key: cord-0467735-8wox5b5a
authors: Brosseau, Quentin; Ran, Ranjiangshang; Graham, Ian; Jerolmack, Douglas J.; Arratia, Paulo E.
title: Flow and aerosol dispersion from wind musical instruments
date: 2022-01-25
journal: nan
DOI: nan
sha: fbe0b25b567bc8acbe6dc62ef9cea23b7b1e6ed4
doc_id: 467735
cord_uid: 8wox5b5a

In the midst of the SARS-COVID-19 pandemic, many live musical activities had to be postponed and even canceled to protect musicians and audience. Orchestral ensembles face a particular challenge of contamination because they are personnel heavy and instrumentally diverse. A chief concern is whether wind instruments are vectors of contamination through aerosol dispersion. This study, made possible by the participation of members of the Philadelphia Orchestra, brings insight on the modes of production and early life of aerosols of human origin emitted by wind instruments. We find that these instruments produce aerosol levels that are comparable to normal speech in quantity and size distribution. However, the exit jet flow speeds are much lower than violent expiratory events (coughing, sneezing). For most wind instruments, the flow decays to background indoor-air levels at approximately 2 meters away from the instrument's opening. Long range aerosol dispersion is thus via ambient air currents.

The SARS-COVID-19 pandemic has disrupted many aspects of our daily lives. Live entertainment, for example, has experienced severe restrictions resulting (in some cases) in the temporary disbanding of large bands, orchestras, and choirs. Numerous live performances and festivals had to be postponed and even canceled to avoid the spreading of the disease [1] [2] [3] [4] . To date, orchestras are still experimenting with new ways of maintaining a high level of artistic production while keeping their audience and personnel safe. Mainly, they have resorted to performing with remote or limited audiences, adapting their repertoire to promote pieces featuring strings, and have made significant changes in the number of musicians and their position in the auditorium 5, 6 .

Among professionals, musicians playing string instruments and percussion can maintain an activity fully compliant with the recommendations of the World Health Organization (WHO) regarding social distancing and the use of personal protections equipment (face masks, screens, etc.) 7-9 . The case of wind instruments, however, poses a unique challenge since they are actuated by the human respiratory system. The constant air stream forced in and out of the body, required to maintain basic tone quality while playing a wind instrument, results in the creation and expulsion of small aerosols from the body. In addition, mouth and tongue movement required for the interpretative aspect of the sound imposes mechanical constraints that further contribute to the production of aerosol particles 10 . Combined, these two process can lead to an enhancement of aerosol flux exiting the instrument. a) Q.B. and R.R. contributed equally to this work. b) E-mail address: parratia@seas.upenn.edu Even in the absence of audiences, the use of wind musical instruments may still pose risks to other musicians as they are likely to release airborne particles, especially given the size of modern orchestra and standard choirs (∼ 100 persons). Airborne particle transport is usually defined as the spreading of pathogens by aerosols of a size smaller than 5 µm, which allows them to travel over a long distance carried by air flow 11 . This transport process is regarded as the main contamination pathway of the COVID-19 virus [12] [13] [14] [15] [16] . Studies have established that the vast majority of the aerosol generated during normal speech is under the size of 1 µm [17] [18] [19] . But larger size (> 100 µm) particles, which travel ballistically at speeds of 5 to 10 m/s 20-22 during coughing and sneezing, can still be a factor in contamination especially over shorter distances 14, 15, 23, 24 . For wind musical instruments, studies have found a particle size distribution similar to normal speech (< 5 µm) 25 , indicating the potential for long-range transport. Moreover, recent experiments have shown the the flow created by some wind instruments can extend to approximately 30 cm away from the instrument 26 ; ambient flow remains undisturbed beyond the distance of 1.5 m from the instrument 27 . Despite these advancements, there is still a dearth of relevant experimental studies regarding the production and transport of aerosols in wind instruments.

In this study, we investigate the flow and (mass) flux of aerosols produced by wind musical instruments using flow visualization techniques and particle counting instruments. We focus on single instruments and combine flow with particle concentration measurements to gain insights into aerosols' early life in the vicinity of a single musician. The data are used to formulate predictions regarding aerosol spreading. (Details regarding the dependency on articulation such as pitch, note attack and intensity of playing can be found in separate studies 25, 28 .) We find that the flow produced by wind instruments is, in general, relatively gentle and that the arXiv:2201.10386v2 [physics.flu-dyn] 6 May 2022 aerosol fluxes produced are similar to those generated by normal speech. Flow visualization reveals that intermittent jets are produced at the instrument bells or tone holes. Using a simple model, we show that the jet velocity decays to the indoor background flow within a few meters.

We begin by defining a few terms specific to musical instruments of the wind class. The air column of a wind instrument is the resonating space contained within the bore of the instruments (Fig. 1a) . It is bounded by the physical walls made of metallic alloys or wood essences; these wall are designed to be impermeable to air under playing conditions 29 . The air column starts at the embouchure (the player's mouth) and ends at the bell, which is an opening, usually with a flared geometry, at the instrument's bell or exit. In modern instruments, bore walls are usually pierced with tone holes or pistons that allow changes in the length of the air column.

All experiments are performed with professional musicians from the Philadelphia Orchestra. To minimize the effects of human activities (e.g. breathing) on the background flow and aerosol generation, musicians were isolated in a large amphitheater (along with the operators). For each measurement, musicians were asked to play their instrument continuously and repeat the same cycle of notes for approximately 2 minutes. We measure aerosol concentration and size distribution, as well as flow velocity in the vicinity of a given instrument using particle counting and flow velocimetry; more details can be found below.

Aerosol detection is performed using a particle counter (Lighthouse Handheld 3016) with 6 discrete particle size channels. The instrument operates at a suction rate of 2.83 L/min and a refreshment rate of 6 seconds to measure aerosol particle concentration. The opening of the aerosol counter is set at a distance of 5 -20 cm from the instrument bell and tone holes. For each experiment, the musicians are asked to play up and down a scale, in the natural range of the instrument, at a comfortable tempo, and at a mezzo forte dynamic range. The musical notes played can be found in Supplementary Fig. 1 . The experiments are purposefully performed in a large amphitheater to reproduce performance conditions, and to avoid the accumulation of released aerosols near the area of the musician. Background measurements are performed before any musician takes place in the auditorium to avoid contamination by human activity in the space. A delay of 20 minutes in between each musician is allowed to renew the air volume in the space.

Flow characterization experiments are performed at the bell for brass instruments and in the region above tone holes for woodwinds, with a custom particle image velocimetry (PIV) setup similar to a previous study 30 . An artificial fog is produced by a commercial ultrasonic humidifier (AquaOasis) and directed towards the instrument (Fig. 1b) . A slice of the fog parallel to the axis of the bell is illuminated by a green laser sheet (517 nm, 50 mW, BioRay). A camera equipped with a lens (AF-D, 80-200 mm, Nikon) records images of the fog at a rate of 60 fps while each musician performed continuous scales up and down in pitch at a comfortable tempo for a duration of 2 minutes. We note that the focus of this study is on a single instruments; ensemble studies will be the subject of future studies.

Aerosol concentration and size distribution produced by each wind musical instruments are characterized using a particle counter. Figure 1c shows aerosol counts, N , as a function of time (∆t = 250 s) for one representative instrument of the brass family (b-flat trumpet) and one of the woodwinds family (b-flat clarinet). Results are shown for 6 discrete particle diameters (d = 0.3 µm, 0.5 µm, 1 µm, 3 µm, 5 µm, 10 µm); also shown is the background count for control. For both instruments, the particle count time signals show deviation from background signal for sizes ≤ 1 µm. We find that the aerosol production range (number of aerosol per unit time) deceases as aerosol size increases by several orders of magnitude; the signals become indistinguishable from background for larger sizes. The data indicate that most of the aerosol is produced in the range of 0.3 µm to 1 µm.

To quantify the above observations, we compute a normalized mean aerosol count N/N 0 , where N 0 is the background count averaged over many runs for the trumpet and clarinet instruments (Fig. 1d ). We find that N/N 0 is non-monotonic in aerosol size, d, with a peak at 0.5 µm for both instruments. We note that non-monotonic size distribution in aerosol production has also been observed in activities based on mouth vocalization [18] [19] [20] 31 . We find that the averaged number of aerosols produced by the trumpet (at the peak) is nearly twice as much as the clarinet. Aerosol emission data, φ (particles/m 3 ), also show that the trumpet produces more aerosols than the clarinet (Fig. 1d, inset) , in agreement with recent results 25 . This may be due to instrument construction. The clarinet, similar to other woodwinds, also possesses a large number of tone holes through which part of the flow is expelled 26 , thus reducing the concentration of aerosol at the bell.

For both trumpet and clarinet instruments, we find that the particle concentration (from instrument) scales with particle size as φ ∼ d −1.5 . That is, most of the aerosols emitted by these instruments are in the smaller, sub-micrometer (≤ 1 µm) range. This phenomenology is similar to normal respiration (10 4 m −3 ) and vocalization (10 5 m −3 ) 19,32 , indicating that our data for these two specific instruments are more consistent with values obtained by the processes involving vocal cords rather than mouth movements (lips of tongue) such as reading or normal breathing. Other studies find flute and oboe emission ranges to be differing up to two order of magnitude more than speech, suggesting that the playing of these instruments (air pressure and mouth shape) can concentrate the amount of aerosol produced 25, 33 . Finally, our measurement indicate that aerosol distribution and concentration values are not affected by the transit inside the instrument bore for particle sizes ≤ 10 µm. It seems that moisture deposition inside bores is a process involving larger aerosol sizes.

Next, we compare aerosol emission by a broader set of wind instruments. Figure 2 shows the normalized mean aerosol count (or emission), N/N 0 , for an extended sample of instruments; only the 0.3 µm and 0.5 µm channels are presented here since they are the most abundant. Data are shown for woodwinds (oboe, b-flat clarinet and bassoon) characterized by small tube length, wooden walls and tone holes; and brass (b-flat trumpet and ftuba), with piston and large tube length. Similar to our previous results, we find that aerosol size distributions for all instruments peak at approximately d = 0.5 µm, except the clarinet, which peaks at d = 0.3 µm. The emission reported here is roughly 1.5 to 2 times that of the background of the room. Surprisingly, for the selected size range (0.3 -0.5 µm), the amount of aerosol emitted is independent of the instrument's tube length. For example, the tuba, with its large cross section and tube (length ∼ 5.5 m), has a comparable emission rate to the trumpet tube (length ∼ 1.5 m) which itself is twice as long as the clarinet (length ∼ 70 cm). Note that the larger volume of air needed for the playing tuba could explain the larger amount of aerosols. This is further ev-idence that deposition of droplet on the instrument wall is minimal for this size range.

Overall, our results show wind instruments emit aerosols mostly in the sub-micrometer range (≤ 1 µm) at concentrations comparable to normal respiration and vocalization. Particle counting data show that woodwind instruments are lower emitters relative to brass instruments. However, the flute stands apart; it has particle concentrations similar to brass instruments, albeit lower. Note that the flute's aerosol measurements are performed next to the instrumentalist's mouth above the mouthpiece, since this is the most significant stream exiting the instrument 34, 35 . Thus, the flute data are not affected by possible losses through the tone holes. The question now is: how far do these aerosols travel? To address this issue, we characterize the flow emanating from the musical instruments in the following section.

We now characterize the flow at the openings (i.e. bells and tone holes) of wind musical instruments using a particle image velocimetry (PIV) technique with a high-speed camera. In short, fog is used as seeding particles that are visualized using a laser sheet (see Fig. 1b and Supplementary Fig. 2 ). Flow velocities are obtained by the cross-correlation between two successive images taken by the camera. We define the reference frame so that the z-axis is oriented parallel to the ground in the direction away from the instrument opening and y-axis points upward (see Fig. 3a ). The region of interest is roughly 20 cm by 20 cm. Figure 3a and b show an example of a flow field extracted at the bell of a trombone. Each time-dependent flow field is then averaged to obtain the instrument's mean flow speed U mean . Figure 3b shows U mean as a function of time for all instruments analyzed here. In general, the values of U mean are relatively similar for all instruments. In fact, our measurements do not show a distinct correlation between the pitch evolution (up of down a musical scale) and the value of the mean velocity; see the SI for more details pitch evolution. Importantly, these flow speeds (∼ 0.1 m/s) are relatively low compared to the speeds of coughing and sneezing (∼ 5 -10 m/s) 21 . Even for the flute, the highest instantaneous mean speed (∼ 0.7 m/s) is an order of magnitude lower than the speeds for coughing and sneezing 22, 36 .

In order to gain further insight into the flow generated by the instruments, we compute and analyze the distribution of U z obtained from PIV over the duration of the recordings (Fig. 4a, 4b) ; note that our measurements interrogate a 20 cm x 20 cm area in the vicinity of the instrument's exit. For all the instruments, the mean of the distribution is approximately 10 −2 m/s, indicating that the flow is quite gentle in accordance to recent results 27 . The maximum velocity, defined as the upper 99-percentile of the distribution, reaches speeds as large as ∼ 10 −1 m/s (Fig. 4c) , which are comparable to normal respiration events ∼ 1 m/s 37 , but small in comparison to coughing and sneezing events 22, 36 . The skewness (Sk) of each distributions has a visible bias towards positive values, which represents the direction away from the instrument opening. We find that Sk ∼ 1 for woodwinds and Sk ∼ 0.5 at the bell of brass instruments, which indicates a stronger directional displacement above tone holes compared to the bell. Curiously, the tuba shows a negative skewness (Fig. 4d) . Tuba is the only measurement in the upright direction, and it is likely that the negative skewness is due to (fog) droplet sedimentation in direction opposite to the bell (Fig. 4d) . Overall, both the skewness and mean velocity data show that rather than a continuous stream, the flow displacement at the opening is better characterized by transient events that dominate the background ambient flow intermittently. The observed intermittency might originate from pressure variations necessary for the inception or "attack" of a pitch 38 , as well as changes in fingering that release or block pistons and tone holes. This results in flow structures that contain puffs and jets 26, 28 ; see Fig. 1b as well as the SI for time lapse images and videos).

It is worth noting that flutes (together with recorders and organ pipes) stand apart as the vibration of the air columns is set in motion by an air jet instability that originates at the mouth of the musician over the embouchure 34, 39 . In that case, our measurements are taken in a direction aligned with the mouth of the musician, instead of above the tone holes. Despite this peculiarity, the flute displays a skewed velocity distribution comparable to other woodwinds.

To better understand the release and dispersion of aerosols in the ambient, we analyze the characteristics of the jets emitted by the musical instruments during play (See Supplementary Fig. 2) . We begin by calculating the maximum Reynolds number (Re) for each instrument. Here, we define Re = U m D/ν, where U m is the maximum (or peak) air velocity obtained from PIV, D is the diameter of the instrument openings (bell or tone hole), and ν is the kinematic viscosity of air. The maximum air velocity is used to provide a conservative estimation. The (maximum) Reynolds numbers for all instruments are well below 300 (Fig. 5a) , which indicates that the jet flow is still laminar. Therefore, we model the flow exiting the instrument opening as laminar jets. We further simplify the problem by assuming steady and an axisymmetric jet. Under such conditions, we can make use of an analytical solution known as the "Schlichting jet" 40 . The steady and axisymmetric assumptions are clear simplifications, but they allow us to estimate the decay of jet velocity without resorting to numerical simulations.

The axial velocity of the laminar jet produced by the instruments can be expressed as (see details in the SI):

where z is the axial direction parallel to the jet flow, r is the radial direction normal to the flow, and Re is the Reynolds number of the jet defined in the above manner. The volumetric flow rate of such jet, Q, increases with axial distance z due to the entrainment of ambient air:

We note that Equation (1) is valid only for distances far away from the jet origin, i.e., for larger z values. Hence, we select a reference distance, z 0 , that matches the volumetric flow rate of the instrument such that Q = 8πνz 0 = U m A, which leads to: ing of the instruments. We can then replace the variable z by (z + z 0 ) and express the centerline velocity of the jet at r = 0 as:

The above equation describes how the jet axial velocity emanating from the instrument's exit decays as a function of axial distance. It predicts that the jet velocity far away from the exit is inversely proportional to the propagation distance z and proportional to the square of the Reynolds number: U c ∼ Re 2 /z. Figures 5b and 5c plot the estimated jet velocity decay versus the (jet) propagation distance for woodwind and brass instruments based both on Equation (4) and PIV measurements. The data show that flute and trombone have significantly higher velocities than the other instruments, as a result of their larger Re values (see Fig. 5a ) due to either larger opening and/or higher flow speeds. In both cases, the distance needed for the flow jet to decay to the indoor air draft (0.1 -0.2 m/s) is of the order of a few meters.

But would the aerosol particles follow the flow? To answer this question, we compute the Stokes number (Stk), which characterizes the "attachment" of a suspended particle to the surrounding flow. For the range of flow speeds measured in this study, we find that the Stokes number are well below unity for all aerosol diameters (Stk < 10 −2 , see Supplementary Fig. 4) . In this regime, the aerosols act as ideal tracers that closely follow the flow streamlines. As the jet velocity decays to room air draft level, the aerosol particles will be carried away by the ambient air flow.

Thus, we can define a length scale, L d , that represents the farthest distance an aerosol particle can travel with the jet until it is carried away by the ambient air flow. Figure 5a shows the values of L d for all instruments as an average between low (0.1 m/s) and high (0.2 m/s) indoor air draft speeds. Results show that aerosols released by the flute and trombone can propagate over a distance of 2 m to 6 m before reaching the room air draft level. For the other instruments, the decay length (L d ) are all shorter than 2 m, the recommended social distancing of the CDC guidelines 41 . Note that the calculation is performed with the instrument's maximum flow speeds, and thus representing the most conservative estimation. Estimations using the average speeds would lead to much lower distances (L d 1 m). We are also interested in the dispersion of aerosol particles in the direction normal to the flow. To this end, we estimate the expansion of the jet versus the propagation distance, and find that the jet diameter is proportional to the axial distance z, and inversely proportional to the Reynolds number: D ∼ z/Re (see the SI). Figures 5d  and 5e show the growth of jet diameter for different wind instruments. We find that the jets generated by instruments with larger Re, flute and trombone, can propagate a longer distance without much expansion in diameter. On the other hand, the jets created by instruments with smaller Re, clarinet and oboe, are more likely to disperse aerosols at short ranges due to their faster expanding diameters, despite unable to travel over long distances.

The combination of flow and particle concentration measurements allow us to draw insight on the early life of aerosols, from production to release in the ambient. Overall, we find that aerosols emitted by wind instruments share similar concentration and size distributions to normal speech and respiration events. We show that in the range of diameter < 10 µm, aerosol particles travel down the instrument bore with little trapping and are either ejected through tone holes or the instrument bell. Flow measurements show that exit jet speeds are much lower (∼ 0.1 m/s) than coughing and sneezing (∼ 10 m/s) events. We use an analytical solution for an axisymmetric laminar jet to estimate each instrument's exit jet speed decay. We find that, for most instruments, the maximum decay length is less than 2 meters away from the instrument's opening. Although very simplified, the jet model predicts plume length that are consistent with studies in controled environment 26 and CFD modelling 28,42 which also predict maximum jet development over a distances shorter than 1 m. The aerosol particles in the size ranged explored here (≤ 10 µm) follow the (jet) flow closely until this decay length is reached. Beyond that, we expect aerosols to be dispersed by the ambient flow.

See the Supplementary Information (SI) for the videos recording of the instruments playing used for the PIV analysis. The derivation for the laminar jet model and the aerosol particles Stokes number and settling times are also provided in the SI. jet analytical models, Q.B., R.R., I.G., D.J.J. and P.E.A. wrote the manuscript. Q.B. and R.R contributed equally to this work.

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The authors thank the members of the Philadelphia Orchestra, instrumentalists, and staff for their willingness to participation in our study. We also thank P.J. Brennan and Tanya Derksen for their invaluable guidance. We also thank Nakul Deshpande and Andrew Gunn for insightful discussions and assistance with experiments. R.R. and P.E.A. are supported by NSF-DMR-1709763, and I.G. acknowledges the support from NSF-DMR-1720530 (Penn MRSEC).