ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-9717-2017Chemistry of riming: the retention of organic and inorganic atmospheric trace constituentsJostAlexanderSzakállMiklósszakall@uni-mainz.dehttps://orcid.org/0000-0002-0261-4802DiehlKarolineMitraSubir K.BorrmannStephanhttps://orcid.org/0000-0002-4774-9380Institute for Atmospheric Physics, University of Mainz, 55099 Mainz, GermanyParticle Chemistry Department, Max Planck Institute for Chemistry, 55218 Mainz, GermanyMiklós Szakáll (szakall@uni-mainz.de)16August20171716971797326March201713March20179June20176July2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/17/9717/2017/acp-17-9717-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/9717/2017/acp-17-9717-2017.pdf
During free fall in clouds, ice hydrometeors such as snowflakes and ice
particles grow effectively by riming, i.e., the accretion of supercooled
droplets. Volatile atmospheric trace constituents dissolved in the
supercooled droplets may remain in ice during freezing or may be released
back to the gas phase. This process is quantified by retention coefficients.
Once in the ice phase the trace constituents may be vertically redistributed
by scavenging and subsequent precipitation or by evaporation of these ice
hydrometeors at high altitudes. Retention coefficients of the most dominant
carboxylic acids and aldehydes found in cloud water were investigated in the
Mainz vertical wind tunnel under dry-growth (surface temperature
less than 0 ∘C) riming conditions which are typically prevailing in
the mixed-phase zone of convective clouds (i.e., temperatures from -16 to
-7∘C and a liquid water content (LWC) of 0.9±0.2gm-3). The mean retention coefficients of formic and acetic acids
are found to be 0.68±0.09 and 0.63±0.19. Oxalic and malonic acids
as well as formaldehyde show mean retention coefficients of 0.97±0.06,
0.98±0.08, and 0.97±0.11, respectively. Application of a
semi-empirical model on the present and earlier wind tunnel measurements
reveals that retention coefficients can be well interpreted by the effective
Henry's law constant accounting for solubility and dissociation. A
parameterization for the retention coefficients has been derived for
substances whose aqueous-phase kinetics are fast compared to mass transport
timescales. For other cases, the semi-empirical model in combination with a
kinetic approach is suited to determine the retention coefficients. These may
be implemented in high-resolution cloud models.
Introduction
Riming is an important process leading to the growth of glaciated
hydrometeors (e.g., ice particles, snowflakes, graupel grains and hailstones) where supercooled liquid droplets collide with frozen drops or ice
crystals and subsequently freeze . Hence, it affects the
formation of precipitation sized ice particles. During riming, soluble species
present in the liquid phase could be scavenged, i.e., removed from the
atmosphere by precipitation, if they remain in the ice phase during freezing.
If they are not removed by precipitation, they may be carried aloft and
released upon detrainment and evaporation at higher altitudes, e.g., in anvil
outflows. Thus, retention during riming in the mixed-phase zone of
cumulonimbus clouds and mesoscale convective systems is crucial for the
vertical redistribution of trace substances. The amount of species
initially dissolved in the supercooled liquid droplets that is retained in the
final glaciated hydrometeor can be quantified by the so-called “retention
coefficient”, which assumes percentages or values between 0 and 1. This
retention is dependent on chemical properties such as solubility and
dissociation (effective Henry's law constant H*) but is also affected by
physical factors such as droplet sizes, liquid water content (LWC), temperature,
and ventilation. Ventilation characterizes the enhancement of heat and mass
transfer due to flow around the collecting, falling hydrometeor. Species with
high values of H* are expected to have 100 % retention. For substances
with lower values of H*, physical factors and ambient conditions become
more important .
These assumptions were confirmed by wind tunnel studies of inorganic species
. Hydrochloric and nitric acids, both
characterized by high values of H*, were found to be fully retained in ice
. For the substances with intermediate values of H*
such as ammonia, hydrogen peroxide, and sulfur dioxide the mean retention
coefficients were found to be 0.92±0.21, 0.64±0.11, and 0.46±0.16, respectively . The retention
coefficient of the most volatile substance, sulfur dioxide, was significantly
affected by the experimental conditions . Thus, one could
expect that between 50 and 100 % of inorganic species stay in the ice
phase during riming, which validates riming as an important process for
scavenging of chemicals by the ice phase.
Water-soluble organics in the atmosphere are mainly carboxylic acids and
aldehydes. Carboxylic acids are ubiquitous components of the troposphere;
their primary sources are anthropogenic and biogenic emissions, and
photochemical transformations of precursors . These
substances were detected in measurable quantities in cloud and rain water, as
well as in snow samples, and even in polar ice . The most abundant carboxylic acids
found in cloud water are formic acid, acetic acid, oxalic acid, malonic acid,
and succinic acid . Especially in remote
regions they are responsible for up to 65 % of acidity in precipitation
. But also in urban regions carboxylic acids may
contribute significantly to the free acidity in precipitation
. Furthermore, they have a low photochemical reactivity
in the atmospheric gas phase (photochemical lifetimes are more than a week),
so that important sinks for these organic acids are dry and wet deposition
.
Comparison between the experimental parameters and the ones observed
in the real atmosphere. Parameter ranges and typical values (not necessarily mean values) are also given.
ParameterExperiment Observed ReferencesRangeTypical valueRangeTypical valueTemperature (∘C)-16 to -7-11.5-15 to -5-101, 2, 3Liquid water content (LWC) (gm-3)0.5 to 1.70.90.5 to 31.03, 4, 5Droplet diameter (µm)2 to 4782 to 140153, 5, 6Size graupel (diameter) (mm)–80.5 to 523, 7Terminal velocity graupel (ms-1)–3.00.5 to 4.01.83, 7, 8Size snowflakes (diameter) (mm)10 to 15132 to 1553, 7, 9, 10Terminal velocity snowflakes (ms-1)1.8 to 2.32.00.5 to 1.51.33, 7, 9, 10, 11
1; 2; 3; 4; 5;
6; 7; 8; 9; 10;
11
Aldehydes are related to human activities and
photochemistry and are involved in many
atmospheric-chemistry processes. Photolysis is the main sink of formaldehyde
producing HOx radicals which contribute to the oxidative capacity of
the atmosphere . However, as formaldehyde is soluble in
water there is a pathway for redistribution by retention. Measurements of
cloud water samples showed that formaldehyde is the dominant aldehyde
followed by acetaldehyde and propionaldehyde . While
in the gas phase the photolysis of formaldehyde produces HOx
radicals, in the aqueous phase the reaction of OH with formaldehyde is
one of the main sinks for this radical. In this way formaldehyde is
responsible for the depletion of approximately 30 % of OH under
typical in-cloud conditions . Moreover, the reaction of
formaldehyde with OH leads to an appreciable amount of formic acid in
the aqueous phase . Furthermore, the aqueous-phase
oxidation of S(IV) to S(VI) can be inhibited by the
reaction of hydrated formaldehyde with free radicals such as OH.
Convective transport is an important process in the distribution of trace
substances in the atmosphere since it rapidly transports atmospheric trace
gases and aerosols from the boundary layer to the upper troposphere. There
they have generally longer lifetimes and are more likely to undergo
long-range transport . Especially in the tropics, convective
overshoots can lead to injection of ice particles loaded with retained trace
substances even in the lowermost stratosphere .
Moreover, the shapes of hydrometeors observed in situ at high altitudes (up
to 14km) often indicate the result of riming .
For global models, the choice of the needed convection parameterization scheme
has a substantial influence on trace gas distributions . There are some studies available in the literature which
investigate the impact of deep convection on the scavenging and
redistribution of trace substances in the troposphere but almost all emphasized the high uncertainty in their modeling
studies arising from the lack of experimentally determined retention
coefficients. This is especially true for water-soluble organic substances.
In contrast to inorganic substances the values for retention coefficients of
organics are almost unknown. The aim of this study is to experimentally
determine retention coefficients for lower carboxylic acids and aldehydes
(formaldehyde) dominantly present in cloud water samples and place the
obtained values into the context of those for inorganic species. Performing
the experiments at the Mainz vertical wind tunnel facility allowed the
simulation of conditions similar to those in mixed-phase clouds. A further
aim was a comparison with previous studies on retention coefficients and to
find a general parameterization for retention coefficients which can be
implemented in high-resolution cloud models.
Experimental
In the present experiments, single-component systems were investigated so that
the chemical properties were mainly determined by the substances themselves.
This implies that possible interactions between various species present in
the liquid phase are not considered (with the exception of CO2). As
liquid water contents and droplet sizes were nearly constant, the experiments
provided insights into the effects of physical factors like temperature
dependency, and the influence of ventilation and different collector shapes
on the retention coefficients. That is, rime collectors such as snowflakes
and ice particles were floated in a vertical air flow at velocities ranging
from 2 to 3ms-1 (i.e., their terminal settling
velocities inside clouds) and at typical temperatures where riming is known
to be effectively leading to precipitation, namely from -16 to -7∘C. Table shows a comparison of the
experimental parameters and the ones observed in the real atmosphere. Note
that only dry-growth conditions were investigated; i.e., the surface
temperatures of the rime collectors were below 0∘C during
riming. The overall methodology adopted to arrive at real retention
coefficients is complex and consists of many steps. Involved are (i)
realistic hydrodynamical considerations, (ii) application of ion
chromatography close to its detection limits, (iii) inclusion of a
concentration tracking tracer, and (iv) reduction of gas-phase concentrations
(see Eq. for the operational mathematical expression of the
retention coefficients).
The flow conditions in the Mainz vertical wind tunnel
In the Mainz vertical wind tunnel hydrometeors from micrometer to centimeter
sizes can be freely floated at their terminal fall velocities in a vertical
air stream. Therefore, ventilation (i.e., mass and heat transfer) is similar
to that in the real atmosphere. Ambient air is continuously sucked through
the tunnel by means of two vacuum pumps. To perform experiments in the ice
phase, the tunnel air can be cooled down to -30∘C. The air
flow is laminar with a residual turbulence intensity below 0.5 %. More
details about the wind tunnel design and experimental characteristics are
given in two review papers by and .
Supercooled cloud droplet characteristics
Droplet number (a) and mass distribution (b) of the
supercooled cloud generated in the wind tunnel. The average error due
to count statistics for the given distributions is 23 %.
Liquid-phase concentrations of the investigated substances and
corresponding pH. Ambient cloud water concentrations are means of three
events . The presence of CO2 (≈400µmolmol-1) was neglected in the pH calculation
except for HCHO.
The droplet size distribution in the wind tunnel air stream was measured by a
Classical Scattering Aerosol Spectrometer Probe Electronics (CSASPE), which is
a special unit designed for the wind tunnel by PMS (Particle Measurement
Systems, Inc., Boulder, CO, USA). The instrument is capable of measuring the
number distribution of droplets from 2 to 47µm (diameter) in
15 channels with a constant bin size of 3µm. The cloud of
droplets was generated in the lower part of the tunnel by two spraying
nozzles (air atomizing nozzles series 1/4 J, Spraying Systems Deutschland
GmbH, Hamburg, Germany) in a way such that clogging by freezing was
prevented. The upper panel of Fig. shows the number concentration
of the supercooled cloud measured in the experimental section of the wind
tunnel, where the actual retention measurements were performed (corrected for
coincidence effects and dead time losses). The average error due to count
statistics for each size bin was 23%. The lower panel of
Fig. shows the mass distribution, i.e., the normalized cloud
liquid water content per size interval. The mass mean diameter of the
produced cloud was 22±14µm. An alternative measurement for
the LWC was obtained from integral measurements by means of a dew-point meter
(MBW Calibration Ltd., Wettingen, Switzerland, DP3-D/SH) coupled with a 5m heated pipe. The wind tunnel air containing droplets was sampled
through the heated pipe isokinetically. After evaporation the dew point and,
thus, the absolute humidity was determined. Afterwards, the dew point of the
air without droplets was measured utilizing a droplet separator at the inlet
of the heated pipe. By subtracting both absolute humidity values an average
LWC of 0.9±0.2gm-3 was obtained. The averaging refers
to at least 100 measurements.
Liquid-phase concentrations
Table summarizes the specifications of the liquid phase (i.e., the
supercooled droplets) during the experiments. The second and third columns
show concentrations measured in atmospheric cloud water
and the concentrations used in the experiments. In
order to avoid analysis too close to the detection limit of the ion
chromatograph (IC) the concentrations used in the experiments were
approximately 1 order of magnitude higher than those found in cloud water.
However, the resulting pH values were in a range which is typically found in
cloud water, i.e., from 3.5 to 5.3 . The solutions,
containing a single substance, were prepared from high purity grade materials (see
Table ). Besides the trace substance of interest, potassium
nitrate (KNO3) was added as a concentration tracking tracer. Since
salts are non-volatile this tracer remained completely in the ice during
freezing. The tracer concentration value was used as a reference in the
retention coefficient calculation to account for processes changing the
concentration of the investigated substance. These processes include
evaporation of the droplets and dilution of the rime ice due to the pure ice
core (see Eq. ).
Experimental procedure
The supercooled solution droplets containing the substance of interest and
the tracer were injected into the wind tunnel upstream from the measurement
section by means of two sprayer nozzles which were driven by 99.999 %
N2 gas. A specially designed drop separator was installed
to avoid high ambient concentrations arising from a part of the wide beam of droplets produced by the spraying
nozzles freezing on the
tunnel walls. In this way, the adsorption of gas molecules of the investigated
substances on the rime ice could be neglected. After a duration of
approximately 8s, the droplets reached the measurement section of
the wind tunnel, where the rime collectors were positioned. Retention is
affected by the ability to transfer latent heat to the environment, which is,
in turn, given by the shape of the collector and its ventilation properties
(including terminal velocity). Therefore, three kinds of rime collectors were
investigated: ice particles, snowflakes, and two Teflon rods (FEP). In
addition, during all experiments a liquid nitrogen (LN) finger which
consisted of a permanently cooled Teflon (PFA) test tube was used for the
determination of the liquid-phase concentration of the droplets just before
riming. The freezing on the surface of the LN finger occurred so fast that
the retention value was 1; thus, the original concentration of the rimed
droplets could be measured from the deposit by IC.
To avoid a high loss rate and contamination from contacts with the wind
tunnel walls the ice particles were “captively floated”, i.e.,
tethered on a thin nylon fiber of 80µm in diameter. In this
manner they were able to move in the airstream without getting lost or contaminated and were able to properly simulate the ventilation effect. Another reason
for this simplification was the size of the ice particles. For the analysis
with IC and the associated minimum injection volume, it was necessary to
produce a relatively large ice core when compared to atmospheric ice
particles which fall at a terminal velocity of approximately 3ms-1 (3–4 mm in diameter, ). The dimension of
such a conical shaped ice particle (produced from IC-grade water) was 8mm in diameter. These ice particles would actually have a much
higher terminal velocity (≈7.5ms-1;
) especially because their density was 0.92gcm-3. However, by suspending them it was possible to ventilate them
at a typical vertical velocity of 3ms-1.
The snowflakes were produced from dendritic ice crystals
. Snowflakes with diameters between 10 and 15mm were positioned on a coarse meshed net. To assure a negligible
influence of the net on the rime process it was produced out of a thin nylon
fiber with a lattice constant of approximately 8mm. To account
for the correct ventilation, the snowflakes were “quasi-floated”, which
means that they were floated at an updraft velocity just before they were lifted from the net. In this manner the velocities were always close to
the terminal velocities of the snowflakes. Due to the different sizes and
slightly different bulk densities of the snowflakes the terminal velocities
varied between 1.8 and 2.3ms-1.
The FEP rods served as a reference since the rimed ice of these
collectors was not diluted after melting as in the case of the ice particles
and snowflakes. The FEP collectors were used to measure the retention
coefficient at different ventilations. Furthermore, the retention coefficients of
these collectors were used for the comparison with previous experimental and
theoretical works .
After a typical exposure time of 10min the rimed samples were
collected and the meltwater from them was analyzed with IC as described in the
next subsection.
Chemical analysis
All five substances were analyzed by ion chromatography using a DIONEX
ICS-1000 system (Dionex Corporation) in combination with the software package
Chromeleon. Prior to analysis, formaldehyde was oxidized with H2O2
to formic acid and analyzed with the same setup as described above
. In order to validate the above method, consistency checks were performed by analyzing solutions of known concentrations.
Calculation of the retention coefficient
The retention coefficient was determined by the following ratio:
R=Csubstancesample/CtracersampleCsubstanceLN/CtracerLN.
Here, the numerator describes the ratio of the concentration for the
substance of interest in the ice sample
Csubstancesample to the tracer concentration in the ice
sample Ctracersample. The denominator describes the
same ratio but sampled using liquid nitrogen cooling. With this description,
it is not required to account for dilution correction or evaporation
correction since these effects change both the substance and the tracer
concentration so that the ratio is not altered. This ratio also includes the
desorption effect prior to riming since the denominator contains this loss
already due to the direct measurement of the liquid-phase concentration. (The
retention coefficient is 1 at such low temperatures.) Therefore, a change
in this ratio is solely an effect of the retention of the substance. The
error of the liquid-phase concentrations is estimated as 4.5 % including
the instrumental error of the IC and the error of the pipette used for
producing the calibration standards for the IC. Taking these errors and
applying error propagation on Eq. () yields a typical error for
the retention coefficients of 9 %.
Results and discussion
Retention coefficients of all measured substances as a function of
temperature for different rime collectors. Red symbols: rimed ice particles.
Blue symbols: rimed snowflakes. See Sect. for details.
Figure shows the retention coefficients as a function of
temperature for all investigated organic substances, namely formic acid (a),
acetic acid (b), oxalic acid (c), malonic acid (d), and formaldehyde (e). The
red symbols depict the rimed ice particles and the blue symbols the rimed
snowflakes. Also given in Fig. are the number of data points
N and the average retention coefficients R (for formic acid and acetic
acid R is the value at -11.5∘C; for the other substances
it is the arithmetic mean including both collector types). The temperature of
-11.5∘C corresponds to the mean temperature of the
measurements and is specified as Tm in the next subsections. In
addition to the 95 % error (2SD) and the minimum/maximum values (labeled
as “Min” and “Max”), the dimensionless effective Henry's law constants
are shown for the pH of the droplets at 0∘C. Note that all
errors in this section correspond to 2 standard deviations (2SD). In Fig. a and b the
(dashed) red and blue curves represent linear regressions of the retention
coefficients of the ice particles and snowflakes, respectively. The black
lines in Fig. a are the linear regression as well as the 95 %
confidence bands of the whole data set, i.e., including all results for ice
particles and snowflakes. The red line in panels (c), (d), and, (e) indicates
a retention coefficient of 1, or 100 %.
Formic acid
For both rime collectors, the ice particles and the snowflakes, a
statistically significant negative temperature dependency (dashed lines in
Fig. a) was found using a statistical regression test
(significance level α=0.05). However, when comparing the linear
regressions of both collectors with the 95 % confidence bands of the
overall regression (solid black lines), the difference in the temperature
dependencies of the retention coefficients is negligible. Therefore, the mean
retention coefficient is determined by the overall regression which yields
R(Tm)=0.68±0.09. Finally, the retention coefficient of formic
acid is only weakly dependent on temperature (when considering the error in the observed temperature range)
with negligible dependencies on the shape of the collector and the
ventilation conditions. The parameterization of the temperature dependency is
given in Table . The weak temperature dependency might be
explained by the intermediate value of H*. In this range H* slowly
loses its dominant influence, which allows physical factors such as
temperature to become more significant. There are three reasons behind the
temperature dependence: first, at higher temperatures ice crystallization
inside a freezing droplet proceeds slowly, which promotes the segregation
process of molecules; i.e., the molecules diffuse more readily into the
liquid phase and are not so effectively immobilized by the growing dendrites.
This process increases the concentration in the liquid phase and drives the
substance into the gas phase. According to this is the
only factor controlling the solute transport out of the freezing droplet.
Second, H* is lower at higher temperatures which additionally shifts the
equilibrium towards the gas phase. Third, at higher temperatures the
formation of an ice shell along the surface of the still supercooled liquid
proceeds more slowly. Thus, the dissolved substances have more time to escape
from the freezing droplet into the gas phase, which eventually reduces the
retention coefficient.
Retention coefficients of the measured substances, their temperature
dependencies, and the effect of ventilation. s.: significant; n.s.: not
significant; IP: ice particles; and SF: snowflakes. Organic species: present
study. Inorganic species: adopted from and
. HC: high concentration. LC: low concentration.
In contrast to formic acid the retention coefficients of acetic acid show a
more pronounced temperature dependency. Additionally, a significant
dependency of the retention coefficients on the shape of the collectors and
the ventilation conditions is evident. The mean retention coefficients of the
ice particles and the snowflakes at Tm are 0.72±0.16 and
0.54±0.11, respectively. The corresponding temperature dependencies at
the 95 % confidence interval of the ice particles and the snowflakes are
listed in Table . These dependencies can be partially
explained by the lower effective Henry's law constant compared to formic
acid. Due to the lower H* the influence of temperature becomes more
pronounced. Furthermore, the temperature dependency of H* of acetic acid
is slightly higher compared to that of formic acid, which in turn increases
the temperature dependency of the retention coefficient. A comparison of the
ice particles and the snowflakes shows that the retention coefficient of the
snowflakes is on average reduced by 0.18. This decrease might be explained
by the combination of the lower value of H* and a slower heat transfer
process for the snowflakes compared to the ice particles which results from
the reduced ventilation effect. First, the snowflakes were floated at
approximately 2ms-1, while the ice particles were floated
at 3ms-1. This difference in the settling velocities
arises from the differences in size, bulk density, and shapes of the
collectors. Second, the flow through the branches and around the snowflakes
reduces the effective ventilation to the total exposed surface of the
snowflakes. Compared to compact spheroidal ice particles this causes slower
freezing times of the droplets and as a result acetic acid has more time to
escape from the freezing droplets.
Comparison of formic acid and acetic acid results
Apparently, the retention coefficients of the snowflakes for formic acid
R(Tm)=0.67 and acetic acid R(Tm)=0.54 differ by
0.13. This difference can be explained by taking the mole fractions of the
ionic species (formate and acetate) and molecular species (formic acid and acetic
acid) into account. Besides the solubility, H* also depends strongly on the
dissociation of a species, which, in turn, is a function of pH. At the pH of the
formic acid solution droplets (pH=4.3), only 21 % of the total
dissolved formic acid is present in the molecular form (calculated at 0∘C) and the remaining 79 % is in the ionic form. In
contrast, at pH=4.5 for the acetic acid droplets 64 % is present
in the molecular form and 36 % is in the ionic form. A dissociative
substance first has to recombine to the molecular form before leaving the
droplet and reenter into the gas phase. Even though association
(recombination) occurs quickly compared to the other timescales involved in
the retention process (e.g., those of aqueous-phase transport, interfacial
transport, gas-phase transport of a molecule, and the freezing time), it
influences the retention of acetic acid less than that of formic acid. This
is because acetic acid is 3 times more present in the molecular form
compared to formic acid which facilitates its escape to the gas phase.
Furthermore, the association timescale for acetic acid is 1 order of
magnitude faster than that of formic acid which further increase the
degassing rate for acetic acid or on the other hand decrease that for
formic acid. Moreover, an acetic acid molecule is larger (and rather linearly
aligned) than a formic acid molecule which promotes the segregation of acetic
acid from ice. This means that the concentration in the liquid part of the
freezing droplet increases faster for acetic acid than for formic acid. This
effect might lead to the formation of a concentration gradient at the
liquid–gas interface forcing the acetic acid molecules to reenter the gas
phase.
Comparing the mean retention coefficients (R(Tm)) of the ice
particles for acetic acid and formic acid shows that they are very close to
each other. Due to the stronger temperature dependency, the retention
coefficients of acetic acid are slightly higher at low temperatures; however,
this enhancement is within the measurement uncertainty.
Dicarboxylic acids – oxalic and malonic acids
Figure c and d represents the results of oxalic acid and malonic acid for which H* are
almost 9 orders of magnitude higher compared to the above discussed
monocarboxylic acids. This high H* dominates the retention process
, which is also reflected by the experimental results.
Application of the statistical regression test on the data of oxalic acid and
malonic acid reveals that the retention coefficients for both collectors do
not significantly depend on temperature, and the retention coefficients can
be given by their average values. The mean retention coefficients of oxalic
acid for the ice particles and the snowflakes are 0.99±0.06 and 0.94±0.06, and between the two rime collectors there are no differences. The
mean retention coefficients of malonic acid for the ice particles and
snowflakes are 1.00±0.08 and 0.96±0.08, respectively. Hence, for
both acids the difference between the two rime collectors is negligible.
Oxalic acid and malonic acid are strong, fully dissociated acids at
pH=4.3 and pH=4.5. This, in combination with their
high intrinsic Henry's law constant results in a large H* that dominates
all other environmental parameters influencing the retention process.
Formaldehyde
Formaldehyde, similarly to the dicarboxylic acids, is almost completely
retained in the ice during dry-growth riming even for a relatively high
concentration (see Table ). From Fig. e it is obvious
that the retention coefficients of the ice particles and the snowflakes are
independent of temperature showing high mean retention coefficients of 0.98±0.06 and 0.95±0.10, respectively. As in the case of the
dicarboxylic acids both values agree within the measurement error. While the
retention of the dicarboxylic acids can be explained by the strong
dissociation and intrinsic Henry's law constant, formaldehyde is only a weak
acid with pKa=13.3. Also, its intrinsic Henry's
law constant is low, comparable to sulfur dioxide or hydrochloric acid.
However, it undergoes hydration in aqueous solutions forming methanediol (see
Reaction ) with a hydration constant of
Khyd=kR1/k-R1=1280 (at T=298K; ).
CH2O(aq)+H2O⇌k-R1kR1CH2(OH)2(aq)
Hence, H* of formaldehyde does not account for the intrinsic Henry's law
constant and dissociation but rather for the intrinsic Henry's law constant
and hydration. Especially at low concentrations the diol form is the favored
one . According to the hydration constant Khyd
at T=298K, 99.9 % of the total dissolved formaldehyde is
present as methanediol, whereas less than 0.1 % is present as monomeric
formaldehyde. Furthermore, at such low concentrations as in the present
experiments all formaldehyde and methanediol are in their monomeric forms
. Nevertheless, the values of H* for formaldehyde are
rather in an intermediate range, comparable to formic acid and acetic acid,
but the retention is 100 % within the measurement error. This indicates
that the retention cannot be fully explained by the value of H*, which only accounts for equilibrium
conditions and gives no information on kinetic aspects. If formaldehyde gets
dissolved in water its equilibrium between monomeric formaldehyde and
methanediol is attained comparatively fast with a rate constant of
kR1=10.7s-1 (at T=298K,
). However, if the equilibrium is shifted towards
monomeric formaldehyde and, thus, the gas phase, methanediol first has to
dehydrate with a very low
rate constant (k-R1=8.4×10-3s-1 at 298K;
). Presumably, the combination of both the strong
hydration of formaldehyde and the low dehydration rate constant are
responsible for the high retention coefficient. This means that, within the
freezing time of a droplet (approximately 1ms for a ventilated
spread 10µm droplet), the methanediol dehydrolyzes to a very
small extent. Therefore, the dissolved formaldehyde gets almost fully
incorporated into the ice phase leading, to a retention coefficient close to
1.
(a) Retention coefficient as a function of retention indicator.
Filled symbols: organic substances of the present study. Open symbols:
wind tunnel data from earlier studies .
The black filled symbol for formaldehyde and the magenta open symbol for
ammonia represent values for equilibrium conditions neglecting the aqueous-phase kinetics (see text for details). Vertical error bars are measurement uncertainties.
Horizontal error bars account for the two limits of adiabatic freezing time and total
freezing time of the droplets. Dotted line: fit according to
. Solid line: new fit of the wind tunnel data.
(b) Retention coefficients as a function of H*. Symbols according to (a).
Solid line: new fit of the wind tunnel data. The H* values are calculated from
literature (see Table ) at given pH and at 0∘C.
Application of a semi-empirical model and comparison with previous works
To the best knowledge of the authors, there are no data of retention
coefficients for organics available in the literature. Therefore, the obtained
values are juxtaposed with the corresponding results for inorganic species as
measured in earlier studies at the Mainz wind tunnel laboratory
. Two questions are to be answered in this
section: (i) is H* the controlling parameter for both inorganic and
organic substances? (ii) Can a reliable parameterization be obtained from
such a comparison?
Model description
A meaningful tool is provided by the semi-empirical model of Stuart and
Jacobson which relates the experimentally
obtained retention coefficients with the so-called retention indicator (RI).
This is the ratio of the expulsion timescale (τexp) of a
species from the liquid phase to the freezing time (τfrz) of
the droplets during riming. In order to find functional dependencies of RI,
first a systematic study was carried out on the influences of chemical factors on the retention process.
These factors included the effective Henry's law coefficient, mass accommodation, aqueous
diffusivity, and gas diffusivity as well as physical factors like temperature, droplet size
and ventilation . In
a later study, the timescale analysis was extended to dry-growth riming
accounting for spreading of the droplets' liquid onto the collector's surface
and the riming conditions prevailing on a ventilated rimed rod
. The most relevant aspects concerning the RI are briefly summarized here (for details see ).
Input parameters for the determination of the retention indicator
and calculated timescales.
SubstanceHCHOHCOOHCH3COOH(COOH)2CH2(COOH)2HClHNO3NH3H2O2SO2 (HC)SO2 (LC)Air temperature, ∘C-11-11-15to-7-11-11-11-11-11-11-15to-7-11Pressure, hPa1.013×1031.013×1031.013×1031.013×1031.013×1031.013×1031.013×1031.013×1031.013×1031.013×1031.013×103Liquid water content, gm-30.90.90.90.90.91.21.21.21.21.21.2Mean volume radius of droplets, µm1010101010131313131313Average collector radius, mm1010101010101010101010Wind tunnel air speed, ms-1332to3333333331 Spreading factor1.41.41.3to1.51.41.41.41.41.41.41.3to1.51.4Height of spread cylinder, µm6.86.87.9to5.96.86.88.88.88.88.810.3to7.78.82 Surface temperature, ∘C-8.7-8.7-12.3to-4.6-8.7-8.7-7.8-7.8-7.8-7.8-12to-3.9-7.8Growth regimedrydrydrydrydrydrydrydrydrydrydryConcentration, molL-11×10-46.5×10-58.3×10-55.6×10-52.9×10-54.7×10-41.6×10-45.9×10-52.9×10-53.6×10-48.6×10-53 pH5.34.34.54.34.53.33.86.45.33.54.14H* at given pH (0∘C)5.3×1056.1×1061.0×1064.5×10141.4×10151.4×10129.4×10138.7×1051.6×1075.0×1032.0×1045 Mass accommodation (0∘C)0.0140.0470.0670.2600.3070.1790.1520.2020.2340.3350.335Thermal velocity in air (0∘C), ms-14393553102532363983035834123013016 Diffusivity in air (0∘C), cm2s-10.150.120.100.080.070.140.100.210.140.100.106 Diffusivity in water (0∘C), cm2s-16.9×10-67.6×10-66.0×10-65.3×10-64.6×10-61.1×10-56.8×10-61.1×10-59.5×10-67.3×10-67.3×10-67 Ventilation coefficient31343032302638273532328τr, s9935.41.6×10-68.9×10-8107.0×10-7101.2×10-6112.2×10-8116.3×10-8121200.06.8×10-72.9×10-72.9×10-7τaq, s6.67×10-26.11×10×10-2137.70×10-28.75×10-21.00×10-17.24×10-21.15×10-17.48×10-28.22×10-21.08×10-11.08×10-1τi, s8.18×10-13.31×100134.31×10-17.21×1071.96×1082.3×1051.02×1068.99×10-21.54×100137.97×10-43.96×10-3τg, s1.66×10-22.20×10-1134.82×10-22.95×1071.02×1081.02×1052.8×1054.15×10-26.64×10-1135.64×10-42.80×10-3τexp, s9.36×1023.59×100135.56×10-11.02×1082.97×1083.34×1051.31×1061.2×1032.28×100131.09×10-11.14×10-1Limiting resistanceτrτiτi+τgτi+τgτi+τgτi+τgτiτrτiτaqτaq13τad, s1.03×10-41.03×10-41.03×10-41.03×10-41.03×10-41.34×10-41.34×10-41.34×10-41.34×10-41.34×10-41.34×10-413τd, s9.93×10-49.93×10-49.93×10-49.93×10-49.93×10-41.79×10-31.79×10-31.79×10-31.79×10-31.79×10-31.79×10-3τfrz, s1.10×10-31.10×10-31.10×10-31.10×10-31.10×10-31.93×10-31.93×10-31.93×10-31.93×10-31.93×10-31.93×10-314 RI2.79×1061.07×1041.65×1033.02×10118.85×10116.57×1082.57×1092.36×1064.50×1032.15×1022.25×10215R0.96±0.040.74±0.100.59±0.110.99±0.030.99±0.030.99±0.030.99±0.040.92±0.210.64±0.140.29±0.070.53±0.09
1 Inter- and extrapolated from
. 2 Calculated for the
corresponding LWCs for 3ms-1. 3 The
presence of CO2 was neglected except for HCHO and
H2O2. The pH of NH3 was measured in the meltwater of the
pure rime ice. The pH calculation neglects the second dissociation stage.
4 Calculated at 0∘C and at the corresponding pH
().
5 The mass accommodation coefficients (α at 273K) are
taken from a review paper or estimated as described
elsewhere . 6 The diffusivities in air Dg and in
water Daq at 273K have been calculated at 273Kp. 78ff.. 7 The convective
enhancement of heat and mass transport due to ventilation is calculated for
the dimension of the rimed rod using the parameterization of
. 8 Calculated from unless
specified otherwise. Values for kf and kr from
. kf and kr specify
the forward and reverse reaction rate constants of dissociation/association.
9 Assumed as 1/k-1 since the mass transport is fast compared to the
dehydration rate constant. 10 Sum of first and second dissociation stage
timescale, i.e.,
τr=τr(1st)+τr(2nd).
11kr assumed to be diffusion controlled
kr=5×1010Lmole-1s-1. 12
Assumed as the desorption timescale determined by .
13 Value for 3ms-1 at -11∘C. 14
Calculated for the geometric mean of the adiabatic freezing time
τad
and the total freezing time τfrz as ice shell formation is more likely to occur shortly after the adiabatic freezing time.
15 Note that the values of the present work are arithmetic means of all
data points of the FEP rod collectors (results not shown here).
The expulsion timescale τexp is the sum of characteristic
timescales which are relevant for an individual substance to leave a water
droplet and enter the gas phase . Formally the individual
timescales are given as
τexp=h2H*3Dgf¯︸τg+h2H*3Dgf¯4hH*3v¯αm︸τi+h2H*3Dgf¯h2Daq︸τaq+τr,
where h=4a/3S2 is the spread droplet height, a the droplet radius, S
the spreading factor, H* the effective Henry's law coefficient, f¯
the mean gas-phase ventilation coefficient (related to the collector's fall
speed), Dg the diffusivity of the chemical in air, ν¯ the thermal
velocity of the chemical in air, α the mass accommodation coefficient,
and Daq the diffusivity of the chemical in water. The first term
on the right-hand side of Eq. () describes gas-phase mass transport
(τg), the second term the interfacial mass transport
(τi) and the third term the aqueous-phase mass transport
(τaq). Here, a fourth timescale (τr) which
describes the kinetics of aqueous-phase reactions (i.e., association,
; dehydration, ; or reaction with
CO2, ) is added to the expulsion timescale.
This timescale has been neglected in the earlier works because acid/base reactions are generally fast compared to the
other processes involved. However, as shown below, it becomes important for
properly determining the retention coefficients of formaldehyde and ammonia
in the presence of carbon dioxide . The dehydration
timescale results from Reaction () as it is the inverse first-order rate constant k-1 of the reverse reaction.
The total freezing time of the droplets is calculated as the sum of the
adiabatic and the diabatic freezing time, viz.
τfrz=τad+τd.
During adiabatic freezing no heat exchange with the environment takes place.
In the associated time the dendrites penetrate through the supercooled liquid
droplet and heat it up to 0∘C. Note that in this time only
a small fraction of the water mass is frozen depending on the supercooling of
the droplets. It is assumed that shortly after this time ice shell formation
is likely to occur. This would inhibit a further removal of the substance
from the freezing droplet and, hence, increase the retention coefficient
. The diabatic freezing time is
determined by the rate of latent heat removal to the underlying rime
substrate and the ambient air . The ventilation decreases
the diabatic freezing time by increasing the heat removal to the ambient air.
Due to the increased ventilation, heat transfer to air dominates that to the
substrate which facilitates ice shell formation. The retention indicator is
calculated as
RI=τexpτfrz.
If this ratio is much higher than 1 then the substance is assumed to be
fully retained in ice. If, in turn, this ratio is much lower than 1 then the
substance is presumably fully expelled from the freezing droplet. Values for
this ratio in an intermediate range are assumed to be directly related to the
experimentally obtained retention coefficients .
All necessary parameters for the calculation of the individual mass transfer
timescales (Eq. ) together with the references of the values as
well as the limiting timescales, the freezing times (Eq. ), the
retention indicator (Eq. ), and the experimentally obtained
retention coefficients for all chemical substances measured in the Mainz wind
tunnel laboratory are compiled in Table .
Application of the model to the present and earlier wind tunnel results
In Fig. a the retention coefficients of organic substances (filled
symbols) investigated in the present study as well as the inorganic
substances (open symbols) from earlier wind tunnel studies
are plotted as a function of the retention
indicator. Note that RI was calculated as the geometric mean of the adiabatic
and the total freezing time. The horizontal error bars indicate the two
limits of adiabatic freezing and total freezing time of the droplets. In this
way, ice shell formation is accounted for, which is assumed to be more likely to occur shortly after the adiabatic freezing
time . The retention coefficient of
SO2 was measured for two different concentrations, one at a high
value of 360µmolL-1 (HC) and one at a low
concentration of 86µmolL-1 (LC) which has a retention
coefficient of 0.53. In the HC case the retention coefficient showed a
significant negative temperature trend and the retention indicator as well as
the retention coefficient was calculated at three different temperatures:
-7, -11, and -15∘C. The same was done for acetic acid,
although in this case a distinction was made between the different rime
collectors in order to account for the ventilation effects. The other
substances did not show any significant temperature and ventilation
dependencies and, hence, the retention coefficients represent average values.
In these cases the retention indicators were calculated at a mean temperature
of -11∘C and at a ventilation corresponding to 3ms-1. The retention coefficients used in the intercomparison
with the semi-empirical model were obtained from the experiments utilizing
FEP rods as rime collectors. This was done because the freezing time
calculations considered the conditions which prevailed on a previously rimed
rod. Therefore, the retention coefficients differ slightly from the ones
discussed in the previous section. This is especially the case for formic
acid, whose retention coefficient is not temperature dependent for the FEP
rods. The heat transfer for these collectors is more efficient compared to
the ice particles and the snowflakes since they consisted of a stainless
steel core. This caused a faster freezing of the droplets, which counteracted
the weak temperature dependency of the retention coefficient for formic acid.
A second result originating from the better heat transfer is that the average
retention coefficient is slightly higher than in the previously presented
results from Sect. . Consequently, the retention coefficient
for formic acid is given as average value and not for three different
temperature values. For NH3 and HCHO, RI was calculated for
two different expulsion timescales: one neglects the aqueous-phase kinetics
(i.e., τr=0 in Eq. ) while the other one includes it
(i.e., τr>0 in Eq. ). This is indicated by the
magenta open symbol for ammonia and the black filled symbol for formaldehyde
for which the aqueous-phase kinetics are neglected. In contrast, the values
represented by the purple open symbol as well as the red filled symbol
include the aqueous-phase kinetics. The results for these two substances are
discussed in more detail in Sect. . For the remaining
substances, RI was calculated including τr, however, it is
negligible for these substances. That is, τr is several orders
of magnitude smaller than the other involved timescales. The dotted line in
Fig. a is an exponential function of the following form:
RSJ=1-exp(a5RI),
where a5=-0.002±0.001, RSJ is the parameterized
retention coefficient, and RI the retention indicator according to
Eq. () . However, the wind tunnel data suggest
a somewhat smoother transition from low to high values. Thus, it is better
represented by
RRI=1+a6/RIb6-1.
Here a6=618±71 and b6=0.64±0.06 are fit parameters with
1σ errors. Note that for this parameterization the values for
NH3 and HCHO with aqueous-phase kinetics are considered. In
order to quantify the accuracy of the parameterizations the average absolute
error ε is defined as
ε=1N∑i=1N|RSJ,RIi-Rexpi|,
where N is the total number of substances i. RSJ,RIi are the
retention coefficients applying Eq. () or () and
Rexpi are the experimentally obtained values. Utilizing
Eqs. () and () on the data yields ε=0.16 and
ε=0.06, respectively. Thus, the presently proposed fit function
(Eq. ) increases the accuracy by a factor of about 2.5 compared
to the formerly used exponential function (Eq. ). This improvement
can be attributed to the consistency of the wind tunnel experiments as well
as to the larger number of investigated substances. While Eq. () is
based on five inorganic substances which were measured under different
experimental conditions, the wind tunnel data of this study represent results
of 10 organic and inorganic substances which were measured under very
similar experimental conditions.
Since the retention indicator is strongly affected by the effective Henry's
law constant it is worthwhile to investigate the
dependency of the measured retention coefficients on H*
(Fig. b). The data points represent average values of the retention
coefficients of the substances. The fit curve is described by the same
functional relationship as in the case of RRI parameterization
(NH3 and HCHO are excluded as discussed below):
RH*=1+a8/H*b8-1.
Here the fit parameters are a8=1.69±1.05×105
and b8=0.26±0.05. From Fig. b it is obvious that the
mean retention coefficients for all investigated acids as well as for
H2O2 regardless of whether they are inorganic or organic can be well
described solely by H*. Application of the RH* parameterization to
the acids and H2O2 yields a high accuracy of ε=0.04. The
overall mass transfer timescales (Eq. ) for the considered
substances are mainly controlled by gas phase or interfacial transport (see
Table ). The presence of CO2 has a negligible effect
on the mass transfer for these substances since it is only a weak acid
(pKa≈6.4) and does not interact with them in the aqueous
phase. Even H2O2 is not affected by CO2 because it is more
or less independent of pH. Thus, aqueous-phase reaction kinetics are
negligible for these substances. This makes the retention coefficients a
strong function of H* as previously pointed out in the literature
. Furthermore, the experimental conditions of
the studies concerning the inorganic substances and the present study are very similar. Therefore, the
negligible aqueous-phase kinetics and the similarity of the experiments are
thought to yield such a small value of ε. However, while the
RRI parameterization (Fig. a) also accounts for
ventilation, temperature, droplet size, and LWC, the RH*
parameterization (Fig. b) only accounts for solubility and
dissociation. Nevertheless, to a first order
approximation, it describes the mean of the retention coefficients quite well, especially because for most
investigated substances temperature and ventilation effects are small.
Consequently, the parameterization given in Eq. () can be applied to
temperatures between -15 and -7∘C within the
corresponding errors.
Note that the most volatile substance depicted in Fig. is
SO2. For even more volatile substances the influence of the physical
factors might become stronger, probably increasing the error of the RH*
parameterization. However, the results of SO2 suggest that the mean
of the retention values can also be obtained by the RH*
parameterization in such cases. While the retention coefficient of
SO2 (LC) showed neither a temperature nor a collector shape
(ventilation) dependency, the retention coefficient R for SO2 (HC)
was dependent on both parameters. Moreover, increasing the concentration from
86 to 360µmolL-1 led to a decreasing pH from 4.1
to 3.5, resulting in a smaller H*. Even then the main part of the strong
decrease in the retention coefficient from 0.53 to 0.29 could be
attributed to the shift in H* (see Fig. b). Therefore, it can be
surmised that also for substances which are more volatile than SO2,
H* is the main factor determining the retention coefficient in the
dry-growth regime. However, these results show that the retention
coefficients for substances which dissociate may be affected by the pH of the
droplets. The effective Henry's law constant H* combines the dissociation
and the intrinsic Henry's law constant. Hence, when at least one of these
constants has a high value, H*
also becomes high making it the controlling factor for retention. In such a
case the substances are more or less independent of the pH of the droplets
because they are either fully dissociated or have a high solubility. On the
other hand, if both values are low or in an intermediate range, that is, if
the substances are not fully dissociated and their solubility is low, they
are dependent on pH. Experiments on the concentration dependency of the
retention coefficients for HCl and HNO3 showed that their
retentions were invariant in a pH range between 2.6 and 3.7. These two
substances are fully dissociated for pH >1, meaning that for higher pH
values these acids are expected to show 100 % retention. Furthermore,
HNO3 possesses besides the high dissociation constant also a high
intrinsic Henry's law constant, which suggests a retention of 100 %, even
for a pH lower than 1. The same is expected for the two investigated
dicarboxylic acids: oxalic acid and malonic acid for low pH values. These two
acids have very high intrinsic Henry's law constants and moderate
dissociation constants. Thus, their high retention values are mainly caused
by the low volatility and not by the dissociation making their retention
coefficients more or less independent of pH. This is not the case for the
monocarboxylic acids for which the intrinsic Henry's law constants as well as
the dissociation constants have moderate values. Hence, the intrinsic Henry's
law constant is not the dominating factor making formic acid and acetic acid
more sensitively dependent on pH, similarly to sulfur dioxide. That means,
for a decreasing pH in the droplets, that the retentions for the
monocarboxylic acids presumably decrease too and vice versa. Finally, the
combined value of the equilibrium constants (i.e., H*) decide to what
extend the pH affects the retention. Therefore, the effect of the pH of the
droplets on retention is included in the derived parameterizations as is
evident from the results of SO2 as well as HCl and
HNO3.
Effects of aqueous-phase reactions on retention
Conceptually, the RH* parameterization is only valid for substances
whose aqueous-phase kinetics and reactions are negligible. This is not the case for NH3 and HCHO.
Ammonia
The solubility of NH3 is increased by several orders of magnitude in
the presence of atmospheric CO2. In the wind tunnel investigations on
the retention coefficient of NH3, the pH of the droplets was measured
at consecutive times . Initially the solution had a pH of
about 9, which decreased approximately 2s after the production
of the droplets to about 8. Finally the pH of the meltwater from the rimed
material was 6.3. This measurement shows that the droplets absorbed
CO2 in the time they were exposed in the wind tunnel (≈8s). However, H* was calculated at pH 6.3 in Fig. b
and, thus, already accounting for such an enhancement of the solubility.
Nevertheless, the RH* parameterization does not reproduce the high
retention value of NH3. In Fig. a, the RI of NH3
(RI ≈400) was calculated neglecting the aqueous-phase kinetics of
the CO2 reaction with NH3 (see Reactions and
in the text below). According to the
RRI parameterization, R should be about 0.4, which is a
deviation much higher than explainable by the measurement error. An
experimental study on the desorption of NH3 in
the presence of CO2 from a water drop revealed that the desorption of
NH3 is determined by two different time constants. The first one is
governed by the mass transfer equivalent to
τaq+τi+τg, which can be considered as
the inverse of the overall mass transfer rate coefficient
kmt-1. However, in the meantime the droplet containing
NH3 absorbs CO2 gradually, which reacts rapidly with
OH- according to the following reaction describing the coupling of
NH3 and CO2 in alkaline aqueous solution:
NH3(aq)+H2O⇌k-R2kR2NH4++OH-,CO2(aq)+OH-⇌k-R3kR3HCO3-.
Initially the system is in equilibrium according to
Reaction (). At the very beginning when the droplets are
exposed to ambient air the desorption process is determined by mass transport
since the acid/base equilibrium adjusts very fast. In the presence of
CO2 (at alkaline pH) the reaction given by Reaction ()
becomes important and inhibits the reverse Reaction ().
CO2(aq) reacts fast with OH- and forms HCO3-
(kR3=2.3×103s-1 at 6.6∘C; ). However, the reverse reaction is very slow
(k-R3=1.4×10-5s-1 at 6.6∘C; ) so that the opportunity of the
OH- ions to recombine with NH4+ in order to form the
volatile aqueous NH3(aq) is hindered. By also applying a convective
diffusion model including internal circulation of the liquid within the
falling drop, it was shown that the time to completely
deplete a drop of 2.88mm in radius from NH3 and to reduce
CO2 back to equilibrium conditions would be 1200s. This
timescale is taken into account in the retention indicator calculation as
τr (Eq. ). Despite the large differences in the
investigated drop sizes it is justified to take that value since desorption
is mainly determined by the slow reverse Reaction (). In other
words, the characteristic time of desorption in case of ammonia is controlled
by chemical reaction rather than by mass transport.
Formaldehyde
A kinetic effect in the aqueous phase was also observed in the case of
HCHO. The high retention coefficient in Fig. b cannot be
explained by H* although hydration is included. In Fig. a, the RI for
HCHO which only accounts for mass transport (i.e.,
kmt-1) is given by the red open circle at RI ≈3000.
It is in the same range as H2O2 and CH3COOH. However, it
shows a retention coefficient of 0.96 which is well above the value
predicted by the RRI parameterization. This indicates that even
mass transport effects, for example mass accommodation, cannot explain
the high retention coefficient. Obviously, the overall expulsion timescale is
strongly controlled by τr, which is the rate-limiting step in
the desorption of HCHO (see Table ). Consequently,
τr=1/k-R1=935.4s (k-R1
extrapolated to 0∘C) is added to the characteristic
timescales for mass transport (Eq. ). Similarly as in the case of
NH3 the chemical reaction timescale τr controls the
desorption of HCHO and, therefore, retention. (Here it is not H* as
in cases of negligible aqueous-phase kinetics.)
The two substances NH3 and HCHO show how aqueous-phase chemical reaction kinetics could influence the retention coefficient.
Particularly for such short timescales as the freezing of a 10µm ventilated spread droplet (τfrz≈10-3s)
the recombination/dehydration kinetics become very important for the
retention process. On these short timescales this kinetic inhibition of
volatilization can be viewed as an increase in solubility. For all other
substances for which recombination is fast the retention can be very well
described by mass transport kinetics alone, which in dry-growth conditions are
predominantly determined by H*. This might not be the case if one considers
wet growth of macroscopic-sized hail where not simply one parameter dominates
the retention of volatile species but rather a combination of the ice–liquid
interface supercooling, the LWC of the hail, and H*. Hence, it is likely that physical factors determining
retention such as ventilation, temperature, LWC, and droplet size become more
important under wet-growth conditions and H* loses its dominant role.
Conclusions
Wind tunnel experiments were carried out to determine the retention
coefficients of lower carboxylic acids and aldehydes during riming. Rime
collectors such as snowflakes and ice particles were investigated under
typical dry-growth riming conditions, i.e., temperatures from -16 to -7∘C and an LWC of 0.9±0.2gm-3. By keeping the liquid water content and the droplet size
distribution (mean mass diameter 22±14µm) nearly constant
during each experimental run the measurements provided information about the
dependencies of the retention coefficients on ventilation effects (such as
heat and mass transfer) and on ambient temperature. The retention
coefficients of the measured monocarboxylic acids, formic and acetic acids,
showed significant negative temperature dependencies. While the results of
formic acid indicated a negligible effect on the ventilation, the results of
acetic acid revealed a significant decrease in retention when comparing the
ice particles (vertical velocity w=3ms-1) to the
snowflakes (w=2ms-1). The measured mean retention
coefficients of formic acid and acetic acid were 0.68±0.09 and 0.63±0.19, respectively. Oxalic acid and malonic acid as well as formaldehyde
showed retention coefficients of 0.97±0.06, 0.98±0.08, and 0.97±0.11 without significant temperature and ventilation dependencies.
The application of a semi-empirical model on the present
experimental results and on the previously obtained retention coefficients
for inorganic substances show that
retention can be well described by the retention indicator, i.e., the ratio
of the sum of kinetic mass transfer timescales to the freezing time of the
droplets on the surface of the collector. For those substances for which
aqueous-phase kinetics (chemical reaction or association) are fast compared to
mass transport the mean values of the retention coefficients can be well
interpreted using the effective Henry's law constant. The derived functional
relationship of retention coefficients on the effective Henry's law constant
suggests a high accuracy, which makes it a very simple estimation tool for
retention coefficients, probably also for substances not investigated so far.
Thus, the parameterization can be easily implemented in high-resolution cloud
models which include retention in the dry-growth riming regime.
However, from the measurements with formaldehyde and ammonia it was found
that retention is primarily controlled by aqueous-phase kinetic effects. The
retention of formaldehyde is controlled by the dehydration of methanediol. On
such short timescales as the freezing of cloud droplets this can be
considered as an increase in solubility and, therefore, retention. The
retention of ammonia is strongly affected by the kinetics of the reaction of
CO2(aq) with OH-. Both cases emphasize the importance of
accounting for chemical reactions when describing retention. However,
modifying the semi-empirical model by adding appropriate
kinetic timescales (e.g., by adding the inverse of dehydration rate) makes it
a well-suited tool for describing retention coefficients even for such
substances for which aqueous-phase kinetics are the limiting factor.
Generally, acid/base reactions are several orders of magnitude faster than
mass transport processes. Nonetheless, before applying the
RH* parameterization it is recommended to first check the
recombination/dehydration kinetics of the substance of interest and compare
them with the mass transport timescales.
Finally, the work contributes to the improvement of high-resolution cloud
models which simulate the redistribution of atmospheric trace gases. For
example, our experiments verify the estimation of the retention coefficients
for formic acid and acetic acid applied in and
. Nevertheless, they underestimated the retention coefficient
values of formaldehyde. However, strictly speaking, the present work is only
applicable to dry-growth conditions and one-component systems in the presence
of CO2. Further experiments which account for more realistic
compositions of chemicals in cloud water, for example by measuring retention
coefficients of categorized mixtures (tropical, urban, rural, etc.), would
give further insight into the process. Moreover, an extension to wet-growth
conditions is necessary in order to quantify the retention of trace
substances throughout all riming regimes in convective storms.
Experimental data are freely available upon request to the
contact author.
Author contributions: AJ, MS, KD, SKM, and SB designed research;
AJ performed research; AJ, and SKM performed and developed the chemical
analysis; AJ, MS, KD, SKM, and SB evaluated the data; AJ, MS, KD, SKM, and SB
wrote the paper.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft under grant MI
483/6-1, as well as by internal funds from the Max Planck Institute for
Chemistry. Edited by: Jennifer G.
Murphy Reviewed by: two anonymous referees
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