# On the risk of infection by infectious aerosols in large indoor spaces

Bardia Hejazi  Oliver Schlenczek  Birte Thiede  Gholamhossein Bagheri
Eberhard Bodenschatz<EMAIL_ADDRESS>Laboratory for Fluid
Physics, Pattern Formation and Biocomplexity, Max Planck Institute for
Dynamics and Self-Organization (MPIDS), Göttingen, NI 37077, Germany
Institute for Dynamics of Complex Systems, University of Göttingen, Göttingen,
NI 37077, Germany  Laboratory of Atomic and Solid State Physics and Sibley
School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY
14853, USA  Sibley School of Mechanical and Aerospace Engineering, Cornell
University, Ithaca, NY 14853,USA

###### Abstract

Airborne diseases can be transmitted by infectious aerosols in the near field,
i.e., in close proximity, or in the far field, i.e., by infectious aerosols
that are well mixed within the indoor air. Is it possible to say which mode of
disease transmission is predominant in large indoor spaces? We addressed this
question by measuring the transport of aerosols equivalent to the size of
human respiratory particles in two large hardware stores
($V>$10\,000\text{\,}\mathrm{{}^{3}}\mathrm{m}$$). We found that aerosol
concentrations in both stores decreased rapidly and almost independently of
aerosol size, despite the different ventilation systems. A persistent and
directional airflow on the order of a few cm/s was observed in both stores.
Consequently, aerosol dynamics in such open settings can be expected to be
dominated by turbulent dispersion and sweeping, and the accumulation of
infectious aerosols in the indoor air is unlikely to contribute significantly
to the risk of infection as long as the occupancy of the store is not too
high. Under these conditions, well-fitting face masks are an excellent means
of preventing disease transmission by human aerosols.

###### keywords:

Aerosol transport, Large indoor settings, Exposure risk

††journal: arXiv

4 [gray]0.87

##  1 Introduction

It is important to keep the indoor air we breathe free of pollutants and other
harmful substances, as we spend most of our time indoors [1, 2]. Airborne
infectious diseases such as Severe Acute Respiratory Syndrome (SARS), avian
flu and swine flu (H1N1), and more recently the coronavirus disease (COVID-19)
are transmitted through near-field and far-field airborne contact with an
infectious [3, 4, 5]; with the predominant route of transmission for SARS-
CoV-2 being via airborne transport of respiratory aerosols released from the
respiratory tract of an infectious person [6]. (In this study, we use the
terms _particle(s)_ and _aerosol(s)_ interchangeably to refer to
<$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ particulate matter suspended in
air, regardless of composition.) The size of human aerosol emissions varies
greatly in magnitude and span length scales of several decades [7]. While
moist exhaled aerosols larger than $50\text{\,}\mathrm{\SIUnitSymbolMicro m}$
(approx. $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ fully dry [7]) settle
within seconds by gravitational deposition, smaller droplets dry while
airborne and shrink in size, and due to their small remaining mass can stay
airborne for extended periods of time [5]. Such aerosols may contain single or
multiple copies of pathogens when exhaled by an infectious individual, and
when inhaled by a susceptible person, there is a risk of infection determined
by the absorbed dose of pathogens [8].

author | room volume ($\text{m}^{3}$) | ACH ($\text{hr}^{-1}$) |  $\tau$ (min) | measurement duration (min) | description
---|---|---|---|---|---
Ishizu [9] | 71 | NA | 7.66 | 21 | cigarette smoke, ventilated room
" | 268 | NA | 6.83 | 21 | "
" | 82 | 45.3 | 7.9 | 15 | outside air intake rate
" | 82 | 8.7 | 8.68 | 22 | "
Leaderer et al. [10] | 34 | 2.3 | 12.9 | NA | cigarette smoke in room
Mage and Ott [11] | 548 | NA | 2.6 | 32 | CO concentration, cigarette in Tavern
Miller and Nazaroff [12] | 36 | 0.03-1.7 | 23-40 | 150-240 | cigarette smoke, 2 compartments
Ott et al. [13] | 34 | 4 | 44 | 225 | CO concentration, cigar smoke, 2 compartments
Ott et al. [14] | 3-5 | 3-56.4 | 0.3-7.8 | NA |  $<2.5\mu\text{m}$ particles, cigarette in car
Qian et al. [15] | 242 | NA | 43 | 70 |  $<10\mu\text{m}$ particles in 2 story house
Stephens et al. [16] | 45 | NA | 23.6 | 59 |  $10-100\text{nm}$ particles, 3D printer emissions,
|  |  |  |  | conditioned air
Poon et al. [17] | 11.9 | 40.6 | 11.8 | 32 |  $<100\text{nm}$ particles, cooking in source room,
|  |  |  |  | 2 compartments
Table 1: Examples of experimental studies on indoor pollutants and their
decay.

Far-field transmission in indoor air is described by the well-mixed room (or
space) model and its extensions. These models assume that the indoor air is
well mixed, in other words, susceptible individuals who can be infected are
far enough away from the infectious so that the infectious aerosols are
homogeneously mixed into the considered volume by the time they are inhaled by
the susceptible [18, 19, 20, 21, 22, 23, 24, 18, 25]. The literature on well-
mixed models is substantial, i.e., the spaces considered include aircraft
cabins [26], buses [27], hospital wards [28, 29], and residential buildings
[30, 31], or recent case study scenarios of different indoor settings [32].
Experiments have investigated the transport dynamics of pollutants in
differently sized indoor spaces [9, 33, 14] and how human presence and
activity can affect these dynamics [15, 34, 35]. Studies have also looked at
how aerosols can transfer from room to room [36, 13, 17]. Best strategies for
ventilation of indoor spaces to minimize disease transmission have been
devised for a long time, recent examples are for schools [37], hospitals and
clinics [38, 39], and homes [40]. The well-mixed model fails when the volume
of the indoor space is large or when the infectious and the susceptible are
close to each other. Extensions for such situations are by subdividing the
indoor environment into near- and far-field [41, 42, 43] or performing
situation-specific approximate numerical simulations with turbulent mixing
models [44, 45, 46]. Aerosol concentration decay in well-mixed rooms can be
well described with an exponential decay. Typical measured exponential time
constants under various air exchange conditions (room volume, air change hours
- or ACH, and measurement duration) are given for later comparisons with the
results reported here in Table 1.

For near-field disease transmission the temporal dynamics of aerosol
dispersion is highly dependent on the activity-duration of the source and the
dispersion mechanism. Mage and Ott [11] introduced three time-scales for the
aerosol concentration evolution, which were further investigated by Klepeis
[47] and Licina et al. [48]. Namely, the time when the source is active
$t_{\alpha}$, the time when the source is no longer active and the space is
not well-mixed $t_{\beta}$ , and the time from when the space is well-mixed to
when the aerosol concentration reaches that of the background $t_{\gamma}$.
For $t_{\alpha}+t_{\beta}\ll t_{\gamma}$ the well-mixed room model can be
considered adequate for exposure risk calculations [11]. Bagheri et al. [49]
investigated the upper bound on the risk of disease transmission for one-to-
one near-field exposure of human exhale in different scenarios of social
distancing for unmasked and masked individuals and found that wearing a well-
filtering face mask is the safest option and greatly reduces the infection
risk. Recently, Li et al. [50] have investigated the effect of ventilation on
the transmission by respiratory aerosols in well-mixed spaces by considering
contaminant concentration in the near-field exhalation cone of an individual.
It is also important to note that exhaled human aerosols can remain airborne
for longer periods of time than previously thought [51].

Large room volumes have found little attention in the literature so far as
shown in Table 1. Mage and Ott [11] investigated a tavern with
$V\sim$550\text{\,}{\mathrm{m}}^{3}$$ where they report relatively short
measured decay times of $\sim 3$min with no information on the ventilation.
Blocken et al. [52] examined how different aerosol removal mechanisms effect
aerosol concentrations of particles emitted by persons performing physical
exercises in a gym with $V\sim$900\text{\,}{\mathrm{m}}^{3}$$. They found that
a combination of ventilation and air filtering units work best in reducing
aerosol concentration. They reported total concentrations at specific time
intervals, but did not report decay times for aerosol concentration. Comparing
the results by Ishizu [9] and Qian et al. [53] shows that knowing the room
volume alone is not sufficient to estimate the aerosol concentration decay
time. These investigations studied two similar sized rooms,
$268\text{\,}{\mathrm{m}}^{3}$ and $242\text{\,}{\mathrm{m}}^{3}$ and found
quite different decay times of $\sim 7$ min versus $\sim 40$ min,
respectively. Ishizu [9] also compared the same room with different ACH values
of 45 and 9 and found decay times of $\sim 8$ min for both scenarios. This was
attributed to non-ideal mixing of the clean air supply with the existing room
air. It is remarkable that similarly puzzling results were found when
comparing Leaderer et al. [10] with Ott et al. [13] where similar rooms have
quite different decay rates. In Ott et al. [13] for the very small
$34\text{\,}{\mathrm{m}}^{3}$ room studied, room compartmentalization and
transport from room to room increased local decay times in spite of the ACH
being almost doubled. These examples (listed in Table 1) show that predicting
decay times in an indoor environment based solely on reported values of ACH
and room volume is a non-trivial task and may lead to significant
uncertainties.

The importance of the room airflow on aerosol transport dynamics was recently
pointed out by Bhagat et al. [54]. Detailing airflow in rooms is challenging,
if not impossible, due to the complexity introduced by boundary conditions,
placement of air-inlets and air-outlets, opening and closing of doors, and
other time dependent factors such as the movement of people. Bhagat et al.
[54] suggest that the room flow becomes a key component in aerosol
transmission of COVID-19 for particle sizes that have gravitational settling
speeds lower than the typical room flow velocities. In the following, our data
shows that room flow velocities in the two measured exemplary hardware stores
are fast, robust to spatio-temporal fluctuations and that settling of
particles is negligible. In other words aerosol concentration decay rates are
short, as shown later. Thus the infection risk will be dominated by near-field
transmission for which we can use our earlier results to calculate an upper
bound for the risk of infection [7]. From this upper bound, we conclude that
presence in these large indoor spaces poses a low risk of infection for
current variants of SARS-CoV-2 as long as well-fitted filtering face masks are
worn and room occupancy is limited.

##  2 Measurements of aerosol decay and transport in two large hardware stores

We performed measurements at two different hardware stores in Germany during
the COVID-19 pandemic and while the stores were open to pre-registered
customers with limits on store capacity. All individuals present in the store
were wearing filtering face masks and practicing social distancing in
compliance with local hygiene rules and regulations. As a result the stores
had low occupancy and people were not present during measurements unless
measurements were performed specifically to study the effects of human
presence and movement. Both stores had the layout typical to large chain
hardware stores with high ceilings ($\sim 10\text{\,}\mathrm{m}$) and large
interiors but different ventilation layout as shown in Fig. 1.

Store 1 had a total volume of approximately
$\sim$$200\,000\text{\,}{\mathrm{m}}^{3}$, while the semi-detached garden
center had a volume of $\sim$$45\,000\text{\,}{\mathrm{m}}^{3}$. The garden
center was an enclosed greenhouse and had less shelving and more open space.
In Store 1 (as shown in Fig. 1(a)) the ventilation units (inlets and outlets)
are spread over the entire retail area at regular intervals on the ceiling, so
that in a given section of the store, a row of inlet units followed a row of
outlet units. Inlets supply air into the indoor space and outlets extract air
from the indoor space. The main retail area, excluding the garden center, had
a maximum air exchange rate of 57800 cubic meters per hour provided by the air
handling units, which results in a nominal ACH of
$0.4\text{\,}{\mathrm{h}}^{-1}$. The store’s air exchange rate was reported to
us by building services. The store had 300 total parking spaces for cars and
with an average of 2 people per vehicle [55], the estimated maximum occupancy
is $\sim$$32\text{\,}{\mathrm{m}}^{2}$/person.

Store 2 had a volume of $\sim$$60\,000\text{\,}{\mathrm{m}}^{3}$ in the main
retail area and $\sim$$40\,000\text{\,}{\mathrm{m}}^{3}$ in the garden center.
For Store 2, the ventilation units were installed on the walls of the store
wile the outlets were on the wall separating the main retail area and the
garden center (see Fig. 1(b)). The inlets of Store 2 were close to the ceiling
and in the main retail area they blew air into the store at a downward angle
of $\leavevmode\nobreak\ 45^{\circ}$, as seen in Fig. 1(b), while in the
garden center they blew air perpendicularly away from the wall (Fig. 12 of the
Supplementary Material). The air exchange rate was reported to us by building
technicians. The main retail area had 3 fans that generated an air exchange
rate of $12\,000\text{\,}{\mathrm{m}}^{3}\text{\,}{\mathrm{h}}^{-1}$ each,
resulting in a nominal ACH of $0.6\text{\,}{\mathrm{h}}^{-1}$ for the whole
retail area. The garden center also had 3 fans with an air exchange rate of
$7000\text{\,}{\mathrm{m}}^{3}\text{\,}{\mathrm{h}}^{-1}$ for each fan, which
in total generate a nominal ACH of $0.5\text{\,}{\mathrm{h}}^{-1}$. As before,
the maximum occupancy of the store is estimated to be
$\sim$$27\text{\,}{\mathrm{m}}^{2}$/person, from the total 180 available
parking spaces and an average number of two people per vehicle.

The values for occupancy based on parking spaces are the extreme maximum and
actual store occupancy as reported by store officials is less, where on normal
operating days the occupancy is $\sim$$100\text{\,}{\mathrm{m}}^{2}$/person,
and during promotional periods the occupancy is
$\sim$$60\text{\,}{\mathrm{m}}^{2}$/person. Furthermore, according to internal
reports, more than $95\%$ of customers stay in these stores for less than one
hour, with more than 50% staying for less than half an hour [55]. The customer
toilets of both stores were small spaces with a volume of approximately
$15\text{\,}\mathrm{m}^{3}$. By German law the ACH of the customer toilets
should be at least $5\text{\,}{\mathrm{h}}^{-1}$ [56].

Figure 1: Schematic top view of the store layout with ventilation systems, as
well as entrances and exits that provide additional air exchange with the
outside air. The locations of test aerosol release and aerosol measurements
are also marked with location numbers and number of experiment performed in a
particular location. To reduce complexity, only the shelving around the
experiment locations are shown.

Figure 1 also shows the locations where the test aerosol was released and the
aerosol measurements took place labeled by location number and additionally
showing the experiment number that was performed in that particular location.
The measurement locations were carefully selected, e.g. the screw and nail
departments, where there can be a high number of customer visits and customers
dwell longer. The location of the shelves near the test sites is also shown in
Fig. 1, as shelves can influence aerosol transport. The Supplementary Material
contains a detailed report of each experiment, showing the locations of the
aerosol release and measurement devices, including the layout of the
surrounding shelves and supporting photographs. Fig. 2 shows panoramic
photographs of the main retail area of both stores and the garden center of
Store 2. The photographs display the large interiors and high ceilings of the
stores. The garden centers of both stores were very similar with less shelving
and more open space as compared to the main retail area.

Figure 2: Panoramic photographs of the stores. (a) The main retail area of
Store 1 and (b) Store 2, showing the large interior space with high ceilings.
(c) The garden center of Store 2 which is a greenhouse with less shelving and
more open space as compared to the main retail area. The garden center of both
stores were very similar.

The aerosol measurements were conducted with four Optical Particle Sizer
spectrometers TSI 3330, all of which were fully calibrated, and had valid
calibration certificates. The individual spectrometers were labeled as
position 1, 2, 3 and 4 in each of the experiments. At the beginning of data
collection all spectrometers were synchronized with each other in time. In
each location they were placed on ladders or shelves at approximately the
typical breathing height of an adult human (about
$1.5$-$2.0\text{\,}\mathrm{m}$ above the ground). The background concentration
in the store was measured at the beginning and end of each experiment. The
spectrometers can measure particle sizes in the range of
$0.3$-$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The spectrometers allow for
a maximum of 16 custom selected bins for size distribution analysis. In this
investigation we used 16 bins that were evenly spaced on the logarithmic
scale. The sampling time was set to 1 second, which yields a sample volume of
$16.7\text{\,}\mathrm{c}\mathrm{m}^{3}$ per scan. The measured range does not
cover the smaller aerosols of human origin, however, this is not an issue
since aerosols with size of approximately
$0.3\text{\,}\mathrm{\SIUnitSymbolMicro m}$ have the longest dwell time in
ambient air, longer than smaller or larger particles. We used dolomite test
dust from DMT GmbH & Co KG with diameters less than
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The aerosol size distribution is
almost flat over the measured size range and is shown in Fig. 3. The test-dust
is harmless to humans at the concentrations used, and furthermore all persons
exposed to the dust wore FFP2 face masks.

Figure 3: Size distribution of the DMT test dust measured immediately after
the release with an spectrometer.

The test dust was released at a height of about 1.0-$1.5\text{\,}\mathrm{m}$
above the ground by first covering both sides of a $30\text{\,}\mathrm{cm}$ x
$30\text{\,}\mathrm{cm}$ microfiber cloth with dolomite dust and then shaking
it in an empty bucket with a volume of about $30\text{\,}\mathrm{L}$ for a
total duration of <$10\text{\,}\mathrm{s}$. An example of the test-dust
release can be seen in Fig. 14 of the Supplementary Material, we have also
provided a video of the release. The utility of this simple method is also
reflected by the fact that repeated experiments gave equal results on the
decay times showing that the variability of the procedure had no significant
impact on the results. After the local dust release, we monitored the time
evolution of the concentrations at the four spectrometer locations. Once the
measured aerosol concentrations decreased to the background level at all
spectrometers, the experiment was terminated.

Two questions about the quality of the test dust measurements come immediately
to mind:
Could the test-dust itself influence the flow of the air?
The volume fraction of particles is defined as $\Phi_{p}=NV_{p}/V$, where $N$
is the total number of particles, $V_{p}$ is the volume of a single particle,
and $V$ is the volume occupied by particles and fluid. To calculate an upper
limit for $\Phi_{p}$, even if we assume that all particles are
$5\text{\,}\mathrm{\SIUnitSymbolMicro m}$, we find that from the concentration
data obtained by the particle counters, in each release the particle volume
fraction was $\Phi_{p}<10^{-7}$, which is well within the dilute one-way
coupling regime [57]. Thus the flow influences the motion of particles, but
the particles do not influence the flow or each other.

Does the procedure of release of the test dust influence the measured aerosol
concentration decay?
The decay time for the turbulent kinetic energy generated by the cloth motion
is approximated as $t=L/U$, where $L$ is a characteristic length scale and in
our experiments this is the opening of the bucket
($L=$0.3\text{\,}\mathrm{m}$$), and $U$ is the mean flow velocity. From videos
of the dust release (see video provided in the Supplementary Material), we
find that in our experiments the mean flow velocity created by the motion of
the cloth is approximately
$U=$1\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$$. Thus the kinetic energy
of turbulence created by the dust generation decays in
$t\sim\mathcal{O}($1\text{\,}\mathrm{s}$)$, which is much shorter than the
measured mean aerosol cloud decay times of about 1-2 minutes. From this we
conclude that the turbulence generated by the cloth is suitable for creating a
test dust cloud and has no influence on the transport and decay time
measurements. All in all, this shows that the release of test dust by the
bucket method provides reliable and reproducible results when the turbulent
large-scale dispersion of aerosols is considered (see the Supplementary
Material section 2 for additional details on the reproducibility of particle
concentrations with aerosol release).

Additionally, to determine whether thermally induced convective currents could
impact aerosol transport, the temperature distribution at the measurement
locations in one of the stores (Store 1) were measured with a thermal imaging
camera (VarioCam head from Jenoptik Laser Optik Systeme GmbH, equipped with an
IR 1.0/25 LW lens).

Figure 4: Normalized aerosol concentration for
0.90-$1.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sized particles as measured
by one spectrometer for the first $300\text{\,}\mathrm{s}$ after aerosol
release in Store 1. (a) Experiment 1 with an exponential decay where
$t_{\alpha}+t_{\beta}\ll t_{\gamma}$, displaying well-mixed room dynamics. The
inset shows the time it takes for the concentration to decay and reach the
initial background concentration. (b) Experiment 7 and (c) Experiment 2 where
$t_{\alpha}+t_{\beta}$ is comparable to $t_{\gamma}$ yet an exponential can be
fitted to the decay to calculate an effective $\tau$. (d) Experiment 6 where
no good estimates for $\tau$ are found but aerosol dwell time $t_{90\%}$ can
still be measured.

Aerosol decay times

Mage and Ott [11] proposed to analyze mixing/dispersion, and decay of aerosol
concentration in similar experiments to ours with the times $t_{\alpha}$,
$t_{\beta}$ and $t_{\gamma}$. In Fig. 4 we present representative examples
from our measurements and show the times $t_{\alpha}$, $t_{\beta}$ and
$t_{\gamma}$ in order to define later the aerosol decay times used in the
analysis of our measurements. The data for the spectrometer bin
0.90-$1.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ are shown as that bin had
the best signal-to-noise ratio. The aerosol rise time $t_{\alpha}$ is
$\sim$$10\text{\,}\mathrm{s}$, $t_{\beta}$ is the time where the concentration
approximately stays constant after release and before the decay starts, and
$t_{\gamma}$ is the time from when the concentration starts to decay until it
reaches that of the background. Figure 4(a) shows the concentration decay of
Experiment 1, which was performed in the customer toilet of Store 1 with one
spectrometer. It can be seen that the decay timescale is much larger than the
other timescales involved ($t_{\alpha}+t_{\beta}\ll t_{\gamma}$) where
$t_{\gamma}$ extends well beyond $300\text{\,}\mathrm{s}$, as shown in the
inset. This shows that this customer toilet can be considered a well-mixed
space, and as a result, the concentration decay can be fitted well with an
exponential (with $0.76<r^{2}<0.97$ for all channels of the spectrometer). The
example shown in figure 4(b) is experiment 7 in the retail space of Store 1
(spectrometer Pos. 2 in Fig. 2 of the Supplementary Material), which was
conducted under a ventilation inlet. Here $t_{\alpha}+t_{\beta}<t_{\gamma}$
and $t_{\gamma}$ can be fitted with an exponential ($0.54<r^{2}<0.83$).
Experiment 2, shown in Fig. 4(c) (spectrometer Pos. 1 in Fig. 1 of the
Supplementary Material), was conducted in a relatively narrow aisle in Store
1. Fluctuations of concentrations occur during mixing/dispersion $t_{\beta}$
and also during the decay $t_{\gamma}$. Nonetheless, if we do not consider the
highly fluctuating parts of the $t_{\gamma}$ an exponential fit with
$0.90<r^{2}<0.94$ can be achieved. Figure 4(d) shows the aerosol concentration
measured for Experiment 6 of Store 1 (spectrometer Pos. 4 in Fig. 1 of the
Supplementary Material), conducted in a relatively wide and open area near the
entrance/exit, which shows strongly fluctuating concentration values. For this
experiment the $t_{\beta}$ and $t_{\gamma}$ regions have an exponential fit
with $0.25<r^{2}<0.75$ (median $r^{2}\sim 0.45$). As these examples show, for
aerosol concentration decay the most important time scale is $t_{\gamma}$. In
the analysis of our data we used two ways to measure $t_{\gamma}$, which we
term the _exponential aerosol decay time $\tau$_ and the _aerosol dwell time
$t_{90\%}$_. These two parameters are correlated and determine how fast the
aerosols are removed from the indoor air.

We calculate the _exponential aerosol decay time $\tau$_ by fitting an
exponential decay to the spectrometer measurements, where we report $\tau$ for
experiments with $r^{2}\geq 0.7$ (median $r^{2}\sim 0.8$) for at least $80\%$
of the spectrometer bins. Overall, 42% of all measurements (54 of 127) met
these stringent requirements. Within the part of the time series where the
exponential fit was applied, the change in concentration was at least a factor
of 1.8 (median: factor 7.5); the smallest change in concentration was found in
the experiments at the cash register of Store 2, the toilets in both stores,
and the garden center of Store 1. The length of the data-fit for 50 out of the
54 measurements was at least one unit of $\tau$.

Exponential fits could not be applied to highly fluctuating decays, such as
the experiment shown in Figure 4(d), and therefore we define as a second
parameter the _aerosol dwell time $t_{90\%}$_ which we were able to find for
all measurements. $t_{90\%}$ is the time it takes for the cumulative
normalised concentration to go from 0.05 (5th percentile) to 0.95 (95th
percentile). Using other thresholds is possible, but this choice worked well
for quantifying all data measured.

In addition, we calculate the _aerosol advection velocity $v$_. For this we
use the 0.05 value of the normalized cumulative aerosol concentration to
calculate the aerosol time of arrival at a spectrometer. By knowing the
distance between the spectrometers and aerosol release and dividing this value
by the aerosol time of arrival, we calculate $v$ (details of all spectrometer
and aerosol release locations of all experiments are in the Supplementary
Material).

##  3 Results

In total, we conducted 31 experiments with four spectrometers each, and three
experiments with only one spectrometer. This yields a total of 127 data sets.
It should be noted that in some experiments, the dust did not reach all
spectrometer locations due to large-scale flows in the stores. And because of
that, we needed to define a concentration threshold for those data sets that
got a significant amount of dust. We calculated the maximum total
concentration for each experiment and compared the total concentration at each
of the other spectrometer locations with this value. If the total
concentration at those locations was at least 5 % of the maximum total
concentration of the experiment, the respective data sets were considered
significant and used for further analysis of decay dynamics. This was the case
for 104 out of the 127 data sets. The experiment where the maximum aerosol
concentration compared to the background aerosol concentration was the lowest,
was still above the background by a factor of 27, so the maximum total
concentration used to define the threshold was never close to or below the
background concentration.

The measured background particle concentrations for both stores as a function
of particle size are shown in Fig. 5. Let us first consider Store 1, for which
the ventilation units circulate filtered outside air into the main retail
area. As shown by Fig. 5(a) for particle size
$<$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$$, the toilet had almost a factor
10 higher particle concentration than the retail spaces, while for larger
particles it was approximately the same. When we took the measurements, there
was very little customer traffic in the toilet and thus little air exchange
with the outside world through the entrance of the toilet. The strong increase
for particles $<$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ shows an
accumulation of small aerosols and zero to little air exchange. The latter was
confirmed by the lack of observed flow at the inlets/outlets at the ceiling.

Store 2 was different not only in layout of ventilation units, but also in
that the fresh air in the main retail areas was unfiltered and thus the
particle concentration in the retail areas was higher than in Store 1. The
lower concentration in the customer toilet of Store 2 compared to the retail
spaces of Store 2 for particles $>$0.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$$
suggests air exchange with filtered air in the toilet.

Figure 5: Background particle concentrations as a function of particle size
for the toilets and main retail areas of (a) Store 1 and (b) Store 2.

Mean aerosol decay times

The mean measured decay times, $\bar{\tau}$ and mean 90% aerosol dwell times,
$\bar{t}_{90\%}$ are summarized in Table 2. The location for each experiment
in the store is identified with the label S for store number and L for
location number as shown in Fig. 1. $\bar{\tau}$ and $\bar{t}_{90\%}$ give the
arithmetic mean of decay and dwell times measured over all bins of all
spectrometers. The range for $\tau$ is given by
$\frac{\tau_{min}}{\bar{\tau}}$ and $\frac{\tau_{max}}{\bar{\tau}}$ by
dividing the minimum and maximum decay time in each experiment for different
bins of the spectrometers by $\bar{\tau}$. The mean aerosol advection velocity
$\bar{v}$ for all spectrometers in an experiment for the
0.90-$1.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sized particles are also
given in Table 2. The 0.90-$1.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sized
particles were chosen as the data has the best signal-to-noise ratio.

Exp. no. | Loc. label |  $\bar{\tau}$ (min) |  $\frac{\tau_{min}}{\bar{\tau}}$ and $\frac{\tau_{max}}{\bar{\tau}}$ |  $\bar{t}_{90\%}$ (min) |  $\bar{v}$ (cm/s) | Description
---|---|---|---|---|---|---
1 | S1 L1 | 34.37 $\pm$ 4.94 | 0.40-2.51 | 32.68 $\pm$ 0.65 | NA | Toilet
2 | S1 L2 | 1.13 $\pm$ 0.05 | 0.72-1.76 | 3.35 $\pm$ 0.1 | 4.7 | Area of interest
3 | S1 L2 | 1.47 $\pm$ 0.03 | 0.87-1.44 | 4.13 $\pm$ 0.16 | 5.9 | "
4 | S1 L2 | 5.82 $\pm$ 0.31 | 0.57-2.58 | 10.58 $\pm$ 0.1 | 3.3 | "
5 | S1 L2 | NA | NA | 2.01 $\pm$ 0.03 | NA | Area of interest, brief event
6 | S1 L3 | NA | NA | 3.07 $\pm$ 0.01 | 9.7 | Out of area of interest
7 | S1 L4 | 1.49 $\pm$ 0.12 | 0.26-3.26 | 2.29 $\pm$ 0.09 | 24.3 | Under inlet
8 | S1 L4 | 1.26 $\pm$ 0.11 | 0.42-3.07 | 2.6 $\pm$ 0.11 | 12.7 | Under inlet
9 | S1 L5 | 3.78 $\pm$ 0.14 | 0.86-1.39 | 6.6 $\pm$ 0.15 | 6.3 | Between two inlets
10 | S1 L5 | 2.49 $\pm$ 0.07 | 0.72-1.70 | 5.37 $\pm$ 0.05 | 2.8 | Between two inlets
11 | S1 L6 | NA | NA | 2.37 $\pm$ 0.06 | 4.4 | Main path
12 | S1 L7 | NA | NA | 7.05 $\pm$ 0.16 | 3.6 | Under outlet
13 | S1 L7 | 2.10 $\pm$ 0.06 | 0.85- 1.30 | 5.3 $\pm$ 0.08 | 2.2 | Under outlet
14 | S1 L8 | 0.55 $\pm$ 0.04 | 0.81-1.85 | 2.16 $\pm$ 0.05 | 4.9 | Cash register
15 | S1 L8 | NA | NA | 2.08 $\pm$ 0.02 | 5.7 | "
16 | S1 L8 | 0.66 $\pm$ 0.02 | 0.89- 1.21 | 2.09 $\pm$ 0.04 | 11.5 | "
17 | S1 L9 | 1.21 $\pm$ 0.04 | 0.80-1.46 | 1.84 $\pm$ 0.07 | 3.7 | Garden center
18 | S1 L10 | 1.37 $\pm$ 0.10 | 0.51-1.72 | 4.5 $\pm$ 0.07 | 3.8 | Aisle to aisle
19 | S1 L10 | 1.55 $\pm$ 0.02 | 0.96-1.14 | 6.14 $\pm$ 0.05 | 7.2 | Aisle to aisle
avg. | - | 1.91 | - | 4.08 | 6.86 | Store 1 average
20 | S2 L1 | 9.34 $\pm$ 0.93 | 0.75-2.36 | 14.59 $\pm$ 0.09 | NA | Toilet
21 | S2 L1 | 10.74 $\pm$ 1.79 | 0.71-3.37 | 11.68 $\pm$ 0.09 | NA | Toilet
22 | S2 L2 | 2.40 $\pm$ 0.22 | 0.49-3.47 | 4.62 $\pm$ 0.07 | 7.7 | High-traffic area
23 | S2 L2 | 1.37 $\pm$ 0.13 | 0.51-4.56 | 3.61 $\pm$ 0.09 | 8.2 | "
24 | S2 L2 | 1.48 $\pm$ 0.07 | 0.85-2.06 | 3.69 $\pm$ 0.06 | 4.5 | "
25 | S2 L2 | 2.46 $\pm$ 0.26 | 0.71-3.61 | 5.7 $\pm$ 0.19 | 5.9 | Aisle to aisle
26 | S2 L2 | 2.67 $\pm$ 0.22 | 0.73-2.1 | 5.97 $\pm$ 0.07 | 5.2 | Across main aisle
27 | S2 L3 | 0.83 $\pm$ 0.07 | 0.66-4.32 | 1.65 $\pm$ 0.07 | 34.9 | Downstream of inlet
28 | S2 L3 | 1.12 $\pm$ 0.11 | 0.79-2.5 | 2.4 $\pm$ 0.07 | NA | Downstream of inlet
29 | S2 L3 | 0.58 $\pm$ 0.04 | 0.82-1.84 | 5.39 $\pm$ 0.03 | 25.7 | Downstream of inlet
30 | S2 L4 | NA | NA | 1.72 $\pm$ 0.06 | 10.4 | Cash register, brief event
31 | S2 L4 | 1.96 $\pm$ 0.19 | 0.44-2.55 | 3.1 $\pm$ 0.04 | 7.7 | Cash register
32 | S2 L5 | NA | NA | 0.5 $\pm$ 0.13 | 10.7 | Garden center, brief event
33 | S2 L5 | 0.59 $\pm$ 0.09 | 0.76-3.05 | 1.52 $\pm$ 0.06 | 16.5 | Garden center
34 | S2 L5 | 1.29 $\pm$ 0.14 | 0.66-2.79 | 5.11 $\pm$ 0.03 | 11.7 | Garden center
avg. | - | 1.54 | - | 3.46 | 12.42 | Store 2 average
Table 2: Mean aerosol decay times $\bar{\tau}$, range of aerosol decay times
$\frac{\tau_{min}}{\bar{\tau}}$ and $\frac{\tau_{max}}{\bar{\tau}}$ where we
divide the minimum and maximum measured decay time in each experiment across
all bins of the spectrometers by $\bar{\tau}$, and mean 90% aerosol dwell
times $\bar{t}_{90\%}$ for experiments performed in the two stores. The mean
aerosol advection velocity $\bar{v}$ for each experiment is also reported.
Here S refers to the store and L to the locations identified in Fig. 1. The
measurements made in the well-mixed environment of the customer toilets are
shown in bold text. Store 1 and 2 averages include all locations except for
the customer toilets and NA values.

Aerosol decay times with customer traffic

In experiments 22-24, four to five volunteers were asked to move within the
trial area during the measurement and behave in a similar way to the
customers. For example, the subjects walked past the spectrometers, stopped at
certain products to inspect them, and then moved on to another section of the
aisle. We observed fluctuations in aerosol concentration at the spectrometer
closest to the subject, while the other spectrometers showed little or no
fluctuations. In the fluctuating areas smallest particles had longer decay
times, which is consistent with the expectation that they are more easily
transported by the turbulent wake created by a walking person. Although the
presence of the people created fluctuations that led to slight variations in
the decay times, the decay times were very close to the store average at 1-2
minutes and the dwell times were very close to the store average at 3-5
minutes. We attribute this to the persistent airflow measured in the stores.
Additional information on the influence of people on the aerosol concentration
measurements can be found in Fig. 9 of the Supplementary Material.

Aerosol decay in the vicinity of ventilation inlets and outlets

Experiments 7 and 8 (see Supplementary Material, Fig. 2) were conducted
directly under an air inlet in Store 1, where the flow velocities at 1.5 m
above the floor directly at the inlet location were $\sim$
$20\text{\,}\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}50\text{\,}\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$,
measured with a testo 405i thermal anemometer probe. As shown in Figure 1a,
the ventilation units were mounted on the ceiling, with fans blowing filtered
air downwards. Dust was released directly below an inlet. The dynamics of the
aerosol decay times were strongly dependent on the distance of the
spectrometers from the inlet area with $\tau_{min}<0.5\bar{\tau}$ and
$\tau_{max}>3\bar{\tau}$. An extremely rapid drop in aerosol concentration was
measured for the spectrometers nearest to the air inlet, which increased with
distance from the air inlet. We attribute this increase above the store
average to the recirculation of the room air driven by the rapid inflow below
the air inlet. This is even more evident in experiments 9 and 10, where the
spectrometers were placed between two air inlets (see Supplementary Material,
Fig. 3). The average decay times were even longer, which we attribute to the
accumulation of aerosols in the stagnation region between the two
recirculations driven by the two air inlets. This is also evident from
$\bar{t}_{90\%}$, where the mean dwell times in experiments 7 and 8 are much
shorter at 2.29 min and 2.6 min than in experiments 9 and 10 at 6.6 min and
5.37 min between the two inlets. Experiments 7 and 8 had higher mean
velocities of $\bar{v}_{exp.7}=24.3$ cm/s and $\bar{v}_{exp.8}=12.7$ cm/s than
experiments 9 and 10 with $\bar{v}_{exp.9}=6.3$ cm/s and
$\bar{v}_{exp.10}=2.8$ cm/s. The air outlets did not significantly influence
aerosol dynamics since the measured $\bar{\tau}$ in Experiment 13 is 2.1 min
and close to the store average of $1.91\text{\,}\mathrm{min}$ (and
$\bar{t}_{90\%}=5.3$ min, with store average being 4.08 min). The air outlets
also don’t appear to create much air flow as $2$ cm/s $<\bar{v}<4$ cm/s and is
less than the store average of
$6.86\text{\,}\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$. Measurements near
ventilation units in Store 2 gave similar results. There the ventilation units
were installed on walls and fans blew unfiltered outside air into the store.
The experiments performed downstream of the inlet in Store 2, Experiments
27-29 (see Supplementary Material Fig. 10 for details on the experiment site),
had relatively short decay times due to strong turbulent advection from the
large scale flow ($0.58$ min $<\bar{\tau}<1.12$ min, which are less than the
Store avg. of 1.54 min), even though the range was still relatively broad with
Experiment 27 having a $\tau_{min}=0.66\bar{\tau}$ and
$\tau_{max}=4.32\bar{\tau}$. Experiments 32-34 were also performed in front of
air inlets in the garden center of Store 2 which show similar behavior to the
main retail areas in terms of their decay times ($0.59$ min $<\bar{\tau}<1.29$
min). These locations also had short event duration in comparison to other
locations in Store 2. The exceptions for these group of experiments are
Experiments 29 and 34, where the spectrometers were intentionally moved to
regions where the aerosol cloud was advected to by the mean air flow created
by the inlets, and as a result, we measure longer $\bar{t}_{90\%}$ since the
aerosol cloud has diffused significantly and spread-out spatially by the time
it reaches the spectrometer locations, so while the event duration is longer
the particle concentration is lower due to dilution with the ambient air
($\bar{t}_{90\%}$ in these locations is larger than the store average of 3.46
minutes). The flow from the inlets also cause the mean advection velocity in
these regions, $10.7$ cm/s $<\bar{v}<34.9$ cm/s, to be approximately the same
or higher than the store average of
$\bar{v}=$12.42\text{\,}\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$$.

Aerosol decay in areas of long customer dwell times

Experiments 2-5 were conducted in the nuts, bolts, and screws aisle in Store
1, an area of interest to store operatives as customers have a longer dwell
time there. Experiments 2 and 3 show short decay and dwell times with
$\bar{\tau}$, $\bar{t}_{90\%}$, and $\bar{v}$ are close to the store averages.
However in Experiment 4 we measured the longest decay and dwell times of the
main retail areas of both stores. With $\bar{t}_{90\%}=10$ min was more than
twice of that measured in the same location (S1 L2) in other experiments. In
that case the measured mean advection velocity was $\bar{v}=3.3$ cm/s, which
is nearly a factor 2 less than the store average of $\bar{v}=6.86$ cm/s. We
attribute this slower velocity to changes in the large scale flow due to
opening and closing of nearby entrance/exit doors. This factor of two in decay
times was measured only once in this experiment and even then it is still
quite fast with a 10 min decay. Details of Experiment 4 are shown in more
detail in Fig. 6.

The majority of experiments performed in the open store areas were areas where
the aerosol dynamics was dominated by advection and diffusion due to turbulent
mixing and sweeping flows. In Fig. 6(a), after the release of the aerosol, the
short delay between rise in concentration levels between spatially separated
spectrometers show the fast transport of aerosols caused by turbulent
advection. Furthermore, the aerosol concentration decays at the same time at
all 4 positions meaning that turbulent mixing rapidly spreads the aerosol in
the aisle and advection removes the aerosol from the environment.
Additionally, there is no significant contribution to aerosol transport from
thermal convection as demonstrated by a thermal image of the experiment aisle
shown in Fig. 6(b). The temperature profile of the store is relatively
constant with no gradients between the floor, ceiling, and walls that would
cause convective motion of air and aerosols. Figure 6(c) shows the schematic
of the experiment site along with a photograph of the aisle displaying the 4
spectrometers that are placed on ladders while researchers in the aisle
monitor spectrometer readings.

Figure 6: (a) Normalized aerosol concentration for particles of size
0.90-$1.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ at different positions in
the aisle for Experiment 4 (S1 L2). (b) Thermal camera image of an aisle with
two people standing in the aisle. The temperatures in the store are relatively
constant with no significant contributions to aerosol transport from thermal
convection. (c) Schematic of the experiment site along with a photograph of
the aisle with spectrometers placed on ladders and researchers present. Main
path refers to areas with high movement where people move from aisle to aisle.

Aerosol decay times at the cash registers

Interestingly, the cash register areas of both stores, which are close to the
main entrance/exit doors of stores, also have relatively short $\bar{\tau}$
and $\bar{t}_{90\%}$ as compared to the store averages. For Store 1 these
values are, $\bar{\tau}\sim 0.5$ min and $\bar{t}_{90\%}\sim 2$ min, and for
Store 2, $\bar{\tau}\sim 2$ min and $\bar{t}_{90\%}\sim 2-3$ min. These
regions can be of importance in regards to the infection risk of customers and
store personnel since they can have a higher density of people present at
checkout lines as compared to other locations in the store. In our experiments
however, the presence of people in the checkout area was minimal due to store
capacity limits and since the measurements were done at closed cash registers.
While the measured characteristic times are relatively short, $\bar{v}$ is not
consistent between different experiments in the same locations for the cash
register experiments and varies between 5 and 11 cm/s for Store 1 and 7 to 10
cm/s for Store 2. We contribute the difference in $\bar{v}$ to the changing
flows created by the opening and closing of the entrance/exit doors of the
stores. At the same time, the opening and closing of doors and the air
exchange with outside air assists in the rapid removal of aerosols and thus
explain the short measured decay times and event duration. The garden center
of Store 1 also has short $\bar{\tau}=1.21$ min and $\bar{t}_{90\%}=1.84$ min,
which is most likely due to the open layout of the greenhouse and close
proximity to service doors used for moving inventory, as shown in Fig. 1. The
mean advection velocity in this area was 3.7 cm/s. We have also examined aisle
to aisle transport of aerosols in Experiment 18 and 19. These experiments have
values of $\bar{\tau}\sim$1-2 minutes and close to the store average. We find
that the aerosol transport to neighboring aisles is not significant and that
the shelving acts as a barrier to transport. Further details of the aisle to
aisle experiments can be found in Fig. 7 of the Supplementary Material.

Aerosol concentration decay in open spaces is by turbulent advection

In order to better characterize the difference between open spaces and small
well-mixed rooms we also measured the customer toilets of the two stores.
Figure 7 shows the measured aerosol decay times for the different measurement
locations as a function of particle size. Fig. 7 confirms the observed low air
exchange of the toilet of Store 1 where the measured decay times are extremely
long in comparison to other locations, commensurate with what one would expect
for pure gravitational particle settling and deposition on the walls as shown
by experiments in room sized chambers [58] (approximately
$>$10\text{\,}\mathrm{min}$$ for most cases). While in Store 2 the particle
decay times in the customer toilets are commensurate with approximately 5-6
times ACH for particles $>$0.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$$. This
is in agreement with German law that requires ventilation systems to have at
least 5 times ACH for customer toilets [56]. The longer decay times for
particles $<$0.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ in the toilet of
Store 2 could be attributed to the filter properties of the ventilation unit
for the smaller particles.

Figure 7: Aerosol decay times $\tau$ as a function of particle size at
different locations. In S2 main the ventilation intake air from outside was
not filtered, leading to larger decay times for small aerosols.

In comparison, for the large open retail spaces the decay times are of the
order of a few minutes and only weakly dependent on particle size. The
uniformly short decay times for all measured aerosol sizes in the main open
retail areas show that, unlike in the toilets that can be considered well-
mixed, the aerosol removal mechanism in the open areas is not dominated by
deposition and settling, which is a strongly size dependent process [59], but
rather by transport through turbulent sweeping flows that remove contaminants.
The latter will only show a weak dependency on particle size as the decay is
fast compared to the settling times of the particles studied.

The longest average decay times were measured in the experiments with the
smallest measured flow velocities, such as the experiments between the two
inlets (Experiments 9 and 10), all other experiments while showing variations
in the measured decay time have an average decay $\bar{\tau}<$3 minutes with
the average of the stores being between 1-2 minutes. Figure 8 shows the
probability distribution function (PDF) of the mean measured advection
velocity $\bar{v}$ in each experiment. We were able to calculate the aerosol
advection velocity using the distance to the aerosol source and the 5% arrival
times for 57 spectrometer locations in Store 1 and 39 velocities in Store 2.
The shaded regions are obtained by a polynomial fit to the data. The overall
higher average velocity in Store 2 agrees with the average shorter decay times
and dwell times and slightly higher nominal ACH of Store 2. While the the
aerosol is mostly advected with a velocity on the order of a few centimeters
per second, which is typical of indoor spaces with air speeds $\sim$1-10 cm/s
[59], however, in our experiments $\bar{v}$ is persistent and directional as
evident by experiments where the spectrometers are more than 10 meters away
from the release location and yet the aerosol is detected by the
spectrometers. such as Experiments 27-29, and 32-34. The measured advection
velocities are consistent with the transport of particles with a size of $<20$
$\mu$m being dominated by the room air flow rather than gravity, which is $<1$
cm/s for particles with a size of $<20$ $\mu$m [59].

Figure 8: Probability distribution function (PDF) of the mean measured aerosol
advection velocity in each experiment for Store 1 and 2. The shaded regions
are polynomial fits to the data.

##  4 Conclusions

In this study, we investigated aerosol transport in two German hardware/DiY
stores with large retail spaces ($V>$10\,000\text{\,}{\mathrm{m}}^{3}$$). The
size distribution of the test aerosol used was similar to that of human
exhaled aerosols. We focused on particle sizes in the range of
$0.3$-$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$, which are known to remain
airborne for long periods of time. We conducted measurements in various
locations that pose a high risk of infection for airborne diseases, such as
frequently visited areas in large open spaces or small rooms such as customer
toilets. We released the test aerosol locally and measured the decay and dwell
times spatially resolved. Although the stores had different ventilation
systems, in the large retail spaces the measured average decay times
($\bar{\tau}\sim$1-2 minutes) were short and only weakly dependent on particle
size. Even when we considered the total time that the aerosol remained at a
given location, we found that the average measured aerosol dwell times of 4
minutes were only twice as long as the typical decay times. The fact that the
decay and dwell times did not depend significantly on particle size suggests
that turbulent transport by sweeping flows dominates over deposition. The
measured advection velocities of the aerosols were very similar at all
locations in the main retail areas of both stores, supporting this assumption.
The rapid decay due to sweeping flows also applied when people were in the
measurement area. Although this led to temporal fluctuations, the measured
average decay times did not change and were 1-2 min. These results need to be
contrasted to the small ventilated spaces of the customer toilets, where the
aerosol concentration decay times were $\bar{\tau}>10$ minutes.

Infection risk in the far-field is limited to the customer toilets

The findings presented here have implications for disease transmission through
infectious human aerosols. As mentioned, airborne transmission could occur
either by far-field transmission, when the susceptible inhales infectious
aerosols that have mixed and accumulated in indoor air, or by near-field
transmission, when the susceptible is in the vicinity of infectious persons.
Far-field transmission is limited to the customer toilets in the stores
studied, where the risk of infection can be calculated by assuming a well-
mixed room [8]. In the main retail areas, our results show that the
accumulation of infection aerosols can be expected to be negligible. To better
bound this, we consider an upper bound for the occupancy of such a store and
the consequences for the accumulation of infectious aerosols. Given the
typical exhalation rate of an adult person, which is
$0.5\text{\,}\mathrm{m}^{3}$ of air per hour when breathing, it should be safe
when the exhaled aerosol concentration by all occupants is <1% of the volume
capped at the height of a person ($\sim$2\text{\,}\mathrm{m}$$) for the
contribution to aerosol accumulation in the room to be insignificant. This
results in a maximum occupancy of $25\text{\,}{\mathrm{m}}^{2}$/person, which
for the stores we studied means a maximum occupancy of 300-800 people in total
(staff, customers, service staff, etc.) at any given time, which is well
within the operating capacity of the stores we studied. In addition, it is
important that there are no cluster infections among staff, which can be
prevented for the example of the current COVID-19 pandemic by regular testing
[60, 61]. With these considerations, we can safely conclude that near-field
one-to-one exposure is the most likely route of disease transmission in stores
with large open retail spaces.

Masks make the safe use of these large indoor spaces possible

In our recent work [49] we have shown that for the current variants of the
SARS-CoV-2 virus, unprotected inhalation of infectious exhale has a more than
90% risk of infection after only a few minutes, even at a distance of 3m.
Direct infection in the near-field is therefore extremely likely.
Consequently, use of the stores would not be advisable without effective
prevention measures, such as universal masking as shown in Bagheri et al.
[49]. With a well-fitting FFP2/KN95 mask (fitted manually without fit testing)
worn by all parties, the conservative estimate of infection risk is
$\sim$0.4%, even after an hour of infectious speaking and in the worst-case
scenario when the susceptible inhales the full undiluted concentration of
aerosols exhaled by the infectious. As we pointed out in Bagheri et al. [49],
this very conservative assumption represents an upper bound, and it is
reasonable to assume that the actual risk can be a factor of 10 or even a
factor of 100 lower, depending on the airflow at the mask. Let us now apply
this to the situation considered here. If we assume a maximum 7-day incidence
rate of about 2000 COVID-19 cases per 100000 households (1% of the population
with 2 persons per household), there are about 3 to 8 infectious persons in
the store at any given time. (Please note that this value is intentionally set
high). An upper bound on the risk of infection can then be estimated by
assuming that all the infectious people in the store are standing together and
at the same time talking continuously to a susceptible in closest proximity
for one hour. Even in this very extreme and unlikely situation, the upper
bound of the risk of infection is only $\sim$3% if everyone is wearing a well-
fitting FFP2/KN95 mask.

In conclusion, our data indicates that large indoor spaces similar to those
studied are safe for employees and customers during the COVID-19 pandemic as
long as (i) everyone wears a well-fitted FFP2 mask, (ii) the occupancy is not
unbounded and (iii) if there is no cluster infection between the employees.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

BH, OS, GB, EB: designing and carrying out the experiments; BH, OS, BT, GB,
EB: analysis and interpretation of experimental data, writing original draft
and final text; BH, OS, GB, EB contributed equally to this work.

## Funding

This work was partially funded by Handelsverband Heimwerken, Bauen und Garten
(BHB). Additional funding by BMBF within the project B-FAST (Bundesweites
Netzwerk Angewandte Surveillance und Teststrategie) (01KX2021) within the NUM
(Netzwerk Universitätsmedizin) and the Max-Planck-Gesellschaft. And also the
Deutsche Forschungsgemeinschaft (project number: 469107130).

## Acknowledgments

The authors would like to thank Alexei Krekhov, Yong Wang, and Taraprasad
Bhowmick for insightful discussions regarding solutions to the three-
dimensional complex source advection-diffusion problem.

## Supplemental Data

Details on all experiment sites showing aerosol release and spectrometer
locations is shown in the Supplemental material along with further details on
the aerosol release procedure. We have also provided a video of the aerosol
release in the supplemental material.

## Data Availability Statement

The data presented here is available upon reasonable request.

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