Since mid-2021, global concerns appear to be focusing on scourges other than the Covid-19 pandemic. This disease could nonetheless go through seasonal resurgences as do other respiratory infections, especially the flu. Covid-19 is transmitted mainly through contact with soiled, previously contaminated objects (also referred to as “fomites”) and through the transport and dispersion of particles emitted by infected people. In this regard, it has been established that virions, the extracellular form of viruses, are present and pathogenic in liquid particles produced by infected people when they sneeze or cough, but also when they speak or simply breathe. Virions are found in the sputum of symptomatic people, but also in that of asymptomatic people, who can unknowingly transmit the infection to others who, in turn, will be unaware that they have been contaminated. Airborne transmission of infectious agents carried in liquid particles of different sizes is discussed later in the introduction. It raises concerns, especially since it is not specific to Covid-19; indeed, it is common in many other respiratory diseases such as the other severe acute respiratory syndromes (SARS), Middle East respiratory syndrome (MERS) or the many types of influenza (H1N1) and their variants.

The sizes of particles expectorated depend on the dissemination event, and even on the human behind it (in other words, two people do not produce the same spectrum of liquid particles when breathing or coughing). The range of sizes extends over several orders of magnitude (from 0.1 to 1000 µm in aerodynamic diameter). A cut-off diameter (around 5 to 10 µm) separates the finer particles, which are “real” aerosols sustainably suspended in the air, from the larger particles, which, according to the conditions of their emission, either settle almost immediately on accessible surfaces or behave like projectiles. In this article, we consider particles of discrete sizes and use the word “droplets” for particles whose diameter is either 1 or 10 µm, whereas the word “drops” refers to particles with a diameter of either 100 or 1000 µm. Also, the word “diameter” implicitly means “aerodynamic diameter.”

On a global level, not all countries agree on the measures to be taken in the face of Covid-19: some apply strict testing and lock-down measures, while others put up with the presence of the disease as long as it remains limited. However, the World Health Organization (WHO) like the health institutions of many countries ended up advocating the mask use as valuable for limiting the dissemination of virions exhaled by infected people during respiratory events. Mask use was systematically made compulsory during the acute phases of the pandemic. It has persisted in places such as hospitals, pharmacies and public transport. Even though mask use currently remains compulsory only in certain countries, it will clearly become advisable again in the event of a Covid-19 resurgence, wherever it may occur.

In a previous article1, we attempted to fully demonstrate the value of Computational Fluid Dynamics (CFD) to account for the three-dimensional space and time dispersion of particles emitted by people infected with diseases leading to expectoration of pathogens such as virions. To illustrate our point, we studied the risk of Covid-19 transmission among public transport passengers. We created a twin experiment by reproducing the numerical mock-up of a commuter train car in which human manikins were placed. We assumed that an infected individual emitted droplets and drops while breathing and during coughing episodes. The particles were transported by the ventilation system of the coach and exhibited totally different aerodynamic behaviour depending on whether they were droplets (which perfectly followed the streamlines) or drops (which separated from the carrier fluid by their inertia and tended to sediment in the immediate vicinity of the spreader). In addition, the cough was characterised by the initial momentum given to the emitted particles. While the droplets adapted very quickly to the flow around them, this was not the case for the largest drops, which adopted a ballistic behaviour. This phenomenology was highlighted in our three-dimensional simulations, which examined the turbulent flow within the coach and the dispersion of particles of different sizes (using an Eulerian approach and a Lagrangian approach that led to similar results).

While our article1 enabled us to present and validate our CFD model, it was limited to the case in which passengers did not wear masks. This situation corresponds to what prevails today in places where the Covid-19 outbreak seems to be behind us, at least in some countries. When the epidemic was active, however, many governments mandated the wearing of masks on public transport; this remains the case in some parts of the world and could become widespread again in the event of a resurgence of Covid-19 or other respiratory diseases. In addition, we thought it would be interesting and useful to attempt to carry out CFD simulations featuring mask use by passengers. We were particularly interested in knowing if mask use could effectively reduce the dissemination of virions in a public space such as a railway coach. This led us to undertake simulations involving, once again, a twin experiment in a railway coach, this time with passengers wearing masks and, among them, one passenger assumed to be infected with the Covid-19 disease. In the simulations reported in this article as in the previous one, the liquid particles are assumed not to evaporate and we study their spatial and temporal distribution around the human manikins occupying the railway coach.

This new research article is structured as follows. We first present a review of the literature: on one hand, we take stock of what is known or still debated at the end of 2022 regarding the transmission of the SARS-CoV-2 virus; on the other hand, we examine the influence of mask use on the droplets and drops produced by an individual breathing and coughing. As there are many types of masks, special emphasis is placed on the surgical mask, which is very widespread due to its particularly low cost. We then devote a part of the article to the results of our modelling and simulation work. First we consider the head and bust portion of a human manikin, which is immersed in a motionless atmosphere; this allows us to examine the situations in which the manikin wears a tight-fitting mask, a loose-fitting mask, or no mask at all. We next present results obtained with complete human manikins wearing masks and placed in a commuter train, with one of the passengers being infected with the Covid-19 disease. In the next section of the article, we present a general discussion about the results obtained and the perspectives offered by our numerical approach in terms of scientific developments and operational applications. Part of the article is devoted to the methods used in the numerical study. In particular, we explain our choices regarding the production of droplets and drops, depending on whether the manikins wear more or less well-fitting masks, and regarding the aerodynamic conditions in the railway coach. We also present the CFD tool implemented in the study, as well as the computational resources and the associated computation times.

Aerial transmission of the SARS-CoV-2 virus and other pathogenic respiratory agents

The mode of transmission of the SARS-CoV-2 virus (which causes Covid-19) was intensely debated in 2020, as the results were to determine the healthcare responses needing to be made. In July 2020, the WHO2 recognised that the SARS-CoV-2 virus could be transmitted from person to person through the air. This virus is known to be carried in liquid particles exhaled through the mouth and the nose, particularly when coughing, sneezing, speaking, singing or breathing3. These particles, whose exact chemical composition remains unclear, contain multiple virions of about 100 nm in size4. The combination of entrainment by the airflow, particle inertia, gravity and evaporation determines the evolution of the exhaled particles.

Historically, particles carrying virions have been separated into two categories according to their aerodynamic behaviour5, on the grounds that this dichotomy should be a source of guidance for national health authorities and the WHO. We therefore make a distinction between drops – “visible” particles with a diameter greater than about 5 to 10 µm, which fall under the effect of gravity without having time to evaporate, finally settling on exposed surfaces (fomites) – and droplets, presenting a diameter of less than 5 to 10 µm, which evaporate more or less rapidly to a dry nucleus and remain suspended in the air in the form of an aerosol6. The droplets are carried by the airflow, which depends on the local ventilation conditions7. They are likely both to cause contamination at longer distances and to penetrate deeper into the respiratory tract in comparison to drops8,9. The threshold of 5 to 10 µm that is usually considered has been discussed and questioned during the pandemic3, and it is clear today that all classes of particles must be taken into account, as well as the two modes of transmission at short and long distances10.

The number and size of particles exhaled by a spreader are highly variable. The overall exhalations of a human being are known to contain particles between 0.1 and 1000 µm in aerodynamic diameter, i.e. five orders of magnitude11. Symptomatic and asymptomatic carriers do not a priori produce the same number or the same size of viral particles. In addition, symptomatic carriers do not necessarily excrete higher viral-load drops and droplets than do asymptomatic infected people12. There are also people called “super-spreaders.” It has been shown, for example, that some individuals produce seventeen times more droplets during a cough compared to other individuals13. It has also been shown that the viral load of the particles changes according to the stage of the disease.

The proportion between exhaled drops and droplets is variable and still subject to debate, as is the potential for aerosol contamination. For example, trials7 have shown that 20,000 particles between 0.8 and 5.5 µm, along with 100,000 virions, are emitted every minute during speech. In a series of analyses, aerosols smaller than 5 µm have been shown to contain more SARS-CoV-2 virions than do particles larger than 5 µm14, while other findings tend to go the other way13. The number of exhaled particles varies depending on whether we consider a low-frequency event or a cyclic event. For example, a sneeze can produce around 10,000 particles15, a cough around 10 to 100 times fewer16 and breathing or speaking a minimum of 50 particles per second, but since breathing and speaking are recurrent phenomena, they are probably ten times more important in contamination than coughing or sneezing17.

Experimental work13 makes it possible to assess both the number of particles produced during coughing and speaking and the corresponding viral load. For instance, this work mentions that during a cough, 98% of the volume of particles is made up of drops of 100 to 1000 µm, with more than 20 106 droplets (with a diameter of less than 10 µm) being produced in a single cough. By comparison, the experiment proposed for speech (“stay healthy” pronounced 10 times) produces more than 7 106 droplets. The authors use a viral load estimate of 7 106 virion copies per millilitre of respiratory sample. Measurement of the volume of the cough droplets shows that it has about 104 copies, i.e. one in 2000 droplets contains at least one virion.

Finally, it should be noted that the diameter of the particles varies in the air under the effect of evaporation. The final particle diameter depends on many factors such as initial size, relative humidity, temperature, ventilation flows and residence time11. For example, an average particle size of 2 to 3 µm can be obtained for an initial size of 10 µm18.

While numerous scientific works carried out during the Covid-19 pandemic have supplemented the knowledge acquired over a long period of time on the transmission of infectious agents, many questions about the SARS-CoV-2 virus are not yet clearly resolved, such as the relative contagiousness of drops and droplets according to their diameters, the “minimum dose” to risk contamination, the number of virions exhaled by infected people or the evolution of the pathogenicity of the virions embedded in evaporating drops and droplets.

Use of surgical masks and their effect on aerial transmission

The surgical mask is a single-use respiratory mask whose purpose is to limit to the immediate environment the spread of bacteria and viruses exhaled from the respiratory tract (mouth and nose) of the wearer. Its main purpose is to filter the largest respiratory drops (above a few tens of micrometers). Originally, this type of mask was worn by healthcare professionals during surgery to protect the sterile operating field and the patient receiving care. It is also worn by patients with a disease whose contagious agent is airborne.

When used correctly, a surgical mask quite successfully contains the dispersion of respiratory drops produced during a sneeze or a cough. It is commonly accepted to be an effective device for blocking drops projected by the wearer and measuring several tens of microns. It has been shown to greatly limit the transmission of airborne viruses (influenza, coronavirus, etc.) by infected people19. That said, it is not very effective in stopping the transmission of fine aerosols smaller than 5 µm20, and its effectiveness depends on its design, the materials used in its manufacture, its dimensions and its fit on the face.

Above all, the surgical mask protects the individuals surrounding the person wearing it – but the wearer is also protected from projections of drops, though it is unknown to what extent exactly. The protection provided by a surgical mask during inhalation is real, but unquantified and extremely variable. Such a mask is not designed to protect the wearer from inhaling airborne bacteria or viral particles.

Generally speaking, filtering facepiece (FFP) masks are personal respiratory equipment defined by standards such as EN 14921 in the European Union. This type of mask protects the wearer of the mask against the inhalation of particles in suspension in the air (average aerosol diameter of 0.6 μm) and drops of larger diameters. Leaks inside the mask are also standardised. There are several types of masks – FFP1, FFP2 and FFP3 – categorized by their filtration of aerosols with an average diameter of 0.6 µm (respectively 80%, 94% and 99%) and their degree of leakage towards the inside of the masks (respectively less than 22%, 8% and 2%).

The surgical mask is not a filtering respiratory device and cannot be certified as such. To be approved, however, it must meet standardised criteria based on bacterial filtration efficiency (BFE; during exhalation only) and splash resistance. For instance, in the EU, types I and II correspond to masks with, respectively, BEF > 95% and BEF > 98% of an expired aerosol with an average diameter of 3 µm, while type III is like type II but is also resistant to splash. There exists a test protocol for evaluating BFE22 whose presentation would be beyond the scope of this article, as would be the description of all standards that apply to masks intended for workers (for instance, medical staff) or the general public. The reader is referred, for example, to an Internet site23 that provides an interesting compilation of the standards that apply in the USA, the EU, China, Japan, South Korea and elsewhere.

Particle filtration efficiency during exhalation

Several authors have studied the filtration efficiency of surgical masks for various particle sizes, including fine particles. In one experiment24, different types of masks were tested with the assumption that they were perfectly fitted, i.e. without leakage between the mask and the wearer’s face. Drops with a diameter greater than 10 µm were generally filtered by the different masks, as were particles with a diameter less than 200 nm, due to the Brownian effect. Still, none of the masks tested, apart from FFP2 N95, could filter 100% of the droplets of intermediate size whose diameter was between 1 and 5 μm. In this experiment, even with a perfectly tight fit, aerosol leakage through the surgical mask represented 0.1% to 0.2% of the exhaled particles. Another experimental work25 involving different types of perfectly fitting surgical masks gave even poorer overall aerosol filtration efficiency results for surgical masks, with about 50% of particles with a diameter between 1 and 8 µm being retained.

In practice, leakage can be very significant at the wearer’s face, because the mask lets a large quantity of air pass around its perimeter. For instance, the presence of fog on eyeglasses shows that a good deal of air is exiting directly without passing through the filter screen. The problem of leaky surgical masks is not new, and it has often been studied already, at least qualitatively, leading to wear and adjustment recommendations for healthcare personnel26. A few precautions can limit the rate of leakage: these include a knot in the ear loops, a well-adjusted nose clip or the use of a cloth mask over the surgical mask, as per CDC recommendations27.

More recently, the problem of leakage from surgical masks has been presented experimentally in a relatively large number of scientific publications. For instance, an experimental reconstitution28 of the cough of a human manikin showed that only 56% of aerosols between 0.1 and 7 µm were filtered by a surgical mask, due to leaks around the edge of the mask. The filtration percentage increased to 77% with adjustment by side knots and the use of a nose clip, and even to 85% when the surgical mask was covered with a cotton mask.

Detailed CFD simulation work carried out on the subject in 2021 by the Riken Scientific Research Institute (Japan)29 also showed that the fraction of aerosols passing through different types of fabric masks without being filtered was larger than 70% with a variable fraction of aerosols leaking through the spaces between the wearer’s face and the mask.

Apart from its more or less effective filtration properties, a surgical mask can significantly reduce the airflow velocity during a sneeze, during a cough or within the respiratory cycle30,31,32,33,34. That said, the inhalation and exhalation phases also increase leaks on the perimeter of the mask due to “pumping” effects. Thus, the air jets resulting from these leaks can be highly turbulent and directional, which increases the effects of aerosol dispersion in the transverse directions but redirects the aerosols in directions that are a priori less problematic than a breath of air emitted directly from the mouth or nose of the wearer35,36.

It is also possible to visualise changes in exhaled airflows through density differences (due to temperature differences between the lukewarm exhalation and the ambient air) by means of the Schlieren process37. In the work cited, the authors showed that the direction and range of the exhaled airflow were modified according to the type of mask worn. Instead of passing through the filtering part of the mask, the air flows partially around the filtering part through leaks. Leakage can be two thirds of the total airflow through all parts of the mask. This fraction is much larger for surgical masks than, for example, FFP masks. The leaks between the mask and the face may be so significant that, according to the authors, the effectiveness of the masks should be considered based on the existence of secondary airflows around the perimeter of the mask, which depends on whether or not the mask is properly worn rather than on its intrinsic filtration efficiency or its ability to reduce the main airflow through the mask.

Looking beyond experimental evaluations, CFD presents the advantage of allowing precise access to airflow velocities and particle trajectories. That said, few simulations involving surgical masks and their inherent leaks have been carried out. One example is given by a CFD study38 of a human manikin wearing a surgical mask, in which the air and droplet leakage through and around the mask were evaluated for a five-second cyclical cough (with 1,008 droplets per cycle and a maximum expectoration velocity of 5 m.s−1). The numerical simulations were carried out with the Open FOAM software using an unsteady RANS approach for turbulence and a Lagrangian approach for particle tracking. The particle diameters were between 1 and 300 µm, and the filtration efficiency of the modelled surgical mask was assumed to be 91%. The authors used these simulations to identify the main locations of the leaks, evaluating the airflow velocities through these leaks to be approximately 0.2–0.4 m.s−1. The results also made it possible to estimate the relative proportions of droplets that were blocked by the mask, that passed through the mask and that escaped through leaks. The positive role of the mask, both in terms of filtration and reduced exhaled flow, was highlighted. Unfortunately, the authors did not establish a connection between the nature of the leakage and the particle diameter.

Particle filtration efficiency during inhalation

There exist no standardised data on wearer protection against incoming aerosols (that can also penetrate inside the mask by passing through the spaces between the wearer’s face and the mask). There have, however, been experimental studies published on this subject39,40,41. Between 20 and 80% of aerosols with a diameter of less than 1 µm passed through the mask, depending on its design, the number of layers, the material used for filtration and the airflow imposed through the mask. In another experimental work42, 20% to 80% of 1– to 3–µm diameter droplets passed through the mask.

On the same topic, an interesting experimental comparison43 was made for different types of masks regarding their filtration efficiency during inhalation (inward) and exhalation (outward). The aerosol diameters were between 0.04 and 1 µm in the first case, and between 2 and 5 µm in the second. The filtration efficiency of the mask was evaluated by tests on a specific test bench using a sample of the mask material (which therefore presents no leaks). In addition, the inward and outward protection efficiencies were determined using tests on manikins (accounting for leaks). For diameters less than 5 µm, the results depend on the diameters, with the exhalation and inhalation filtration efficiencies found to be between 25 and 75%. There is a significant deficiency in the effectiveness of the surgical mask for diameters below 2 µm, whether the wearer is inhaling or exhaling. Above 5 µm, the exhalation and inhalation efficiencies of the surgical mask were comparable (around 75%).

Very few CFD simulations have focused on the filtration of inhaled aerosols through a surgical mask. The study44 considers the head of a human manikin inhaling aerosols through a perfectly fitted surgical mask (with no leaks). The aerosols were between 1 and 20 µm in diameter. The filtration efficiency of the mask was set to 65% for all diameters. The originality of this study resides in its consideration of both the upper airways (nose and pharynx) and the lower airways (mouth and larynx), with the results showing that mask use clearly alters the flow near the nose and mouth. The air velocities were significantly lower and the particles entered less deeply into the respiratory tract favouring the deposition of aerosols in the upper airways (nose). Overall, wearing the mask reduced the quantity inhaled by three and five, respectively, for the 3–10 µm and 15 µm aerosols. For the aerosols of 1–3 µm in diameter, the quantity inhaled was almost the same regardless of whether a mask was worn or not.

Another publication35 presents a CFD and experimental study featuring the head of a human manikin equipped with an FFP2 mask. Even though the mask studied was not a surgical mask, this study enabled the assessment of leak sites around the perimeter of the mask and the way in which these leaks were distributed. The results indicated that, on average, leaks occurred mainly at the level of the nose (35 to 50%), to a lesser extent near the cheeks (20 to 25%) and least of all near the chin (6 to 12%).

Summary of the literature review focusing on surgical masks

A number of studies have examined the effectiveness of surgical masks, though most of them have not been carried out in the context of the Covid-19 pandemic, but instead for other infections (especially influenza). In addition, most of these studies have been experimental and solely qualitative, with different areas of focus (samples of filtering materials, masks placed on human manikins or patient cohorts). Due to differences among the protocols and the challenges involved in making the various measurements, the conclusions of these studies can be contradictory. Nevertheless, the following information can be derived about surgical masks:

  • Filtration efficiency in experiments implying real people or human manikins is lower than that measured using devices for testing masks.

  • A surgical mask contains the dispersion of respiratory drops of more than 10 µm in diameter according to standards. That said, it is much less effective in stopping the transmission of aerosols of less than 3 µm in diameter.

  • For a perfectly fitted surgical mask, the overall filtration efficiency during exhalation is around 50% for 1–8 µm droplets25 or between 50 and 75% for droplets smaller than 2 µm43. Still, for 1–5 µm droplets, leakage is limited to 0.1 to 0.2%24.

  • A surgical mask primarily protects those around the person wearing it. The wearer is also protected from projections of drops without it being known in which proportions exactly. The protection provided to the wearer during inhalation is not standardised. Experimental studies show that 20–100% of 1–3 µm particles pass through the mask39,40,41,42,44.

  • In practice, leakage is significant, and the mask allows large quantities of air and large numbers of particles to pass around it. While these leaks are not precisely quantified, their location is relatively well known. We can retain the following results:

  • During a cough, 56% of 0.1–7 µm droplets are blocked, while the others escape via side leaks28;

  • During a cough, the fractions of droplets blocked by the mask, passing through it and escaping through the leaks have been evaluated, and the velocity through the leaks is 0.2–0.4 m.s−138;

  • In respiratory events, leaks around the edge of the mask are distributed on average as follows: 35 to 50% around the nose, 20 to 25% on each side of the cheeks, and 6 to 12% along the chin35;

  • In respiratory events, the outward and inward filtration efficiencies of a surgical mask are between 25 and 75% for droplets of less than 5 µm in diameter, and they are of the same order for particles larger than 5 µm43.

  • Apart from its filtration properties, a surgical mask can greatly reduce the velocity of the breath of air emitted during the respiratory cycle30,31,32.

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