key: cord-0812877-6s2rprd4
authors: Ahmed, Tanvir; Wendling, Hannah E.; Mofakham, Amir A.; Ahmadi, Goodarz; Helenbrook, Brian T.; Ferro, Andrea R.; Brown, Deborah M.; Erath, Byron D.
title: Variability in expiratory trajectory angles during consonant production by one human subject and from a physical mouth model: Application to respiratory droplet emission
date: 2021-07-23
journal: Indoor Air
DOI: 10.1111/ina.12908
sha: 7d496517162c530b32c27301438208440a440c88
doc_id: 812877
cord_uid: 6s2rprd4

The COVID‐19 pandemic has highlighted the need to improve understanding of droplet transport during expiratory emissions. While historical emphasis has been placed on violent events such as coughing and sneezing, the recognition of asymptomatic and presymptomatic spread has identified the need to consider other modalities, such as speaking. Accurate prediction of infection risk produced by speaking requires knowledge of both the droplet size distributions that are produced, as well as the expiratory flow fields that transport the droplets into the surroundings. This work demonstrates that the expiratory flow field produced by consonant productions is highly unsteady, exhibiting extremely broad inter‐ and intra‐consonant variability, with mean ejection angles varying from ≈+30° to −30°. Furthermore, implementation of a physical mouth model to quantify the expiratory flow fields for fricative pronunciation of [f] and [θ] demonstrates that flow velocities at the lips are higher than previously predicted, reaching 20–30 m/s, and that the resultant trajectories are unstable. Because both large and small droplet transport are directly influenced by the magnitude and trajectory of the expirated air stream, these findings indicate that prior investigations of the flow dynamics during speech have largely underestimated the fluid penetration distances that can be achieved for particular consonant utterances.

Voiced speech is produced when a critical air pressure is achieved in the lungs, which pushes the adducted vocal folds apart. The resultant fluid-structure interaction produces self-sustained oscillations, characterized by a periodic opening and closing of the glottis, that is, the gap between the vocal folds. The VF motion produces an unsteady flow and pressure field, which forms the raw acoustic source of sound production. 9 The resulting resonances of the vocal tract, soft palate, and oral cavity produce intelligible sound. Articulation of the tongue, lips, and soft palate is used to generate different resonances, and hence, sounds. 9 Unvoiced speech sounds, produced without the vocal folds oscillating, can be classified as: (1) fricatives, which are produced by turbulent air being forced through a narrow constriction (eg, phones [s] , and [f]), (2) plosives, or stops, which arise from the sudden release of pressure at an occlusion in the vocal tract (eg, phones [p] , and [g]), (3) nasals, which are produced as air is redirected through the nasal cavity (eg, phones [m] , and [n]), (4) semivowels, or glides, which include slight variations in vowel production (eg, phonemes /w/, and /y/), (4) affricates, which are stopfricative pairs (eg, phonemes /j/, and /c/), and finally (5) the aspirant /h/, which is a phoneme produced by turbulent air passing through the glottis. For all of these scenarios, the expulsion of airflow is the common connector. However, the time-varying change in vocal tract shape during speech produces a highly transitory and irregular flow pattern exiting the mouth. Surprisingly, investigations aimed at quantifying these flow patterns [10] [11] [12] [13] [14] with application to transmitting infectious diseases are in short order, but are greatly needed.

To accurately predict infection risk arising from an expiratory emission source, two fundamental characteristics of the source must be quantified: the emission rate (quantity per time) and size distribution of the droplets being emitted, and the expiratory flow field that transports the droplets into the ambient surroundings. There is a significant body of work that has quantified droplet emissions during counting and sustained phonation. 10, [15] [16] [17] Additional work related to the COVID-19 pandemic has been performed more recently. 8, [18] [19] [20] [21] It is well understood that droplet emissions during speech span the range of ≈0.1-200 µm, with a mean size of ≈1-2 µm. 16, 18 More recently, droplet size distributions and production rates have been correlated with specific phonemes, 18 which has provided important insight into transient behaviors in speech; information that is needed to develop accurate models of disease transmission from speaking. Investigating droplet dynamics as a function of the most fundamental building blocks of speech can also identify the impact of linguistic differences on transmission rates. 22, 23 The importance of speech loudness on droplet production has also been highlighted, demonstrating that increased vocal intensity can drastically increase droplet production rates. 8 Recently, a review of techniques for quantifying exhaled airflows has highlighted the surprisingly small number of existing articles focused on quantifying the expiratory fluid dynamics of speech. 24 Efforts that connect flow behavior with specific speech patterns/ utterances are even more limited. Early work focused on quantifying general flow behaviors based on mouth area and expelled flow rate for running speech as well as specific utterances. 25 Similar work has measured velocities at the exit of the mouth when counting, reporting a maximum value of 4.6 and 3.6 m/s for male and female volunteers, respectively, when speaking loudly. The timeaveraged velocity across all participants was reported as 3.9 m/s. 26 Unfortunately, the time history of the flow field was only estimated at the mouth, which does not elucidate the spatial evolution of the flow during speech, and more importantly, the penetration of the expirated flow structures into the surrounding environment. 10 More recently, this penetration distance has been explored for specific utterances using particle image velocimetry. It was found that plosives achieved the highest penetration distance, followed by both fricatives and nasal sounds. 27 Similarly, correlation image velocimetry has been utilized to quantify the flow field at the exit of the mouth arising from a variety of phrases. Both the trajectory of the expelled air and the structure of the flow field were found to vary as a function of phrase. For example, plosive production was characterized by the formation of individual vortices. 11 Interestingly, while both of these recent studies noted significant unsteadiness in the expiratory flow field, it was not specifically investigated. Variations in the trajectory angle of the expiratory flow will directly influence both large and small droplet transport, and the associated infection risk, and the prescription of a safe distance. The identification of varying trajectory angles would also have significant implications on infectious modeling approaches, as most models assume that expiratory flow is emitted parallel to the ground. 13, 21, [28] [29] [30] While early work has provided some insight into expiratory trajectories during speech, such as identifying spreading angles of the speech plume that were as high as 60°, 26 most prior work was performed using time-averaged measures, 25 which obscure the dynamics of the specific utterances, or were based on investigating only a single utterance. 26 Of note is recent work that

• Highly variable flow fields exiting the mouth during consonant production highlight the complex physics of respiratory droplet emissions.

• Wide-ranging trajectory angles of the flow exiting the mouth will influence the distance large-droplets travel as well as how small droplets interact with, and are transported by, indoor air currents.

• The sensitivity of the flow field to small changes in mouth, lip, and tongue positioning, as well as the observed variations in repeated utterances by the same speaker, emphasize the need to investigate speech behaviors across a broader range of utterances and subjects.

• Stochastic models of the expiratory flow field supported by observations of human speech will enable more accurate prediction of droplet transport.

showed ad hoc prescriptions of varying trajectory angles greater than 0° greatly increased droplet transport distances. 31 Consequently, there remains a need to identify how expirated velocity patterns of speech can be expected to vary for different intonations. Consonant production is of greatest interest because expirated velocities at the mouth are usually the highest. This work aims to determine if the expirated flow field, and the resultant trajectories, change across a wide variety of consonant sound productions. The results highlight how different enunciations and small variations in oral posturing can lead to drastic differences in the expiratory flow behavior. Although results are only presented for one subject, due to institutional restrictions during the pandemic, this limited investigation still provides a useful and important first look at the broad variability and unsteadiness in expiratory flows during speech. The experimental facilities and methods are introduced in Section 2, the results are presented in Section 3 and discussed in Section 4, while Section 5 is left for the conclusions. 

Due to the health concerns associated with the COVID-19 pandemic, one human subject was recruited to produce repeated [a]consonant-[a] utterances in order to measure the expiratory flow trajectory as a function of the consonant. A schematic of the facility in which the measurements were acquired is presented in Figure 1 .

All measurements were performed by having the subject speak into an enclosed 121.9 cm wide, by 243.8 cm long, by 121.9 cm high box.

A cut-out resembling the projected frontal area of a face was placed into an end face of the rectangular box, centered in both width and height, through which the subject spoke. One side of the box included a 61.0 cm high by 182.9 cm wide acrylic window for optical

access. An IDT MotionPro camera with a 50 mm Nikkon lens was placed outside the box, looking through the window. The 8-bit camera had a spatial resolution of 1280 × 1024 pixels and acquired images at 30 fps. A planar light sheet was created by placing a 400 mW, 532 nm Aixiz laser inside the box. The laser beam first passed through a beam splitter, with one portion of the beam exiting vertically, and the other continuing horizontally. The vertical beam passed through a planoconcave −10° divergent lens. The horizontal beam also passed through a planoconcave −10° divergent lens before being reflected by a planoconvex mirror (see Figure 1 ). In this manner the beam optics produced two overlapping laser sheets in the midsagittal plane of the subject. The two overlapping sheets were necessary to generate sufficient beam spreading to span the desired field of view. Care was taken to ensure both beams were precisely aligned. The optics were aligned such that the left most edge of the laser sheet was positioned ≈5 cm from the mouth exit. The illuminated field of view captured by the camera was ≈43.8 cm long by ≈35.1 cm high.

To visualize the intonations, a teaspoonful of all purpose flour was placed on the middle to base of the tongue of the subject to minimize disruptions due to the flour coming into contact with the upper palate or teeth during the pronunciations. During voice production, the expiration of flour from the mouth into the laser sheet produced a high-contrast field that was visualized and captured by the camera. . Conversely, during the consonant production, the flour could be observed. Five instances were captured for each utterance. Care was taken to ensure that each utterance and trial was produced at the same constant loudness (measured to be 70-75 dB), using the same intonation patterns that were representative of comfortable speaking.

Repeatability of the approach during post-processing was challenging due to the uncontrollable amount of flour that was ejected during the utterances. This resulted in the algorithm that was em- 

Benchtop physical models of fricative consonant production were fabricated to investigate the sensitivity of the expirated flow field to small variations in the mouth geometry, and loudness of speech; perturbations that are prohibitively difficult to asses with in vivo investigations due to the confounding variables that will inherently exist across subjects and that will influence the outcomes (eg, different mouth geometries, prosody, linguistic subtleties, hydration, etc.) To ensure physiological relevance, the geometry was carefully prescribed based on magnetic resonance imaging (MRI) of human oral geometry during intonation of the consonants of interest, and the flow conditions were matched to those produced during normal speech production.

The experimental flow facility for the benchtop, physical experiments, was constructed to be twice life-size to improve the spatial resolution of the velocity field measurements. Dynamic similarity 33 ensures that if the appropriate nondimensional parameters that govern the flow are matched, the dynamics between the life-size and scaled-up model will be identical. To this end, the flow parameters were scaled according to Reynolds and Euler number. Reynolds number, which is the ratio of inertial to viscous forces, is given as All geometries and parts were machined on a computer numerically controlled mill. Mounting pins were implemented into the construction to ensure precise and accurate geometrical alignment.

A constriction was produced by inserting a tooth model that could be precisely adjusted in the vertical direction, which controlled the tooth gap area. The tooth gap height was prescribed as the minimum wall-normal distance, h, between the tooth and the tongue/lip (see the inset of Figure 3 ). Three tooth geometries were investigated (see The 3D tooth profile was created by transcribing an arc of radius 6.9 cm on the tooth such that the secant connecting the two points was the width of the vocal tract, thereby mimicking, to the first order, the elliptical orifice area at the mouth exit that is produced during human fricative pronunciation. 35 The different choice of tooth geometries enables comparison between 2D and 3D approaches for solving the flow behavior (as 2D assumptions are often utilized in computational fluid dynamics investigations to reduce computational cost). Additionally, varying the tooth gap height identifies the sensitivity of the expirated flow field to small changes in tooth position relative to the lips/tongue during fricative consonant production. Note that for the 3D tooth geometries, the tooth profile is transcribed in the vertical direction, while the lower palate is angled at 46° for the [f] geometry, and 50° for the Table 1 .

Examples of the specific consonant sounds that were produced are Table 1 . The angle of the expirated trajectories was then directly measured from the video acquisitions using the frame image that corresponded to the initiation of the consonant sound, computed using a custom Matlab script that determined the trajectory of the expirated cloud. Figure 4A shows an example of this approach with a zoomed-in video image for the utterance [a ∫ a], with (B) presenting the line fit to the cloud, from which the trajectory angle was calculated.

To compute the trajectory angle, a threshold value was first applied to the video image to create a binary image. Figure 4B shows a binary representation of the video image from Figure 4A over the first 200 columns of data. The threshold value varied with each utterance due to changes in the lighting conditions caused by the amount of flour that was expelled. The threshold value was individually chosen for each utterance to ensure the structure of the expelled cloud was visible, and that no trajectory information was lost. Each column of pixels in the image was then scanned to find the longest consecutive sequence of rows that were greater than, or equal to, the prescribed threshold value, and the average position of these rows were then calculated. In this manner, the center of the emitted cloud was determined as a function of distance from the mouth for the first 200 columns of data, which corresponded to a length of 6.8 cm. This length was constrained to minimize bias in the flow velocity due to gravitational effects that caused the larger flour particles to settle.

For each utterance, the sensitivity of the computed trajectory angle varied by ≈±3° over a reasonable span of threshold values (ie, threshold values that were too low introduced obvious background noise, while threshold values that were too high clearly removed data from the expirated cloud). The sedimentation velocity can be quantified by assuming Stokes flow, such that where g is gravity, p and f are the particle and air density, respectively, D is the average diameter of a flour particle, and µ is the dynamic viscosity of the air. The density of all purpose flour is ≈525 kg/m 3 , with diameters ranging between ≈50 and 300 µm. 36, 37 In air ( f = 1. Table 2 reports the parameters of the geometry and flow conditions that were investigated using the physical models. In speech, the subglottal pressure drives the flow, and is directly correlated with loudness. 9 Three subglottal (ie., plenum) pressures (p s ) were investigated for each vocal tract geometry and tooth orientation: 300, 600, and 860 Pa, which are representative of soft, normal, and loud speech, respectively. These conditions resulted in a broad range of Reynolds numbers that spanned from laminar to transitional. For comparison, comfortable breathing usually occurs at a flow rate of ≈80-130 cm 3 /s, but can increase significantly during exercise, with peak expiratory flow rates reaching as high as ≈10 000 cm 3 /s. in geometry to the tooth gap area, produces a highly asymmetric jet that predominantly attaches to one wall. [39] [40] [41] [42] [43] Analogous work has shown that this behavior can, however, be exaggerated due to the two-dimensionality of the flow. 44, 45 These observations, in tandem with the in vivo flour flow visualizations of Section 3.1 that exhibit a straighter trajectory, indicate that the assumption of a 2D tooth gap likely produces non-physical flow behaviors that do not accurately predict the flow trajectories of human fricative consonant production.

To investigate the role of the three-dimensional mouth geometry, the tooth gap was changed to the aforementioned 3D geometry, which is more physiologically realistic. Figure 9 presents 

For the first time, the flow trajectories of consonant productions have been quantified through a combination of human and physical model investigations. Significant inter-and intra-consonant variability has been observed, indicating that consonants, and therefore speech in general, produces a highly unsteady flow field that exhibits complex flow dynamics, with widely varying trajectory angles.

These findings demonstrate that the expiratory fluid mechanics due to speech is likely more complex than previous models have considered. 13, 21, [28] [29] [30] The measurement of human expiratory trajectories as a function of consonant utterance shows that there is wide variability, spanning 

, which is consistent with prior observations. 26 While a statistical representation of the flow trajectories was not possible with the limited data set, it is anticipated that there will be wide variation in the specific expirated trajectories due to both subject-to-subject variability, as well as utterance-to-utterance variations by the same speaker. MRI studies of the mouth geometry during consonant production 35 have shown that tongue placement during fricative production can vary from speaker to speaker. In addition, as previously discussed, during running speech, the articulatory mouth trajectories that produce the oral geometry for a specific utterance are known to vary based on the sound that both precedes and follows the specific utterance, as well as speaking rate. 46 to exit area. 33, 52 This unsteady "transitory stall" behavior is most pronounced when the included divergence angle of the divergent channel geometry assumes angles between ≈5° and 40°, with the precise flow regime dependent upon the aforementioned variables.

In the current configuration, the physics are likely even more complicated as the expected presence of vortex shedding as the flow separates from the teeth (not captured in the PIV measurements) will introduce additional alternating pressure signatures in the flow between the lip(s)/tongue as the vortices advect through the gap. In addition, ambient flow conditions where large regions of recirculating flow may be present are also known to influence the trajectory of a jet exiting an orifice. 45 Finally, comparing flow behaviors between two similar, but slightly different, oral geometries produced by the fricative con- Consequently, a change in the ejection angle will directly influence the distance the droplets travel. Similarly, variations in the expiratory angle will influence aerosol transmission, as aerosols are small enough that they faithfully follow the flow patterns. Hence, even though they are not as likely to be forcefully expelled over long distances due to their decreased size (ie, momentum), an upward trajectory to the flow increases the probability that they will rise to a height where they are drawn into, and spread by, ventilation and air circulation units. The implications for modeling source emissions, which historically rely upon assumptions of horizontally oriented emissions, 13, 21, [28] [29] [30] are therefore, of significant importance.

The ability to measure the velocity between the lips, as opposed to at some point downstream, also revealed that the velocities of consonant production were three to ten times higher than previously reported values. 10, 26 Velocities at the tooth gap are expected to be even higher, as the tooth gap constriction is much narrower than the constriction at the lips. For example, the minimal gap at the lip(s)/tongue is ≈4 mm whereas the tooth gap, h, is (0.1 mm).

This is another important observation as the momentum with which droplets are expelled is driven by the local flow as the droplets accelerate through the mouth. Consequently, predicting droplet transport based on velocity measurements downstream of the mouth will drastically underpredict the maximum expiratory velocity, and the subsequent calculation of the penetration distance of droplets into the environment.

It is important to note that a significant simplification in the current work is the experimental investigation of consonant expiration as a steady jet, as opposed to a temporally varying puff. It remains to be seen how, or if, this will influence the flow momentum, trajectory angles, and flow unsteadiness, and is a thrust of ongoing work. In addition, there is still a significant gap in the quantification of the expirated flow dynamics; particularly, the structure and importance of the three-dimensional flow physics, and how this influences behaviors such as turbulent dispersion of the jet, as well as the entrainment and transport of droplets. Finally, the importance of buoyancy effects arising due to the temperature difference between the expelled and ambient air has been highlighted as an important component of transport dynamics in coughs and sneezes, 3,53,54 but remains largely unexplored in speech.

A combination of in vivo and physical investigations of the flow expirated during consonant production has been investigated. This work has direct application to modeling droplet spread to identify safe social distancing metrics and the transport of infectious droplets into the ambient surroundings, specifically during the COVID-19 epidemic.

The identification of in vivo trajectory angles that span from +27.2° to −31.5° as a function of consonant utterance is a crucial finding that highlights the need to consider non-zero trajectory angles when predicting/modeling both large and small droplet spread.

The observation that flow velocities at the lip can easily reach velocities of 30 m/s is similarly impactful, as the ballistic-like behavior that governs large-droplet spread depends on both the angle and momentum of the ejected droplet, with increased velocities projecting droplets over farther distances. Even higher velocities are expected at the gap produced by the tooth constriction, in comparison to the velocities at the lips that are reported herein. Aerosol spread will also be influenced by non-horizontal expiratory trajectories, with positive angles more likely to direct aerosols to a higher elevation where they can be drawn into, and distributed through, air ventilation.

Finally, the highly unsteady nature of the flow exiting the mouth for fricative consonants has been highlighted. Small variations in mouth geometry, tooth gap shape and height, and flow rate (eg, subglottal pressure) have been shown to drastically influence the mean expiratory angle of the flow as well as the temporal variation of the instantaneous angle. Flow configurations ranging from a fully separated jet to flow attached to either the upper or lower lip were all observed. The implication is that the expiratory trajectory angles are highly unsteady, suggesting that time-averaged representations over long time scales are likely insufficient for capturing the key dynamics of the flow, and that a stochastic approach to modeling the expiratory velocities of speech may be more appropriate. This also highlights the need for additional work, beyond what is reported herein, to determine how linguistical variables influence expirations.

This work was supported by the National Science Foundation [CBET:2029548] .

There is no conflict of interest. 

All human subject studies were approved by the Clarkson University Institutional Review board.

https://orcid.org/0000-0001-5277-7960

Brian T. Helenbrook https://orcid.org/0000-0002-6369-6805

Byron D. Erath https://orcid.org/0000-0003-0057-6731

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