# Joint Size and Velocity Statistics of Droplets Exhaled While Speaking, Coughing, and Breathing.

Livia Grandoni, Loïc Méès, Nathalie Grosjean, Giovanni Leuzzi, Paolo Monti, Armando Pelliccioni, Pietro Salizzoni

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Livia Grandoni, Loïc Méès, Nathalie Grosjean, Giovanni Leuzzi, Paolo Monti, et al. Joint Size and Velocity Statistics of Droplets Exhaled While Speaking, Coughing, and Breathing. Physical Review Fluids, 2025, 10, pp.043102. 10.1103/PhysRevFluids.10.043102. hal-05037458v1

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Submitted on 17 Apr 2025 (v1), last revised 9 Dec 2025 (v2)

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Distributed under a Creative Commons Attribution 4.0 International License
Joint Size and Velocity Statistics of Droplets Exhaled While
Speaking, Coughing, and Breathing.

Livia Grandoni1,2,3, Loïc Méès1, Nathalie Grosjean1, Giovanni

Leuzzi2, Paolo Monti2, Armando Pelliccioni3, Pietro Salizzoni1,4

1Ecole Centrale de Lyon, CNRS, Universite Claude Bernard Lyon 1,

INSA Lyon, LMFA, UMR5509, 69130, Ecully, France

2Department of Civil, Building and Environmental Engineering,

Faculty of Civil and Industrial Engineering,

University of Rome La Sapienza, Piazzale Aldo Moro, 5, 00185, Rome, Italy

3Italian Workers' Compensation Authority (INAIL),

Department of Occupational and Environmental Medicine,

Epidemiology and Hygiene, Monte Porzio Catone (Rome), Italy and

4Department of Environmental, Land and Infrastructure Engineering (DIATI),

Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin

(Dated: February 20, 2025)
Abstract

Human respiratory activities induce the exhalation of a cloud of air laden with droplets. These droplets can harbor pathogens and play a role in the transmission of infectious diseases. Experimentally determining the size and velocity of these droplets, along with the properties of the exhaled air cloud, is crucial for predicting their behavior post-emission and developing effective strategies to mitigate infection transmission. Despite the efforts of the scientific community, there is still a lack of comprehensive characterization of exhaled droplet size distribution, with different studies yielding significantly varied results. Additionally, while several studies have measured airflow rate and velocity, droplet velocity is rarely measured and typically only within a limited size range.

In this study, we use an enhanced version of the Interferometric Laser Imaging for Droplet Sizing (ILIDS) technique to simultaneously measure the size and velocity of droplets exhaled by 23 volunteers during speaking, coughing, and breathing. This method allows us to detect droplet diameters as small as 2 µm, extending the size range reported in the literature for the coupled measure of droplet size and velocity. The ILIDS technique addresses several issues encountered in previous studies by: (i) directly measuring droplets larger than 20 µm, (ii) conducting measurements close to the mouth to reduce droplet evaporation and dilution effects, and (iii) distinguishing between ambient air dust and exhaled droplets, eliminating the need for air filtration.

Additionally, this study assesses the impact of protective masks on droplet size and velocity distributions, as well as the variability of the results among different volunteers and the same volunteers repeating the tests multiple times.

I. INTRODUCTION

Since the end of the 19th century, the scientific community has recognized that humans exhale droplets during any respiratory activity. Here, the term *droplet* is used in its general sense to refer to particles mainly composed of water, regardless of their size. These droplets can contain pathogens, facilitating disease transmission. Exhaled droplets can contaminate surfaces and objects around the emitter or be inhaled by a susceptible person while still suspended in the air. The fate of these droplets and the phenomena they undergo depend on the properties of the droplet-laden air cloud at the emission. Therefore, experimental
characterization of this cloud is crucial for quantifying and potentially reducing the risk. Specifically, measurements of droplet size, velocity, and air velocity close to the mouth and nose are essential.

Several studies in the literature provide droplet size distribution for breathing, speaking, coughing and sneezing activities. For a comprehensive review of the literature works the reader is referred to [1], [2] and [3]. Different measurement techniques have been used in the past to gain information on the quantity of the emitted droplets and on their size. Pioneers work by [4], [5], [6] and [7] employed liquid and solid impaction methods. More recently, the most common measuring tools are the Aerodynamic Particle Sizer [8–10], the Optical Particle Counter or Optical Particle Sizer [11–14] and the Scanning Mobility Particle Sizer [15, 16], nominally able to capture droplets sizes in the approximate range of 0.5 ÷ 20 µm, 0.3 ÷ 10 µm and 0.01 ÷ 0.04 µm, respectively. Other measurement tools exploit laser light scattering properties of the droplets, such as the laser diffraction droplet sizer [17, 18], Interferometric Laser Imaging for Droplet Sizing or Interferometric Mie Imaging [19, 20] and holography [21]. Also, using Particle Tracking Velocimetry technique, each droplet can be identified and its size can be inferred from the intensity of the scattered light [22, 23]. Some studies employed a combination of measurement tools in order to cover the wide droplet size range (o(0.01) ÷ o(1000) µm). Two examples are the works by [24] and [25]. In the former, the authors measure droplets in the size range o(0.5) ÷ o(1000) µm by combining the Aerodynamic Particle Sizer and an impaction method. In [25], the Scanning Mobility Particle Sizer, the Optical Particle Sizer and holography are instead used to detect droplet from 0.01 µm to 1000 µm. Note that the old impaction methods have been used also recently as they allow largest exhaled droplets [24, 26] to be detected. However, as pointed out by [25], these are indirect methods, in which droplet actual size has to be estimated from the impact size. More advanced techniques based on laser light scattering allow droplet sizes larger than 20 µm to be measured directly.

No standardized respiratory maneuver exists, leading to the use of various experimental protocols in the literature to study the same type of respiratory activity. For instance, [12] tested different levels of airways closure during air expiration to assess the effects on droplet size distribution of different droplet formation mechanisms. Similar tests have been conducted by [15] and [27]. Other researchers focused on the differences between nose and mouth breathing instead (e.g. [11], [9]) only. To simulate the speaking activity, volunteers

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were usually asked to count in English ([19], [4], [5], [24], [9], [11], [26]). However, in some
studies standard text are employed [8, 25]. Besides, [8] and co-authors investigated the
effect of language and speech loudness. Studying coughing and sneezing is more complex
because these activities are generally characteristic of symptomatic individuals, whereas
most studies consider healthy volunteers. Note that, in these studies, coughs and sneezes
are never spontaneous, the former being forced by the volunteers and the latter induced by
stimulation. Besides, quantity and properties of the mucosal fluids in respiratory airways
change between healthy subjects and symptomatic individuals. Among the above-mentioned
works, only [10], [7], [28] and [14] considered symptomatic volunteers.

As recently highlighted by [29] through numerical simulations, different droplet size dis-
tributions at the emission “cause dramatic differences in the reach of airborne droplets”.
However, despite the great effort devoted by the scientific community in recent years, the
measured size distributions of the exhaled droplets is still poorly characterized, with sig-
nificant discrepancies between data produced in different studies [2, 3, 30, 31]. There are
numerous reasons for these discrepancies. One reason is the wide variability among vol-
unteers, necessitating robust statistics, which are difficult to obtain due to the nature of
involving human subjects. Another possible reason is that, once ejected, droplets evaporate,
which makes their size to reduce while travelling in the ambient air. Therefore, the further
the measuring device from the ejection point the smaller the droplet size measured. Mod-
elling the evaporation process to estimate the droplet size at the ejection point (provided the
measured size at a given distance) is not an easy task. The evaporation process is inherently
complex [2], as it depends on both the composition of the droplets and the ambient condi-
tions, such as temperature and relative humidity, which evolve over time as the turbulent,
moist, and hot air cloud carrying the droplets disperses. For this reason, the measure should
be carried out as closer as possible to the emission point. Another reason for the discrepancy
in literature data is the wide range of droplet sizes, which span over five orders of magnitude
(o(0.01) – o(1000) µm). Measurement techniques commonly used in this field are typically
capable of detecting droplet size only within a limited range. Additionally, each technique
is based on specific assumptions about droplet properties (such as aerodynamic, optical, or
mobility diameter) and relies on different physical phenomena, which can sometimes result
in varying size values for the same droplet [1]. Another important factor is the interference
of naturally occurring dust in the air. To mitigate this issue, measurements are often con-
ducted in filtered air chambers. An alternative method involves using tracer substances, although these can potentially affect the measurements [26]. **Another way to distinguish solid, irregular particles form spherical droplet would rely on high resolution imaging or Digital Holography, as suggested in [21]. Note however that the high magnification required to resolve the smallest particles shape would imply a drastic reduction of the measurement volume.**

Regarding velocity measurements, numerous studies have characterized air velocity. Studies that focus on droplet velocity are rarer. Notable examples of research examining the velocity of air expelled by volunteers during activities such as speaking, breathing, coughing, and sneezing include [32], [19], [33], [34], [35], [36], [37]. Particle Image Velocimetry (PIV) with different kinds of seeding were used, except for [37] who employed a shadowgraph imaging technique. [38] and [39], [40] and [41] measured the airflow rate by means of spirometry. For the breathing and speaking activities, air ejection velocity is of order $o(0.1) - o(1)$ m/s, while for coughing and sneezing $o(1) - o(10)$ m/s. Droplet velocity for violent respiratory activities (coughing or sneezing) has been measured in [22],[36], [42], [43], [44], and [45]. To our best knowledge, droplet velocity has been measured for speaking only in a few studies ([22], [23], [21]) and never for breathing. Among these, only [22], [23], [42] and [45] investigated the correlation between droplet size and velocity. For droplet sizing, [42] and [45] relied on analyzing in-focus images, limiting measurements to sufficiently large droplets (e.g., the minimum detected size is 36 µm in [45]). Differently, [22] and [23] inferred droplet size from the scattered light intensity. In [23], droplet sizes in the range 50 ÷ 150µm could be measured, whereas in [22] the minimum measurable droplet size varied with droplet's speed (3.2 µm for speeds lower than 5 m/s, 9 µm for a speed of 35 m/s). The four works, [22], [23], [42] and [45], employed Particle Tracking Velocimetry to track the droplets in time and obtain their velocity. However, only the streamwise and vertical droplet velocities were determined in [42] and [45]. Although droplet velocity is comparable to that of air, droplets appear to disperse from the mouth over a wider angle compared to air, as observed in the visualizations by [46]. Additionally, comparisons between droplet and air velocity in [45] indicate that droplets and air share almost the same velocity only at the beginning of a cough or sneeze.

The aim of the present work is to measure size and velocity distributions of droplets ejected by humans while speaking, coughing and breathing. Measurements are here per-
formed for droplets sizes down to 2 µm. Concerning velocity measurements, it extends
significantly the range investigated in the literature. As droplet size and velocity mea-
surements are performed simultaneously, the correlation between the two quantities is also
assessed. Besides, all the three velocity components are measured. The measurements have
been conducted using the Interferometric Laser Imaging for Droplet Sizing (ILIDS), adopt-
ing an improved setup with respect to its classical application (see [20] for details). ILIDS
allows the size of the largest droplet to be directly measured. Besides, it overcomes some
of the problems encountered in the literature, notably to i. carry out the measure close to
the volunteers' mouth, reducing evaporation and dilution effects and ii. distinguish between
dusts and exhaled droplets, making air filtration in the testing chamber unnecessary. On the
other hand, ILIDS is not suited for high droplet concentrations and the analysis is limited
to liquid spherical particles. Another objective of this study is to evaluate how surgical
and tissue masks worn by volunteers impact droplet size and velocity distribution. To our
knowledge, only a few studies have assessed the effectiveness of masks worn by humans,
taking into account real exhaled particles and various breathing activities. Some examples
are [47], [48], [49] and [50]. [51] considered real humans but only measured airflow velocity.
The reason for the scarcity of this type of analysis is probably the fact that it is difficult to
standardise. Nonetheless, it does provide interesting information in that the actual effective-
ness of protective masks in terms of infection source control may be reduced in comparison
to the filtration efficiency of the materials assessed with standardised tests [52]. The reduced
efficiency may be attributed to the mask not fitting snugly to the face, resulting in leakage.
To assess mask fit, tests have been conducted with real humans, measuring the ratio of
particle concentration inside and outside the mask. [53, 54]. However, artificial particles are
usually employed and inward - instead of outward - mask protection effect is evaluated. Be-
sides, size-dependent mask efficiency can be useful for infection risk estimation [53], whereas
literature data generally do not provide this information and they are limited to particle
sizes smaller than ≈ 1 µm. The final aim of this study is to evaluate the variability of results
when the same volunteer repeats the experiments multiple times.

Note that some of the results for the speaking activity (without mask and excluding the
repetitions by one volunteer) have already been presented in a previously paper [20], and
they are here re-adapted for comparison with other respiratory activities and to assess the
effect of protection masks and the between and within volunteer variability.
The work is organized as follows. Section II describes the measurement campaigns and the working principles of the measurement technique. Some preliminary considerations are reported in Section III B, while the main results are presented and discussed in Sections III C-III H. Summary and conclusions are reported in Section IV.

## II. MATERIALS AND METHODS

### A. Experimental set-up and protocol

Two measurement campaigns were conducted at the Laboratoire de Mécanique des Fluides et d'Acoustique of the École Centrale de Lyon, the first in May 2021 and the second in November and December 2021, involving 23 volunteers. An enhanced configuration of ILIDS, was used for these measurements. The ILIDS equipment includes a laser light source, a camera, and a specialized optical setup for capturing and imaging light. A brief overview of the ILIDS working principles is provided in Section II B. The optical setup was completely dismantled and reinstalled between the two campaigns. Calibration procedures were repeated for the second campaign to adjust for minor variations in distances, effective aperture, and laser profile.

A sketch of the setup is drawn in Figure 1. The volunteer sits on the chair and places his face in front of a mask with a hole in the mouth, used as a positioning aid. For safety, the volunteer's eyes are fully covered during the procedure. The height of the chair is adjustable according to the volunteer's height. The laser light is produced by a double pulse Nd:YAG laser (Litron Bernoulli-PIV 200-15, wavelength: 532 nm, pulse duration: 8 ns, power: 2*200 mJ). An articulated light arm conveys the laser beam close to the volunteer's position, directing it from the ground towards the ceiling. At the exit of the arm, the beam passes through a cylindrical lens to create a divergent laser light sheet parallel to volunteer's mouth. At volunteer's mouth height the laser sheet is ~ 10 cm wide. A black panel separates the body of the volunteer from the laser sheet. A double frame camera (Lavision imager sCMOS, 16 bit, 2560x2160 pixel, pixel size: 6.5x6.5 µm, sensor size: 16.6x14 mm) and the optical system (two lenses and a diaphragm) are aligned and fixed over a plate. The plate can rotate around three axes so that the optical system and the camera can be positioned horizontally and perpendicularly to the laser sheet. The double frame camera and the double pulse
laser are connected to a programmable timing unite and to a personal computer in order
to be synchronized. As the volunteer speaks and coughs without wearing protection masks
during the experiments, he/she is alone in the testing room to ensure COVID-19 safety.
The operator, the computer and the programmable timing unite, that controls the laser,
are located outside the room. Before entering the testing room, the volunteer is asked to
disinfect his/her hands and between one volunteer and the next the mask, the chair and the
safety panels are disinfected. The testing room is ventilated for about 40 minutes by means
of a powerful air extractor.

<figure><img src="image_2.png" /><figcaption>FIG. 1: Sketch of the experimental setup. The volunteer sits on the chair and locate his/her face in correspondence of the mask, whose mouth is open to let the exhaled droplet pass. The laser light is conveyed by means of a tube close to the volunteer. The laser light passes through a cylindrical lens forming a laser light sheet parallel to the volunteer's mouth. The optical system and the camera are located on a rotating plate. The angle formed between the laser sheet and the axis of alignment of the optical system and the camera is the observation angle $\theta$. The angle that forms between an observed droplet and the effective lens aperture is the collection angle $\alpha$. The laser and the camera are connected to a programmable timing unite (PTU) and to a personal computer to be synchronized. The computer and the PTU are outside the testing chamber, together with the operator for COVID-19 safety reasons.</figcaption></figure>

The present study investigates three respiratory activities: speaking, coughing, and
breathing. Additionally, speaking and coughing while wearing both tissue and surgical masks are assessed. Each respiratory activity adheres to a specific protocol designed to minimize volunteer discomfort as much as possible. To simulate speaking activity, each volunteer performed ten tests, consisting in counting aloud from "one" to "one hundred". This protocol allows for comparison with existing literature data and is chosen because using a standard text is impractical due to the volunteers having their eyes covered. The duration of each test is not predetermined but typically lasts about 2 minutes, ending when the counting is completed. After each test, volunteers are permitted a short break and are provided with water. For the coughing activity, each volunteer performs five tests. During each test, the volunteer coughs ten times consecutively, starting with their mouth closed. Volunteers are not required to cough with maximum force to avoid undue strain. Similar to the speaking tests, volunteers are allowed a short break and offered water after each test. In the case of breathing tests, each volunteer undergoes ten sessions. They breathe in through the nose and exhale through the mouth at their own pace for approximately 67 seconds, corresponding to 1000 images captured. The same protocol applies to the speaking and coughing tests conducted while wearing masks. Furthermore, one volunteer repeated the protocols for speaking and coughing six times (six sets of ten speaking tests and six sets of five coughing tests) to assess intra-volunteer variability. The protocol, the measurement campaign and the number of available volunteers for each respiratory activity are summarised in Tables I and II.

## B. Measurement technique

The ILIDS is used to measure the size and velocity of droplets ejected by volunteers during speaking, coughing, and breathing. We outline below a concise explanation of the working principles of this technique

The light scattered by particles passing through the laser light sheet is collected by a lens arrangement and captured by the camera. The camera is positioned to produce out-of-focus images, where particles appear as large, bright circles instead of standard in-focus images (Figure 2). These circles are projections of the particle scattering pattern collected by the circular lenses. Thus, the shape and size of these out-of-focus images are not directly related to the particle shape and size. The large circle's, size and shape depend solely on the lens
<table><caption>TABLE I: Summary of the respiratory activity investigated and the related protocol, number of available volunteers and measurement campaign.</caption><thead><tr><th>Activity</th><th>Protocol</th><th>Number of volunteers</th><th>Campaign</th></tr></thead><tbody><tr><td></td><td>10 tests for each volunteer.<br>Each test consists in<br>counting loudly from "one"<br>to "one hundred".<br>Breaks with the possibility<br>of drinking water are<br>allowed after each test.</td><td>20</td><td>First<br>(May 2021)</td></tr><tr><td></td><td>5 tests for each volunteer.<br>Each test consists in<br>coughing ten time consecutively,<br>starting with mouth<br>closed.<br>Breaks with<br>the possibility of<br>drinking water are<br>allowed after each test.</td><td>23</td><td>First<br>(May 2021)</td></tr><tr><td></td><td>10 tests for each volunteer.<br>Each test consists in<br>breathing at the comfortable<br>frequency (inspiring<br>through the nose and<br>expiring through the mouth)<br>for about 1 minute<br>(1000 images taken<br>at a frequency of 15 Hz).</td><td>3</td><td>Second<br>(November<br>-December 2021)</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>FIG. 2: In panel a) an example of acquired out-of-focus image is shown. In the example image, droplets of different size (d) and position within the laser sheet thickness (x) are present. Each circle in the image correspond to a detected droplet. It is evident how droplet size is related to the fringe frequency, while droplet x-position to the circle radius.</figcaption></figure>

Some circles without fringes are visible. These are either very small droplets (not measurable) or dusts. In panel b) an example of a droplet with possible solid or gaseous inclusions preventing its sizing is shown.

configuration and the defocusing distance. In contrast, the interference pattern within the circle is related to the shape and size of the scattering particle. For spherical transparent droplets, this pattern consists of regular interference fringes, primarily resulting from the interference between the light reflected and refracted by the droplet. The spacing among the fringes provides direct information on the droplet size, according to the following relation:

$$d = \kappa \frac{1}{\Delta\theta} = \kappa \frac{N_f}{\alpha} \qquad (1)$$

where $\Delta\theta$ is the angular fringes spacing, $N_f$ is the number of fringes appearing within the circle and $\alpha$ is the collection angle (angle between the observed particle and the lens aperture). The proportionality coefficient $k$ depends mainly on the laser light wavelength $\lambda$, the droplet refractive index $n$ and the observation angle ($\theta$ in Figure 1). In the present work, $k \sim 34\mu m$ (considering water droplets with $\lambda = 532$ nm and $\theta = 90^{\circ}$). To measure fringe spacing on recorded images, at least two fringes must be observable within the circle. Since fringe spacing increases as droplet size decreases, large collection angles are required to measure the smallest droplets. Unfortunately, practical difficulties arise when using large aperture optics, primarily due to prominent spherical aberration effects, which prevent ac-
<table><caption>TABLE II: Summary of the respiratory activity investigated and the related protocol, number of available volunteers and measurement campaign.</caption><thead><tr><th>Activity</th><th>Protocol</th><th>Number of volunteers</th><th>Campaign</th></tr></thead><tbody><tr><td>Speaking with tissue mask</td><td>Same as speaking but wearing a tissue mask.</td><td>3</td><td>Second (November -December 2021)</td></tr><tr><td>Speaking with surgical mask</td><td>Same as speaking but wearing a surgical mask.</td><td>3</td><td>Second (November -December 2021)</td></tr><tr><td>Coughing with tissue mask</td><td>Same as coughing but wearing a tissue mask.</td><td>3</td><td>Second (November -December 2021)</td></tr><tr><td>Coughing with surgical mask</td><td>Same as coughing but wearing a surgical mask.</td><td>3</td><td>Second (November -December 2021)</td></tr><tr><td>Speaking for intra-volunteer variability</td><td>The speaking protocol is repeated by 1 volunteer for six times in different days.</td><td>1 (x6)</td><td>Second (November -December 2021)</td></tr><tr><td>Coughing for intra-volunteer variability</td><td>The coughing protocol is repeated by 1 volunteer for six times in different days.</td><td>1 (x6)</td><td>Second (November -December 2021)</td></tr></tbody></table>
curate measurement. Optical angles of approximately 45° and 43° were used in the first and second measurement campaigns, respectively, enabling measurement of droplet sizes down to 2µm. It is important to note that this is an absolute lower limit for the ILIDS technique, as the inverse proportionality between droplet size and fringe spacing does not hold for smaller droplets. To use such large collection angles while avoiding spherical aberration effects, a specific lens arrangement was developed and tested. This setup consists of two large aspherical lenses (Thorlabs ACL7560U, focal length: 60 mm, lens aperture: 75 mm) and a diaphragm that covers the outermost part of the lenses. A side effect of using aspherical lenses is the amplification of other geometric aberrations and associated image distortions. These distortions are corrected through calibration and custom image processing software [20].

Note that solid irregular particles do not exhibit regular interference fringes. Consequently, dust naturally present in the environment can be recognized and excluded from droplet measurements, eliminating the need for conducting measurements in a filtered air chamber.

The use of a double-frame camera synchronized with a double-pulse laser allows for the measurement of droplet velocity by evaluating the displacement of the circles corresponding to the same droplet in the two consecutive frames. This method provides the two velocity components within the image plane (in the y and z directions). The third velocity component, perpendicular to the image plane (in the x direction), is also measured. The radius of the circle containing the fringes is directly related to the droplet's, distance from the lens, enabling the determination of the x coordinates and the corresponding velocity measurement. Based on geometrical considerations specific to the setup used in this work, the following relations can be obtained:

$$ \Delta z_{out} \approx -\gamma_1 \Delta z \qquad (2) $$

$$ \Delta y_{out} \approx -\gamma_1 \Delta y \qquad (3) $$

$$ \Delta R \approx \gamma_2 \Delta x \qquad (4) $$

where $\Delta z_{out}$ and $\Delta y_{out}$ are the displacement observed on the out-of-focus image, $\Delta z$ and
$\Delta y$ are the related droplet displacements, $R$ is the radius of the circle on the out-of-focus image and $\Delta x$ is the displacement of the droplet in the direction perpendicular to the image plane and to the laser sheet. The proportionality coefficients have been inferred by means of ad-hoc calibrations. Their values are $\gamma_1 \sim 0.9$ for both the measurement campaigns and $\gamma_2 \sim 0.38$ and $0.34$ for the first and the second campaign, respectively. To obtain the velocities, the displacements are finally divided by the time lag between the frames. The time lag varies for different respiratory activities as it must be short enough for the droplet to stay in the measurement volume and long enough for the droplet displacement to be measurable. Therefore, it is fixed to 700 $\mu$s for speaking and breathing and to 50 $\mu$s for coughing. The time lag is shorter for coughing, as higher velocities are expected. The acquisition frequency is always fixed at 15 Hz, so that one couple of frames is recorded each 1/15 s.

Unlike what is commonly done for measurement techniques involving a laser light sheet, the measurement volume is explicitly estimated in this work. This estimation is not straightforward, which is why it is often omitted (with only the number of detected droplets provided) or assumed to be equal to the thickness of the laser sheet, even when the profile deviates from a top hat shape. The scattered intensity is approximately proportional to the square of the droplet diameter (refer to [55] for more details). Consequently, the detection of a droplet is influenced by its size and its position within the laser sheet. To put it simply, larger droplets are detectable at the very edge of the laser sheet, while smaller droplets are only detectable near the center, close to the intensity peak. Therefore, the effective measurement volume strongly depends on both the droplet size and the laser sheet profile, from the center to the very edge. A method to estimate the measurement volume in the ILIDS technique is proposed by [56]. The position of each droplet within the laser sheet profile (in the $x$ direction) is deduced from the circle radius. At the end of the image processing, all droplets detected across all tests have known sizes and $x$ locations. This allows for a statistical inference of the effective depth in which droplets of a given size class have been detected. By multiplying this effective thickness by the field of view area (approximately 2.3 $cm^2$), the measurement volume for each droplet diameter class is obtained.

The enhancements made to the standard ILIDS technique enable simultaneous and correlated measurements of: i. droplet sizes down to 2 $\mu$m, ii. the three components of droplet velocity, and iii. droplet concentration while accounting for variations in measurement volume with droplet size. Further details about these advancements can be found in [20].
### III. RESULTS AND DISCUSSION

#### A. Measurement volume

As discussed in Section II B, the measurement volume varies with droplet size. Its estimate is then required to compare the quantity of droplets detected in different size classes and to obtain unbiased droplets concentrations and size distributions. The measurement volume for a given droplet class can be inferred *a posteriori* by analyzing the position of the droplets actually detected along the *x* direction, perpendicular to the laser sheet (Eq. 4). Figure 3 illustrates the measurement volumes obtained during the first and second measurement campaigns. In both campaigns, the volume increases with droplet diameter from approximately 0.2 $cm^3$ to around 0.4-0.5 $cm^3$ for droplets ranging from 2 to 50 $\mu m$. However, the evolution of measurement volume with diameter differs between the two campaigns, primarily due to changes in the laser profile. Additionally, it is noteworthy that the total number of droplets detected in the second campaign is significantly lower than in the first campaign, resulting in reduced statistical significance.

<figure><img src="image_4.png" /><figcaption>FIG. 3: Variation of the measurement volume with droplet size inferred for the first (red) [20] and the second (blue) measurement campaigns.</figcaption></figure>
## B. Preliminary considerations about coughing activity

As expected, cough droplets are emitted in high concentrations over a short period. Consequently, few images show high concentrations while many images exhibit low concentrations. Considering the ILIDS configuration and the associated image processing, it is feasible to manage droplet concentrations up to approximately 70 #/cm³, corresponding to about 35 droplets per image, each with a circle diameter of around 800 pixels. Therefore, some images with higher concentrations cannot be fully analyzed with the ILIDS configuration and processing methods used in this study.

High concentration images do not occur for all the volunteers tested. Specifically, for 9 out of 23 volunteers no high concentration images are observed. For 7 volunteers, high concentration images occur only rarely (a maximum of 4 images out of approximately 300). In contrast, for the 7 remaining volunteers, high concentration images are common (ranging from 5 to more than 30 images out of approximately 300). In some cases, the circles appearing in the very high concentration images are not fringed, indicating droplets smaller than the minimum size measurable by ILIDS, i.e., < 2 µm. Among the 14 volunteers with very high concentration images 5 mainly contain non-fringed circles. Therefore, about 4% of the images cannot be analyzed by the image processing software. Excluding the images where droplets are outside the measurable size range (non-fringed circles), this percentage is reduced to approximately 2.5%. In these images, the detection of the circles is hindered due to their high number and significant overlap. As a result, circles corresponding to the droplets are either poorly detected (with incorrect radius and position) or not detected at all. Poorly detected circles could lead to imprecise measurements of droplet size. However, fringe frequency analysis mitigates this issue. Incorrectly detected circles are discarded and not validated as droplets since they do not present a regular interference pattern. Therefore, while droplet concentration may be underestimated, the size distribution remains accurate. Droplets for which an error was made in the validation or size measurement in two of the most critical cases are 2.3% and 4%. Therefore, the results concerning the coughing activity are reported with this caveat. It is important to note that the number of detected droplets is somewhat reduced compared to the total amount.

In future work, several solutions could be tested to improve the results for the coughing activity. These include modifying particle detection in image processing by using filters on
image intensity values and frequencies, considering images on a logarithmic scale instead of a linear scale, or making experimental adjustments. Experimentally, improvements could be achieved by reducing the laser sheet thickness to decrease the number of particles per image and by reducing the out-of-focus distance to minimize circle diameter and overlapping.

### C. Droplet size

In Figure 4 a,b,c the droplet size distributions are depicted for the activities of speaking, coughing, and breathing, respectively. Each volunteer's size distribution is averaged over the performed tests (10 for speaking and breathing, and 5 for coughing). Subsequently, these averaged distributions are further averaged across all volunteers, as illustrated in the figures.

The distributions are expressed as droplet number concentrations ($C_N$) divided by the width of the size class considered (the logarithmic difference between the minimum and maximum sizes defining the bin). This normalization facilitates comparisons of concentrations measured in size classes of varying widths. In this study, bin sizes range between 0.5 and 20 µm. Note that droplet number concentration is used instead of droplet number to enable comparison across different size classes, considering the varying measurement volumes.

For both speaking and coughing, droplets are detected in the range of 2 - 60 µm, while for breathing, the range is narrower at 2 - 8 µm. The absence of droplets larger than 60 µm for speaking and coughing is noteworthy and may be attributed to the presence of gas or solid inclusions in the largest droplets, altering their scattering patterns and hindering their detection. An example of a large droplet (larger than 60 µm) possibly containing inclusions is shown in Figure 2b. Note that the scattering pattern of irregular objects has been mathematically described in the literature [57]. However, even including this kind of analysis in the image treatment software, it would be hard to distinguish between dusts and exhaled droplet with inclusions.

The maximum droplet concentration occurs between 2 and 2.5 µm across all investigated respiratory activities. Specifically for speaking, the concentration sharply declines from around ~2 µm to ~10 µm, followed by a gradual increase leading to a local maximum at ~28 µm, after which it decreases again. For coughing, the concentration declines more slowly and almost monotonically with size up to ~10 µm. A local maximum is observed at ~20 µm.
For the breathing, the decrease is even slower until the concentration reaches is no more measurable for droplet larger than 8 µm. Considerations on the shape of the size distributions for the three activities are more apparent looking at the cumulative frequency in Figure 4d, calculated as the percentage of droplets smaller than a cutoff size with respect to the total concentration. The smaller the cutoff size the less scattered the size distribution. Up to a cumulative frequency of about 87 %, the cutoff size is larger for coughing than for speaking, indicating a more scattered distribution for coughing in the range between 2 and 10 µm. The higher cutoff size for speaking for cumulative frequencies higher than about 87 % is due to the relative concentration maximum around 28 µm. In other words, considering a droplet size of 20 µm, almost all the droplets exhaled while coughing are smaller. Differently, in the case of speaking there is still about 5 % that is larger than 20 µm. These are the droplets contributing to the local concentration maximum around 28 µm. The cutoff sizes are larger for breathing than for both speaking and coughing until about 85 and 75 %, respectively.

Table III lists the droplet number concentrations across all sizes for all volunteers. It includes the average value, as well as the minimum and maximum concentrations detected among all volunteers. Note that the number of detected droplets during the coughing activity is underestimated, as discussed in Section III B, due to challenges in processing images with extremely high droplet concentrations. Additionally, speaking is a quasi-continuous process in the protocol adopted here (counting continuously), whereas volunteers naturally take brief breaks (one or two seconds) between coughs. Furthermore, the volunteers were not symptomatic during the test, likely producing fewer secretions compared to symptomatic individuals. Despite the potential underestimation of droplet concentrations during coughing, the total droplet concentration measured is higher than during speaking, which in turn is higher than during breathing. However, due to the less frequent occurrence of coughing compared to speaking and breathing, the role of the latter activities in disease transmission should not be overlooked, particularly in cases of prolonged indirect exposure, as highlighted in the literature (e.g., [8]) and recognized by health authorities.

In Figures 4 a,b,c size distributions obtained for speaking, coughing and breathing are compared with literature data. For speaking activity, we refer to size distributions measured by [24], [9], [4], [5], [26], and [11]. These studies involved volunteers counting to simulate speaking, albeit with slightly different protocols. Additionally, we include the recent study
<figure><img src="image_5.png" /><figcaption>FIG. 4: Droplet size distributions, expressed as droplet number concentration normalized with the bin size width, measured for speaking (a) [20], coughing (b) and breathing (c). Data from the present work are in red, whereas literature data are in black. Panel (d) depicts the cumulative frequency of occurrence for the three respiratory activities.</figcaption></figure>

<table><caption>TABLE III: Average, absolute minimum and maximum droplet number concentration over all sizes for speaking, breathing and coughing activity</caption><thead><tr><th>Activity</th><th>C<sub>N</sub> average [#/cm<sup>3</sup>]</th><th>C<sub>N</sub> minimum [#/cm<sup>3</sup>]</th><th>C<sub>N</sub> maximum [#/cm<sup>3</sup>]</th></tr></thead><tbody><tr><td>Speaking</td><td>0.055</td><td>0.005</td><td>0.184</td></tr><tr><td>Coughing</td><td>0.081</td><td>0</td><td>0.459</td></tr><tr><td>Breathing</td><td>0.015</td><td>0</td><td>0.038</td></tr></tbody></table>

by [25] for comparison, despite employing a different protocol. In this study, volunteers read a standard text to simulate speaking at two different voice loudness levels. We specifically consider the size distribution associated with "normal speaking" for comparison.
In [4], [5], [58], and [11], droplet counts are reported as results, necessitating assumptions to express the data as number concentrations. The approach proposed by [24] is adopted in this study. It assumes that volunteers expel an average of 7.5 liters per minute while speaking and pronounce about 2 words per second. The concentration is then normalized by the bin size to facilitate comparability. Discrepancies arise in the size distributions regarding the range covered by detected droplets and the location of maximum concentration. The size range is influenced by the measurement technique employed, as no single tool can capture the entire droplet size spectrum. Furthermore, the position and intensity of concentration peaks can be influenced by dilution and evaporation processes.

The results from this study align well with the distributions presented by [24] and [9] in the 2-10 µm range. Both studies used the Aerodynamic Particle Sizer (APS) and adjusted their data for dilution (both) and evaporation (only [24]). Since our measurements were taken close to the mouth, no such corrections were applied here. Despite slight differences in experimental protocols, good agreement is also observed with [25] up to approximately 5 µm. [25] used an Optical Particle Sizer for droplets in the 0.3 to 10 µm range and accounted for evaporation effects.

For droplets larger than 10 µm, our findings notably diverge from those of [24]. Specifically, our distribution exhibits a relative concentration peak between 20 and 30 µm, whereas concentrations in [24] are nearly negligible in this range. This discrepancy coincides with the upper limit of the APS (20 µm) and the lower limit of the Droplet Deposition Analysis used by [24] for detecting droplets in the 20-1000 µm range. Besides, the efficiency of the APS decreases near its limits (as noted in [9]). Other distributions, such as those from [26], differ significantly from ours, [24], and [9]. [26] reports size distributions primarily for the largest droplets that settle or impact the walls of a containment box where volunteers speak or cough. While the exact detection limit for smaller droplets is not specified, it is likely that many droplets smaller than approximately 5 µm were not detected using [26]'s method.

[5] and [4] employ a combination of two techniques so that they can theoretically detect droplets larger than 1 µm. While these studies do not specify an upper detection limit, they report detecting droplets up to approximately 1500 µm. Both studies indicate the presence of a concentration peak around 100 µm, although the reported concentration values differ significantly. It is important to note that these concentrations are inferred based on the above-mentioned assumptions rather than direct measurements. The findings of [4] and [5]
appear to support the non-zero concentrations observed in the present work around 20-30 µm, although [4]'s distribution may be shifted towards smaller sizes due to what [24] suggests as an overly excessive correction for evaporation effects. Interestingly, [25] also identifies a relative concentration peak around 30 µm, similar to our measurements, although the concentration value reported by [25] is notably higher.

For the coughing activity, our results are again compared with those by [24], [9], [4], [5], [26] and [11]. Droplet number provided by [4], [5] and [26] are expressed in terms of concentration, considering that a volume of 1400 ml is exhaled in one cough [24]. Although the droplet concentration presented for coughing in this paper are underestimated, our results agree well with the APS measurement by [24] and [9], at least in the range 2-10 µm. For larger droplets, considerations similar to those reported previously for the speaking activity can be made. Namely, literature data show high discrepancy. Besides, also for coughing a peak around 100 µm is observed in the literature, while it is not detected in the present work.

For the breathing activity, the works by [12], [15], [24], [9], [25], and [59] are considered. These studies generally assess tidal breathing, except for [24], which uses a more rigid protocol. When considering only the works where the droplet size range overlaps with the present data ([24], [9], [59], and [25]), some differences appear with the first three, while good agreement is observed with the latter. The discrepancies can be attributed to evaporation and dilution effects, which are not corrected in [24], [9], and [59], but are accounted for in [25]. If evaporation and dilution effects were considered, the size distributions reported by [24], [9], and [59] would shift towards higher concentrations and sizes, aligning more closely with the present data. Note that some differences in the measured size distributions could be attributed also to the slightly different protocols used.

In addition to the discrepancies ascribable to evaporation and protocol, the primary difference between the literature and the present data is the size range of detected droplets. Literature data shows that droplets much smaller than 2 µm are exhaled by humans while breathing (as well as speaking and coughing), even if they are not detectable with ILIDS. Other measurement tools, such as the Optical Particle Sizer and the Fast Mobility Particle Sizer, could be used in future developments of the work to detect droplets smaller than 2 µm. Note however that, in several other works (e.g., [29], [60], [61] and [62]), larger droplets are considered as more effective in infection transmission, as they may contain a larger number
of viruses of a given size (about 100 nm for SARS-Cov 2). This assumption is here deemed reasonable, but it may not be accurate. In fact, particles formed in different areas of the respiratory system may have different concentrations of virus, depending on whether or not it is present in the area. Several works attempted to understand the formation mechanisms of the droplets into the respiratory apparatus (e.g. [9] and [24]) and outside by atomization of larger agglomeration of saliva exhaled (e.g. [63] and [64]). Nonetheless, to the best of our knowledge, there is no certainty about the concentration of virus copies in droplets of different sizes. Besides, it is worth noting that the risk of infection is rather complex to define, as several other factors are involved which are not completely known, such as particle penetrability in the respiratory apparatus, virus inactivation (depending on environmental conditions) and virus dose needed for infection (varying among individuals).

### D. Droplet velocity

Droplet velocity distribution for the speaking, coughing and breathing activity are depicted in Figure 5 a, b and c, respectively. The distributions are expressed as frequency of occurrence. The three components of droplet velocity—stream-wise ($x$), span-wise ($y$), and vertical ($z$)—are determined from the displacement of each droplet between two frames recorded in quick succession. The statistical sample used to compute droplet velocities is smaller compared to that used for size distribution, mainly because some droplets are detected in only one frame. Often, droplets are missed in either the first or the second frame due to entering or leaving the measurement volume between the frames. Specifically, the number of droplets detected in both frames for speaking, coughing, and breathing activities are 3334, 555, and 58, respectively, which should be compared with the total number of detected droplets: 4842, 853, and 145, respectively. A time lag between the two consecutive frames of 700 µs was employed for speaking and breathing, while for coughing, a shorter time lag of 50 µs was utilized due to the expectation of higher velocities. In fact, the maximum measurable streamwise velocity is limited by the thickness of the laser sheet where the droplets can be detected and on the chosen time lag between the frames (see [20] for more details). With the time lag set here, the maximum x-velocity is about 2.5 m/s for speaking and breathing, while for coughing it is about 35 m/s. The minimum detectable velocity depends on the chosen time lag as well and it is different for the specific velocity component
considered. For the span-wise and vertical velocity components, the minimum detectable displacement is ~ 1 pixel, corresponding to ~ 7 µm for both the measurement campaigns, considering a pixel size of 6.5 µm and the coefficient $γ_1$ in Equations 3 and 2. Therefore, the minimum span-wise and vertical velocity detectable for speaking and breathing is ~ 0.01 m/s, while for coughing it is ~ 0.1 m/s. The stream-wise velocity component is determined by the change in the circle radius corresponding to the droplet between the first and second frames. The minimum detectable circle radius variation is ~ 1 pixel, that is ~ 17 µm and ~ 19 µm droplet displacement in the stream-wise direction for the first and the second measurement campaign, respectively, considering Eq. 4 and the coefficient $γ_2$ calibrated for the two campaigns. Hence, the minimum measurable velocity for speaking (first campaign) is ~ 0.024 m/s, for breathing (second campaign) is ~ 0.028 m/s and for coughing (first campaign) is ~ 0.34 m/s. Bins for the velocity distributions are chosen based on the minimum measurable velocities: 0.2 m/s – wide bins are used for speaking and breathing, while 1 m/s – wide bins are used for coughing.

In Figure 5, for all the three respiratory activities, the stream-wise velocity component (in red) is asymmetric with prevailing positive values. This is expected, as the droplets are ejected from the mouth. Negative values may result from vortices forming downstream of ejection or from inhalation. The span-wise velocity distribution appears almost symmetric across all respiratory activities, with a mean velocity near zero (see Table IV). Vertical velocity distributions are slightly asymmetric towards positive values for speaking and coughing, possibly due to the beginning of the sedimentation of the larger droplets. The asymmetry observed on the velocity distribution is well reflected in the case of speaking by a skewness value of 2.3. Table IV summarizes the overall mean velocity values of the three velocity components and the velocity magnitude among the volunteers. Examining Figure 5 and Table IV, we can compare the characteristic droplet velocities for speaking, coughing, and breathing activities. The velocities measured during coughing are about one order of magnitude higher than those for speaking. For instance, the stream-wise velocity value ranges between -5 and 20 m/s for coughing and between -1 and 2 m/s for speaking. For breathing, the velocities are of the same order as those for speaking. Another quantity of interest - reported in Table IV as well- is the maximum velocity, especially for the stream-wise component, which is responsible for the transport of the ejected droplets away from the mouth. A greater difference in maximum droplet velocity is observed between speaking and breathing, with
the former being higher (3.68 m/s against 0.71 m/s). The highest maximum droplet velocity is observed during coughing (28.1 m/s). [22] detected average velocities of 3.4 m/s and 7.2 m/s for droplets in the size range 3.2 ÷ 100 µm for speaking and coughing, respectively. Both values are higher with respect to those measured here, but confirm the higher velocity characteristic of coughing. Note that a different protocol has been used in [22] with respect to the present work, which may partially account for the observed discrepancy. Particularly, for the speaking, they asked to the volunteers to pronounce the sentence "protect better against COVID", which contains several explosive syllables, supposed to produce higher velocities. Furthermore, the results are based on data from a single subject, which may not be representative of the entire population due to the significant variability observed among individuals (see Section III H for more details on between volunteers variability). From the measurements of the distance traveled by the droplets as a function of time provided in [23], the average velocity of droplets exhaled while speaking can be inferred. Droplets in the size range 40 ÷ 50 µm are, then, characterized by a stream-wise average velocity of 0.5 ÷ 1 m/s, while droplets in the size range 80 ÷ 160 µm by 1.2 ÷ 1.8 m/s. These values are closer to those presented here, even though slightly higher. The discrepancy can be explained again by a different protocol, consisting in pronouncing several explosive sounds. Also, droplets in the work by [23] are larger compared to those reported here. In the works by [45] and [42], the velocity of ejected droplets has been measured during coughing. [45] detected stream-wise and vertical velocities for droplets ≥ 36 µm, with measured velocity magnitudes ranging between 0 and 14 m/s. [42] measured velocity values mainly in the range 4-8 m/s for droplets larger than 250 µm. Even though the droplet sizes investigated in [42] and [45] are not directly comparable to those considered here, the order of magnitude of the measured droplet velocities is in agreement with our results. As far as we are aware, there are no reported measurements of droplet velocity for the breathing. However, for the three activities considered here - speaking breathing and coughing - the velocity measurements of the ejected air can be considered for comparison. [32] reports an average air ejection velocity of tent of centimetres per seconds for the speaking, with peaks of the order of ~ 1 m/s, measured by means of the Particle Image Velocimetry (PIV) technique. [19] and [33] also used PIV and measured a maximum air ejection velocity of ~ 4 m/s. These values are in agreement with our results, even if they are referred to the gaseous phase instead of the droplets. On the other hand, [39] measured a mean air velocity of ~ 4 m/s based on the
airflow collected by a spirometer. Similarly, they measured a velocity range of ~0.3-2 m/s in the case of breathing activity. [37] measured a maximum velocity of the ejected air while breathing velocity equal to 1.13 m/s based on shadowgraph imaging technique. Examples of maximum air ejection velocities in the coughing activity are 28.3 m/s by [38], 22 m/s by [34], 13.2 m/s by [19] and 14 m/s by [37]. [35] found a range 1.15-28.8 m/s for the maximum air ejection velocity for coughing, while [33] measured 10.6 m/s and 15.3 m/s for coughing of female and male subjects, respectively. [36] detected velocities higher than 6 m/s. All these values are in agreement with our findings, taking into account the wide variability among volunteers. Note that ejected air velocity (as well as droplet velocity) for coughing is higher than for speaking and breathing, indicating a stronger intensity of the former respiratory activity. Also, literature data suggest that the higher maximum velocities detected for speaking with respect to breathing can be related to the pronunciation of plosive sounds.

For speaking and coughing, the number of samples is sufficiently large to analyze the droplet velocity distribution across different size classes (Figures 6 and 7). However, the size classes used are wider than those previously considered, due to the weaker statistical sample available for velocity measurements. Specifically, five size classes are now considered, with the last class omitted for coughing due to having a sample of only seven droplets. Figure 8 shows the mean value of the three velocity components and of the velocity magnitude for the different droplet size classes. The error bars in the plot represent the statistical error, calculated assuming that the sample mean follows a Gaussian distribution and that it is inversely proportional to the square root of the number of available samples. For both speaking and coughing, the stream-wise velocity distribution varies slightly with droplet size. Notably, higher velocities become more frequent with increasing droplet size. In the case of speaking, the mean stream-wise velocity for each size class increases from approximately ~0.1 to 0.3 m/s for droplets between ~2.25 and ~40 µm (Figure 8a). In the case of coughing, stream-wise velocity values range from 1 to 4 m/s for droplet sizes from 2 to 60 µm. For both speaking and coughing, the mean span-wise velocity is zero on average, as the distribution is symmetric regardless of droplet size, as expected. A slight increase with droplet size is also observed for the vertical velocity, supporting the hypothesis that slightly positive (downward) values of the vertical velocity are due to droplet settling. For coughing, the variation in vertical velocity with droplet size is more pronounced. Specifically, the velocity distribution is symmetric with a mean value of about 0 m/s for the smallest
<table><caption>TABLE IV: Mean velocity overall droplet sizes (stream-wise $v_x$, span-wise $v_y$ and vertical $v_z$ components and velocity magnitude $|v|$). Absolute maximum values of stream-wise component and velocity magnitude are also reported</caption><thead><tr><th>Activity</th><th>v<sub>x</sub> [m/s]</th><th>v<sub>y</sub> [m/s]</th><th>v<sub>z</sub> [m/s]</th><th>|v| [m/s]</th><th>v<sub>x</sub> max. [m/s]</th><th>|v| max. [m/s]</th></tr></thead><tbody><tr><td>Speaking</td><td>0.16</td><td>-0.02</td><td>0.04</td><td>0.33</td><td>3.68</td><td>6.47</td></tr><tr><td>Coughing</td><td>1.7</td><td>0.0</td><td>0.4</td><td>2.5</td><td>28.1</td><td>29.0</td></tr><tr><td>Breathing</td><td>0.09</td><td>-0.02</td><td>-0.05</td><td>0.23</td><td>0.71</td><td>1.01</td></tr></tbody></table>

droplets, while for droplets around 12.5 µm, the vertical velocity increases with a mean value reaching 1 m/s. The increasing stream-wise velocity with increasing size is probably due to different formation mechanisms of droplets of different sizes. If, for instance, the larger particles were generated at the level of the mouth, due to impulsive forces related to the pronunciation of certain phonemes, they would undergo a rapid acceleration. Therefore, after a short time they would have greater velocities than the smaller particles generated deeper in the respiratory system and whose velocity would be more similar to that of air. If, on the other hand, both the larger and smaller particles were formed in the same zone of the respiratory system, the difference in their velocity could be due to the greater inertia of the former ones. Besides, droplets of different sizes could escape with a different velocity and direction from the air recirculation zones that may form into the mouth. However, these are only hypotheses, as the formation mechanism has not been studied in detail in the present work.

Note that a wide range of velocities (0–29 m/s) is observed for coughing, which can be attributed to several factors. Firstly, a cough is an inherently unsteady event, causing both the air and exhaled droplet velocities to fluctuate over time from the onset to the end of the cough. In the first 0.1 seconds after the beginning of the cough, velocities mostly in the range of 8-10 m/s were detected by [45]. Then, the velocity decreased, with the mode shifting to between 0 and 2 m/s. [42] also noted a decreasing velocity magnitude over time from the start of the cough. Analogously to droplet, ejected air velocity also decreases from the beginning of a cough to its end [35, 38]. The measurements conducted in this study
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>FIG. 5: Stream-wise (red), span-wise (yellow) and vertical (blue) droplet velocity distributions measured for the speaking (a), coughing (b) and breathing (c).</figcaption></figure>

are not time-resolved, meaning we cannot directly observe the temporal variability of the phenomenon. However, this limitation still leads to a broad range of measured velocities. Furthermore, the range of velocity detected can vary with droplet size, and therefore, it can be related to different droplet formation mechanisms. Notably, larger droplets are characterized by a wider velocity range. Note that analogous range of velocity have been detected for coughing in [22] (0-20 m/s) and in [45] (0-14 m/s).
<figure><img src="image_9.png" /><figcaption>FIG. 6: Stream-wise (a), span-wise (b) and vertical (c) droplet velocity distributions measured for four sizes in the case of the speaking activity. Droplet velocity data in different size classes for speaking have already been presented in [20], but shown here again for comparison.</figcaption></figure>

E. Droplet emission rate

Due to the discrete image acquisition (15 Hz sampling frequency) employed in this work, not all ejected droplets are detected. However, provided the measure of droplet velocity and the estimation of the measurement volume for different droplet size classes, the emission rate, i.e. the total number of droplets ejected by unit time, referred here to as *E*, can be
<figure><img src="image_10.png" /><figcaption>FIG. 7: Stream-wise (a), span-wise (b) and vertical (c) droplet velocity distributions measured for four sizes in the case of the coughing activity.</figcaption></figure>

evaluated as:

$$E = C_N S v_x \qquad (5)$$

where $C_N$ is the droplet number concentration, $S$ is the surface corresponding to the field of view and $v_x$ is the stream-wise droplet velocity (perpendicular to $S$). Assuming that no droplet can be detected twice, $C_N$ can be calculated as the number of detected droplet in a given size class ($N_{det}$) divided by the total volume, i.e., the measurement volume ($V$) multiplied by the number of acquired images ($N_{im}$):
<figure><img src="image_11.png" /><figcaption>FIG. 8: mean velocity for different droplet size classes in the case of speaking (a) and coughing (b). Stream-wise $v_x$, span-wise $v_y$ and vertical $v_z$ components and velocity magnitude $|v|$ are shown.</figcaption></figure>

$$C_N = \frac{N_{det}}{V N_{im}} \qquad (6)$$

Then, defining the thickness of the measurement volume as $l = V/S$, equation 5 can be simplified as follows:

$$E = \frac{N_{det}}{l N_{im}} v_x \qquad (7)$$

Note that $C_N$, $v_x$, $V$, $l$, and consequently $E$, depend on the droplet size $d$. Notably, mean values of these quantities in five droplet size classes are considered for the calculation. The ratio between $l$ and $v_x$ represents the time taken by a droplet in a given size class to cross the measurement volume thickness. The estimated emission rates $E$ for the five size classes selected and the three respiratory activities considered are presented in Table V.

For the speaking activity, a value of 2.3 #/s is reasonable and consistent with other results in the literature. This value can be directly compared to the findings in [8]. From the results of one volunteer reported as an example, an emission rate of 0.44 - 3.3 #/s for droplets in the range of 2-20 µm can be deduced; the smallest value corresponds to the lowest voice amplitude, while the largest value corresponds to the loudest voice. It should be noted that this measurement was taken farther from the mouth compared to our measurements. These results are in good agreement with those of the present study. [65] measured the number of particles emitted per unit time to be significantly higher compared
to the present study (≈ 400#/s for droplets in the range 1÷25 µm). Additional comparisons
can be made by considering the total amount of exhaled droplets. Assuming that counting
from "one" to "one-hundred" takes about 50 seconds, the total amount resulting from the
estimated emission rate is 115 #. [4] reported 230 # for droplets with 2 < d < 75µm. A
value of approximately 370 # can be deduced from [24] for droplets in the range 2 < d <
1000µm, considering the measured concentration and assuming an exhaled airflow of 7.5
L/min and a speech duration of 50 seconds. It should be noted that [24]'s measurements
were taken farther from the mouth compared to this study, but were corrected for dilution
and evaporation. Therefore, the total amount of exhaled droplets estimated in the present
work is smaller than the values obtained from [4] and [24]. However, the agreement can be
considered reasonable, given the assumptions made. Considering that a cough lasts about
1 second, approximately 35 # droplets in the size range 2-20 µm are exhaled according
to our results. Note that the acquisition was not interrupted between consecutive coughs,
and volunteers took brief pauses between each cough. Therefore, the total duration of the
acquisition is longer than the actual duration of 10 coughs, i.e., the number of coughs in
one acquisition. However, the underestimation of the droplet number emitted per unit time
due to this issue can be corrected by assuming that a cough lasts approximately 1 second,
resulting in an emission of approximately 65 #/s across all sizes. [4] reports a total amount
of 3700 # droplets in the size range 2-24 µm, while [24] reports about 112 # in the range
2-1000 µm. The value for [24] has been obtained from the measured total concentration of
droplets in the size range 2-1000 µm, considering a total exhaled volume of 1.4 L. Therefore,
discrepancies among data in the literature are quite large. The emission rate shown for
coughing in the present thesis is underestimated due to the detection problem mentioned
in Section III B. Despite the underestimation of droplet numbers, droplet emission during
coughing is about ten times higher than during speaking and about a hundred times higher
than during breathing.

F. Droplet ejection direction

Once the stream-wise, span-wise, and vertical droplet velocities are determined, it is
possible to calculate the droplet direction. This is an interesting quantity, as droplets do
not strictly follow the ejected air cloud but can diverge in different directions [46, 66].
<table><caption>TABLE V: Estimation of the total number of droplet of different sizes emitted in time while speaking, coughing and breathing.</caption><thead><tr><th>Activity</th><th>E (#/s)<br>2 ≥ d > 2.5 µm</th><th>E (#/s)<br>2.5 ≥ d > 3 µm</th><th>E (#/s)<br>3 ≥ d > 5 µm</th><th>E (#/s)<br>5 ≥ d > 20 µm</th><th>E (#/s)<br>20 ≥ d > 60 µm</th><th>E (#/s)<br>for all sizes</th></tr></thead><tbody><tr><td>Speaking</td><td>1.27</td><td>0.33</td><td>0.273</td><td>0.216</td><td>0.223</td><td>2.31</td></tr><tr><td>Coughing</td><td>9.97</td><td>8.93</td><td>10.1</td><td>6.24</td><td>-</td><td>35.3</td></tr><tr><td>Breathing</td><td>0.129</td><td>0.106</td><td>0.0827</td><td>-</td><td>-</td><td>0.317</td></tr></tbody></table>

Droplet direction is here expressed by means of two angles, i.e. $\beta_h$ and $\beta_v$. Taking the stream-wise direction as the reference, $\beta_h$ is the angle formed between the droplet y-velocity and the reference, while $\beta_v$ is the angle formed between the droplet z-velocity and the reference (Figure 9). The percentage of droplets moving in a given range of directions is reported in Table VI. Note that only forwards moving droplets are considered in this calculation, while backward moving droplets corresponding to recirculating or inspiratory flows are neglected. For coughing, about one half of the ejected droplets move at angles between $\beta_h$ and $\beta_v$ in the range $\pm 30^\circ$, while for speaking and breathing the percentage is slightly lower, suggesting a wider angular spread of droplet. However, the same analysis applied to the range $\pm 70^\circ$ leads to the opposite conclusion.

Horizontal and vertical spread angles are almost equal in the case of speaking and coughing, but they slightly differ in the case of breathing. The higher vertical angle observed for breathing is related to buoyancy which induces an upward movement of the warmer (with respect to the ambient) exhaled air. This effect is more pronounced in case of breathing due to a lower ejection velocity. Indeed, breathing droplets mostly move upwards: among the droplets within $\pm 70^\circ$, about 70% move between 0° and $-70^\circ$ and only 30% between 0° and $+70^\circ$.

In [66] the cone shape formed in the vertical plane by trajectories of the droplets ejected in a cough is 90° wide ($\beta_v$ within $\pm 45^\circ$). In [45] most of the droplets move with $\beta_v$ in the range 0-60° at the beginning of a cough.
<figure><img src="image_12.png" /><figcaption>FIG. 9: Sketch representation of the two angles defining droplet direction.</figcaption></figure>

<table><caption>TABLE VI: Percentage of droplets moving with a direction in a given range defined by the two angles $β_h$ and $β_v$. Data for speaking are from [20].</caption><thead><tr><th></th><th>angle β<sub>h</sub> speak β<sub>h</sub> cough β<sub>h</sub> breath β<sub>v</sub> speak β<sub>v</sub> cough β<sub>v</sub> breath</th><th>± 30°</th><th>± 45°</th><th>± 60°</th><th>± 70°</th></tr></thead><tbody><tr><td>46</td><td>48</td><td>42</td><td>44</td><td>49</td><td>31</td></tr><tr><td>65</td><td>61</td><td>61</td><td>61</td><td>60</td><td>50</td></tr><tr><td>78</td><td>66</td><td>78</td><td>75</td><td>67</td><td>67</td></tr><tr><td>85</td><td>69</td><td>83</td><td>83</td><td>67</td><td>75</td></tr></tbody></table>

## G. Effects of masks on droplet size distribution and velocity

Droplet size distributions measured for speaking and coughing when either surgical or tissue masks are worn by the volunteers are shown in Figure 10. Size distributions without wearing masks are also depicted for comparison. Note that data from the same three volunteers are considered, given the high between-volunteer variability (discussed in Section III H). Here, concentrations are not normalized by the bin size width as it is not required to study the masks effect for a given droplet size class. Droplet concentrations are expressed in both number and volume. The latter being more relevant if a proportional relationship between pathogen load and droplet volume is assumed (discussed in Section III C). In Table VII mean droplet number and volume concentration over all sizes is reported for the same study cases as in Figure 10, along with the percentage of reduction obtained with the two mask types considered. Globally, the tissue mask reduces droplet number concentrations by ~77% and ~86% for speaking and coughing, respectively. For the surgical mask, the number concentration reduces by ~74% and ~81%. It is important to note that the slightly
higher filtration efficiency of the tissue mask observed here cannot be generalized to all ex-
isting fabric masks. In fact, although there are guidelines for the fabrication of tissue masks
[67], several fabrics and materials can be used and their choice is left to the single manu-
facturer (even private people). This results in a variable filtration efficiency among fabric
masks. It is worth noting that the filtration efficiency of the masks varies with droplet size.
In fact, in neither of the cases analyzed here droplet larger than 8 µm are detected with
mask. Consequently, droplet reduction in terms of volume is far higher with respect to the
reduction in terms of number (about −99 ÷ 100% against −74 ÷ 86%). Droplets smaller
than 8 µm are still present when volunteers wear protection masks, however, their number
is reduced. Comparison with the literature is difficult as there are only few papers that
consider similar conditions. In the experiments by [54], [49], [68] human volunteers wear
protection masks. However, [54] assessed mask efficiency in preventing artificial ambient
particles of size smaller than 2 µm to be inhaled. Differently, [49] and [68] considered real
exhaled particle. For the former, the results are hardly comparable with the ones in the
present work as the size of droplets smaller than 120 µm is not precisely measured. In the
latter case, mask efficiency is evaluated based on virus copies rather than droplet number
or volume concentration. [53] measured the *total inward leakage* (TIL) for different kind
of masks and for particles ranging in 10 nm ÷ 10 µm. Particle concentration inside and
outside the mask is measured and their ratio is computed, giving the TIL. Dusts naturally
present in the ambient air are used as test particles. Ambient dusts can enter the mask either
through the filtering material or through possible leakages. [53] observed high variability for
different models of surgical masks and measured on average a TIL of ≈ 35 ÷ 5% for droplets
of ≈ 2 ÷ 10 µm. The complementary to 100 of the TIL can be in some way compared to
the present data (in the size range ≈ 2 ÷ 10 µm), if the same behaviour of the mask for
inward and outward flows is assumed and if the specific respiratory activity and the different
nature of particles are neglected. [48] and [50] carried out experiments where real human
volunteers wear KN95, surgical and cloth masks and perform different respiratory activities.
[48] measured the number of droplets in the range 0.3 ÷ 20 µm exhaled by unit time.
Number of droplets in the range 1 ÷ 20 µm is reduced of ≈ 75% in the case of coughing
and ≈ 100% in the case of speaking. [50] measured the number of droplet in the range
0.5 ÷ 10 µm exhaled by unit time while coughing without protections and wearing different
kind of masks. For cloth and surgical masks [50] measured a reduction of ≈ 77% and of
≈ 94%, respectively. Droplet reduction in number obtained by [48] for coughing agrees well with the ones in the present work, whereas the value obtained for speaking by both [48] and [50] is higher. Note, however, that even though more standardized with respect to cloth mask, surgical mask provided by different producer show different efficiency, as pointed out by [53]. Also, when the masks are tested on real humans, one must take into account that they may adhere differently to the faces of the different volunteers.

The effect of masks on ejected droplet velocity is also assessed. Table VIII summarizes the mean stream-wise, span-wise and vertical components and magnitude of velocity over all sizes for speaking and coughing activities with and without masks. Absolute maximum stream-wise component and velocity magnitude are reported as well. In addition to their filtering effect, masks are also very effective in reducing droplet velocity, especially the stream-wise component. The latter, which is responsible for the horizontal distance traveled by the droplets away from the mouth, has a zero-mean value for both the mask types, except for coughing with a surgical mask. Besides, its maximum value is reduced of about one order of magnitude irrespective to the type of masks worn. Note that a reduced stream-wise droplet velocity can beneficial as it can help the droplet to be entrained in the thermal plume of the emitter person, and therefore, to be transported upwards and away from the breathing zone of a susceptible individual. This aspect was pointed out by [51], who measured the velocity of ejected air with and without masks for different respiratory activities.

In the present study, both droplet concentration and velocity are measured just in front of the mouth and not in correspondence with mask sides, where a part of the airflow carrying droplets can be redirected. It would be interesting to extend the measurements in these zones, near the sides of the mask in future developments. Besides, taking the measurements on a larger sample of volunteers would make it possible to assess the variability between them, which includes both variability related to the different emission itself and to the different shape of the face, and thus, to the different adherence of the protective masks.

## H. Between and within volunteers variability of droplet size and velocity

Table IX summarizes *between* an *within* volunteer variability in droplet concentration, stream-wise velocity and velocity magnitude. In this section, no distinction is made between different droplet size classes. Between volunteers, variability is assessed by examining the
<figure><img src="image_13.png" /><figcaption>FIG. 10: Droplet size distribution measured for speaking (a) and coughing (b) when wearing surgical or tissue protection masks. Droplet concentration is expressed either in number (blue) or in volume (red). Droplet size distribution obtained for the same three volunteers, without mask are also reported.</figcaption></figure>

minimum and maximum values of droplet concentration or velocity measured among the 20 volunteers for speaking and the 23 volunteers for coughing. Additionally, the relative variation with respect to the mean value is computed as (maximum – minimum)/mean. For clarity, the mean value of the quantity of interest is also reported. The variability of droplet size and velocity distributions across different tests performed by the same volunteer is also investigated. For this purpose, one volunteer repeated the speaking and coughing tests six times. As with the between-volunteer variability, the minimum and maximum values of the
<table><caption>TABLE VII: Droplet number ($C_N$) and volume ($C_V$) concentration measured for speaking and coughing with and without protection masks. Either tissue or surgical masks are used. Droplet concentration reduction expressed as a percentage is also reported (ratio between i. the difference in concentration without and with mask and ii. concentration without mask).</caption><thead><tr><th>Activity</th><th>C<sub>N</sub> [#/cm<sup>3</sup>] reduction [%]</th><th>C<sub>V</sub> [µm<sup>3</sup>/cm<sup>3</sup>] reduction [%]</th></tr></thead><tbody><tr><td>Speaking (3 volunteers)</td><td>0.067</td><td>-</td></tr><tr><td>Speaking surgical</td><td>0.017</td><td>-73.8</td></tr><tr><td>Speaking tissue</td><td>0.015</td><td>-77.0</td></tr><tr><td>Coughing (3 volunteers)</td><td>0.161</td><td>-</td></tr><tr><td>Coughing surgical</td><td>0.030</td><td>-81.2</td></tr><tr><td>Coughing tissue</td><td>0.022</td><td>-86.3</td></tr></tbody></table>

quantity of interest and the relative variability are used to quantify the within-volunteer variability.

The measurements show significant variability among volunteers, consistent with findings in the literature (e.g., [19], [5], [26], [25]). The difference between the minimum and maximum droplet concentration exceeds the mean value, with relative variations of 2.2 for speaking and 2.6 for coughing. Additionally, the results of the present study confirm that individuals who emit more droplets than average in one respiratory activity are not necessarily the same in another, as shown in [8]. For example, the highest emitters are volunteers 14 and 19 for coughing, and volunteers 1 and 9 for speaking.

The variability in droplet concentration remains notably high even among different rep-
<table><caption>TABLE VIII: Mean droplet velocity (three components and magnitude) measured for speaking and coughing with and without protection masks. Either tissue or surgical masks are used. Maximum stream-wise velocity and velocity magnitude are also reported.</caption><thead><tr><th>Activity</th><th>v<sub>x</sub> [m/s]</th><th>v<sub>y</sub> [m/s]</th><th>v<sub>z</sub> [m/s]</th><th>|v| [m/s]</th><th>v<sub>x</sub> max [m/s]</th><th>|v| max [m/s]</th></tr></thead><tbody><tr><td>Speaking (3 volunteers)</td><td>0.21</td><td>0</td><td>0.08</td><td>0.44</td><td>3.68</td><td>3.69</td></tr><tr><td>Speaking surgical</td><td>0</td><td>0.01</td><td>0.03</td><td>0.07</td><td>0.45</td><td>0.71</td></tr><tr><td>Speaking tissue</td><td>0</td><td>0</td><td>0.02</td><td>0.07</td><td>0.34</td><td>0.35</td></tr><tr><td>Coughing (3 volunteers)</td><td>2.1</td><td>0.1</td><td>0.2</td><td>3.4</td><td>28.1</td><td>29.0</td></tr><tr><td>Coughing surgical</td><td>0.3</td><td>-0.1</td><td>0.2</td><td>3.4</td><td>2.0</td><td>2.1</td></tr><tr><td>Coughing tissue</td><td>0</td><td>0</td><td>0</td><td>1.2</td><td>4.0</td><td>11.1</td></tr></tbody></table>

etitions performed by the same volunteer, with relative variations of 1.0 for speaking and 1.4 for coughing. Although substantial, within-volunteer variability appears to be smaller than between-volunteer variability. Similarly, [25] observed that the number concentration of droplets smaller than 5 µm varies by about two orders of magnitude between volunteers and approximately one order of magnitude across multiple repetitions by the same volunteer. For droplets larger than 5 µm, the variation is significantly reduced. [25] attributes such large between-volunteer variation to differences in age. This could explain why the variability found in this study is lower. In our study, volunteers' ages ranged from 23 to 65 years, whereas in [25], they ranged from 5 to 80 years. Furthermore, the entire size range is considered in our computations, which differs from the approach in [25].

Analogous considerations can be done about droplet velocity variability. Particularly, the variation between different volunteers is higher than the one observed for several repetitions
<table><thead><tr><th rowspan="2">Activity</th><th colspan="3">minimum, maximum, mean, relative variation</th></tr><tr><th>C<sub>N</sub> [#/cm<sup>3</sup>]</th><th>v<sub>x</sub> [m/s]</th><th>|v| [m/s]</th></tr></thead><tbody><tr><td>Speaking between</td><td>0.013, 0.134, 0.055, 2.2</td><td>0.05, 0.36, 0.16, 2.0</td><td>0.18, 0.64, 0.33, 1.4</td></tr><tr><td>Speaking within</td><td>0.018, 0.063, 0.045, 1.0</td><td>0.09, 0.13, 0.11, 0.4</td><td>0.21, 0.29, 0.24, 0.3</td></tr><tr><td>Coughing between</td><td>0.012, 0.291, 0.081, 2.6</td><td>0.1, 6.7, 1.7, 3.9</td><td>0.4, 8.9, 2.5, 3.4</td></tr><tr><td>Coughing within</td><td>0.004, 0.023, 0.015, 1.4</td><td>0, 5.6, 3.2, 1.8</td><td>0.1, 8.3, 4.5, 1.8</td></tr></tbody></table>

TABLE IX: Minimum, maximum and mean values of droplet number concentration, stream-wise velocity and velocity magnitude detected among different volunteers (between) and several repetitions of the same volunteer (within). Relative variation is calculated as the ratio between i. the difference between the maximum and minimum value and ii. the average value of the quantity considered.

tions by the same volunteer (relative variation in stream-wise velocity of 2.0 against 0.4 for speaking and of 3.9 against 1.8 for coughing).

## IV. SUMMARY AND CONCLUSIONS

In this study, two measurement campaigns involving 23 volunteers were conducted to characterize droplet emission during speaking, coughing, and breathing. An improved configuration of the Interferometric Laser Imaging for Droplet Sizing, along with enhanced image processing techniques, was used to collect data. Particularly, droplet size and velocity were measured simultaneously for droplets down to 2 µm, extending the knowledge provided by the existing literature. Notably, the simultaneous measurement of size and velocity allows for the assessment of the correlation between these two quantities. Additionally, as all three velocity components were measured, the direction of the droplets could be determined. The effect of tissue and surgical masks on droplet size and velocity distributions was also
analyzed. Lastly, the variability of the results for the same volunteer, as well as between volunteers, was tested.

For both speaking and coughing activities, droplets were detected in the range of 2-60 µm, while for breathing, the range was limited to 2-8 µm. The highest concentrations were found for the smallest droplets, irrespective of the activity. The prevalence of smaller droplets was more pronounced during speaking, with a steeper decrease in concentration as droplet size increased. For both speaking and coughing, local maxima in concentration were observed at 28 µm and 20 µm, respectively. Coughing exhibited the highest droplet concentration across all sizes, though the concentrations reported in this study for coughing are underestimated. As expected, the lowest concentrations were measured during breathing.

Comparisons with the literature are challenging due to differences in setup, measurement tools, and protocols. However, the results of this study reasonably agree with the literature for droplets in the range of 2-10 µm. The absence of droplets larger than 60 µm in this study warrants further investigation. In the 10-50 µm range, literature results vary significantly, making it difficult to draw definitive conclusions.

As anticipated, the velocity of coughed droplets was significantly higher—by about an order of magnitude—than that of droplets ejected during speaking and breathing. This is particularly true for the streamwise component, which extends the potential contamination range further from the emitter. Consistent with the literature, mean droplet velocities are approximately $o(0.1)$ m/s for speaking and breathing and $\sim 2.5$ m/s for coughing. It is important to note that most literature values refer to the velocity of exhaled air rather than droplets. In all cases, the streamwise velocity is the highest and is predominantly positive, while the spanwise and vertical components fluctuate around an average of $\sim 0$ m/s. Maximum streamwise velocities detected were 3.68, 28.1, and 0.71 m/s for speaking, coughing, and breathing, respectively. For both speaking and coughing, a correlation between the streamwise velocity of the droplets and their size was observed, with larger droplets exhibiting higher velocities. Different velocity distributions based on droplet size could serve as initial conditions in computational fluid dynamics simulations [69].

As reported in previous studies, droplets depart from the mouth at a wide range of angles; about 60% of the droplets move in a direction forming an angle of $\pm 45^\circ$ with the axis passing through the mouth centre.

Significant variability in both droplet size and velocity measurements was observed among
volunteers, with slightly reduced variability when considering repeated tests by the same volunteer. Understanding how within-volunteer variability relates to different volunteer or environmental conditions requires further analysis and testing.

Finally, tests conducted with volunteers wearing surgical and tissue masks revealed a significant reduction in both droplet concentration and velocity.

ACKNOWLEDGMENTS

Data were processed using the high performance computer of the PMCS2I (Pôle de Modélisation et de Calcul en Sciences de l'Ingénieur et de l'Information) of the École Centrale de Lyon. The authors gratefully acknowledge Laurent Pouilloux, the technical manager of the computing center.

This study was supported by the Italian workers' compensation authority, Istituto Nazionale Assicurazione e Infortuni sul Lavoro (INAIL), who founded the University of Rome La Sapienza, and by the Eiffel grant program proposed by the Ministère de l'Europe et des Affaires étrangères.

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