Introduction
Inorganic and organic aerosols constitute an important fraction of aerosols
which influence climate and health
. A large fraction of
inorganic and organic aerosols are not directly emitted, but they are formed
in the atmosphere by the condensation of condensable compounds, which are
often semi-volatile; i.e., they exist both in the gas and in the particle
phases. The modeling of the mass transfer of condensable compounds (inorganic
and organic) from the gas phase to the particle phase is important because
it determines the fraction of the condensable compounds in the particle
phase and therefore the particle concentration. It is usually modeled by
three approaches: the dynamic approach, the equilibrium approach and the
hybrid approach. In the dynamic approach, the mass transfer between the gas
and the particle phases is explicitly calculated by solving the mass flux
equation e.g.,. In the equilibrium
approach, instantaneous equilibrium is assumed between the gas and particle
phases . The dynamic approach provides a more accurate
representation of the gas–particle mass transfer but is computationally more
expensive than the equilibrium approach. The hybrid approach combines these
two approaches. As gas-phase molecules condense more rapidly on fine than on
coarse particles (and therefore reach equilibrium more rapidly with fine
particles), the mass transfer is explicitly computed for coarse particles
using the dynamic approach, and instantaneous equilibrium is assumed for fine
particles in the hybrid approach
.
Several previous studies showed that organic aerosols can be highly viscous
.
The diffusion of organic compounds from the particle surface inside the
particle is influenced by the viscosity of organic aerosols, which depends on
relative humidity and aerosol composition . The
diffusion is very slow when the particle-phase state is semisolid, solid or
glassy solid . By influencing the diffusion inside the
particle, viscosity influences the mass transfer between gas and particle
phases, which is much slower than for nonviscous particles
. Several models explicitly treat the particle-phase
diffusion of organic compounds .
However, the use of these models is limited in three-dimensional (3-D) air
quality models because particles need to be discretized with a high number of
particle layers, which leads to an expensive computational cost.
Although the equilibrium approach is widely used in 3-D air quality models
because of its computational efficiency, the dynamic approach is also
sometimes used in 3-D air quality models for inorganic aerosols
. However, to our
knowledge, the impact of viscosity of particles on gas–particle phase
partitioning and organic aerosol concentrations has not yet been taken into
account in 3-D air quality models.
The mass transfer of condensable organic compounds between the gas and
particle phases is influenced by interactions with other compounds. The
activity coefficients reflect the non-ideality of aerosols and the influence
of the interactions between compounds on the mass transfer between the gas
and particle phases.
Organic aerosol models often assume ideality, and they do not take into
account the influence of activity coefficients on the formation of secondary
organic aerosols (SOAs). Activity coefficients may be determined by
thermodynamic models. For example, the UNIQUAC Functional-group Activity
Coefficients (UNIFAC) thermodynamic model is based on a
functional group method, which estimates short-range activity coefficients
(interactions between uncharged molecules) by using the structure of the
molecules present in the particles. However, in the aqueous phase, for
hydrophilic organic compounds, due to the presence of ions, such as inorganic
ions, medium- and long-range activity coefficients (resulting from
electrostatic interactions) may also influence activity coefficients. These
medium- and long-range activity coefficients are described by the Aerosol
Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC)
model . The effect of activity coefficients was
already investigated by a previous study by using the
UNIFAC model. Compared to assuming ideality, computing activity coefficients
was found to decrease the concentrations of hydrophobic SOA (condensing onto
the organic phase of particles) but also to increase the concentrations of
hydrophilic SOA (condensing onto the aqueous phase of particles). AIOMFAC and
UNIFAC are used in this study to compute the activity coefficients for
organic–inorganic mixtures. These models were developed using a group
contribution method. Eighteen main functional groups and 45 subgroups in AIOMFAC
are used in this study. The SOA surrogates are split into these functional
groups. The computation of activity coefficients depends on the functional
groups that are present in the SOA surrogates. It is assumed here that the
SOA surrogates represent the major SOA compound types in terms of functional
groups. However, considering more compounds in the model may affect the
computation of activity coefficients and enhance their effect as a stronger
variability of composition would be simulate.
obtained a reduction of the bias in SOA for routine monitoring stations
taking into account the non-ideality via activity coefficients. However, this
study did not take into account the effect of interactions between inorganic
and organic compounds.
The Secondary Organic Aerosol Processor (SOAP) model
was developed to represent the condensation and evaporation of organic
aerosols using both the equilibrium and dynamic approaches. The SOAP model
was designed to be implemented in 3-D air quality models and can be used to
implicitly represent the diffusion of organic compounds inside the particle
phase, using a low number of particle layers. Compared to an explicit
representation of the diffusion of organic compounds with a high number of
particle layers, the SOAP model showed good agreements of modeled organic
concentrations of viscous particles, using a lower number of aerosol layers.
In this study, we present the implementation of the SOAP model in the 3-D air
quality model Polyphemus, and present differences between SOAP and the
hydrophilic/hydrophobic organic (H2O) model and
how the new processes implemented in the SOAP model influence SOA formation
(absorbing mass, non-ideality, viscosity). showed that
organic-phase water uptake leads to an increase in total organic aerosol
concentration. Water uptake is taken into account in the SOAP model to
estimate the absorbing mass. We estimate for the first time in a 3-D air
quality model the maximum influence of aerosol viscosity on particle organic
concentrations over Europe. To do so, we compare simulations assuming
inviscid or extremely viscous aerosols. We also estimate the influence of
non-ideality, in particular the influence of inorganic concentrations via
medium- and long-range activity coefficients on SOA concentrations. The SOAP
model and differences with H2O, the previously used SOA model in
Polyphemus, are described in Sect. .
Section details the modeling of the newly
added processes studied here: medium- and long-range activity coefficients,
aerosol dynamics and viscosity. Finally, Sect. presents the
simulations and the sensitivity to these processes.
Description and implementation of SOAP in Polyphemus
The SOAP model was implemented in the chemistry transport model Polair3D
of the air quality platform Polyphemus version 1.8
. The aerosol dynamics (coagulation,
condensation and evaporation) is modeled with the SIze REsolved Aerosol Model
(SIREAM; ). The particle size distribution is
divided into sections, each section corresponding to a range of diameters.
Similarly to H2O, the SOAP model is based on the molecular surrogate
approach. It distinguishes hydrophobic compounds from hydrophilic compounds.
In the molecular surrogate approach, organic compounds are represented by
surrogates, which are model compounds chosen depending on their sources
(anthropogenic vs. biogenic) and their properties, such as their affinity with
water (hydrophilic vs. hydrophobic) and their volatility. Oxidation of the SOA
precursors differs depending on the regime of nitrogen oxides
(NOx) (low NOx regime vs. high
NOx regime). Different reactions were added
to the gas-phase chemistry model of Polyphemus (CB05 is used here;
) to model the formation of organic compounds from five
classes of SOA precursors (intermediate and semi-volatile organic compounds
of anthropogenic emissions, aromatic compounds, isoprene, monoterpenes and
sesquiterpenes). As detailed in , surrogates from
anthropogenic precursors are mostly hydrophobic, while those from biogenic
precursors are mostly hydrophilic. Table summarizes the
surrogates and their properties (volatility and hydrophilicity).
Description of the SOA surrogate compounds .
Surrogate
Typea
Precursors
Conditions of formationb
Volatilityc
BiMT
A
isoprene
Oxidation by OH (low NOx)
high
BiPER
A
isoprene
Oxidation by OH (low NOx)
high
BiDER
A
isoprene
Oxidation by OH (low NOx)
medium
BiMGA
A
isoprene
Oxidation by OH (high NOx)
medium
BiNGA
B
isoprene
Oxidation by OH (high NOx)
high
BiNIT3
B
isoprene
Oxidation by NO3
high
BiA0D
A
monoterpenes
Oxidation by OH and O3
very low if the aqueous aerosol is acidic
BiA1D
A
monoterpenes
Oxidation by OH and O3
medium
BiA2D
A
monoterpenes
Oxidation by OH and O3
medium
BiNIT
B
monoterpenes
Oxidation by NO3
high
BiBlP
B
sesquiterpenes
Oxidation by OH
very low
BiBmP
B
sesquiterpenes
Oxidation by OH
medium
AnBlP
B
aromatics
Oxidation by OH (low NOx)
low
AnBmP
B
aromatics
Oxidation by OH (low NOx)
high
AnClP
B
aromatics
Oxidation by OH (high NOx)
nonvolatile
POAlP
B
–
Primary SVOC
low
POAmP
B
–
Primary SVOC
high
POAhP
B
–
Primary SVOC
very high
SOAlP
B
POAlP
Oxidation by OH
very low
SOAmP
B
POAmP
Oxidation by OH
low
SOAhP
B
POAhP
Oxidation by OH
high
a Type A and B correspond to hydrophilic and
hydrophobic compounds, respectively. b Hydroxyl radical (OH),
nitrogen oxides (NOx), ozone (O3) and semi-volatile
organic compounds (SVOCs). cVery low for compounds with
Kp>100 m3 µg-1, low for compounds with
100 m3 µg-1≥Kp>1 m3 µg-1, medium for compounds with
1 m3 µg-1≥Kp>0.1 m3 µg-1, high for compounds with 0.1 m3 µg-1≥Kp>0.01 m3 µg-1
and very high for compounds
with Kp≤0.01 m3 µg-1 .
In previous studies using Polyphemus , the H2O model was used to partition organics
between the gas and particle phases; instantaneous equilibrium was assumed
between the gas and particle phases, and only short-range activity
coefficients were taken into account. They were computed with UNIFAC
, i.e., without taking into account the impact of
inorganic compounds, as if the aqueous phase is only constituted of water and
organics. In other words, H2O only takes into account solvents in
the computation of short-range interactions, and H2O implicitly
assumed that organics have no interaction with inorganics.
However, AIOMFAC is a thermodynamic model designed
for the calculation of activity coefficients of different chemical species in
inorganic–organic mixtures. It takes into account the short-range,
middle-range and long-range interactions between molecules and ions. For
short-range interactions, AIOMFAC differs from UNIFAC because it takes
inorganics into account in short-range interactions by taking relative van
der Waals subgroup volume and surface area UNIFAC parameters. It assumes that
interaction parameters of inorganics with organics for short-range
interactions are zero; i.e., the short-range organic–inorganic interactions
are ideal.
The SOAP model inherits all the characteristics of the H2O model, and
new processes (such as modeling of inorganic–organic interactions via
activity coefficients and dynamic evolution of gas–particle partitioning)
are added . However, SOAP differs from H2O not
only because of the possibility of modeling inorganic–organic interactions via
activity coefficients and of dynamically modeling the gas–particle
partitioning of viscous aerosols, but also differences occur in the
gas–particle partitioning due to the computation of the absorbing mass.
In SOAP and H2O, ideality is defined by reference to the pure state
for hydrophobic compounds (activity coefficients are equal to one when the
compound is pure) and to the infinite dilution state for hydrophilic
compounds (activity coefficients are equal to one when the compounds is
diluted into an infinite amount of water). The partitioning is computed
according to Raoult's law for hydrophobic compounds and to Henry's law for
hydrophilic compounds.
The differences between SOAP and H2O are now detailed, and their
impact on previously published simulations using the H2O is
quantitatively assessed.
Computation steps for the gas–particle partitioning and the water
absorption.
Gas–particle partitioning for the aqueous and organic phases
The equilibrium approach is used in the H2O model, and it can be used
in the SOAP model. In this approach, the partitioning between the gas and
particle organic phases is done following :
cp,icg,i=Kp,icp,
where Kp,i is the organic-phase gas–particle partitioning
coefficient (m3 µg-1),
cp,i is concentration of the compounds i in the organic phase
(µg m-3), cg,i is the gas-phase concentration
(µg m-3) and cp is the total concentration of the
particles in the organic phase (µg m-3). Whereas in the
H2O model cp is only the concentration of the organic
compounds in the particles, in the SOAP model the absorption of water by the
organic phase, cwater,p (µg m-3), is also
included in cp.
The absorption of water by the organic phase is computed using
Eq. () following :
cwater,p=cpMwaterRHγwater,pMp,
where Mwater is the molar mass of water (g mol-1), RH is
the relative humidity, γwater,p is the activity coefficient
of water in the organic phase and Mp is the averaged molar mass
of the organic phase (g mol-1). Figure shows the
computation steps for the gas–particle partitioning and the water absorption.
The partitioning between the gas and the aqueous phases is done similarly as in
the organic phase:
caq,icg,i=Kaq,icaq,
where caq,i is the aqueous-phase concentration of the compound
i (µg m-3), Kaq,i is the aqueous-phase
gas–particle partitioning coefficient (m3 µg-1) and
caq is the total concentration of the particles in the aqueous
phase (µg m-3). Kaq,i is computed as detailed in
and depends on the activity coefficient. In the
H2O model, caq corresponds only to the liquid water
content (LWC) calculated using a thermodynamic model, e.g., ISORROPIA
, for inorganic aerosols. However, caq
includes inorganic aerosols, hydrophilic organic aerosols and absorbed water
by hydrophilic organic aerosols in addition to LWC in the SOAP model. The
larger concentrations of caq in the SOAP model than in the
H2O model lead in return to larger compounds concentrations in the
aqueous phase (caq,i).
Impact on SOA concentrations
Sensitivity simulations are performed to quantify the impact on organic
concentrations of the differences between the H2O and SOAP models in
the formulation of the absorbing mass used in the modeling (cp
and caq: the total particle concentrations of the organic and
aqueous phases respectively). Within the Polyphemus platform, the two SOA
models are implemented with the SIREAM aerosol
module . The simulations of are
rerun using the SOAP model instead of H2O. The model configuration is
detailed in . The simulation domain covers Europe (see
Fig. ) with a horizontal resolution of 0.5∘×0.5∘ and nine vertical levels (20, 80, 210, 550, 1150, 1950, 2950,
4750, 9000 m). The initial and boundary conditions are calculated using data
from global models MOZART (gas) and ECHAM5-HAMMOZ (particles). Anthropogenic
emissions are taken from the EMEP (European Monitoring and Evaluation
Programme) inventory (http://www.ceip.at/, last access: 25 January 2019) and biogenic emissions are estimated with MEGAN (Model of
Emissions of Gases and Aerosols from Nature) .
Sensitivity simulations are conducted for June 2002 and detailed in
Table . Domain-averaged concentrations of SOA are
used to compare the sensitivity simulations in
Fig. . In the SOAP-Reference simulation,
caq is computed by considering the water absorbed by inorganic
aerosols and by hydrophilic aerosols (inorganic aerosols and hydrophilic
organic aerosols), while cp is computed by considering hydrophobic
organic aerosols and the water absorbed by hydrophobic organic aerosols.
Overall, the average difference in SOA concentrations between the
SOAP-Reference and H2O-Reference simulations is 15 %. The
differences between these two simulations are mostly due to the influence of
the different compounds included in the absorbing mass used for the
partitioning of the gas and particle phases, i.e., in the computation of
cp and caq (the total particle concentrations of the
organic and aqueous phases). Simulations using the same absorbing mass in
SOAP and H2O (water absorbed by inorganic aerosols for
caq and hydrophobic organic aerosol for cp) lead to
similar concentrations (see the comparison of the simulations
H2O-Ideal and SOAP-Ideal in Fig. ). Adding
water absorbed by organic aerosols in the absorbing mass leads to a slight
increase in SOA concentration (comparisons of the simulations SOAP-no_inorg
and SOAP-no_water). Adding inorganic aerosols in the absorbing mass of
hydrophilic aerosols (caq) has a larger impact than the addition
of water absorbed by organic aerosols (5 %, see the comparison of the
simulations SOAP-Reference and SOA-no_inorg). Adding organic aerosols in the
absorbing mass of caq has an impact as large as inorganic
aerosols (6 %, see the comparison of the simulations SOAP-no_inorg and
SOAP-basic).
Simulation domain and location of observation stations.
List of the sensitivity simulations to compare the H2O and
SOAP models.
Simulation name
SOA model
Aqueous-phase particle included in caqa
Organic-phase particle included in cpa
Activity coefficient
SOAP-sr
SOAP
– Water absorbed by inorganic aerosol – Inorganic aerosol – Hydrophilic organic aerosol – Water absorbed by hydrophilic organic aerosol
– Hydrophobic organic aerosol – Water absorbed by hydrophobic organic aerosol
UNIFAC-src
SOAP-Reference
SOAP
– Water absorbed by inorganic aerosol – Inorganic aerosol – Hydrophilic organic aerosol – Water absorbed by hydrophilic organic aerosol
– Hydrophobic organic aerosol – Water absorbed by hydrophobic organic aerosol
UNIFAC
SOAP-no_inorg
SOAP
– Water absorbed by inorganic aerosol – Hydrophilic organic aerosol – Water absorbed by hydrophilic organic aerosol
– Hydrophobic organic aerosol – Water absorbed by hydrophobic organic aerosol
UNIFAC
SOAP-no_water
SOAP
– Water absorbed by inorganic aerosol – Hydrophilic organic aerosol
– Hydrophobic organic aerosol
UNIFAC
SOAP-basic
SOAP
– Water absorbed by inorganic aerosol
– Hydrophobic organic aerosol
UNIFAC
SOAP-Ideal
SOAP
– Water absorbed by inorganic aerosol
– Hydrophobic organic aerosol
idealb
H2O-Reference
H2O
– Water absorbed by inorganic aerosol
– Hydrophobic organic aerosol
UNIFAC
H2O-Ideal
H2O
– Water absorbed by inorganic aerosol
– Hydrophobic organic aerosol
idealb
a Total particle concentration of the organic phase
(cp) and aqueous phase (caq). b Ideal
mixture, activity coefficient is set to 1.0. c Short-range
activity coefficients are calculated taking into account
inorganic aerosols.
Not only does the absorbing mass strongly influence the SOA concentrations,
but it also influences the interactions between compounds, as modeled by activity coefficients.
The influence of taking into account organic–organic interactions by
short-range activity coefficients is as high as 18 % (see the comparison
between the simulations H2O-Reference and H2O-Ideal). The
difference between the SOAP-Reference and SOAP-Ideal simulations is much
larger (35 %) because of differences in the computation of the absorbing
mass between SOAP and H2O.
An additional sensitivity simulation SOAP-sr is used to estimate UNIFAC
sensitivities when inorganic aerosols are added in the computation of the
short-range activity coefficient as in AIOMFAC. The averaged SOA
concentrations in SOAP-sr increase by 15 % compared to those of
SOAP-Reference. This difference is further discussed in
Sect. . As inorganic–organic interaction parameters are
set to zero in UNIFAC, taking into account inorganics in the computation of
short-range activity coefficients (simulation SOAP-sr) leads to activity
coefficients closer to the pure compound state and therefore to a decrease of
the activity coefficients (as organics are generally more stable at pure state
than in water). As activity coefficients are lower in SOAP-sr than in
SOAP-Reference, organic concentrations are higher.
The differences between the simulations SOAP-basic and SOAP-Ideal are larger
during nighttime than those during daytime. This shows that the effect of
ideality is larger during nighttime than daytime. This is due to the lower
temperature, leading to the condensation of a larger number of organic
compounds (some compounds are too volatile to condense during daytime but
condense during nighttime).
Temporal variation of the average SOA concentrations over the domain
(see Table for the description of simulations).
(a) SOA concentrations in the SOAP-Reference simulation
(µg m-3), (b) the differences of the SOA
concentrations between the SOAP-Reference and H2O-Reference
simulations (µg m-3) and (c) concentration of total
condensed water in the SOAP-Reference simulation (µg m-3).
Figure a shows the horizontal distribution of SOA
concentrations obtained by the SOAP-Reference simulation, and Fig. b shows the
differences between the SOAP-Reference and H2O-Reference simulations.
As expected, the SOA concentrations are higher in the SOAP-Reference
simulation than in the H2O-Reference simulation. Depending on the
location, the differences in the SOA concentrations between the simulations
are due to different compounds used to compute the partitioning between the
gas and particle phases. Over northeastern Europe, the differences are due
to the large hydrophilic biogenic organic aerosol concentrations. Taking them
into account in the computation of caq strongly increases the
concentrations of monoterpene SOA over southwestern Europe (especially in
northern Italy, where simulated concentrations of nitrate are high). Over
northern Italy, large differences are also observed for anthropogenic
aromatic organic aerosol concentrations. Even though these compounds are
hydrophobic, taking into account the water they absorbed when computing
cp leads to an increase in their concentrations. Similarly, near
North Africa and the Iberian Peninsula, the concentrations of hydrophilic
surrogates from isoprene oxidation are higher with SOAP than with
H2O because of the large concentrations of sulfate from shipping
emissions. Taking sulfate into account (but without taking into account its
influence on activity coefficients) when computing the partitioning between
the gas and particle phases leads to an increase in the concentrations of
hydrophilic organic compounds in the particle phase.
The coupling of inorganic and organic aerosol formation influences the water
absorption by particles. This coupling consists of two effects: the influence
of organic species on the inorganic aerosol formation and the influence of
inorganic species on the organic aerosol formation. The latter is implemented
in the SOAP model, but the influence of organic species on the inorganic
aerosol formation is not included. According to , the
organic species can either reduce or enhance the water absorption of
inorganic species, which in turn can lead to a change in the condensation of
organic species.
Figure c shows the concentration of total condensed
water in the SOAP-Reference simulation. The coupling of inorganic and organic
aerosol formation may lead to changes in the aerosol concentrations in the
regions where both the concentrations of total condensed water and
hydrophilic organic species are large, e.g., Barcelona, Milan and eastern
Spain.
Description of the newly added processes
Interaction of inorganic–organic aerosols using the AIOMFAC model
Although activity coefficients are computed with the UNIFAC model for
H2O, depending on the user's choice, in the SOAP model, activity
coefficients can be calculated using the UNIFAC or the AIOMFAC model. UNIFAC
was developed to reproduce the short-range interactions between water and
organic compounds, which are dominant for a nonelectrolyte liquid mixture.
In UNIFAC, organic compounds are represented by different functional groups
including alkane, aromatic carbon, alcohol and carbonyl. Interaction
coefficients between water and these functional groups are calculated.
However, for an electrolyte liquid mixture, the mixed organic and inorganic
system may influence activity coefficients by middle-range and long-range
interactions in addition to the short-range interaction. This influence of
inorganic aerosols on the calculation of activity coefficients in the SOAP
model can be estimated by the AIOMFAC model that considers this mixed
organic–inorganic system.
The activity coefficient in the AIOMFAC model is calculated by the following
equation:
γ=γLRγMRγSR,
where γLR, γMR and γSR
are the contributions of long-range interactions (electrostatic force between
ions), middle-range interactions (interactions between ions and molecular
dipoles) and short-range interactions (group-contribution method as in
UNIFAC).
Equilibrium and dynamic approaches
Typically, 3-D air quality models mostly use an equilibrium approach to
represent condensation and evaporation of aerosols. However, using a dynamic
approach may be necessary if the kinetic effects are large (for example if
the diffusion in the organic phase is low due to the high particle viscosity
or if condensation over coarse particles occurs). In the SOAP model,
depending on the user's choice, either the equilibrium approach or the
dynamic approach can be used to model condensation and evaporation. An explicit
representation of diffusion inside particles, which would involve
discretizing the particle along the radius of the particle, cannot be used
in 3-D air quality models due to the heavy computation time of such a
method. To solve this issue, a method was developed by
to implicitly represent the
condensation, evaporation and diffusion of organic compounds for a specified
organic-phase diffusion coefficient. This method separates the particle into
a low number of layers that represent different areas of the particle (the
gas–particle interface, the core of the particle and intermediate layers).
To use the dynamic approach in this study, several simplifications are
carried out for hydrophilic compounds. As a dynamic approach is not used to
simulate the formation of inorganic aerosols, the thermodynamic model
ISORROPIA with the equilibrium approach is used to estimate
the partitioning of inorganics, the aerosol liquid water content and the pH.
The pH given by ISORROPIA is used for each size section, and the liquid water
content is redistributed over sections proportionally to the amount of
inorganics.
In the dynamic approach, the mass transfer rate, J
(µg m-3 s-1) by condensation and evaporation at the
gas–particle interface is calculated as follows:
Jcond/evap=kabsorptioncg-ceq,
where kabsorption is the kinetic rate of absorption (s-1),
cg is the gas-phase concentration (µg m-3) and
ceq is the gas-phase concentration at the interface of particles
(µg m-3).
The ceq value is calculated taking into account a deviation from an
equilibrium concentration. This deviation is presented in
(Eqs. 52 to 55).
The kinetic rate of absorption kabsorption is defined as
follows :
kabsorption=2πdpDairNfKn,α,
where dp is the particle mean diameter (m), Dair is
the diffusivity of the condensing compounds in air (m2 s-1) and N
is the number concentration of particles (n m-3). The function fKn,α depends on the Knudsen number (Kn=2λdp), which is calculated using the mean free path
in air λ (m), and the accommodation coefficient α, which
accounts for imperfect surface accommodation. It is taken equal to 0.5
following and .
For viscous particles, the condensation and evaporation is limited by the
diffusion flux in the internal layers of the particles.
We assume that in each particle layer the evolution of concentration
cp,ilayer of species i can be described as a
deviation of an equilibrium concentration (cg,iKp,ilayercplayer) when the
condensation and evaporation of the species is limited by the diffusion of
organic compounds in the organic phase.
This deviation can be described by taking into account the flux of diffusion
with the mass transfer rate by condensation and evaporation for each particle
layer (Eq. 36 of ).
Jdifflayer=kdifflayercg,iKp,ilayercplayer-cp,ilayer
The kinetic rate of diffusion kdifflayer (s-1)
is computed as follows :
kdifflayer∝1τdiff.
The τdiff value is the characteristic time (s) for diffusion in the
particle:
τdiff=Rp2π2Dorg,
where Rp is the radius of the particle (m) and Dorg
is the organic-phase diffusivity (m2 s-1).
The sum of the diffusion fluxes over all aerosol layers is obtained as follows:
Jdiff=∑layerJdifflayer.
The final mass flux by the mixed phenomenon
condensation, evaporation and diffusion for the particle is computed by
assuming that the characteristic time of the combined effect of
condensation, evaporation and diffusion is equal to the sum of the
characteristic time of condensation and evaporation (Jcond/evap)
and the sum of the diffusion fluxes over all aerosol layers
(Jdiff) as follows:
1Jtot=1Jcond/evap+1Jdiff.
More details on the model are obtained in .
Particle-phase diffusion cases and impact of viscosity on SOA formation
To assess the maximum impact of viscosity on SOA formation, two theoretical
studies are studied. The first case, referred hereafter as the “Dynamic
inviscid” simulation, assumes that particles are inviscid; i.e., SOA
formation is not limited by the particle-phase diffusion, and the particle-phase
diffusion is so fast that there is no difference in concentrations inside the
particle. In this case, compounds condense or evaporate until reaching
equilibrium over the whole particle.
Schematic representation of SOA formation for a growing (a)
and shrinking (b) highly viscous aerosol. The blue curved arrows
describe the behavior of an organic compound A (blue), and the red curved
arrows describe the behavior of a low-volatility organic compound B (red).
The other case, referred as the “Dynamic viscous” simulation, assumes that
the particle is “infinitely viscous” (i.e., too viscous for diffusion to
occur inside the particle even at high relative humidity). A very low
diffusivity of 10-30 m2 s-1 is assumed in order to investigate
the maximum deviation of SOA concentrations from the inviscid condition. The
diffusivity of organic species is modeled using a bulk viscosity of the
mixture estimated by the Refutas method . According to measurement
studies, the diffusivity of organic species in SOA can be lower than
10-21 m2 s-1 e.g.,.
and showed that scaled
values from measured viscosities and predicted values can pass through a
viscosity of 1012 Pa s, which is on the order of a diffusivity of
10-30 m2 s-1, at low relative humidity. In addition,
reported that at a diffusivity of
10-24 m2 s-1, diffusivity does not influence the mass of the
condensed organic species as the diffusion is too low to significantly affect
the formation of organic aerosol that still occur by condensation and evaporation
of organic compounds at the interface. Therefore a diffusivity lower than
10-24 m2 s-1 may not affect the concentrations of organic
aerosols compared to simulation results with a diffusivity of
10-24 m2 s-1.
Practically, for simplification purposes, two aerosol layers (the interface
and an internal layer) are used in the “Dynamic viscous” simulation. The
internal layer and the interface represent 99 % and 1 % of the aerosol
mass, respectively, following the method of , in which
condensation at interface is not limited by particle-phase diffusion.
The SOA formation for a highly viscous particle is complex. The evolution of
the concentration of an organic compound depends on the volatility of the
compound with respect to the other compounds. The SOA formation for a highly
viscous particle is schematized in Fig. in the case of the
growth and the shrinking of an extremely viscous particle.
Figure theoretically presents different behaviors of
volatile and low-volatility organic species in a highly viscous aerosol. For
these theoretical cases, mass transfer between the interface and the core is
neglected because of an extremely low diffusion flux. The condensation of
low-volatility compounds influences the behavior of higher volatility
compounds.
In the case of an organic particle growth (mass increase), the condensation
of a low-volatility organic compound B (its behavior is described by the red curved arrows in
Fig. ) onto a particle can favor the condensation of a
compound A of higher volatility (its behavior is described by blue curved
arrows in Fig. ) at the interface of the particle (even if
the total concentration of A inside the particle exceeds equilibrium). Compound A condenses onto the new layer created by compound B to respect
Raoult's law at the interface. Even though compound A would evaporate if
the particle was inviscid and the concentration of A exceeds equilibrium, for
the extremely viscous case, the condensation of compound B at the
interface can prevent the evaporation of compound A stuck in the core of
the particle (because of the absence of diffusion) and can lead to its
“entrapment”.
In the case of a shrinking particle (mass decrease), a volatile compound A
would evaporate from the inner layers to meet the equilibrium condition if
the particle is inviscid and concentration of A in the particle exceeds
equilibrium. However, if the particle is viscous, this evaporation can be strongly slowed down because there is no diffusion of compound A from
the core to the interface.
Even though the total particle mass reduces, a low-volatility compound B may
condense at the interface and may therefore slow down the shrinking of the
particle. This condensation at the interface prevents the evaporation of
compound A from the core of the particle.
In SOAP, a redistribution is done every time step to keep the interface thin
and the mass fraction of layers constant (to prevent numerical issues, only
the mass of the interface would change for a very viscous particle). This
redistribution represents the fact that if the particle grows the compounds
that have previously condensed are not at the interface anymore (because
other compounds have condensed onto the particle) or that if the particle
shrinks the compounds that were previously at the core of the particle will eventually
be at the interface. Using two layers, compounds are immediately
transferred between the core and the interface. A more accurate
representation of the particle dynamics would be obtained using more inner
layers to better represent the position of the compounds inside the particle.
Nonetheless, the simulation using two layers should give a good estimation on
the effect of viscosity on SOA formation.
These SOA formations for a highly viscous particle are discussed more in
Sect. .
Impact on SOA formation
Simulation setup
The Polair3D model coupled to the SOAP model is evaluated during summer 2012.
The modeling domain covers Europe with a horizontal resolution of
0.5∘×0.5∘ (see Fig. ). Anthropogenic
emissions are generated with the EMEP inventory for 2012. Intermediate and
semi-volatile organic compound (IVOC and SVOC) emissions are estimated as detailed
in by multiplying the primary organic aerosol
emissions by a factor of 4 and by assigning them to compounds of different
volatilities (POAlP, POAmP and POAhP). Biogenic emissions are generated with
the MEGAN model . ECMWF (European Centre for
Medium-Range Weather Forecasts) meteorological reanalysis data
(http://www.ecmwf.int/, last access: 25 January 2019, ERA-Interim) are used to calculate meteorological fields. Initial and boundary
conditions are obtained from the simulation data of MOZART-4 and GEOS-5
(http://www.acom.ucar.edu/wrf-chem/mozart.shtml, last access: 25 January 2019). The aerosols are assumed to be internally mixed in this model.
The number of aerosol bins is 5 covering from 0.01 to 10 µm. An
adaptive time step is used to solve the dynamics of organics. The minimum
time step is 1 s and the maximum time step is set to 10 min in the
simulations of this study. The 10 min duration corresponds to the time step used to split
the different processes in the 3-D model (advection, diffusion and
chemistry). When concentrations are computed by the dynamic approach, the
second-order Rosenbrock scheme is used for time integration
. Further details about the model configuration may be
found in .
List of the sensitivity simulations using different options in SOAP.
Simulation
Absorption
Activity
Viscous
Number of
name
approach
coefficient
aerosol
aerosol layers
Equilibrium UNIFAC
equilibrium
UNIFAC
No
1
Equilibrium Ideal
equilibrium
ideal mixture
No
1
Equilibrium UNIFAC-sr
equilibrium
UNIFAC-sr*
No
1
Equilibrium AIOMFAC
equilibrium
AIOMFAC
No
1
Dynamic inviscid
dynamic
UNIFAC
No
1
Dynamic viscous
dynamic
UNIFAC
Yes
2
* activity coefficients are calculated taking into account
inorganic aerosols.
Six sensitivity simulations are conducted over Europe to study the effect of
non-ideality and nonequilibrium phenomena on SOA formation. The list of the
simulations is presented in Table . The
reference simulation (named “Equilibrium UNIFAC”) uses the default model
options; thermodynamic equilibrium between the gas and particle phases is
assumed, and activity coefficients are computed with UNIFAC. To evaluate the
impact of activity coefficients on concentrations, a simulation (named
“Equilibrium Ideal”) is run. The impact of inorganic aerosols on the
short-range activity coefficients using UNIFAC is estimated with a simulation
(named “Equilibrium UNIFAC-sr”). To evaluate the impact of inorganic
concentrations on activity coefficients, a simulation (named “Equilibrium
AIOMFAC”) using AIOMFAC to compute activity coefficients instead of UNIFAC
is run.
To evaluate the impact of the particle viscosity on SOA concentrations, two
other simulations are run: one with
a dynamic approach to model condensation and evaporation of inviscid particles
(simulation named “Dynamic inviscid”) and one with a dynamic approach but
extremely viscous particles (simulation named “Dynamic viscous”). The
simulations that use the equilibrium approach for condensation and evaporation
are run from 1 June to 31 August 2012. However, the sensitivity simulations
using the dynamic approach are run for only 3 weeks starting 1 June 2012
because of expensive computational time.
The used absorption approaches for the simulations are presented in
Table . The absorbing mass includes
inorganic aerosol, hydrophilic organic aerosol and water absorbed by
inorganic aerosol and hydrophilic organic aerosol for caq.
The cp value includes hydrophobic organic aerosol and water absorbed by
hydrophobic organic aerosol as listed in Table .
The algorithm of SOAP was developed in order to consider both the organic
and the aqueous phases inside a particle. It assumes that the organic and the
aqueous phases coexist in a particle but evolve separately in different
regions of the particle. For example, for the dynamic representation, if a
compound tends to go from the aqueous to the organic phases, it has to first
evaporate to the gas phase and then condense to the organic phases instead of
a direct mass transfer between the phases. It is due to the complexity of properly
representing these transfers. This assumption is discussed in more
details in Sect. 2.3 of .
Model evaluation
To evaluate the general performances of the model, the concentrations of
organic aerosols given by the Equilibrium UNIFAC simulation are compared
to the concentrations of organic matter (OM), organic carbon (OC) and
inorganic aerosols measured at stations of the ACTRIS observation network
(http://actris.nilu.no, last access: 25 January 2019) in
Europe. OC concentrations are measured by high and low volume samplers, and those
of OM and inorganic aerosols are measured by aerosol mass spectrometers. The
locations of stations are presented in Fig. . To compare the
simulated OM concentrations with the measured OC, the simulated OM
concentrations are converted into OC concentrations using the OM / OC
ratio for each surrogate of the organic aerosols, as described in
.
Comparison of the simulated concentrations to the measurements. Performance statistics are calculated with daily mean concentrations.
Station
Particle
Measurementb
Simulationb
RMSE
MFB
MFE
Correlation
typea
(µg m-3)
(µg m-3)
(µg m-3)
Košetice
OC2.5
2.36
1.94
0.86
-26 %
37 %
0.73
Melpitz
OC2.5
1.41
1.67
0.56
16 %
27 %
0.85
OC10
2.05
1.67
0.63
-23 %
28 %
0.86
OM1
3.83
2.75
2.21
-20 %
38 %
0.81
NH4,1
0.66
0.46
0.32
-30 %
36 %
0.72
NO3,1
0.84
0.53
0.59
-47 %
60 %
0.56
SO4,1
1.60
0.84
0.91
-62 %
63 %
0.74
Montseny
OC1
1.89
2.06
0.57
6 %
20 %
0.76
OC2.5
2.41
2.20
0.70
-10 %
23 %
0.66
OC10
2.72
2.06
0.99
-30 %
35 %
0.64
OM1
7.56
3.90
4.80
-60 %
64 %
0.26
NH4,1
1.14
0.59
0.78
-60 %
60 %
0.49
NO3,1
0.58
0.36
0.77
-51 %
66 %
0.04
SO4,1
2.54
1.23
1.84
-65 %
66 %
0.44
Ispra
OC2.5
2.79
3.16
0.88
16 %
27 %
0.75
Aspvreten
OC10
2.26
1.29
1.14
-56 %
56 %
0.63
Birkenes
OM1
1.55
1.07
0.54
-39 %
39 %
0.80
Cabauw
OM1
2.86
2.59
1.11
0 %
20 %
0.94
NH4,1
1.04
1.09
0.52
11 %
30 %
0.78
NO3,1
2.82
2.65
2.00
12 %
49 %
0.75
SO4,1
0.88
0.95
0.31
8 %
21 %
0.79
a Subscripts are used for the particle size. For
example, OC2.5 is organic carbon of aerodynamic diameter lower than
2.5 µm. For ammonium (NH4), sulfate (SO4) and
nitrate (NO3), e.g., SO4,1 is sulfate of aerodynamic
diameter lower than 1 µm.
b Mean concentration from 1 June to 31 August 2012.
To evaluate the model ability to reproduce SOA concentrations, the standard
metrics of the model performance for particulate matter of
are used: the mean fractional bias (MFB), the mean
fractional error (MFE), the root mean square error (RMSE) and the
correlation. proposed a performance evaluation
criteria (|MFB|<60 % and MFE<75 %) and a goal
evaluation criteria (|MFB|<30 % and MFE<50 %).
Model performance statistics are presented in Table . For
organic compounds, the model performance and goal criteria are satisfied for
the stations Košetice, Melpitz, Ispra, and Cabauw (|MFB|<30 %
and MFE<50 %, see Fig. ). For the Birkenes
station, the performance criteria are satisfied, but the goal criteria are
almost satisfied, although the concentrations of OM1 are quite
underestimated (MFB: -33 %). For the Aspvreten station, the model
performance criteria are satisfied, but the OC10 concentrations are
significantly underestimated (MFB: -56 %). For the Montseny stations, the
goal criteria are satisfied for OC, and the performance criteria are satisfied
for OM1 with a significant underestimation.
For inorganic PM1 aerosols, the performance biases and errors are
satisfied at the Cabauw station. However, inorganic PM1 concentrations are
underestimated at the Montseny and Melpitz stations, even though the MFE
satisfies the model performance criteria.
Comparison of modeled SOA concentrations (blue) with observations
(black) for (a) OC2.5 concentrations at Ispra and
(b) OM1 concentrations at Cabauw.
Modeled hydrophilic SOA concentrations in (a) the
Equilibrium AIOMFAC simulation, (b) the Equilibrium UNIFAC
simulation, (c) the differences between the simulations
(µg m-3) and (d) the temporal evolutions of domain-averaged concentrations.
Differences in concentrations of several SOA compounds between
AIOMFAC and UNIFAC over Europe (AIOMFAC – UNIFAC in µg m-3).
The definition of the compounds is given in Table .
Impact of inorganic–organic interactions
Figure shows the modeled hydrophilic SOA
concentrations. The choice of thermodynamic model affects the spatial
distribution of hydrophilic SOA, with a decrease of concentrations when using
AIOMFAC over the Netherlands, Belgium, parts of Italy, Spain, over the
Mediterranean coast and southeastern Europe and an increase of concentrations
over northern Europe, parts of the Alps, southern France, parts of Italy and
parts of Spain. The area with the strongest decrease of concentrations
corresponds to areas with strong inorganic concentrations. For example, the
decrease of concentrations over Netherlands corresponds to high ammonium
nitrate concentrations, while the decrease in southeastern Europe corresponds
to high ammonium sulfate concentrations.
The changes in concentration of specific SOA compounds using AIOMFAC and
UNIFAC are illustrated by Fig. . The local increases
of concentrations can be due to nonlinear effects. Indeed, while the
concentrations of the less oxidized hydrophilic compounds (BiA0D with a ratio
of oxygen to carbon atoms (O/C) of 0.2 and BiA1D with a O/C of
0.5) mainly decrease over Europe (-2 % for BiA0D and -27 % for
BiA1D), the concentrations of the more oxidized compounds (BiPER with a
O/C of 1.2 and BiDER with an O/C of 0.8) mainly increase (6 %
for BiPER and 16 % for BiDER). This finding is in agreement with
, who found that in the eastern US, particle-phase
interactions of organic and inorganic compounds increase partitioning toward
the particle phase (vs. gas phase) for highly oxidized compounds
(O/C≥0.6) but decrease particle-phase partitioning for low
O/C.
Figure d shows the temporal evolution of the
domain-averaged concentration of hydrophilic SOA for different simulations.
Modeling organic interactions by activity coefficients strongly influences
hydrophilic SOA. It leads on average to a concentration increase of 33 %
(Equilibrium UNIFAC simulation compared to Equilibrium Ideal simulation). When the computation of short-range interactions
between inorganic and organic aerosols is taken into account in UNIFAC, the
SOA concentrations increase because of a decrease of activity coefficient
(see Equilibrium UNIFAC-sr simulation in Fig. d).
Long-range and medium-range interactions in the Equilibrium AIOMFAC
simulation lead to an increase of activity coefficients as concentrations
decrease compared to the Equilibrium UNIFAC-sr simulation by 28 %. This
evaporation of hydrophilic organic concentrations by the medium- and
long-range inorganic–organic interactions agrees with the results of
, who showed that the activity coefficients of
hydrophilic organic aerosols increase because of the interactions with
inorganic aerosols.
The SOA concentrations simulated with the AIOMFAC model are close to the
concentrations simulated with the UNIFAC model (without taking into account
inorganics in the computation of short-range interactions). It suggests that
computing activity coefficients for hydrophilic organic compounds by only
taking water and organic compounds (and therefore by ignoring inorganics)
could give a good first approximation of activity coefficients. Medium- and
long-range interactions compensate the decrease of activity coefficients due
to the inclusion of inorganic ions in short-range interactions. We estimated
the contributions of long-range and medium-range interactions in this
decrease by an additional simulation. In this additional simulation, only the
medium-range interactions are taken into account in the AIOMFAC model.
According to the results of this simulation, the differences in the
concentrations of hydrophilic SOA are due to the medium-range interactions by
65 % and the long-range interactions by 35 %.
Impact of the thermodynamic equilibrium assumption
The aqueous phase of the particles is assumed to be inviscid, and organics are
strongly influenced by inorganic concentrations because they constitute an
absorbing mass for hydrophilic organics. However, in the organic phase, the
particles may be viscous, and the dynamic evolution of the SOA concentrations
by condensation and evaporation may be limited by diffusion due to the particle
viscosity .
To evaluate the impact of particle viscosity on SOA concentrations,
condensation and evaporation need to be solved using the dynamic approach.
Because condensation and evaporation are solved using the equilibrium approach in
the previous simulations, the impact of using the dynamic approach, while
still assuming particles to be inviscid, is assessed by running the “Dynamic inviscid” simulation.
Differences between the Equilibrium UNIFAC and the “Dynamic inviscid”
simulations are very low for hydrophobic compounds (less than 1 %), whereas
a decrease of concentrations by about 6 % is found for hydrophilic
compounds in the “Dynamic inviscid” simulation. The differences are due to
the non-ideality of the aerosols as low differences are found when assuming
ideality (3 %). In the Equilibrium UNIFAC simulation, activity
coefficients are computed by taking the composition of the aerosols averaged
over size sections. However, for the “Dynamic inviscid” simulation,
activity coefficients are computed for each size section. The section
activity coefficients of the “Dynamic inviscid” simulation are therefore
different from the activity coefficients of the Equilibrium UNIFAC
simulation.
For hydrophobic compounds, the differences are mainly due to the variations
of the mass transfer rate computed by Eq. (). In the
dynamic approach, the condensation and evaporation process is slower than in the
equilibrium approach. Therefore, using the dynamic approach reduces the
magnitudes of the peaks in the temporal variations of the SOA concentrations,
although the average concentrations do not change much with the temporal and
spatial resolutions used here. In the dynamic approach, in opposition to the
equilibrium approach, low-volatility secondary compounds formed by gas-phase
chemistry are found to not be completely into the particle phase due to the
kinetics of condensation. For example, 97 % of SOAlP is absorbed inside the
particle, and 3 % of SOAlP is still present in the gas phase.
Modeled hydrophobic SOA concentrations in (a) the “Dynamic inviscid” simulation, (b) the “Dynamic viscous” simulation,
(c) the differences between the simulations (µg m-3)
and (d) the temporal evolutions.
Temporal evolution (left) and differences between the “Dynamic viscous” and “Dynamic inviscid” simulations (right) of modeled SOA
concentrations for (a) SOAhP, (b) SOAlP and
(c) POAlP (µg m-3).
Impact of viscosity of the organic phase
In the “Dynamic viscous” simulation, as expected, the dynamic evolution of the
hydrophilic SOA concentration does not change from those of the “Dynamic inviscid” simulation, but the organic hydrophobic phase is strongly
influenced by the viscosity.
Assuming that the organic phase is very viscous leads to an increase in
concentrations of hydrophobic SOA: 6 % on average of the total
concentrations (see Fig. ). The increase can exceed
20 % over areas with low concentrations in the “Dynamic inviscid”
simulation (Spain and northern Europe). This increase of concentrations of
hydrophobic SOA is due to the absence of evaporation (because of the absence
of diffusion) when concentrations exceed equilibrium. The hydrophobic SOA
concentrations in the “Dynamic viscous” simulation decrease, where they are
very high in the “Dynamic inviscid” simulation (the Strait of Gibraltar
and Istanbul). As shown in Fig. d, the increase of
concentrations in the “Dynamic viscous” simulation happens mainly during
daytime.
The influence of viscosity differs depending on the volatility of the
surrogate. For example, in the model, the emitted anthropogenic IVOC and SVOC are
represented by surrogates of different volatility classes: high volatility
(POAhP, Kp=0.00031 m3µg-1), average volatility
(POAmP, Kp=0.0116 m3µg-1) and low volatility
(POAlP, Kp=1.1 m3µg-1). The chemical kinetic
mechanism used for the SOAP model includes the oxidation of these surrogates
to other surrogates with lower volatilities: SOAhP (Kp=0.031 m3µg-1), SOAmP (Kp=1.16 m3µg-1) and SOAlP (Kp=110 m3µg-1) with the
following equations .
POAhP+OH→SOAhPPOAmP+OH→SOAmPPOAlP+OH→SOAlP
In Fig. a, the concentrations of SOAhP (one of the most
volatile compounds of the mechanism) strongly increase in the “Dynamic viscous” simulation (by 44 % in average). This increase is especially
strong in southeastern Europe, where concentrations double and increase by
0.1 µg m-3. In the “Dynamic viscous” simulation,
concentrations increase strongly at the beginning of the day and reach a
maximum during daytime. On the contrary, in the “Dynamic inviscid”
simulation, concentrations decrease at the beginning of the day and reach a
minimum during daytime (as the volatility of the compound increases during
daytime). In the “Dynamic viscous” simulation, the diurnal variations of
SOAhP follow those of the low-volatility compound SOAlP
(Fig. b). Figure shows the deviation of the
particle–gas partitioning from equilibrium for SOAhP (defined as the
particle–gas concentration ratio in the “Dynamic viscous” simulation over
that in the “Dynamic inviscid” simulation, which is close to equilibrium).
This deviation often exceeds 50 % and particle-phase concentrations exceed
equilibrium over most of Europe. As presented in Sect. ,
condensation of a semi-volatile compound can happen without respecting
equilibrium as long as the particle is growing (growth that can be due to the
condensation of a low-volatility compound such as SOAlP). The condensation
during the day of low-volatility compounds formed during daytime stops the
evaporation of SOAhP captured inside the particle (evaporation that would
occur for an inviscid organic phase) and is even able to bring further
condensation of the compound.
Comparison of the time elapsed for the simulations. The elapsed time for
the Equilibrium UNIFAC simulation is set to a reference time.
Ratios between the reference time and the time elapsed for other simulations are
presented.
Equilibrium
Equilibrium
Equilibrium
Dynamic
Dynamic
Ideal
UNIFAC
AIOMFAC
inviscid
viscous
Ratio of computation time
0.97
1
1.45
9.74
10.02
Concentrations for the low-volatility compound SOAlP slightly decrease (see
Fig. b). This decrease is mainly due to the increase of the
POAlP particle-phase concentration during daytime (see
Fig. c). In the chemical kinetic mechanism used in this study,
SOAlP is formed from the gas-phase oxidation of POAlP by OH radicals (mainly
present daytime). The increase of POAlP in the particle-phase during daytime
slows down the formation of the compound SOAlP. On the contrary, at the end
of the day, concentrations of POAlP become higher in the “Dynamic inviscid”
simulation due to the decrease of volatility (because of the decrease of
temperature). However, in the “Dynamic viscous” simulation, the decrease of
the volatility has a small effect on concentrations (because the inner layer
cannot absorb more compounds to reach equilibrium due to the absence of
diffusion).
The large deviations from equilibrium suggested by this study agree with the
measurements of and , who
observed that the concentrations of pinonic acid in SOA are much higher than
predicted ,with the equilibrium assumption using saturation vapor pressures.
It could also be possible that this phenomenon is due to nonideal effects and
the possibility for pinonic acid to be absorbed onto an aqueous phase with an
acidic dissociation.
The viscosity effect is very low for low-volatility compounds
. Here, extremely low-volatility compounds from the
oxidation of monoterpenes are not modeled . Taking
them into account may decrease the viscosity effect estimated in this study.
Comparison of computation times
Table presents the time elapsed for each simulation. The
elapsed time for the Equilibrium UNIFAC simulation is set to a reference
time. The time elapsed for the Equilibrium AIOMFAC simulation increases
by 45 % compared to the reference time. Using the dynamic approach leads to
an increase of the computation time by a factor of 10, making it difficult to
represent viscous aerosols in long-term 3-D simulations. However, these
computation times are acceptable for short-term 3-D simulations.
Equilibrium deviation for compound SOAhP. A deviation close to 1
means that the compound reaches equilibrium, above 1 means that
particle-phase concentrations are above equilibrium and under 1 means that
concentrations have not reached equilibrium.
Conclusions
The SOAP model, which uses either the equilibrium approach or the dynamic
approach for the mass transfer of organic compounds from the gas phase to the
particle phases, was implemented in the 3-D air quality model of Polyphemus.
Compared to its predecessor, SOAP provides a more complete description of the
partitioning of semi-volatile compounds, in particular, by taking into
account the effect of inorganic aerosols on SOA formation based on the
computation of activity coefficients given by AIOMFAC. Sensitivity
simulations indicate that including inorganic aerosols and hydrophilic
organic aerosols in the absorbing mass of the aqueous phase can lead to an
increase of concentrations around 5 % and 6 %, respectively. Overall,
hydrophilic SOA concentrations using AIOMFAC are higher than those with the
ideality assumption by about 33 %. The results of this study suggest that
non-ideality via organic–organic and inorganic–organic interactions strongly influence the condensation of hydrophilic organic compounds.
For an inviscid aerosol, the results of this study show that the equilibrium
assumption is an efficient approximation when assuming ideality for organic
aerosols. However, assuming equilibrium can lead to significant differences
in the concentrations of hydrophilic compounds when non-ideality is taken
into account. Indeed, with a dynamic approach, different values of activity
coefficients can be simulated for the different size sections. These results
indicate that differences in the composition of particles with particle size
can impact the formation of SOA. Note that in this study, an equilibrium
approach is used for the condensation of inorganics. Using a dynamic approach
to model the condensation and evaporation of both inorganic and organic compounds
may be necessary to properly estimate the formation of hydrophilic SOA.
The dynamic approach in the SOAP model is used to account for the viscosity
of aerosol to study SOA formation via two theoretical cases: the inviscid
case, where diffusion is extremely fast and concentrations inside the
particle are homogeneous, and the infinite viscosity case, where viscosity
is too high for diffusion to occur inside the particle but where condensation
or evaporation of compounds at the gas–particle interface can still occur.
Even if the two cases presented in this study are theoretical, the results
provide a first insight on how viscosity may affect SOA formation. For the
inviscid case, concentrations of hydrophobic compounds are close to those
in the equilibrium simulation. However, assuming a highly viscous
organic phase leads to an increase of hydrophobic SOA concentration during
daytime (by stopping the evaporation of the most volatile compounds without
stopping their condensation). SOA formation for a highly viscous particle can
therefore significantly deviate from thermodynamic equilibrium; e.g.,
condensation can happen when evaporation occurs if equilibrium is assumed.
This deviation may explain why some observed concentrations in the literature
are significantly different to concentrations calculated with the equilibrium
assumption and saturation vapor pressures.
Those results emphasize the need to study the effect of the dynamics of SOA
formation. Next modeling studies should focus on the sensitivity of results
to the organic-phase diffusion coefficient and try to take into account the
effect of temperature, the aerosol water content and also aerosol composition
on this parameter.
The estimation of the computation time shows that the dynamic approach used
in the SOAP model can be applicable to the 3-D air quality modeling for a
short period or with high computation time capability. Although, the results
emphasize the need to study the effect of a dynamic approach compared to an
equilibrium approach, the computation-time issue is probably a limiting
factor in the possibility for the implementation of dynamic approaches in 3-D
air quality models.
Finally, the effect of morphology for a highly viscous aerosol may be
critical for a highly viscous aerosol. The coagulation of two highly viscous
spherical particles may form a nonspherical particle composed of two spheres
stuck together. Nonspherical particles may lead to higher surface-to-volume
ratios and faster condensation, evaporation and diffusion.