules. In the atmosphere, diffusiophoresis results
in a force whose direction is the opposite of the water vapour gradient.
Electro-scavenging could also have an important contribution when both
droplet and aerosol particles are electrically charged, resulting in an
attractive (or repulsive) force when they have opposite (or identical)
polarity. Moreover, Tinsley et al. (2000, 2006) theoretically
showed that electrically charged aerosol particles can induce an image
charge on droplets that results in a short-range electrical attraction that
increases collection efficiency even with neutrally charged droplets.
For each of these elementary mechanisms, theoretical expressions of the
elementary collection efficiencies have been derived (Table 1).
References of theoretical expressions for the calculation of each
collection mechanism.
Elementary mechanismReferenceInertial impactionSlinn (1977); Park et al. (2005)InterceptionSlinn (1977); Park et al. (2005)Brownian motionSlinn (1977); Park et al. (2005)DiffusiophoresisWaldmann (1959); Davenport and Peters (1978);Andronache et al. (2006); Wang et al. (2010)ThermophoresisDavenport and Peters (1978); Andronache et al. (2006);Wang et al. (2010)Electro-scavengingDavenport and Peters (1978); Andronache et al. (2006);Wang et al. (2010)Image forcesTinsley and Zhou (2015)
Finally, the droplet total collection efficiency can be theoretically
deduced by adding all these elementary collection efficiencies together. The
use of these theoretical models seems justified for cloud droplets since
they have very small Reynolds numbers. However, for raindrops with larger
sizes and Reynolds numbers, there are many additional uncertainties. This is
because, once they reach their terminal velocity, the Reynolds and Weber
numbers of these large drops are very high. They thus oscillate at high
frequency (Szakáll et al., 2010), which greatly complicates the
simulation of flows inside and outside the drop. Furthermore, the boundary
layer separation in the wake of the drop results in significant
recirculating flows. Therefore, there are currently few methods for
numerically simulating such flows (although the work of Menard et al., 2007, shall be mentioned). The most common approach continues to be to
use the Slinn model (Volken and Schumann, 1993; Laakso et al.,
2003; Chate, 2005; Depuydt, 2013), essentially for its ease of use and
despite its simplifying assumptions. It should be kept in mind that
Slinn models the flow around the drop as a Stokes flow, which results in
ignoring the convective terms of the Navier–Stokes equation. Such flows have
a similar kinematic field to that of a potential flow. The Slinn model
cannot therefore capture the separation of the boundary layer in the wake of
the drop. The flow on the front side of the drop is, however, relatively
well modelled.
Beard and Grover (1974) have developed a numerical model that is more
sophisticated than that of Slinn (1977) to numerically simulate the
collision between particles and a drop. The main difference is that they do
not assume Stokes flow. Flow around the drop is computed by solving the full
Navier–Stokes equation including the convective term. However, Beard and
Grover (1974) made two simplifying assumptions: the drop is assumed
spherical and the flow axisymmetric. These simulations capture the
separation of the boundary layer in the wake of the drop and the resulting
recirculating flows. Using these simulations, Beard (1974) derived the
collision efficiencies between drops and particles of different sizes. For
this, he computed the particle trajectory in the flow considering drag and
gravity forces. For the drag force, they followed the Stokes–Cunningham
expression that takes into account non-continuum effects, which are
important for the smallest particles. These simulations highlight, for the
first time, the capture of submicron-sized particles in the rear of the
drop, due to wake recirculations.
Until recently, no measurements in the numerous experimental studies (Kerker
and Hampl, 1974; Grover et al., 1977; Wang and Pruppacher, 1977a;
Lai et al., 1978; Pranesha and Kamra, 1996; Vohl et al.,
1999) could be used to validate these two models since very few use
submicron particles. Quérel et al. (2014a) showed that, for
their dataset, the Slinn model underestimates by 2 orders of magnitude the
measured collection efficiencies for particles with submicron sizes. As
stated in the introduction, if they concluded that their data could confirm
the Beard model, they were required to extrapolate the simulations of
Beard to confront their observations.
In this paper, the collection efficiency is investigated experimentally for
drops within the size range simulated by Beard (1974) to address these
uncertainties in the collection efficiency of raindrops with large Reynolds
numbers by accurately measuring them in the laboratory with the ultimate aim
of theoretically deriving a scavenging coefficient.
The new BERGAME facility.
Experimental facility
The new experimental facility follows the one described and deployed by
Quérel et al. (2014b). The equipment is called BERGAME (French
abbreviation for a facility to study the aerosol scavenging and measure
collection efficiency).
Presented in detail in the following subsections, the three stages are
(Fig. 1)
a mono-dispersed drop generator,
a free-fall shaft and
an aerosol chamber.
The main changes with respect to Quérel et al. (2014b) concern
the drop generator and the aerosol chamber. Indeed, those authors concluded
that drop generation has to be improved if direct comparisons with the Beard (1974) results were to be made. Improvements are presented in
Sect. 2.1. In addition, the aerosol chamber has been modified not only to increase
the particle number concentration but also to better control relative
humidity, to neutralise the aerosol particles and to minimise
uncertainties. The objective of these modifications is also to be consistent
with the hypothesis of the Beard (1974) model, which considers only drag and
gravitational forces on the aerosol particles. The modifications are thus
intended to minimise electro-scavenging (discussed in Sect. 2.1 and 2.3),
diffusiophoresis (discussed in Sect. 2.3 and Appendix A1) and
thermophoresis. Both the drop generator and aerosol chamber are described in
the following sections.
Production of drops representative of rain
In order to enable the generation of finer drops, a new generator (Fig. 2)
was developed, characterised and installed at the top of the free-fall shaft
of the BERGAME facility. The generator was placed 8 m above the new
aerosol chamber. The total height of the drop shaft has been reduced by 2 m
because, as the drops are smaller than those investigated by Quérel
et al. (2014a and b), they reach their terminal velocity in a
shorter distance.
Diagram of operation of the generator opening valve.
The drop generator consists of a valve operated by piezoelectric actuators
which transmit their movement to a rod. A ceramic sealing ball is attached
to the rod and lifts to open the valve by enabling the fluid to flow (see
Fig. 2). The water circuit is maintained under
pressure by a compressed air system.
Classical piezoelectric drop-on-demand systems may produce electrically
charged droplets (Ardon-Dryer et al., 2015). However, we want to
limit electro-scavenging as Beard (1974) did in his simulations. To control
electro-scavenging, the net charge of each drop produced by this system has
been measured with the help of a Faraday pail connected to an electrometer
(Keithley model 6514; Sow and Lemaitre, 2016). Any electrical charge on the
drop was detected by our sensitive electrometer (limit of 10 fC). This might
be explained by the fact that, unlike classical piezoelectric drop-on-demand
systems (such as those of microdrop Technologies and MicroFab Technologies),
the piezoelectric transducer in our drop generator is not in direct contact
with the liquid (Fig. 2).
Drop size measurements
The generator was calibrated in order to produce drops of a prescribed
diameter. Two parameters govern the size of the drops: the water supply
pressure and the valve opening time. The different tests performed showed
that when the pressure in the water circuit is too high, the drops break up
at the injector outlet. Maintaining pressure below, or at 0.3 bar, avoids
these effects. These tests were therefore performed at a positive pressure
of 0.3 bar. For this water circuit supply pressure, the valve opening time
was between 4 and 11 ms. The raindrops' size is determined after a free-fall
acceleration over a height of 8 m. For each opening time, shadowgraph
measurements were taken in the aerosol chamber of the BERGAME facility. An
optical window is used to trigger the photographing of each drop entering
the BERGAME aerosol chamber. Our optical device is a camera (Andor: neo,
sCMOS) with a resolution of 2560 × 2160 square pixels. It
is equipped with a Canon macro lens (MP-E 65 mm, f/2.8, 1–5x) for a
magnification of 3:1 (experimentally checked with a calibration chart). The
pixel size is 6.5 µm, for a spatial resolution of 2.1 µm.
Drops are backlit with a 9 ns strobe to freeze their fall on the sensor.
An example of a shadowgraph image is shown in Fig. 3.
Example of a shadow image.
Due to the oscillations, the millimetric drops exhibit an oblate spheroid
shape. To define the size of the raindrops, the notion of “diameter
equivalent to a sphere of the same volume” has been adopted. Since
shadowgraphy yields only 2-D information, the diameters are equivalent to
a disc. For axisymmetric objects, equivalent spherical diameter and equivalent disc diameter are
equal. Szakál et al. (2009) experimentally verified this
axial symmetry of the drop of that size range at terminal velocity. Thus, shadow
images are used and processed to deduce the projected surface area of the
drop (Sdrop) and derive the diameter of the disc of equal surface
area (Deq).
Deq=4Sdropπ
For each injection configuration, the equivalent diameter of the drops is
measured for 100 images. Finally, the mean equivalent diameter and
the standard deviation are calculated. Figure 4
shows all the measurement points investigated. For all operating points, the
standard deviation is approximately 20 µm, i.e. approximately
1.5 % of the size of the drop.
Measured equivalent diameter of the drop produced by our generator as a
function of the valve opening time (for an overpressure of 0.3 bar).
Drop velocity measurements
In order to be representative of rain, the drops must cross the BERGAME
aerosol chamber at their terminal velocity. For each of the drop sizes
produced by our generator, the drop fall velocity is also measured at the
entrance of the aerosol chamber, below the 8 m free-fall shaft. Two
consecutive pictures of the same drop are taken during its fall. By knowing
the time interval between these two images and measuring the displacement of
the centre of the drop, we derive its velocity. The results are shown in
Fig. 5 and compared to the theoretical values
computed from Beard (1976), often taken as the reference in the literature,
as it was validated both in wind tunnel tests and in the environment.
We note in this figure that, up to a drop diameter of 1.4 mm, the 8 m
distance is sufficient for accelerating the drops to their terminal velocity.
This is consistent with the results of the theoretical calculations of Wang
and Pruppacher (1977b), which predict that 6.5 m free fall is enough for a
1.4 mm drop to reach 99 % of terminal velocity. Furthermore, to ensure
that our drops are representative of the hydrometeors described in the
literature, we compare in Fig. 6 the axis ratios of the drops in the
BERGAME chamber with the model of Beard and Chuang (1987). For the drop
sizes investigated, the drop can be considered as horizontally aligned oblate
spheroids (Fig. 3); no tilt angle was measured, which is consistent with
Pruppacher and Beard (1970) measurements. This is why the axis ratio is
computed as the ratio between the vertical and horizontal dimensions of the
drop.
Comparison of velocities measured in BERGAME with the Beard (1976) model.
Figure 6 shows that, up to a diameter of 1.4 mm, the drops entering the
aerosol chamber are perfectly representative of the hydrometeors observed in
the atmosphere.
In this study, we focus on the collection efficiency of drops with a
diameter of 1.25 mm. We have selected this size because it is the only one
produced by our systems for which comparisons with Beard (1974) simulations
will be direct. This model is particularly interesting as we have previously
shown that, for 2 mm diameter drops (Quérel et al., 2014b), it
is the only one able to predict the sharp rise in the collection efficiency
observed experimentally for submicroscopic particles, which is due to the
eddies that develop within the wake of the drop. These vortices will capture
the particles and draw them back onto the rear of the drop. For a drop
diameter of 1.25 mm, an 8 m free-fall distance is enough for the drops to
represent atmospheric raindrops, both in terms of velocity and axis ratio.
Comparison of axis ratios measured in BERGAME with the model of Beard and Chuang (1987).
Schematic design of the new BERGAME aerosol chamber.
Description of the new BERGAME aerosol chamber
A new aerosol chamber (Fig. 7) has been designed
to increase the concentration of particles within the volume swept by the
drops during their fall. Its geometry is strongly influenced by the one
developed by Hampl et al. (1971). It consists of a 1300 mm high
stainless steel cylinder with an internal diameter of 100 mm.
Various taps are provided for injecting the aerosols, taking samples and
characterising the thermodynamic conditions of the gas. These various
sampling points serve to measure, in particular,
the aerosol particles' size distribution,
their mass concentration and
the temperature and relative humidity.
In Fig. 7, each valve is labelled with a Greek
letter to structure the explanations in the text. The chamber is fitted with
two gate valves, one at the top (κ) and the other at the bottom
(φ). These two valves isolate the chamber while it is being filled
with particles. The particle size distribution of the aerosols is measured
by means of an aerodynamic particle sizer (APS, χ) and an electrical
low-pressure impactor (ELPI, δ). The injected particles are pure
fluorescein particles so that they may be easily measured by fluorescence
spectrometry. The mass concentration of the particles in suspension inside
the chamber is determined by venting the entire content of the chamber onto
a high-efficiency particulate arresting (HEPA) filter (α) and
measuring the mass of particles on the filter using fluorescence
spectrometry.
The size distribution of the particles produced by the ultrasound aerosol generator vibrating at 2400 kHz
(a) for a fluorescein concentration of 0.11 g L-1 and (b) for a fluorescein concentration of 10 g L-1.
The distribution on the left is measured using an electrical low-pressure impactor (ELPI, δ) and the one on the right using an aerodynamic particle sizer (APS, χ).
Finally, the relative humidity and the temperature are given, respectively, by
a capacitive hygrometer and a thermocouple (ω).
After having accelerated in free fall over 8 m, the drops are representative
of rain in terms of size, velocity and axis ratio (Sect. 2.1). They enter
the aerosol chamber via a circular opening with a 4 cm
diameter. After crossing the aerosol chamber, the drops are collected in a
removable container (τ). One of the principal difficulties of these
experiments relates to the sedimentation of the cloud of particles that
settles directly inside the drop collector. Indeed, Rayleigh–Taylor
instabilities can arise when a dense cloud of aerosol particles overlies a
layer of clean air. These instabilities induce a downward motion of the
aerosol cloud much faster that the settling velocity of individual particles
(Hinds et al., 2002). In order to avoid this effect, a layer of
argon (which is denser than the cloud of particles) is formed in the bottom
of the aerosol chamber, located below the second gate valve in
Fig. 7. A large number of experiments was performed. These experiments show that, regardless of the concentration and
the size of the particles in the aerosol chamber, until 4 min after
opening the gate valves, the drop collector is free from any particulate
contamination. Beyond 4 min, traces of fluorescein are detected on the
drop collector.
Aerosol particle characterisation and generation
The aerosol particles size distributions are measured using an ELPI (δ) and an APS (χ).
ELPI is a quasi-real-time aerosol spectrometer (Marjamäki et al., 2000).
It is composed of a corona charger and a 12-stage cascade low-pressure impactor. Each stage of the impactor is connected to an
electrometer. The corona charger is used to set the electrical charge of the
particles to a specific level. Then, the low-pressure impactor classifies
the aerosol particles into 12 size classes according to their aerodynamic
diameter (from 7 nm to 10 µm). Finally, the electrometers measure the
electrical charge carried by the particles collected by each impaction
stage. This charge is finally converted to the number of particles collected
according to the charging efficiency function of the corona charger.
APS is also a quasi-real-time aerosol spectrometer (Baron, 1986). It
measures the time of flight of individual particles accelerated by a
controlled accelerating flow imposed by a calibrated nozzle. The
time of flight of each aerosol particle is then converted into its
aerodynamic diameter. Thus, the APS classifies the aerosol particles in
terms of aerodynamic diameter from 500 nm to 20 µm over 52 size
classes.
APS and ELPI are both used for their complementary size ranges so all the
particles produced in our laboratory can be sized. For particles with a
median aerodynamic diameter less than 0.8 µm, the size distribution
is measured using an ELPI. For the others, we favour the use of an APS
because of the better size resolution.
The aerosol particles are produced with two ultrasound generators. The key
part of these generators is a piezoelectric ceramic immersed in a solution.
When subjected to an appropriate electric current, this ceramic vibrates at
a frequency of 500 or 2400 kHz depending on the generator used.
These oscillations transform the surface of the liquid into a mist of
microscopic droplets with a narrow size distribution. These drops are
transported to the upper part of the generator by a flow of dry filtered
air at a flow rate of 20 L min-1. More dry air is added in the upper
part of the generator at a flow rate of 30 L min-1 to dry the
particles.
These drying and dispersal flow rates have been selected to obtain the
following characteristics:
the aerosol particle size distributions are narrowly spread (geometric standard deviation less than or equal to
1.5);
the particle concentration inside the aerosol chamber is high
(∼ 2 × 105 particles cm-3); and
the relative humidity measured in the aerosol chamber is approximately 77 ± 1%. This humidity corresponds to
relative humidities observed during rainfall events (Depuydt et al., 2012). Furthermore, we will show that this
humidity is high enough to make diffusiophoresis negligible (see the discussion of Fig. 12 in Sect. 3).
Changing the concentration of the solute dissolved in the water varies the
size of the produced particles. The chosen solute is sodium fluorescein
(C10H10Na2O5). This molecule has been selected for its
very large fluorescence properties. It can be easily detected by
fluorescence spectroscopy down to a concentration of
5 × 10-11 g mL-1. The generator is placed inside a negative pressure
enclosure to prevent any possible fluorescein particle contamination of the
laboratory. Figure 8 shows two examples of number
particle size distributions of fluorescein measured in the BERGAME aerosol
chamber.
Both of these distributions fit well to log-normal distributions (red curves
on the graphs). For a fluorescein concentration of 0.11 g L-1
(respectively, 10 g L-1) in the solution, the median diameter of the
fitted distribution is 220 nm (respectively, 820 nm) and the geometric
standard deviation is 1.5 (respectively, 1.34).
For each of the particle sizes produced, the fluorescein mass concentrations
in the aerosol chamber derived from APS and ELPI measurements are compared
with ones derived from filter measurements (Sect. 2.2). These comparisons
provide slight differences (∼ 10 %) that can be attributed
to both the purity of fluorescein sodium salt used (∼ 97 %)
and the shape of the aerosol particles that is not perfectly spherical.
Thus, for improving the accuracy of collection efficiency measurements, the
fluorescein concentration inside the aerosol chamber is derived from filter
measurements, and APS and ELPI are used to provide a precise measurement of
the particle size.
In order to neutralise the charge of the aerosol particles prior to
injecting them into the BERGAME aerosol chamber (β), the particles go
through a low-energy X-ray neutraliser (< 9.5 keV, TSI 3088), at a
flow rate of 1.5 L min-1. At this flow rate, the residence time of the
particles in the neutraliser is sufficient to neutralise them.
As we have seen in the previous section, our aerosol generator produces
aerosols at a flow rate of 50 L min-1 (20 L min-1 of
dispersion air and 30 L min-1 of drying air). Therefore, we use a flow
divider to ensure that the particles pass through the
neutraliser at 1.5 L min-1. This divider includes an 8 L buffer
volume, provided with one inlet and two outlets. A flow rate of 48.5 L min-1 is drawn off from one of these outlets by means of an air
suction pump. This flow is filtered and vented. The remaining flow passes
through the neutraliser. After neutralisation, the particles are injected
into the aerosol chamber.
Test procedure
The aerosol chamber is flushed at the start of each experiment with
synthetic air to ensure that initial conditions are free of any fluorescein
particle contamination. After flushing, the previously neutralised aerosol
particles of chosen diameter are injected at a flow rate of 1.5 L min-1
via valve β (Sect. 2.3).
The two knife gate valves (φ and κ) are closed during
this filling phase in order to isolate the enclosure. In addition, valve
ε is opened to exhaust the excess pressure towards a
HEPA filter. The injection process lasts 20 min, during which we form a
layer of argon within the zone located below knife gate valve ϕ. This
injection is carried out in two stages. First, we inject the argon during
10 min via valve η, with the drop collector unscrewed and valve
γ closed. Second, the drop collector is refitted and valve
γ is opened. At the end of this phase, the aerosol chamber
is filled with neutralised particles of a prescribed diameter at a
concentration of approximately 2 × 105 particles per cubic centimetre.
This filling phase of the enclosure is followed by a relaxation period
lasting no less than 15 min. During this time period, all the valves of
the aerosol chamber are closed, with the exception of valve ε,
which remains open in order to perfectly balance the pressures. This period
is used to bring the train of drops produced by the generator to the
centre line of the aerosol chamber. Once the drop generator is adjusted,
valve ε is closed and both knife gate valves (φ and κ) are opened to enable the drops to cross the aerosol
chamber. A cumulated volume of 1 cm3 of solution is necessary for
performing a measurement by fluorescence spectrometry, i.e. approximately
1000 drops of 1.25 mm diameter. As a result of the frequency at which drops
cross the enclosure, 10 min are needed to collect this volume. As
mentioned above, the drop collector remains free of any particulate
contamination if the valves remain open for less than 4 min. The 10 min needed
to collect the 1000 drops are therefore divided into three
periods of 200 s each. At the end of these 200 s phases, the
gate valves are closed again and the buffer volume between gate valve ϕ and the drop collector is flushed with argon
(Fig. 9). During flushing, the argon is injected
through valve η and removed through valve γ,
which ensures an upward flow within this buffer volume and minimises the
risk of contamination of the drop collector.
Once 1 cm3 of drops is collected, both knife gate valves close, and the
buffer volume is flushed, to avoid any contamination of the collected water
when removing the drop collector.
In order to determine the collection efficiency, we need to know the mass
concentration of fluorescein within the volume swept by the drops (Eq. 3).
The concentration is measured by filter analysis, and for this purpose the
aerosol chamber of the BERGAME experiment is flushed with synthetic air at
the end of each experiment. This is done by injecting the synthetic air
through valve φ, at a flow rate of 5 L min-1 for 10 min, and collecting the particles on a HEPA filter.
This filter is then placed in 100 mL of ammonia water Vsol for 24 h in order to dissolve all the fluorescein particles it
contains. Finally, the mass concentration of fluorescein in this water
(fluofilter) is measured by fluorescence spectrometry.
The mass concentration of fluorescein particles in the aerosol chamber
(fluochamber) is then determined using the following
equation:
fluochamber=fluofilter⋅VsolVchamber.
In this equation, the term Vchamber is the volume of the aerosol
chamber, i.e. 10.2 L.
As the mass concentration of particles is only quantified once the
measurements are completed, we have attempted to quantify its variation over
the duration of a measurement (approximately 15 min). For this, we have
first verified the reproducibility of characteristics of the aerosol
produced by the aerosol generator in size, number and concentration. This
is performed by repeating the injection phase with exactly the same
operating conditions. No variation of the fluorescein concentration greater
than the uncertainty of the fluorimeter (±2.5 %;
Appendix A) has ever been measured. We have then compared the mass
concentration in the aerosol chamber just after the relaxation phase and
after a complete measurement procedure. At last, we measured a reduction in
concentration of less than 8 % regardless of the particle diameter. These
particles are essentially lost through deposition on the sides of the
aerosol chamber. This decrease of the particle concentration during the
experiments is the main source of uncertainty on the measurement of the
collection efficiency.
The collection efficiency is defined as the ratio between the mass of
particles (of a given diameter) collected by a drop as it falls and the
total mass of particles (of the same diameter) within the volume it has
swept. The mass of fluorescein in the drops during the experiments Mdrop is easy to calculate:
Mdrop=πDdrop36fluodrop,
where fluodrop is the mass concentration of fluorescein
in the drops.
The mass of particles within the volume swept by the drops M2 is calculated with
M2=πDdrop2H4fluochamber,
where fluochamber is the mass concentration of
fluorescein in the aerosol chamber and H the height of the aerosol chamber
(1.3 m; Fig. 1).
The collection efficiency is derived from the following expression:
Edaero,Ddrop,RH=MdropM2=2Ddrop⋅fluodrop3H⋅fluochamber.
In order to precisely determine the size distribution of the particles for
which the collection efficiency has been measured, we repeat the injection
of particles into the BERGAME aerosol chamber following each efficiency
measurement under exactly the same operating conditions (generator, ceramic
excitation frequencies, injection times, dispersal and drying flow rates and
fluorescein concentration). The size distribution of the aerosol particles
produced by the generator is then measured in the aerosol chamber.
Results and discussion
All the measurements taken are summarised in Table 2 with the associated expanded relative uncertainties. The first column of
this table provides the median aerodynamic diameter daero of each particle size distribution measured
using the APS or the ELPI. The detailed calculation of the uncertainties is
presented in Appendix A1 (Lira, 2002).
This median aerodynamic diameter is converted into a physical diameter
(dap) by means of the following expression (which is solved
iteratively):
dap=daeroCc,daeroCc,dapρ0ρp.
In this equation, Cc is the Cunningham slip correction factor and
ρ0 the water density. The density of the particle
ρp is calculated from the growth factor
(GF) of the fluorescein aerosol particle.
ρp=ρC10H10Na2O5+ρ0GF3-1GF3
This factor has previously been measured using a hygroscopic tandem
differential mobility analyser (HTDMA; Quérel et al., 2014b).
For our experiments, performed at a relative humidity of 77 ± 5 %,
we deduce a GF of 1.25 ± 0.05. Stöber and
Flachsbart (1973) have measured a density of 1.58 g cm-3 for a dry
fluorescein aerosol particle. Using Eq. (10), we therefore calculate the
density of our aerosol in the aerosol chamber to be 1.30 ± 0.05 g cm-3.
Comparison of our measurements for a drop of 1.25 mm diameter with the results of the models of Beard (1974) and Slinn (1977).
The aerodynamic diameters measured in the aerosol chamber by the APS and the
ELPI can then be expressed as physical diameters (dap):
dap=0.88×daero.
All our measurements are summarised in Table 2 and plotted in
Fig. 10 as a function of the median diameter of
the distribution of the physical diameter of the particles. Figure 10
compares our dataset against the efficiencies computed by both Slinn (1977)
and Beard (1974) models. In this figure, the Slinn model includes the
contributions of inertial impaction, Brownian diffusion and interception
(Table 1). It should be remembered that the in situ scavenging
measurements (Volken and Shumann, 1993; Laakso et al., 2003; Chate,
2005) are only compared to the Slinn model. In the aerosol size range investigated,
the collection efficiencies measured vary considerably as a function of the particle size. On a logarithmic scale, the efficiency
curve obtained has a “V” shape with a minimum around 0.65 µm. The
increase in the collection efficiency for particles larger than 0.65 µm
is attributed to the mechanism of impaction on the front side of the drop.
Within this size range, the increase in the diameter of the particle
increases its inertia. The particle can then no longer follow the
streamlines and impacts the drop.
The reasons for the increase in the collection efficiency for particles smaller
than 0.65 µm in diameter are not as easy to figure out. Indeed,
particles of this size range are not expected to be affected by Brownian
motion since their diameter is 7 times bigger than the mean free path of
the air molecules.
The Slinn model does not predict this increase and underestimates the
collection efficiency for a 0.22 µm particle by 2 orders of
magnitude. This is linked to the assumptions of Stokes flow around the drop.
Yet, at Reynolds numbers larger than 20 (for a 280 µm drop at its
terminal velocity), recirculation eddies develop in the wake of the drop.
Beard (1974) has shown the major influence of these wake vortices on the
collection of submicron-sized particles. In fact, he showed that the
smallest aerosol particles are trapped in these eddies in the wake of the
drop and then collected on its rear side.
This model is not referred to in the literature, as it has never been
validated by experiments until now. Yet, we observe that, for particles below
this minimum efficiency, our measurements are in almost perfect agreement
with the model and seem to validate it.
For particles with a diameter greater than 1 µm, we observe that the
Beard or Slinn models yielded almost the same values. This result is
expected since their only difference stands in the Stokes flow around the
drop for Slinn model. This assumption prevents the capture of boundary layer
separation in the wake of the drop and the resulting recirculating flows
even if it makes very little difference to the flow on the leading edge of
the drop. Yet, particles with a diameter greater than 1 µm are very
sensitive to inertial effects and are captured on this front side. Moreover,
as the Stokes number of these large particles is high, they pass through the
recirculations without being trapped.
For particles with a diameter greater than 0.65 µm, our measurements
show the same trends as these two models but with an average difference of
1 order of magnitude. This is probably related to the fact that, during
our experiments, the aerosol particles in the aerosol chamber are not
perfectly mono-disperse. Indeed, the particles have log-normal distributions
with geometric standard deviations between 1.3 and 1.5
(Fig. 8). The collection efficiency varies very
sharply with particle size. Thus, in order to compare more rigorously our
measurements with the Beard (1974) model, we need to calculate, for each
measurement, the average theoretical collection efficiency (〈E(Dgtte,dap)〉)
resulting from the integration of the Beard (1974) model over the
entire range of particle sizes in the aerosol chamber (Eq. 12).
In this equation, the term f(dap)
is the probability density function according to the number of the particles
in the BERGAME aerosol chamber, and E(Ddrop=1.25mmdap) is
the collection efficiency calculated by the Beard model (1974) for a drop
1.25 mm in diameter. The numerator and denominator of this equation are both
weighted by a term dap3, which reflects the fact that,
experimentally, we measure intensities of fluorescence and therefore masses
of particles. We use the rectangle method to numerically solve this
integral. In addition, the functions E(Ddrop=1.25mmdap) and
fdap are both interpolated using Hermite interpolation
polynomials (Fritsch and Carlson, 1980) with a step size of 0.1 µm.
We note a significant improvement of the agreement between our measurements
and the Beard (1974) model since it is integrated over the entire particle
size distribution measured during our experiments in BERGAME (red dots in
Fig. 11). Larger differences are nevertheless
observed for the first (dap=0.22µm) and last measurement points
(dap=2.54µm). These differences could be attributed to the fact
that, for these points, the resolution of Eq. (12) requires an
extrapolation of Beard (1974) calculations beyond the size range he
investigated (continuous line in Fig. 11).
Integration of the Beard (1974) model over the particle size distribution of each of our experiments for a drop of 1.25 mm diameter.
Moreover, for the collection efficiency measured for the finest aerosol
particles (dap=0.22µm), the discrepancy observed with the Beard
model could also be explained by the hypothesis of the simulations. Indeed,
the Brownian motion was neglected. This can be justified in the particle
size range investigated; however, it is much less justified when
extrapolating the simulations to finer aerosol particles.
Furthermore, it is interesting to compare our measurements with the ones
from Lai et al. (1978) since they are the only ones in the
literature in the same drop size range. As the aerosol particles produced in
these experiments are composed of silver chloride (ρAgCl= 5.6 g cm-3), which is much denser than sodium fluorescein
(ρC10H10Na2O5= 1.3 g cm-3), it is more appropriate to
plot all the collection efficiencies as a function of the Stokes number of
the particle (Stap).
Stap=ρpU∞Ddropdap2Cc,dap9Ddropμair
In this equation, μair is the dynamic viscosity of the air and ρp the density of the aerosol particles. This comparison is presented in
Fig. 12.
For particles with a Stokes number greater than 6 × 10-2, the
motion of the particles is driven by their inertia, leading us to expect to
observe the same trends in our measurement and those of Lai et al. (1978).
The comparison for a Stokes number smaller than 6 × 10-2
is much less obvious. Indeed, for these particles, the measurements of Lai
et al. (1978) indicate an increase in the collection efficiency, while
our measurements continue to decrease down to a Stokes number of
1.6 × 10-2. At that point, the slopes of the increases of both
collection efficiency measurements are similar, while the Stokes number
decreases.
Collection efficiencies measured in this study and by Lai et al. (1978). Both measurements are compared to the Slinn (1977)
and Beard (1974) models. The contribution of diffusiophoresis in both studies is computed following the description of Davenport and Peters (1978).
Semi-empirical parameterisation of rear capture.
A precise analysis of the procedure for the aerosol particle injection in
the experiments of Lai et al. (1978) indicates that the carrier gas
is pure nitrogen without any subsequent humidification. As a consequence, it
is reasonable to consider that their measurements were performed with 0 %
relative humidity. In order to compare the contribution of diffusiophoresis
for both our experiment and that of Lai et al. (1978), we plot in
Fig. 12 the elementary contribution of diffusiophoresis
(Edph) to the collection efficiency. This contribution is
calculated with the Davenport and Peters (1978) model for 0 % relative
humidity (as expected for the experiments of Lai et al., 1978) and
77 % (as measured in our experiments). From this figure, it will be noted
that, for the experiments of Lai et al. (1978), the contribution of
diffusiophoresis is more than 1 order of magnitude higher than in ours.
Furthermore, while in our experiments the contribution of diffusiophoresis
is smaller than the collection efficiency simulated by Beard (1974), the
opposite is observed with Lai et al. (1978). Thus, it appears that
the experiments of Lai et al. (1978) cannot be compared directly to the model
of Beard (1974), because they seem to be dominated by diffusiophoresis.
Based on these comparisons, we can consider that the Beard (1974) model is
validated for addressing the collection of the aerosol particles of the
accumulation mode by raindrops. Finally, it seems necessary to provide, to
facilitate its use, an analytical expression to assess the contribution of
the rear capture (ERe-capture) to the raindrop collection
efficiency. Indeed, the Slinn (1977) model which neglects rear capture
underestimates the collection efficiency by 2 orders of magnitude in the
submicron range compared to Beard's model (1974). Furthermore, Beard (1974) noticed from his theoretical simulations that rear capture plays a
main role in the collection efficiency for aerosol particles with a Stokes
number smaller than 5 × 10-2. Thus, to derive an analytical
expression for the elementary collection efficiency resulting from rear
capture alone (Erear capture), we gather in Fig. 13 the collection
efficiencies numerically simulated by Beard (1974) for a Stokes number
smaller than 5 × 10-2 (crosses in Fig. 13). These
collection efficiencies are plotted as a function of the Reynolds number of
the drops and the Stokes number of the particles.
This figure suggests that the Reynolds number of the drop and Stokes number
of the aerosol particles are the two parameters influencing rear capture.
The dependency on these two dimensionless numbers is physical, as the
Reynolds number of the drop Redrop reflects the
intensity and the size of the areas of recirculating flow in its wake and
the particle Stokes number Stap reflects the
susceptibility of the particle to pass through the recirculating flow in the
wake of the drop without being trapped.
Applying a power law fit to the simulations of Beard (1974) yields Eq. (14).
ERear-capture=13×107Redrop×Stap-1.23
This correlation is presented in solid lines in Fig. 13 and shows a
satisfactory agreement with Beard's simulations (crosses) in the
corresponding range of the drop Reynolds number and particle Stokes number.
However, it should be kept in mind that this relationship is only valid for
the drop Reynolds numbers larger than 20 (a 280 µm drop at its terminal
velocity), since below this critical value there is no recirculating flow
behind the drop (Le Clair et al., 1972). Finally, this new
contribution should be added to those presented in Table 1 for raindrops.
Conclusions
This study is a follow up of the paper by Quérel et al. (2014b)
and treats questions raised therein. In particular, Quérel et al. (2014b) showed that their efficiency measurements of submicron
particles could only be explained by rear capture. The present paper
confirms the impact of recirculating flows at the rear of the drop on the
collection of submicron particles. This was done by directly comparing our
measurements against the numerical simulations of Beard (1974). The BERGAME
experimental facility was optimised to considerably reduce the measurement
uncertainties, as well as to perfectly control the electric charges of both
the drops and the aerosol particles.
As in Quérel et al. (2014b), we show that the collection
efficiency of the accumulation mode aerosol particles by drops
representative of rain varies significantly with the size of the particles.
On a logarithmic scale, the efficiency curve obtained shows a V shape
with a minimum around 0.65 µm. The increase in the collection efficiency
for particles larger than 0.65 µm is attributed to the mechanism of
impaction on the front side of the drop. Within this size range, the
increase in the diameter of the particle increases its inertia, and the
particle can no longer follow the streamlines and thus impacts the drop. It
was not possible for the measurements of Quérel et al. (2014b),
but here we can directly compare our results with the numerical simulations
carried out by Beard (1974). This comparison highlights the robustness of
his model for predicting the efficiency of capture of particles by raindrops
over the entire accumulation mode. It should be noted that it is the only
model to predict the significant increase in the collection efficiency that we
measured for submicron particles. This is related to the fact that Beard (1974) first simulated the flow around the drop by solving the complete
Navier–Stokes equation (without ignoring the convection terms; Beard and
Grover, 1974). Therefore, he captured the separation of the boundary layer
at the rear of the drop and the resulting recirculating flows; then, he
simulated the trajectory of the particles in this velocity field.
Beard thus showed that the increase in the collection efficiency of
submicron particles as observed in experiments is due to the fact that these
particles are captured in the recirculating flows to the rear of the drop
and drawn back into its rear side.
Furthermore, we have also shown that, for particles larger than 1 mm, the models of Beard and Slinn are very similar.
Finally, we propose a new semi-analytical expression to calculate the
elementary efficiency of capture by the rear recirculating flows. It is
important that this mechanism should be systematically taken into account to
avoid errors of at least 2 orders of magnitude on the collection
efficiency and consequently on the scavenging coefficient.
In the near future, we plan to integrate these new measurements within the
DESCAM model (Flossmann, 1986, 1991; Querel et al.,
2014a) and to compare the scavenging coefficient derived from the
theoretical approaches and the experiments conducted in the environment by
Volken and Shuman (1993), Laakso et al. (2003) and Chate (2005).
Finally, we plan, in a more distant future, to look at other hydrometeors
such as snow and hail.
Evaluation of uncertainties
The collection efficiency is calculated by means of Eqs. (5) and (8)
from which we derive the equation below by substitution:
Edaero,Ddrop,RH=2DDrop⋅fluodrop⋅Vchamber3H⋅fluofilter⋅Vsol.
The expanded relative measurement uncertainty of the collection efficiency
(UR,Edaero,DDrop,RH) is determined with
the help of the law of propagation of variances, considering an expansion
factor of 2 (Lira, 2002):
UR,Edaero,DDrop,RH=2uR,Ddrop2+uR,fluodrop2+uR,Vchamber2+uR,H2+uR,fluofilter2+uR,Vsol2.
In the right-hand member of this expression, the terms uR,X
correspond to the relative measurement uncertainty of X. Each experimental
uncertainty is discussed in a separate subsection.
Uncertainty in drop size
Shadowgraph measurements of the size of the drops have shown that our drop
generation system is very stable and reproducible for the parameters adopted
(Sect. 2.1). The standard deviation of the drop size distribution is 20 µm; we use this standard deviation to determine the relative
uncertainty in the diameter of the drops.
uR,Ddrop=σDdropDdrop=20×10-31.3≈0.015
Uncertainty in fluorescein concentration measurements
For the range of concentrations within which fluorescence spectrometry is
used, the calibration certificate of the spectrometer indicates an expanded
relative measurement uncertainty (UR,fluo) of
less than 5 %.
We then derive the relative measurement uncertainty of the fluorescein
concentration in the drops (uR,fluodrop). This relative uncertainty has two contributions. The
first one is due to the spectrometer relative measurement uncertainty on the
fluorescein concentration (uR,fluo), and the
second one is due to a potential variation of the volume of water collected
(in the drop collector; Fig. 7) due to vaporisation during the
experiments (uR,Vcollected).
uR,fluodrop=uR,fluo2+uR,Vcollected2uR,fluo=UR,fluo2=0.052
The uncertainty on the volume of water collected (uR,Vcollected)
is estimated with the maximum variation of the volume of liquid water in the
drop collector due to vaporisation (EMTVcollected).
uR,Vcollected=EMTVcollected3Vcollected
In this equation, the volume of water collected (Vcollected) is greater
than 1 cm3 (Sect. 2.4). The maximum variation of the volume
of liquid water in the drop collector (EMTVcollected) is evaluated
supposing that during the experiment period (Sect. 2.4) the entire volume
of the buffer (Vbuffer) becomes saturated with water vapour. This leads
to
EMTVcollected=3MH2OPsat(Tair)VbufferRTairρliquid-water=1.2×10-2cm3.
In this equation, R is the perfect gas constant, Psat is the saturation
vapour pressure, ρliquid-water is the density of liquid water,
MH2O is the molar mass of water and Tair the gas
temperature in the buffer. The coefficient of 3 in the numerator comes from
the fact that the buffer volume is flushed three times during the
measurement period (Sect. 2.4).
uR,fluodrop=0.0522+1.2×10-23×12≈0.025
For the fluorescein concentration measured in the aerosol chamber fluochamber, we have the same uncertainty
associated with the fluorescence spectrometry measurement. In addition to
this measurement uncertainty, there is a second uncertainty associated with
the reduction in concentration during the course of the experiment. We have
calculated this reduction to be less than 8 % over the duration of
the measurement. The total relative uncertainty in the fluorescein
concentration inside the aerosol chamber is therefore approximately 8 %
(equation below).
uR,fluochamber=0.0252+0.082≈0.08
Uncertainty in height of aerosol chamber
The aerosol chamber measures 1.3 m (plus or minus 1 mm). However,
over the duration of the measurement, the particles diffuse and move
slightly outside the geometric boundaries of the aerosol chamber. We
calculate the maximum error in the height of interaction between the drops
and the particles (EMTH) to be approximately 2 cm (one
above and one below the chamber). We therefore calculate the relative
uncertainty for this height of interaction (uR,H) by means
of the following equation:
uR,H=EMTH3H≈0.005.
Uncertainty in volume of dilution
The uncertainty in the volume of dissolution is very low; we estimate its
maximum error (EMTVsol) to be 1 mL. We derive a relative
uncertainty in the dilution uR,Vsol:
uR,Vsol=EMTVsol3Vsol≈0.003.
Uncertainty in volume of aerosol chamber
The uncertainty in the volume of the aerosol chamber is low, we estimate its
maximum error (EMTVchambre) to be 20 cL. We derive the
relative uncertainty in the dilution uR,Vchamber:
uR,Vchamber=EMTVchamber3Vchamber=20×10-23×10≈0.007.
Uncertainty in relative humidity
The relative humidity is not directly involved in the calculation of
collection efficiency. However, it is established, for the finest droplets,
that the efficiency increases considerably when the relative humidity
reduces, due to diffusiophoresis. For example, Grover et al. (1977)
calculated that the collection efficiency of a 0.5 µm aerosol
particle by a 80 µm, can increase by a factor of 104 when the
relative humidity falls from 100 to 20 %.
However, our recent measurements, for the largest hydrometeors forming rain
(between 2 and 2.6 mm; Quérel et al., 2014b) showed no
dependency of the collection efficiency on relative humidity.
During our experiments, the aerosol generator settings were optimised in
such a way that, at the end of the aerosol chamber filling phase, the
relative humidity in the chamber was 75 ± 1 %.
For each measurement, during the 10 min needed to collect 1 mL
of drops (Sect. 2), the relative humidity increased by 5 ± 1 %.
This increase is related to an accumulation of water on the slightly
inclined bottom of the aerosol chamber.
We consider therefore that the measurement uncertainty for the relative
humidity is approximately 5 %.
The authors declare that they have no conflict of interest.
Acknowledgements
We give special thanks to Denis Boulaud for his confidence and support.
Edited by: B. Ervens
Reviewed by: two anonymous referees
ReferencesArdon-Dryer, K., Huang, Y.-W., and Cziczo, D. J.: Laboratory studies of collection efficiency of sub-micrometer
aerosol particles by cloud droplets on a single-droplet basis, Atmos. Chem. Phys., 15, 9159–9171, 10.5194/acp-15-9159-2015, 2015.Andronache, C., Gr¨nholm, T., Laakso, L., Phillips, V., and Venäläinen, A.: Scavenging of ultrafine particles by rainfall at a
boreal site: observations and model estimations, Atmos. Chem. Phys., 6, 4739–4754, 10.5194/acp-6-4739-2006, 2006.
Baron, P. A.: Calibration and use of the aerodynamic particle sizer
(APS 3300), Aerosol Sci. Technol., 5, 55–67, 1986.
Beard, K. V.: Experimental and numerical collision efficiencies for
submicron particles scavenged by small raindrops, J. Atmos. Sci., 31, 1595–1603, 1974.
Beard, K. V. and Grover, S. N.: Numerical collision efficiencies for
small raindrops colliding with micron size particles, J. Atmos. Sci., 31, 543–550, 1974.
Beard, K. V.: Terminal velocity and shape of cloud and precipitation
drops aloft, J. Atmos. Sci., 33,
851–864, 1976.
Beard, K. V. and Chuang, C.: A new model for the equilibrium shape
of raindrops, J. Atmos. Sci., 44,
1509–1524, 1987.
Charlson, R. J., Schwartz, S. E., Hales, J. M., Cess, R. D., Hansen, J. E.,
and Hofmann, D. J.: Climate Forcing by Anthropogenic
Aerosols, Science, 255, 423–430, 1992.
Chate, D. M.: Study of scavenging of submicron-sized aerosol
particles by thunderstorm rain events, Atmos. Environ., 39, 6608–6619, 2005.
Davenport, H. M. and Peters, L. K.: Field studies of atmospheric
particulate concentration changes during precipitation, Atmos. Environ., 12, 997–1008, 1978.
Depuydt, G.: Etude expérimentale in situ du potentiel de
lessivage de l'aérosol atmosphérique par les
précipitations, Doctoral dissertation, available from Toulouse
University, 2013.
Depuydt, G., Masson, O., Gomes, L., and Brenguier, J. L.: Micro and
macro-physical characterizations of precipitations in continental and
Mediterranean environments, in: 16th International
Conference on Clouds and Precipitation, ICCP-2012, July 30–August 3 2012, Leipzig, Germany, 2012.
Flossmann, A. I.: A theoretical investigation of the removal of
atmospheric trace constituents by means of a dynamic model, PhD thesis,
Phys. Dep., Johannes Gutenberg-Univ. Mainz, Mainz, Germany, 186 pp., 1986.
Flossmann, A. I.: The scavenging of two different types of marine
aerosol particles calculated using a two-dimensional detailed cloud
model, Tellus, 43B, 301–321, 1991.
Fritsch, F. N. and Carlson, R. E.: Monotone piecewise cubic
interpolation, SIAM J. Numer. Anal., 17,
238–246, 1980.
Greenfield, S. M.: Rain scavenging of radioactive particulate matter
from the atmosphere, J. Meteorol., 14, 115–125, 1957.
Groëll, J., Quélo, D., and Mathieu, A.: Sensitivity analysis
of the modelled deposition of 137 Cs on the Japanese land following the
Fukushima accident, Int. J. Environ.
Pollut., 55, 67–75, 2014.
Grover, S. N., Pruppacher, H. R., and Hamielec, A. E.: A numerical
determination of the efficiency with which spherical aerosol particles
collide with spherical water drops due to inertial impaction and phoretic
and electrical forces, J. Atmos. Sci., 34, 1655–1663,
1977.
Hampl, V. M. D. D. E., Kerker, M., Cooke, D. D., and Matijevic, E.:
Scavenging of aerosol particles by a falling water droplet, J. Atmos. Sci., 28, 1211–1221, 1971.
Hinds, W. C., Ashley, A., Kennedy, N. J., and Bucknam, P.:
Conditions for cloud settling and Rayleigh-Taylor
instability, Aerosol Sci. Technol., 36, 1128–1138, 2002.
Jaenicke, R.: Aerosol physics and chemistry, Zahlenwerte und
Funktionen aus Naturwissenschaften und Technik, 4, 391–457, 1988.
Kerker, M. and Hampl, V.: Scavenging of Aerosol Particles by a
Failing Water Drop and Calculation of Washout Coefficients, J. Atmos. Sci., 31, 1368–1376, 1974.
Laakso, L., Grönholm, T., Rannik, Ü., Kosmale, M., Fiedler, V.,
Vehkamäki, H., and Kulmala, M.: Ultrafine particle scavenging
coefficients calculated from 6 years field measurements, Atmos. Environ., 37, 3605–3613, 2003.Ladino Moreno, L. A., Stetzer, O., and Lohmann, U.: Contact freezing: a review of experimental studies,
Atmos. Chem. Phys., 13, 9745–9769, 10.5194/acp-13-9745-2013, 2013.
Lai, K. Y., Dayan, N., and Kerker, M.: Scavenging of aerosol
particles by a falling water drop, J. Atmos. Sci., 35, 674–682, 1978.
Le Clair, B. P., Hamielec, A. E., Pruppacher, H. R., and Hall, W. D.:
A theoretical and experimental study of the internal circulation in water
drops falling at terminal velocity in air, J. Atmos. Sci., 29, 728–740, 1972.
Lira, I.: Evaluating the Measurement Uncertainty: Fundamentals and Practical Guidance, Taylor & Francis, Institute of Physics, Bristol, UK, 2002.
Marjamäki, M., Keskinen, J., Chen, D. R., and Pui, D. Y.:
Performance evaluation of the electrical low-pressure impactor
(ELPI), J. Aerosol Sci., 31, 249–261, 2000.
Ménard, T., Tanguy, S., and Berlemont, A.: Coupling level
set/VOF/ghost fluid methods: Validation and application to 3D simulation of
the primary break-up of a liquid jet, Int. J.
Multiphas. Flow, 33, 510–524, 2007.
Mircea, M. and Stefan, S.: A theoretical study of the microphysical
parameterization of the scavenging coefficient as a function of
precipitation type and rate, Atmos. Environ., 32, 2931–2938, 1998.
Mircea, M., Stefan, S., and Fuzzi, S.: Precipitation scavenging
coefficient: influence of measured aerosol and raindrop size distributions,
Atmos. Environ., 34, 5169–5174, 2000.
Park, S. H., Jung, C. H., Jung, K. R., Lee, B. K., and Lee, K. W.:
Wet scrubbing of polydisperse aerosols by freely falling
droplets, J. Aerosol Sci., 36, 1444–1458, 2005.
Pranesha, T. S. and Kamra, A. K.: Scavenging of aerosol particles by
large water drops: 1. Neutral case, J. Geophys. Res.-Atmos., 101, 23373–23380, 1996.
Pruppacher, H. R. and Beard, K. V.: A wind tunnel investigation of
the internal circulation and shape of water drops falling at terminal
velocity in air, Q. J. Roy. Meteorol.
Soc., 96, 247–256, 1970.
Pruppacher, H. R., Klett, J. D., and Wang, P. K.: Microphysics of
clouds and precipitation, Kluwer academic publishers, Dordrecht, Boston,
London, 852 pp., 1998.
Quérel, A., Monier, M., Flossmann, A. I., Lemaitre, P., and Porcheron,
E.: The importance of new collection efficiency values including the
effect of rear capture for the below-cloud scavenging of aerosol
particles, Atmos. Res., 142, 57–66, 2014a.Quérel, A., Lemaitre, P., Monier, M., Porcheron, E., Flossmann, A. I., and Hervo, M.: An experiment
to measure raindrop collection efficiencies: influence of rear capture, Atmos. Meas. Tech., 7, 1321–1330, 10.5194/amt-7-1321-2014, 2014b.
Quérel, A., Roustan, Y., Quélo, D., and Benoit, J. P.: Hints
to discriminate the choice of wet deposition models applied to an accidental
radioactive release, Int. J. Environ.
Pollut., 58, 268–279, 2015.
Slinn, W. G. N.: Some approximations for the wet and dry removal of
particles and gases from the atmosphere, Water Air Soil
Pollut., 7, 513–543, 1977.
Sow, M. and Lemaitre, P.: Influence of electric charges on the
washout efficiency of atmospheric aerosols by raindrops, Ann.
Nucl. Energy, 93, 107–113, 2016.
Stöber, W. and Flachsbart, H.: An evaluation of nebulized
ammonium fluorescein as a laboratory aerosol, Atmos.
Environ., 7, 737–748, 1973.
Szakáll, M., Diehl, K., Mitra, S. K., and Borrmann, S.: A wind
tunnel study on the shape, oscillation, and internal circulation of large
raindrops with sizes between 2.5 and 7.5 mm, J. Atmos. Sci., 66, 755–765, 2009.
Szakáll, M., Mitra, S. K., Diehl, K., and Borrmann, S.: Shapes
and oscillations of falling raindrops – A review, Atmos.
Res., 97, 416–425, 2010.Tinsley, B. A., Rohrbaugh, R. P., Hei, M., and Beard, K. V.: Effects
of image charges on the scavenging of aerosol particles by cloud droplets
and on droplet charging and possible ice nucleation
processes, J. Atmos. Sci., 57, 2118–2134, 2000.
Tinsley, B. A., Zhou, L., and Plemmons, A.: Changes in scavenging of
particles by droplets due to weak electrification in
clouds, Atmos. Res., 79, 266–295, 2006.
Tinsley, B. A. and Zhou, L.: Parameterization of aerosol scavenging
due to atmospheric ionization, J. Geophys. Res.-Atmos., 120, 8389–8410, 2015.
Twomey, S.: Pollution and the planetary albedo, Atmos.
Environ., 8, 1251–1256, 1974.
Vohl, O., Mitra, S. K., Wurzler, S. C., and Pruppacher, H. R.: A wind
tunnel study of the effects of turbulence on the growth of cloud drops by
collision and coalescence, J. Atmos. Sci., 56, 4088–4099, 1999.
Volken, M. and Schumann, T.: A critical review of below-cloud
aerosol scavenging results on Mt. Rigi, Water Air Soil
Pollut., 68, 15–28, 1993.
Waldmann, L.: Über die Kraft eines inhomogenen Gases auf kleine
suspendierte Kugeln, Z. Naturforsch., 14,
589–599, 1959.
Wang, P. K. and Pruppacher, H. R.: An experimental determination of
the efficiency with which aerosol particles are collected by water drops in
subsaturated air, J. Atmos. Sci., 34,
1664–1669, 1977a.
Wang, P. K. and Pruppacher, H. R.: Acceleration to terminal
velocity of cloud and raindrops, J. Appl.
Meteorol., 16, 275–280, 1977b.
Wang, R., Tao, S., Shen, H., Huang, Y., Chen, H., Balkanski, Y., Boucher,
O., Ciais, P., Shen, G. F., Li, W., Zhang, Y. Y., Chen, Y. C., Lin, N., Su,
S., Li, B. G., Liu, J. F., and Liu, W. X.: Trend in global black
carbon emissions from 1960 to 2007, Environ. Sci.
Technol., 48, 6780–6787, 2014.Wang, X., Zhang, L., and Moran, M. D.: Uncertainty assessment of current size-resolved parameterizations for below-cloud
particle scavenging by rain, Atmos. Chem. Phys., 10, 5685–5705, 10.5194/acp-10-5685-2010, 2010.
Whitby, K. T.: On the multimodal nature of atmospheric aerosol size
distribution, in: VIII International Conference on Nucleation,
Leningrad, USSR, September, 24–29, 1973.