Toward unraveling the mechanisms of aerosol generation during phonation Open Access

During the COVID-19 pandemic, the route of airborne transmission of respiratory viruses seems to play a main role in the infection of the upper airways.¹ Consequently, since the outbreak of the pandemic at the end of 2019, virus transmission under different conditions (e.g., temperature, wind speed, and relative humidity) has been investigated in detail.^2–5 However, the place of origin and formation mechanism of virus-laden aerosol particles still remain unclear. Typically, respiratory droplet formation processes are associated with three modes of generation:^6–9 

1. A bronchiolar mode: a liquid film/bridge burst mechanism in the terminal bronchioles, which occurs during normal breathing as the smallest airways contract during exhalation and reopen during inhalation. Typical aerosol particle sizes are in the range of $d ≤ 1 μ m$⁠.

2. A laryngeal mode: aerosols with a particle size of $d ≥ 1 μ m$ are generated in the laryngeal region due to vocal fold oscillation during vocalization and coughing.

3. An oral mode: larger droplets (⁠ $d ≥ 100 μ m$⁠) are generated in the oral cavity by speech and coughing.

While the aerosol formation process in the alveolar region (bronchiolar mode: liquid films rupture during inhalation and produce aerosol, which is subsequently transported into the alveoli and leaves the body during the following exhalation process) has been intensively investigated^10–12 and is now widely understood and accepted,^8,9,13 the exact generation mechanisms of larger aerosol particles and droplets in the upper airway region still remain unclear and are rather the subject of assumptions.^9,13,14 Studies on aerosol formation in the upper airways do, to the best of the author's knowledge, not exist. However, in the most infectious period of COVID-19, which occurs within the first five days after the onset of symptoms, a viable virus was typically isolated in the upper respiratory tract, i.e., in the nose and throat.¹⁵ Thus, it can be assumed that virus containing aerosols are predominantly generated in the upper airway tract. The hypothesis that virions occur primarily in particles of the size that presumably arises in the laryngeal mode is further supported by the studies from Chia et al.¹⁶ and Fennelly.¹⁷ However, the probability that a small particle of about 10 μm in diameter (at initially wet conditions) contains any virion (e.g., SARS-CoV-2) is only 0.37%.¹⁸ This probability is based on the average number of virus ribonucleic acid (RNA) copies of 7 × 10⁶ found in a 1 ml throat swab.¹⁸ The particles from the alveolar mode are suggested to be much smaller than 10 μm, and hence, their probability to contain any virion should be even below. In contrast, a 50 μm particle at initially wet conditions contains one virion with a probability of 37%.¹⁸ Nevertheless, it should be kept in mind that a high probability of virions within a large droplet (e.g., from the oral mode) does not account for the fact that smaller particles (e.g., from the laryngeal mode) are emitted with a considerably higher number density. Thus, the total amount of exhaled virions within the fraction of small, aerosolized particles might be similar or even larger than in the fraction of large droplets. Since these small particles can travel much longer distances before depositing, they are assumed to enhance disease transmission.

It is furthermore important to note here that at a relative humidity RH < 80%, particle diameters reduce to 20%–40% of their original size after complete dehydration, depending on the amount of nonvolatile contents.¹⁹ Thus, a 50 μm droplet can dehydrate to a size of 10 μm. This particle is able to suspend in air for up to 8 min and possesses a deposition efficiency of 81% in the upper airways.¹⁹ 

Hence, it is the overall objective of this paper to understand the generation process of the aerosol particles during phonation and derive the most influential parameters on their size distributions. Interestingly, Smith et al.²⁰ suggest that aerosol transmission is not a very efficient route for non-symptomatic or mildly symptomatic individuals with low viral load. Superspreaders, who produce a high amount of aerosol, are considered much more dangerous. Therefore, it is of great interest to identify parameters which, during phonation, potentially lead to an increased aerosol production within the relevant size range.

For high expiratory flow rates, i.e., during maneuvers such as coughing and sneezing, Wei and Li⁸ suggest that strong shear forces acting on the mucus–air interface lead to surface wave instabilities, where the growth of perturbations results in droplet formation. However, empirical evidence to support this mechanism is less well established.⁷ For speaking and phonation, the shear force provided by the respiratory air flow is not sufficient to induce such instabilities of the mucus layer. Instead, Patterson and Wood⁷ assume that close apposition of the vocal folds (VF) potentially produces liquid bridges of mucus that burst, creating aerosol, but evidence is still missing. At least, Asadi et al.²¹ have observed that droplet number formation increases with loudness. A higher oscillating amplitude and air flow rate are associated with increasing loudness. Furthermore, Asadi et al.²² analyzed particle numbers during different types of vocalization. They found higher particle emission rates for voiced consonants and that vowels release more aerosol particles than voiceless fricatives. They, hence, hypothesized that vocal fold vibration is an important mechanism of aerosol particle generation. However, the exact relations have not been investigated yet and still remain unclear. Especially, we are not aware of studies about the atomization of respiratory liquids at the oscillating VF.

Vadivukkarasan et al.²³ investigated the breakup of soap bubbles and deduced possible hydrodynamic instabilities leading to atomization during the expelling of respiratory liquid, e.g., sneezing by a human. Yet, droplet sizes strongly exceed the typical droplet size generated during voicing. In a recent study, Kim et al.²⁴ have shown that, based on measurements with polyacrylic acid (PAA) solutions, viscoelastic properties suppress aerosol formation. However, in how far the rheological properties of PAA solutions agree with human airway liquids is not discussed by the authors.

Due to this lack of information about aerosol formation mechanisms and their influencing parameters, we aim to provide a first piece of the puzzle. Thus, a simplified in vitro model is created that emulates the human vocal folds performing sustained phonation and, hence, allows the atomization of an artificial mucus layer, which covers these ligaments. We visualize the aerosol formation process by high-speed videos and determine particle size distributions based on a large number of images received from shadowgraphy. We will present the influence of vibration frequency, amplitude, and air flow rate on the process of mucus breakup at the VF and on the particle size distribution.

The VF model divides the complex shape of the human VF into a rigid, physiologically shaped contracting part (the flow guides) and two elastic, deformable cylinders made of silicone (hereafter referred to as the model VF). The main dimensions of the overall VF model, especially the shape of the flow guides, are based on the M5 model introduced by Scherer et al.²⁵ The length and diameter of the silicone cylinders are adapted to physiological values²⁶ with a length of 20 mm and a diameter of 4 mm. A schematic setup of the test section is presented in Fig. 1(a), and Fig. 1(b) shows a cut through the CAD (computer-aided design) model of the perspex channel with the VF.

In order to match the elastic properties of the VF tissue, very flexible and soft silicone is used here (KauPo EcoFlex^® 00‐20). With a Young's modulus of 0.06 N/mm², it closely resembles the mechanical behavior of physiological VF.^27,28 Since the surface of silicone is originally hydrophobic, the surface treatment gas phase fluorination was employed to reduce the contact angle. Additionally, fluorination lowers the materials stickiness so that the model VF will not adhere to one another during oscillation.

In contrast to the real VF, which are agitated by the respiratory air flow, the model VF are driven by a motor (Robitronic Razer ten 3652 3000 KV) of high speed. An eccentrical unit has been integrated for translating the rotational motion of the motor into a translatory motion and is connected to the VF by a rigid threaded rod. The rotational speed of the motor can be freely adjusted by variation of the servo signals or the applied voltage. The adjusted frequency of the VF was verified with the help of a laser Doppler vibrometer (Polytec OFV-3001/353). To account for different oscillation amplitudes, the size of the eccentric was varied. This way, the oscillation frequency and amplitude of the VF can be tuned individually. Since only one motor was employed, only one of the VF is actively induced to oscillate, while the other one remains fixed. For our investigations, this opening and closing mechanism of the model VF is, nevertheless, considered sufficient to mimic the physiologic glottal cycle. According to Padday et al.,²⁹ the formation and breakup of liquid bridges occurs symmetrically between two endplates, even though only one plate is moving apart. Hence, it can be assumed that the droplet formation process is not altered although only one VF is moving. Moreover, other parameters like oscillation frequency, amplitude, and air flow rate as well as the rheological parameters of the respiratory liquid are expected to have a dominant effect on particle generation. The frequency was varied between 75 and 150 Hz at amplitudes of 0.5, 0.7, and 1.0 mm (complete glottal opening gap of 1.0, 1.4, and 2.0 mm). Maximum glottal gaps of $O ( 1 mm )$ and fundamental frequencies between 80 and 220 Hz are typical for human vocalization.³⁰ The adjusted amplitudes and frequencies of the model VF are thus well in the range of physiological values.

The model VF are attached at the end of a simplified trachea, which consists of an entrance tube of rectangular cross section. This way, humidified air can enter the model trachea and exits through the VF. A constant air flow rate is adjusted to 10, 20, and 30 l/min by a mass flow controller (MFC; Bürkert Type 8742) in order to account for typical air flow rates during voicing.³¹ During the measurements, the exhaled air had a temperature of 23 °C and RH $≈ 75 %$⁠. All flow parameters are summarized in Table I. Particle size distributions are supposed to show the influence of oscillation frequency and amplitude as well as air flow rate on mucus atomization. Absolute particle numbers are not in the focus of interest within the scope of the study.

The model liquid mimics the respiratory liquid. That means the non-Newtonian behavior of the respiratory liquid is emulated by a shear-thinning and thixotropic behavior of the model liquid. We used a cell culture medium (DMEM GlutaMAX) to which 5% bovine serum has been added. This model liquid has a physiological density^11, ρ of 1014 kg/m³. We measured the shear rate $γ ̇$ dependent dynamic viscosity η of the artificial mucus with a rotational rheometer (Anton Paar Physica MCR 101, cone-and-plate system) at 20 °C and obtained values that can be fitted with the power-law function $η ( γ ̇ ) = 4.845 mPa s n · γ ̇ n − 1$ (with n = 0.756; η in mPa s; $γ ̇$ in s⁻¹). For shear rates $γ ̇ ≳ 5 s − 1$⁠, these values are in the same order of magnitude as for human saliva.³² It should be noted that the viscosity of the model mucus is lower than for airway mucus.³³ The surface tension of the model liquid was measured with two approaches: the Du Noüy ring method and the capillary rise method. The obtained average value of $σ = 51.9 ± 2.1 mN / m$ also corresponds to physiological values of saliva, as measured by Kirkness et al.³⁴ with $σ = 57.4 mN / m$⁠. Tracheal mucus has an even lower surface tension of about 32 mN/m.³⁵ However, the exact shear rate dependent viscosity and surface tension values of human VF mucus have not been documented yet and might still be different from airway mucus since the glands of the ventricular folds generate their own mucus. The only study we are aware of on the rheology of human laryngeal mucus from the vocal folds was published quite recently by Peters et al.³⁶ Yet, their focus is exclusively on the viscoelastic properties of mucus.

During the experiments, the VF are continuously fed by the respiratory model liquid. A silicone tube (inner/outer diameter = 0.8/1.6 mm) connected to a syringe pump (B|BRAUN Perfusor^® with 50 ml syringe) is used to continuously apply the liquid to the VF surface with a flow rate of 10 ml/h. Since physiological values regarding the rate at which laryngeal mucus flows onto the VF are unknown, the value was set based on test experiments with the premise of ensuring constant wetting of the entire VF without significant amounts running off the model.

Two different setups were used to perform two separate measurement procedures (detailed description below): one to study phenomenological aspects (atomization process visualization) and one to measure particle size distributions (particle size measurements by shadowgraphy). Connecting the results of these measurements is supposed to reveal which processes are responsible for the formation of the different sizes of droplets and how the exhalation parameters influence the atomization mechanisms and the particle size distributions.

The VF movement and the process of atomization at the VF are visualized in top view [Fig. 1(c)]. Here, a high-speed camera (Phantom VEO 710L; resolution $1280 × 800 px 2$⁠) with a 100 mm focal length macrolens (aperture set to f/8) combined with 110 mm spacer rings records the formation of liquid bubbles and bridges and their subsequent breakup into droplets at a frame rate of 5000 fps. Due to the high air flow speed, and thus particle velocities, short illumination times of 60 μs were used in order to reduce motion blur. Furthermore, short illumination times require high light intensities. We, thus, used a focused high-power LED (light-emitting diode; Osram OSTAR LE B P3W 01) for illumination purposes in this top view setup. A total field of view of $16.8 × 10.5 mm 2$ with a resolution of 13.1 μm per pixel could be attained.

For a quantitative view of the atomization process, that is, analyzing particle sizes, the spray is observed directly above the VF exit (distance: 25 mm). We employed a shadowgraphy setup to record the generated aerosol particles [Fig. 1(d)]. For illumination purposes, an LED (Mouser LZ4–40B208) is used, whose light is converged and parallelized by a short focal-length (25 mm) Fresnel lens. The droplets are backlit via an LED flash and their shadows, i.e., the particle images, are recorded with a FLIR Grasshopper^®3 (GS3-U3–41C6M) USB 3.0 camera at a frame rate of 34 fps and $2048 × 2048 px 2$ image resolution. The extremely short LED flash duration of 2 μs (=illumination time) ensures that there is no motion blur in the particle images. With a short shutter time of 0.1 ms, the ambient light does not contribute to the illumination of the image but only the bright light flash of the LED. The frame rate is set below the VF frequency to prevent particles from being recorded twice on subsequent images. By employing a 180 mm focal length macrolens (aperture set to f/11) in combination with 110 mm spacer rings, a resolution of 2.6 μm per pixel could be achieved with a total field of view of $5.3 × 5.3 mm 2$ and a depth of field of about 1.5 mm. The measurement volume is considered to comprise a representative section of the mucus spray. Altogether, a number of about 8000 images were recorded for each parameter set in order to obtain statistically reliable results.

The images recorded in the previously described shadowgraphy measurements [see also Fig. 1(d)] are processed in the following manner: Prior to the actual image processing, all frames that do not contain any particles are sorted out in order to reduce the subsequent computation time. This results in about 5000 remaining images per measurement case, in each of which the imaged droplets will be detected and sized. The software for the imaged particle detection is written in python and makes use of the OpenCV program library to detect the particle contours and to measure their sizes. Figure 2 graphically represents the basic steps of the image evaluation for the detection of the particles. For the purpose of demonstration, a section of an exemplary measurement image with only a few, relatively large droplets was selected.

Since some mucus droplets hit the Fresnel lens during the recordings, and thus cause local darkening of the image background, the images of a measurement case are evaluated in intervals of 50 images. The background of 50 consecutive images can be considered as constant. For each interval, a mean image is created from all included measurement images, with the help of which the background of the raw images is removed by division. The resulting gray values are rescaled by 255, according to the image color depth of 8 bits. To avoid optically falsified particle sizes due to out-of-focus particles, a so-called trinarization is performed, whereby two thresholds of different strengths are applied to the image. The threshold values were determined in test evaluations by adjusting them until the particles that are considered to be in focus (assessed visually) would be detected correctly. On both resulting binary images, the software detects the particles and stores, among other things, their size and position. Based on the number of pixels per particle and assuming perfectly spherical particles, an equivalent diameter for each particle can be derived. A diameter difference (i.e., particle size at upper minus the size at lower threshold) can then be determined for each particle as a decision criterion for the maximum permissible blur. If the diameters of a particle vary too much between the two different thresholds, it is considered blurred and is, therefore, discarded since the size of an out-of-focus (i.e., blurry) particle is distorted in the image, and thus, its true size cannot be derived. A blurry particle would appear smaller at the lower and larger at the upper threshold, while a particle in focus would barely change in size by applying the thresholds. Using the image resolution, the real particle diameters in micrometers can be calculated. The program also determines the eccentricity value for each particle as a measure of circularity. For each measurement case, the sizes and eccentricities of all detected in-focus particles are stored for subsequent postprocessing. The eccentricities show that the majority of the detected particles are almost perfectly circular, and thus, the previously made assumption is valid.

A subsequent postprocessing step is used to visualize and further evaluate the particle size distributions. After the particle size data are log-transformed (base 10), a kernel density estimator (KDE) with a Gaussian kernel—gaussian_kde from the scipy.stats Python package—is used to predict the underlying probability density function (PDF). Figure 3 shows, for an exemplary case, how the estimated PDF fits the histogram data. For the purpose of visualization, the particle size data were back-transformed and then plotted on a log-scaled x-axis. It has to be noted that due to the logarithmic scaling, any modes at higher diameter values will be accentuated.

Due to the sinusoidal excitation of the motor, the gap between the VF is cyclically opened and closed. A top view of the VF is shown in Fig. 4, where the primary atomization of the model mucus can be observed. Here, the four different observable atomization processes presented by means of case Nos. 1 and 2 are considered as exemplary. Each row shows five consecutive steps of mucus breakup at the model VF within one period of oscillation. Atomization processes observed in this study always take place during the first half of a period. The high-speed images shown in Fig. 4 were acquired at a frame rate of 5000 fps for cases with an oscillation frequency of 100 Hz; therefore, one full period comprises 50 time steps (0.2 ms per step). The start of a period is defined with the glottis closed at $t 0 = 0$⁠. In Fig. 5 (Multimedia view), slow-motion video sequences visualize the mucus atomization over a number of complete oscillation periods for the measurement case Nos. 1–5 and 8. Further information that can be derived from these videos will be included in the following description of the four different breakup mechanisms observed in our investigations and depicted in Fig. 4. Additionally, in the video sequences, the generated droplets and their dispersion are visible much more clearly, while also the further course of atomization (subsequent to what is depicted in Fig. 4) can be observed. Table II lists all observed particle generation mechanisms for each parameter combination.

Figure 4(a) shows the mechanism we call “double bubble burst” (2B). Two connected bubbles, which could also be considered as one large bubble with a necking area, span the complete glottal region. One side of this constricted bubble is inflated further than the other. The larger bubble part ruptures first and the rim retraction is then passed over to the smaller part, driven by the surface tension. Ligaments form on the rim of the punctured bubble cap which break apart producing a large number of small particles.

In Fig. 4(b) only one smaller bubble (B) ruptures. It extends across one half of the glottis leaving the other side uncovered. Similar to the double bubble burst, when the single bubble ruptures, ligaments of a receding rim are fragmented into small droplets. Yet, single bubbles also produce larger droplets, mainly at their thickened outer edge that forms a bridge over the center of the glottis. Single bubbles are always observed in combination with other mechanisms (see Table II). Jetting (J) and filament breakup (F), which will be explained below, sometimes even act simultaneously with the burst of single bubbles.

The mechanism we refer to as “jetting” is shown in Fig. 4(c). Two opposing surfaces of a thicker liquid bridge connecting the VF accelerate toward each other as the VF begin to move apart. This leads to a breakup due to instabilities being introduced as the surfaces collide in the middle. The exposure to the exhalation flow hinders the surface tension from contracting the liquid back to a stable state. Jetting produces visibly larger droplets than the bubble burst mechanisms, as one compact liquid region is fragmented. Sometimes jetting also occurs at the edges of bubbles.

When a thinner liquid bridge is stretched out by the VF pulling apart, as seen in Fig. 4(d), the bridge constricts into a thin filament due to the increasing glottal gap. These filaments do not have enough time to form a single large satellite droplet, as the aerodynamic forces cause the filament to stretch further and become unstable. The existing instabilities in the ligaments can be considered as Rayleigh instabilities,³⁷ which are enhanced by the aerodynamic forces of the perpendicular air flow. Hence, due to the effect of the surface tension, pressure differences in the ligaments cause liquid to flow from high- to low-pressure regions and, thus, smaller droplets are generated from the constrictions. Filament breakup produces larger droplets than bubble burst since the filament diameter is far greater than the bubble film thickness and they also breakup within a shorter period of time.

It can be concluded, from the observations of the atomization process visualization, that the bubble burst mechanisms generally produce significantly smaller droplets than jetting and filament breakup. Furthermore, it needs to be added that the shear-thinning behavior of the mucus and model liquid cause a reduction of the viscosity by deformation, thus reducing the resistance against additional strain. This means, the deformation rate in a shear-thinning liquid increases exponentially, helping to breakup into smaller droplets.³⁸ 

In Fig. 6, St and Re for the cases listed in Table II are plotted against each other and the observed droplet generation mechanisms are matched to the points. The double bubble burst mechanism, which produces by far the most and smallest particles, only occurs at $St ≳ 0.02$⁠. The lower St the stronger the influence of the jetting and filament breakup mechanisms, leading to an increased formation of larger particles. Reynolds numbers of $O ( 10 3 )$ within the glottis are typical for human phonation.³⁹ For our cases, there appears to be a transitional region at about $Re ≈ 1800$⁠, where all four different droplet formation mechanisms have been observed, while at higher Re, the double bubble burst mechanism is no longer active. Also note that, with our current setup, we were not able to adjust our parameters to reach quadrants II and IV as defined in the St–Re diagram.

Particle size distributions are shown in Fig. 7. An average of about 4300 in-focus particles contribute to each distribution, thus creating statistically reliable results. While the left side shows box plots giving a general overview of the size distributions, the right side presents their PDFs for a more detailed insight into the characteristic size distributions. The horizontal lines in the box plots mark the median particle diameters while the upper and lower bounds of boxes denote the upper and lower quartile, i.e., the length of the box represents the interquartile range (IQR), which is a measure of dispersion of the data. The median values vary between 16 μm for case No. 8 and 32 μm for case No. 3. Very few particles in the size of up to 800 μm are generated, as can be seen from the outliers marked by crosses.

Considering first the air flow rate variation [Figs. 7(a) and 7(b)] from 10 to 30 l/min, the box plots show an increasing median particle diameter from 20 to 32 μm. Moreover, the IQR almost doubles. Focusing on the PDFs, the first and highest peak occurs for all flow rates at a value of 13.5 μm. The height for this peak is, however, reduced as the flow rate increases. For 20 l/min (case No. 2) and 30 l/min (case No. 3), a second peak arises at about 130 μm, which grows further with increasing flow rate. Thus, the particle generation mechanisms cause a bimodal particle size distribution. This further indicates that at least two different aerosol formation mechanisms appear for higher flow rates, which do obviously not both occur at 10 l/min (case No. 1). This is consistent with the findings from visualizing the atomization processes (see Table II), where at the lowest flow rate (case No. 1) exclusively double bubble burst (2B) occurs, while at higher flow rates (case Nos. 2 and 3) not only bubbles burst (2B, B) but also filament breakup (F) and jetting (J) can be observed. It can, thus, be assumed here that higher flow rates cause a higher amount of larger droplets, with a reduction of smaller particles.

In contrast to flow rate dependencies, the particle sizes become smaller with increasing frequency [Figs. 7(c) and 7(d)] and also the IQR reduces. The median diameter decreases from 26 μm (case No. 4; 75 Hz) to 17 μm (case No. 6; 150 Hz). Similar to the distributions for the flow rate variation, second peaks arise at diameters between 100 and 200 μm. Here, however, increasing the frequency leads to a shift toward smaller particle sizes rather than to a stronger manifestation of the peak. While all distributions for frequencies 75–125 Hz present this second peak, it disappears for 150 Hz, resulting in an even more pronounced first peak, i.e., a considerably larger proportion of very small particles. Hence, for an increase in the vibration frequency, the atomization mechanisms have to occur in a shorter period of time, due to the higher velocities and accelerations of the vocal folds, which apparently causes a breakup into smaller particles. However, at 150 Hz (case No. 6) it cannot be ensured that the disappearance of the second peak is a clean effect, since the test rig reached its mechanical load limit at this frequency. The oscillating vocal fold was damaged during the measurement and had to be replaced. Anticipating this to happen, case No. 6 was conducted last in the shadowgraphy measurement campaign.

Finally, we will consider the variation of the oscillation amplitude [Figs. 7(e) and 7(f)]. There seems to be a threshold amplitude at which the behavior substantially changes. For $x ̂ = 0.5 mm$ (case No. 7) and $x ̂ = 0.7 mm$ (case No. 2) the PDFs, medians (⁠ $≈ 20 μ m$⁠) and IQRs do not differ significantly from each other. The PDFs are bimodal, similar to the ones for varying flow rate and frequency. If we increase the amplitude further to 1.0 mm (case No. 8), however, the second peak again no longer persists, as solely the double bubble burst (2B) mechanism is generating the droplets (cf. Table II). Thus, the amount of small particles in the size range of 10 μm rises drastically. This lowers the median value to 16 μm. It can, hence, be derived that the larger amplitude causes the liquid region to be stretched more extensively, which is then atomized into smaller particles by the aerodynamic forces of the air flow. Moreover, as smaller particles are generated from the same amount of liquid, their number has to be larger due to the conservation of mass. In general, higher amplitudes are associated with speaking louder.⁴¹ This coincides with the findings from Asadi et al.,²¹ who already observed higher droplet numbers by increasing loudness. For louder speech, Bagheri et al.⁴² (PREPRINT) also found an increased proportion of particles with a wet size of $O ( 10 μ m )$⁠, whose origin they assigned to the laryngeal mode and which are corresponding to our first peak in the PDFs. However, higher flow rates are also associated with louder phonation, yet our findings for increasing this parameter suggest a contradictory impact on the generated droplet sizes than for enlarging the amplitude. As shown above, larger flow rates cause higher amounts of larger particles. It has to be further investigated in which way these two effects superimpose in order to be able to predict the behavior of particle sizes during loud speech.

The second peak in the PDFs at larger particle sizes of $O ( 100 μ m )$ is most likely to be caused primarily by jetting (J) and filament breakup (F), but also the burst of smaller (single) bubbles (B) is assumed to contribute to this second peak. For all parameter variations, there is a value at which the atomization mechanisms that cause a second peak in the PDFs at larger particle sizes are no longer active. In the investigated cases, this happens at the lowest flow rate (10 l/min; case No. 1) and highest frequency (150 Hz; case No. 6) and amplitude (1.0 mm; case No. 8). It becomes apparent that in the cases where the PDFs are unimodal and show an especially high amount of very small particles, solely double bubble burst (2B) was observed during atomization process visualization (cf. Table II). Therefore, it is reasonable to assume that bubbles extending across the entire glottis (2B) inhibit mechanisms that might produce larger droplets, such as jetting (J) and the breakup of filaments (F) and small bubbles (B). The strongly increased proportion of small droplets of $O ( 10 μ m )$ is of particular importance for the transmission of pathogens, as the resulting aerosol particles—large enough to carry various pathogens—can remain in the ambient air for a prolonged period of time and might also accumulate there. Additionally, as stated before, based on the conservation of mass, higher particle numbers are expected. It has to be the subject of future investigations to verify this assumption.

Important to be noted is that for all particle size distributions the initial (wet) diameters were measured, as the spray was captured directly at the vocal folds. The distance from the VF to the center of the measurement region is 25 mm. The average velocity within this distance was approximated with 2 m/s for the lowest flow rate of 10 l/min, and hence, the available time for a droplet to lose some of its water content due to evaporation is $Δ t = 12.5 ms$⁠. This time period represents just about 11% of the time which a 10 μm particle needs to fully dehydrate at RH = 75% (rough approximation based on a water droplet according to Ferron and Soderholm⁴³). For larger particles, the time they would need to fully dehydrate is substantially longer than the time it takes for them to travel from the glottis to the measurement area. For instance, at the moment of image acquisition, particles with an initial diameter of 100 μm have only been existing for 0.1% of the time that would have been needed to completely evaporate. Higher flow rates also reduce the ratio of the particle age to the dehydration time, as the particles reach the measurement area faster, i.e., losing less water on their way. Since even at the lowest flow rate the smallest particles experience only a negligible loss of water, the assumption of all particle sizes under wet conditions is legitimate here. In fully dehydrated conditions (subsequent to the image acquisition), the particles of the first and highest peak (diameter $≈ 14 μ m$⁠) will reduce to an equilibrium size of 2.8–5.6 μm depending on the proportion of nonvolatile matter.¹⁹ This size agrees well with typical sizes, measured in vivo during sustained vocalization and speaking.^6,44 In humans, particles of $O ( 100 μ m )$⁠, corresponding to the second peak in the PDFs, would probably not leave the mouth, as they are too large to closely follow the exhalation air flow. It can be expected that their higher inertia causes them to collide with the upper airway walls. Nevertheless, further atomization might occur as they impact on the mucus layer lining the airways. This issue, too, should be the subject of further research.

Additionally, a rough prediction of mean particle sizes was derived from the top view high-speed images (atomization process visualization). Comparing these results with those from the shadowgraphy measurements is intended to give a better understanding of the different droplet formation mechanisms and their influence on the particle size distributions. Initially, the base area of the emerging bubble is measured (by counting the number of pixels) in the top view images at the moment when a puncture in the bubble surface first becomes visible. In Fig. 8, the base area of an exemplary bubble is marked in one of the high-speed images.

For the mucus–air interface, $l c = 2.28 mm$⁠, given the mucus surface tension $σ = 51.9 mN / m$⁠, mucus density $ρ = 1014 kg / m 3$⁠, and the gravitational acceleration $g = 9.81 m / s 2$⁠. Hence, in our case, $R ≲ 11.4 mm$ is required for Eq. (5) to be applied. This condition is met for all bubbles formed at the model VF (see Table III).

Based on these data, Fig. 9 shows the comparison of the mean diameter calculated from the bubble sizes measured in the top view images and the mean diameter from the particle size distributions. Only the results for the variation of frequency and volume flow rate are considered here since due to limited data points the evaluation regarding the amplitude would be inconclusive. The curves for the measured and calculated values have a very similar course, with the measured values being shifted upwards. The deviations can be explained by the fact that the calculated approximation is fundamentally quite rough and does not take account of other formation mechanisms than bubble burst (measured values also include jetting and filament breakup) and the additional air flow acting on the bubbles formed at the VF. Moreover, as stated before, the formula (5) underestimates the particle sizes. Looking at Fig. 9, it becomes evident that within the investigated parameter range the mean particle diameter grows linearly for increasing flow rates, while it declines exponentially for increasing frequencies. Bubble breakup (2B and/or B) seems to be the dominant mechanism since the calculated mean values only consider bubble aerosol and yet behave similarly to the measured values. The highest (first) peak is thus assumed to be caused by bubble breakup (2B and/or B). According to Eq. (5), a thinner bubble cap wall results in smaller particles. Therefore, the results obtained from measuring the bubble sizes (Table III) explain the behavior of decreasing particle sizes observed from the particle size distributions (Fig. 7) for increasing frequency and amplitude and for decreasing flow rate quite well.

This section addresses and summarizes the limitations of the test rig and of the measurements that were conducted during this study. We used a simplified and abstracted model of the human vocal tract, which only comprises the trachea and the vocal folds. The entire airways located above the vocal folds (false vocal folds, epiglottis, pharynx, and mouth) were neglected in order to first investigate the atomization of mucus and the resulting droplet sizes directly at the vocal folds. Examining the influence of the upper respiratory tract (e.g., the trapping of larger droplets or their breakup into smaller droplets due to splashing upon impact) on the final droplet size distribution the mouth releases to the ambient air will be part of further studies. The vocal fold model, in the narrower sense, consists of two silicone cylinders, with only one side being actively induced to oscillate rather than being passively agitated by the respiratory air flow. Although the model and its motion represent a strong abstraction of reality, they sufficiently cover the essential components and influencing factors in relation to the process under investigation: the primary atomization of mucus at the vocal folds. The respiratory air flow was at room temperature (23 °C), instead of body temperature (37 °C), yet this is expected to have a negligible effect on the atomization process in this setting. It also has to be noted that the artificial mucus used here is less viscous than tracheal mucus.

With our optical (shadowgraphy) setup, it is not possible to detect particles smaller than 5 μm. In addition, systematic errors occur due to the optical imaging and during the software-based evaluation of the raw images. The photography inherent representation on a pixel grid leads to a diameter deviation of up to $± 1 px ( = ̂ 2.6 μ m )$⁠. Furthermore, background correction, threshold application and contour detection altogether result, again, in a diameter deviation of up to $± 1 px ( = ̂ 2.6 μ m )$⁠. In combination, the total absolute deviation of up to $± 5.2 μ m$ translates to the following relative uncertainties: up to 100…50% for particle sizes 5…10 μm; up to 50…25% for sizes 10…20 μm; up to 25…10% for sizes 20…50 μm; and up to 10…5% for sizes 50…100 μm. The relative uncertainty drops rapidly with increasing particle diameter. For large particles > 100 μm, the diameter deviation is below 5%. However, this shows that the detected particle sizes for small particles, especially very small ones < 10 μm, have to be considered with caution. Nevertheless, we assume that the qualitative shape of the particle size distributions is not affected by this relatively high diameter deviation of up to $± 5.2 μ m$⁠.

This study did also not allow to quantify and compare the absolute number of generated particles that might give indications for potential superspreader parameter settings. This will be the subject of further research.

To the best of our knowledge, this is the first study that considers aerosol formation at a VF model. This allows an isolated observation of the atomization processes directly at the VF without overlapping mechanisms from other sources such as lower airways or mouth/lip motions. The droplet formation process during phonation has been visualized, and droplet size distributions have been deduced. Despite a simplification of the VF model, the comparison with literature data has shown that the generated particle sizes agree well with the typical range as produced during phonation.

Typical parameters characterizing phonation have been varied. An increase in the maximal glottal gap opening during VF oscillation leads to a higher number of smaller particles. At this point, it has to be considered that larger amplitudes and higher flow rates are both associated with louder phonation. However, as our results have shown, higher flow rates lead to a reduction of smaller particles with a simultaneous increase in larger particles. It is, hence, not clear yet which of these mechanisms is dominating and thus the subject of further studies. Increasing frequencies, which are associated with higher voices, also cause a higher amount of smaller particles, and thus a higher potential risk of exhaling a larger amount of virus-laden particles which can travel with the air flow over large distances before falling down. As larger droplets are assumed to collide with the upper airway walls before they can leave the mouth, their contribution to a particle size distribution emitted from real human airways is expected to be much lower.

The visualization of the aerosol formation processes revealed different but very reproducible generation mechanisms. Thereby, the aerosol formation process is dominated by the breakup of large, thin bubbles which form in the glottal gap. Aerosol particle sizes (order of magnitude) and their variation with flow rate and frequency changes could even be predicted based on the bubble sizes. Other processes, such as filament elongation and breakup, which have been frequently assumed to be the dominating mechanisms, seem to play a minor role here. However, it still remains unclear which parameter triggers certain breakup mechanisms and should thus be addressed in future studies.

The authors gratefully acknowledge Professor Uwe Liebert and Dr. Corinna Pietsch, Institute of Virology, University of Leipzig Medical Center, for providing the artificial mucus. The authors also would like to thank Professor Michael Fuchs and Lennart Pieper, Division of Phoniatrics and Audiology, University of Leipzig Medical Center, for fruitful discussions.

The authors declare no conflict of interest.

Lisa Fritzsche: Formal analysis (lead); Investigation (lead); Methodology (supporting); Software (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Ruediger Schwarze: Conceptualization (equal); Resources (lead); Supervision (lead); Writing – review & editing (equal). Frauke Junghans: Investigation (supporting); Writing – review & editing (equal). Katrin Bauer: Conceptualization (equal); Investigation (supporting); Methodology (lead); Project administration (lead); Writing – original draft (supporting); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.