T he rapid spread of COVID-19, the disease caused by the virus SARS-CoV-2, highlights the lack of guidelines and mitigation strategies for reducing the impact of airborne viruses in the absence of a vaccine. The inherent structural features of the air flows created by exhalation and inhalation during speech or simple breathing could be a potent yet, until recently, unsuspected transport mechanism for pathogen transmission. This important topic surrounding viral transmission has largely been absent from the fluid mechanics and transport phenomena literature, and even absent more generally from quantitative studies of virus transport in the public health realm. We take steps toward quantifying fluid dynamic characteristics of this transmission pathway, which in the case of COVID-19, has been suggested to be associated with asymptomatic and presymptomatic carriers during relatively close social interactions, like breathing, speaking, laughing and singing. We focus on identifying and quantifying the complex flows associated with breathing and speaking; important areas for future research are indicated also. We recognize that much remains to be done, including integrating the findings and ideas here with potential mitigation strategies.

There are many recent news articles reporting on the pos-23 sibility of virus transmission during everyday social interac-24 tions. For example, documented cases include parties at homes, 25 lunches at restaurants (1), side-by-side work in relatively con-26 fined spaces (2), choir practice in a small room (3), fitness 27 classes (4), a small number people in a face-to-face meeting (5), 28 etc. Also, an editorial in the New England Journal of Medicine 29 summarizes differences between SARS-CoV-1, which is primar-30 ily transmitted from symptomatic individuals by respiratory 31 droplets after virus replication in the lower respiratory tract, 32 and SARS-CoV-2, for which viral replication and shedding 33 apparently occur most in the upper respiratory tract and do so 34 even for asymptomatic individuals (6). These differences were 35 suggested to be at least one reason why public health mea-36 sures that were successful for SARS-CoV-1 have been much 37 less effective for SARS-CoV-2.

Much has been written over many decades about droplet 39 shedding and transport during sneezing and coughing (7)(8)(9)(10)(11). 40 There remain open questions about the long-range transport 41 of droplet nuclei or aerosols resulting from droplet evaporation 42 (12), which is important to understand virus transmission from 43 symptomatic individuals in all airborne respiratory diseases. 44 In addition, researchers in the last decades have shown that

in human breathing and speaking reported in the literature. We assume a typical length scale for the orifice or mouth of diameter 2a = 2 cm for calculating the Reynolds numbers, Re = 2ua/ν, where u is the average speed at the mouth or orifice exit and the kinematic viscosity of air ν ≈ 1.5 × 10 -5 mfoot_0 /s.

The typical human adult has a head with approximate radius 7 cm. We may define the characteristic length scale of the mouth, whose shape is approximately elliptical, with the radius a of a circle having the same surface area. Measurements show that the average mouth opening areas are approximately 1.2 cm 2 for breathing and 1.8 cm 2

(with peak values of the order of 5.0 cm 2 ) for speaking (22).

For an order-of-magnitude estimate of the Reynolds numbers, a = 1 cm is chosen. It is perhaps surprising to many that typical air flow speeds are u ≈ 0.5 -2 m/s (volumetric flow rates ≈ 0.2 -0.7 L/s) when breathing and u ≈ 1 -5 m/s (volumetric flow rates ≈ 0.3 -1.6 L/s) when speaking; see Table 1. When breathing, exhalation and inhalation occur approximately evenly over a cycle with period about 3 -5 seconds (22,29), while during speaking the exhalation period is generally lengthened so that 2/3rds or even greater than 4/5ths of the time may be spent in exhalation.

The local fluid mechanics of exhaled and inhaled flows of speed u are characterized by Reynolds numbers Re = 2ua/ν (the kinematic viscosity of air ν ≈ 1.5×10 -5 m 2 /s), which have typical magnitudes Re= O 7 × 10 2 -3 × 10 3 when breathing and Re= O 1 × 10 3 -7 × 10 3 when speaking; larger values will be associated with loud or excited speech. Inertial effects are expected to dominate these flows, which will also generally be time dependent and turbulent, as discussed below.

Breathing and Blowing as Jet-like Flows. We characterize first the nature of breathing and blowing flows (Fig. 1). We set up a laboratory experiment with a laser sheet (1 m × 2 m × 3 mm), where no light hits the speaking subject, who sits adjacent to the sheet. A fog machine generates a mist of microscopic aqueous droplets whose large-scale motions are observed with a high-speed camera oriented perpendicular to the sheet. We obtain the velocity field of exhalation (both during breathing and speaking) by observing how the air stream drags and deforms the cloud in the sheet of light using correlation image velocimetry (see typical images in Fig. 1A and C, with details in Materials and Methods).

The flows are qualitatively similar during breathing or strong blowing (Fig. 1A and C), though the velocity magnitudes can be quite different (Fig. 1B and D). For instance, typical velocities observed in the air flow while breathing with a slightly open mouth (∼ 1 cm × 2 cm) remain of the order of 0.3 m/s to 1 m/s as visible in Fig. 1B (see Movie S1 in Supplementary Information (SI)), while velocities can be as high as a few meters per second in the blowing stream (Fig. 1D) (see Movie S2 in SI). Most significantly, a jet-like, conical structure is visible for the two different situations as depicted by the white lines in Fig. 1A and C, with a cone angle 2α ≈ 20 • . We can expect stronger propagation when breathing after exercising, as the volumetric flow rates are increased, which could make breathing in such a case closer to blowing. These observations call for comparison for the more complex situation relevant for pathogen transport, which is the case of speaking, where aerosols are produced during speech (13,14). Next, though, we comment on a fundamental asymmetry of exhalation and inhalation.

At these Reynolds numbers, we expect exhalation and inhalation to be asymmetric. A reader may be aware that one extinguishes a candle by blowing, but it is not possible to do so by inhalation (Fig. 1E which is a characteristic of the flows for breathing and speak-154 ing. Long exhalation should produce starting jet-like flows 155 propagating away from the individual over a significant dis-156 tance of the order of a meter (e.g. Fig. 1A-D), while inhalation 157 is more uniform and draws the air inward from all around 158

the mouth (Fig. 1F); it is this asymmetry that explains the 159 phenomenon related to extinguishing a candle (Fig. 1E). These 162 For such inertially-dominated flows, a continuous or long 163 out-flow should be similar to an ordinary jet (30), and during 164 the initial instants over a time T the propagation distance, 165 while smaller than the naive estimate L = uT = O(1) m (see 166 below), is still larger than the typical size of the head (e.g. 167 Fig. 1). Moreover, since L a, it follows that, in ordinary 168 circumstances, one breaths in little of what is breathed out. 169 Wearing a mask (as recommended as a mitigation strategy for 170 COVID-19) should be expected to produce more symmetric 171 flow patterns during exhalation and inhalation, localizing air 172 flow around the face. Speaking, Plosive Sounds and Jet-like Flows. Flows exiting 174 from an orifice are well-known to produce vortices, even in the 175 absence of coughing, and these drive the transport about the 176 head, as evident in Fig. 1. Speaking introduces two further differences: (i) the typical time of inhalation is about 1/4-1/2 of the exhalation time (29) and (ii) language includes rapid 179 pressure and flow rate variations associated with sound pro-180 ductions (plosives, fricatives, etc.), as previously characterized 181 acoustically by linguists (26). We also note that the stop 182 consonants, or what are referred by linguists as plosives con-183 sonants, such as ('P', 'B', 'K', ... ), have been demonstrated 184

recently to produce more droplets (14). In these cases, the 185 vocal tract is blocked temporarily either with the lips ('P', 186 'B') or with the tongue tip ('T', 'D') or body ('K','G'), so that the pressure builds up slightly and then is released rapidly, producing the characteristic burst of air of these sounds; in contrast, fricatives are produced by partial occlusion impeding but not blocking air flow from the vocal tract (31).

We now visualize flow during speaking, which seems different than breathing as, for instance, when saying a sentence like 'We will beat the corona virus', as shown in Fig. 2A (and visible in the Movie S3 of SI). A color code illustrates the average speeds (averaged over the time to say the phrase), but note that these are not representative of the true instantaneous velocities, which in the remainder of this section were estimated from the movies in the SI. Over the approximately 2.5 s to say the sentence, the air flow is more jerky and changes direction depending on the sound emitted. In this particular case, the sentence contains starting vowels (in 'We' and 'will') and pulmonic consonants as fricatives (as 'V' and 'S' in 'virus') and plosives (like 'B' and 'K' in 'beat' and 'corona'). Three different directions are revealed when averaging the velocity field over the time to say the sentence in Fig. 2A: 'We will beat' being slightly up and to the front with a typical velocity of about 5-8 cm/s, 'the corona' being directed downward between -40 • and -50 • with higher velocities of almost 8-12 cm/s while saying the two syllables 'coro'. Finally, the short air puff associated to 'virus' is directed upward at about 50 • with speeds of 5-7 cm/s. We believe that an interlocutor and potential receiver of the exhaled material will be most exposed after a few seconds by the horizontally directed part of the flow, whose velocity reaches, in this case, the ambient circulation speed at about half a meter at most. Next, we illustrate a sentence of the same time lapse of about 2.5 s containing many times the same starting fricative 'S' as in 'Sing a song of six pence' (25) with only one starting bilabial plosive sound 'P' in the last word: most of the air

D R A F T 0 . 0 5 0 . 1 0 . 1 5 0 . 2 0 . 2 5 0 . 3 V e l o c i t y m a g n i t u d e [ m / s ] 0.005 0.010 0.015 0.020 0.025 0.005 0.01 0.015 0.02 0.025 Velocity magnitude [m/s] 0 . 0 0 5 0 . 0 1 0 . 0 1 5 0 . 0 2 0 . 0 2 5 V e l o c i t y m a g n i t u d e [ m / s ] We will b ea t c o r o n a v ir u s 0.1 m ' We will beat the corona virus ' th e ' Peter Piper picked a peck ' 0.1 m 0.05 0.10 0.15 0.20 0.30 0.05 0.1 0.15 0.2 0.25 0.3 Velocity magnitude [m/s] 0.25 Velocity Magnitude (m/s) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Velocity magnitude [m/s] 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 7 0 . 0 8 0 . 0 9 V e l o c i t y m a g n i t u d e [ m / s ] ' Sing a song of six pence ' S in g a song s ix of pence L a s e r S h e e t L im it 0.1 m Table A B D Velocity Magnitude (m/s)

Velocity Magnitude (m/s)

< l a t e x i t s h a 1 _ b a s e 6 4 = " J J h 7 H j q R S S q l q b j L g 2 puffs produced are emitted downward at an estimated angle of 221 -50 • from the horizontal (and become visible in this sequence 222 only when the air flow hits a nearby table and crosses the laser 223 sheet, see Fig. 2B and Movie S4 in SI). However, a distinct, 224 directed air puff appears in front of the speaker when 'pence' 225 is pronounced (Fig. 2B), which propagates forward at initially 226 high speeds of about 1.4 m/s as visible in Movie S4, but 227 decelerates rapidly to ≈ 1 m/s at half a meter distance from 228 the mouth; the puff has a speed of 30 cm/s at about 0.8 m 229 (see Movie S4). 230 These images of typical speech raise the question of the 231 dynamics of individual puffs. In Fig. 2C we report the dis-232 tance L travelled by the air puff as a function of time t when 233 pronouncing 'pence'. The data demonstrates that the starting 234 plosive sounds like 'P' induce a starting jet flow, which grows 235 initially for very short timescales of under 10-100 ms as t 1/2 ,

but rapidly transitions to a slower movement characterized 237 by a t 1/foot_1 response, typical of puffs (32) and vortex rings (33).

238

In fact, when looking at the flow, a vortex ring stabilizes the 239 transport over a distance of almost a meter. This transition 240 between two different dynamics, ending with the dynamics of 241 an isolated puff, is also measured in coughs (10).

In contrast, when we speak a sentence with many 'P' sounds, 243 such as 'Peter Piper picked a peck' (PPPP) (25), as illustrated 244 in Fig. 2D, the distribution of the average velocity field ap-245 proaches that of a conical jet with average velocities of tens of 246 cm/s and over long distances of about a meter. Peak velocities 247 are seen at the emission of the sound 'P' with values close to 248 1.2-1.5 m/s (Movie S5 in SI). This more directed flow situation 249 shares features of breathing and blowing and thus material 250 will be transported faster and further than individual puffs. 251 But, unlike breathing, we believe that this distinct feature of 252 language is more likely to be important for virus transmission 253 since droplet production has been linked to the types of sounds 254 (14).

It should be evident that language is complicated (Fig. 2A, 256 B). Given the possibility of asymptomatic transmission of virus 257 by aerosols during speech, we have focused on the phrases in 258 language, those usually containing plosives, that produce di-259 rected transport in the form of approximately conical turbulent 260 jets (Fig. 2D, and also see Figs. The transition from puff-like dynamics associated to single 281 plosives and the development of turbulent jet-like flow during 282 longer sentences seems to be associated with the sequential 283 accumulation of 'puff-packets' pushing air exhaled from the 284 mouth. We will explore this transition in more detail using 285 the numerical simulations below.

To assist with the interpretation of the experimental results 288 just presented, and the numerical results we will report below, 289 for completeness we summarize a few results of well-known 290 mathematical models.

Reynolds-number steady turbulent jet, it is of interest to 293 characterize the volume flux, linear momentum transport and 294 kinetic energy transported by the jet, as well as the entrain-295 ment of the surrounding air that dilutes the jet (34) properties also help to understand the fluid dynamics of breathing and speaking. There are at least three significant conclusions that characterize the flow: (i) Denoting the direction of the jet as x, the typical axial speed of the jet as v(x), and its cross-sectional area as A(x), in a steady jet issuing in an environment at a constant pressure, the flux of linear momentum is constant, or v 2 A = constant. If the exit flow near the mouth is characterized by a speed v0, volumetric flow rate Q0

and area A0, we conclude that v(x)/v0 = (A0/A(x)) 1/2 < 1.

For a conical jet-like configuration of angle α (Fig. 1), then beyond the mouth A(x) ∝ (αx) 2 . (ii) The corresponding volume flux Q = vA, so that the out-flow leads to a volume flux below.

On the other hand, a rapid release of air, or puff, injects a finite linear momentum into the fluid, e.g. Fig. 2. For the inertially dominated flows of interest here, the linear momentum of the puff is conserved, so that the distance travelled is (32,35), similar to interrupted jets, i.e., starting jets when the flow is suddenly stopped.

However, during breathing or speaking, the interrupted jet and the puffs are released one after the other and interact with each other in front of the source, as illustrated by Fig.

3. The jet is neither continuous like in starting jets nor isolated like in classical puffs. What is then the dynamics of such a "train of puffs"? In the next section, we use numerical simulations to investigate the dynamics of puff trains and quantify their 339 growth in space and time. 340 Three-dimensional Numerical Simulations: Character-341 izing the "Puff Trains" of Breathing and Speaking 342 To explore quantitatively the various flows we have introduced 343 above, we report 3-D simulations of the incompressible Navier-344 Stokes equations (the flow speeds are much smaller than the 345 speed of sound). To highlight the dynamics of breathing 346 and speaking, simulations are driven by representative time-347 periodic flow rate variations (25) from an elliptical orifice 348 comparable to a large open mouth (of radii 1 cm × 1.5 cm). 349 Speaking produces relatively high-frequency changes to the 350 volume flow rate (or fluid speed) during exhalation, though 351 the variations are much smaller than sound frequencies; we 352 do not study the initial formation of the sounds of speech at 353 the glottis (36). Furthermore, as we have seen above, natural 354 plosive sounds also create special characteristic features that 355 we investigate. Nevertheless, it has to be stressed that the 356 simulations are a model and lack the phonetic complexity 357 introduced by the tongue and the cavity of the mouth, yielding 358 flows directed in front of the mouth only. 359 Contrasting Four Situations of Exhalation. We contrast four 360 situations with comparable period and given volumes exhaled 361 and inhaled, with zero net out-flow over one cycle (Fig. 4A-D): 362 (i) normal breathing with a 4-second period split into intervals 363 of exhalation (2.4 s) and inhalation (1.6 s); (ii) a breathing-like 364 signal but with a (slow) speaking-like distribution of exhala-365 tion (2.8 s) and inhalation (1.2 s), (iii) a spoken phrase, 'Sing 366 a song of six pence' (25), and (iv) a phrase with many plosive 367 sounds, 'Peter Piper picked a peck' (25). We either ran 1-cycle 368 simulations using the flow rate profiles over a single period, 369 followed by no further out-flow, to quantify a single "atom" of 370 breathing and speaking, and for many periods (or cycles) to 371 understand how the local environment around an individual 372 is established and changes in time. Different volumes of ex-373 halation typical of speaking, from 0.5 -1 L per breath, were 374 studied (see the full table of runs in the SI, Table S1).

The results of simulations of these different flow rate profiles 376 are shown in Fig. 4E-H For every case, a conical jet flow is produced, with similar cone angles as well, which is reminiscent of typical features of turbulent jets studied in laboratory experiments and many applications, e.g. (34,37); see also Figs. 12. Qualitatively, we observe that breathing produces a jet with an axial flow comparable to speaking, which some may find surprising. Jet lengths in particular are very similar, despite a factor of 2.6 in the peak flow rate of cases P75 and C75 for instance (see Table S1). The phrase with plosives produces qualitatively a rougher jet (Fig. 4G) due to the ejection of vortex rings away from the main jet and vortex interactions. Speaking jets (P75 and S75) yield the largest cone angles and consequently an axial extent somewhat reduced compared to breathing (B75 and C75). Short high-speed puffs associated with speaking thus seem to increase the jet entrainment, but do not enhance the long-range transport in the axial direction.

For all cases, even those with complex phonetic characteristics, we observe that the resulting jets display many of the features of a turbulent jet, which leads to transverse spreading and mixing of the exhaled contents with the environment.

These features actually build up over the continual cycles of exhalation and inhalation in both breathing and speaking.

Particle residence time (Fig. 4E-H 90% of the exhaled tracer particles (Fig. 5A). The included angles differed from case to case, but were of the order of 10 -14 • (see Table S1). The typical jet lengths, L(t), were 416 also calculated based on the criterion that 90% of the tracers 417 are located upstream of x = L at time t. Raw data of L(t) are 418 presented in the SI, Fig. S2, and the jet angles are reported in 419 Table S1. First, higher mean flow rates (exit speeds) produce 420 longer lengths, as expected. For a given exhaled volume per 421 cycle, different types of exhalation produce comparable jet 422 lengths, as suggested by the qualitative analysis of Fig. 4E-H. 423 Modulation of the in-flow signal (cases P and S) systematically 424 tends to increase the lateral growth of the jet, increasing the 425 jet angle and decreasing the jet length.

A Train of Puffs. We ran the multi-cycle simulations over many 427 periods to quantify the development of the transient velocity 428 field. In order to filter the turbulent fluctuations that prevent 429 direct comparisons of the velocity fields as a function of time, 430 we performed time averages over each period (see Fig. 5B) to 431 produce an approximate profile for the distribution of axial 432 speeds in the exhaled jet. In the far field, though time varying, 433 breathing and speaking may be viewed as periodic processes 434 where the time scales are much longer than an individual pe-435 riod. Moreover, we have already explained that inhalation has 436 little effect on exhalation because of the differences expected 437 of high-Reynolds-number motions. Indeed, when we plot the 438 axial speed as a function of axial distance we find that for each 439 period of exhalation, the axial velocity falls along the curve 440 v(x) ∝ x -1 for both speech and breathing, shown, respectively, 441 in Fig. 5C and D. Not only does the head of the jet evolve 442 as that of a starting jet, but the whole flow downstream of 443 a certain distance from the mouth behaves similarly to as 444 a steady turbulent starting jet. This is particularly striking 445 as the near-mouth flow is laminar and completely different 446 from a steady jet (Fig. 5C-D). Thus, at the Reynolds num-447 bers characteristic of breathing and speaking, a train of puffs 448 transitions to a turbulent, jet-like flow that dominates the 449 transport associated with breathing and speaking. A Diffusive-like, Directed Cloud of Exhaled Air. For growing 451 jets at constant angle, we can estimate the spreading of the 452 cloud with time. The time t it takes to reach an axial distance 453 from the orifice, or the mouth, is estimated by

or (using a to make the equation non-dimensional)

acts as a unique large puff (32), and L ∝ t 1/4 is obtained, which is consistent with the experiments (Fig. 2C).

These results allow the quantification of concentration of exhaled material in the far field. From the previous results, we expect the concentration field of the exhaled cloud is quasisteady and falls off with distance, c(x)/c0 ∝ a/ (αx). Note that for a = 1 cm, α = 10 • , and L = 2 m (the six-foot rule), then for directed jets the concentration of any exhaled material has fallen off by a factor of (a/ (αL)) ≈ 0.03. Typical dilution levels of 0.04-0.05 have been found in the different simulations at 1.5 m, which is consistent with this estimate. It is evident that this result is not an especially large dilution and the concentration is much larger than might be estimated based on a model of diffusion from a sphere.

To complement the numerical simulations and to further characterize the propagation of the exhaled jets we placed a laser sheet perpendicular to a speaker (Fig. 6 inset). We measured the time t for the laser sheet to be visibly disturbed when placed a distance L in front of the speaker, who said the sentence 'Peter Piper picked a peck' (PPPP) N times. The data of L(t) (circles), including breathing (diamonds), along from the speaker, exhaled material is delivered in a fraction of a second with flows directed upwards (about 40 • from the horizontal), downwards about 40 • from the horizontal) and directly in front (especially the bilabial plosives), where the latter regime obeys a t 1/2 starting-jet power law; (ii) out to about 1 m, longer, though slower, transport occurs driven by individual vortical puffs created by syllables with single plosives, where the time variation follows a t 1/4 power law; (iii) finally, out to about 2 m, or even further, due to an accumulation of puffs, the exhaled material decelerates to about a few cm/sec and becomes susceptible to the ambient circulation (in our ventilated lab). In this last regime, we discovered that the series of puffs, from plosives in a spoken sentence, produces a conical, jet-like flow, again similar to a starting jet, with a t 1/2 power law.

In the absence of significant ventilation currents, or air motions driven by other speakers, we have seen that often the exhaled cloud will largely be in front of the speaker, with a modest angle as shown in this paper. The dynamics of "puffs" associated with individual breaths or sounds have a distinct dynamics with the very early-time formation phase having a distance that scales with t 1/2 after which the puff advances a downstream distance that varies with t 1/4 ; these dynamics are common to starting jets of all types (e.g. ( 32)), including coughs (10). However, speech is similar to a train of puffs, effectively generating a continuous turbulent jet, which mimics many of the features of exhalation in breathing and speaking, where the local exhaled cloud increases in size approximately as L ∝ (v0t) 1/2 ; both longer times and louder speech (or increased breathed volume in the case of exercise for instance) increase the affected environmental volume. So, someone that speaks twice as long and "loud", which corresponds approximately to a change from 60 dB to 70 dB in sound pressure levels (out-flow velocities would be larger by about a factor of three) creates an exhaled cloud more than twice as long. Moreover, the increased loudness will also be accompanied by more droplets (13). With social situations in mind, in hindsight, it should perhaps not be surprising that droplet and aerosol generation, and possible virus transmission, are enhanced during rapid and excited speech during parties, singing events, etc. (3,4) The results presented in this paper do not account for some real features, e.g. movement of the head or trunk of the speaker and the influence of background motions of the air due to the ventilation. There is obviously much to be done to quantify the many details and nuances, especially as the different sounds in speech produce vortical structures of different strengths that influence the spread (axial and transverse) of the exhaled jet.

The authors are not trained in public health, nor have professional standing in the public health arena, so we should be cautious in conclusions to be drawn from our results regarding social distancing guidelines. Nevertheless, there are general results that can be extracted from this work. Our results show that typical airflow speeds at 1 -2 m distances from a speaker are typically tens of centimeters per second. This means that the ambient air current may be dominant at such distances from a speaker, which makes the definition of guidelines difficult. When thinking about quantitative features to discuss social distancing guidelines (six feet, approximately 2 m, in the United States or 1 m in the World Health Organization's interim guidance published on June 5, 2020 (38)), both spatial and temporal characteristics matter, e.g., during conversations, is approximately 3 mm. To maintain safe use, the laser light shines from above so that no light hits the speaker who sat adjacent to the sheet. Laser safety glasses were worn by the speaker.

The flow is seeded by a fog machine (Mister Kool by American DJ), which uses a water-based juice (Swamp Juice by Froggys Fog) and generates droplets with diameters of about one micrometer. The fog can last for tens of minutes and no notable sedimentation of the droplet is observed throughout the course of the experiments. Therefore, the droplets can track the local flow, effectively as passive tracers. Images are captured via a high-speed camera (v7.3, Phantom) with frame rate f = 300 fps (frame per second). However, we note that there is inevitable background flow in the experiments due to the droplet emission by the fog machine, as well as the natural ventilation in the room. Specifically, the background flow is of the order of O(1) cm/s and moves from the left to the right in the experiments reported in the main text (e.g., Fig. 1) and only slightly enhances the propagation of the jets. Although we do not pursue it here, the effect of the background flow due to ventilation on the transport of the out-flows from breathing and speaking is an interesting and fundamental problem for future investigations.

A similar setup is used when speaking a distance L in front of a laser sheet to determine the axial structure of the out-flows, e.g., the measurement presented in Fig. 6. The laser sheet is perpendicular to the flow and the camera is perpendicular to the laser sheet.

In order to quantify the structure of the jets from breathing and speaking, the seeded image sequences captured on video are processed using PIVlab (40). The crosscorrelation method is applied to the image sequences to measure the local velocities in the particle image velocimetry (PIV) analyses. Square interrogation windows of 16 pixels × 16 pixels (approximately 2 cm × 2 cm) with an overlap step of 50 % (8 pixels, 1 cm) are used to obtain the velocities, e.g. those presented in Fig. 1B. Numerical simulations. The computations are performed with the in-house flow solver YALES2BIO (41-45) (https://imag.umontpellier. fr/~yales2bio/). These are large eddy simulations (46), which are well suited to study transport in turbulent flows, in particular in the context of speech production (35). In addition, they are well adapted to intermittent/transitional regimes (41,42). The spatially filtered, incompressible form of the Navier-Stokes equations are solved. The so-called sigma model ( 47) is used to treat the effect of the numerically unresolved scales on the resolved scales. Particles are injected into the flow to characterize the jets issuing from the orifice (mouth). They are perfect Lagrangian tracers displaced at the local fluid velocity, and do not affect the flow. In the simulations buoyancy effects are not considered; the temperature, density and dynamic viscosity are constant. The geometry of the model of the mouth remains constant over time and does not depend on the type of in-flow signal (breathing or speaking). The mouth opening is an ellipse of semi-axes 1.0 cm and 1.5 cm, which corresponds to the upper limit of the range of mouth surface area observed during speaking (22)

for travel support, as well as K. Meersohn for pointing out the importance of plosives in almost all languages of the world. S.M. thanks V.

Moureau and G. Lartigue (CORIA, UMR 6614) and the SUCCESS scientific group for providing YALES2, which served as a basis for the development of YALES2BIO. Simulations with YALES2BIO were performed using HPC resources from GENCI-CINES (Grant No. A006 and A0080307194) and from the platform MESO@LR. S.M. acknowledges the LabEx Numev (convention ANR-10-LABX-0020) for support for the development of YALES2BIO. We thank A. Smits for loaning the fog machine and P. Bourrianne and J. Nunes for help measuring flow rates during breathing.