Experimental framework to examine turbulent puffs generated by human coughing

Outbreaks of infectious diseases and epidemics raise questions about transmission modes and safeguards against respiratory infections. In the context of respiratory infections, transmission involves the transfer of pathogens from one individual to another. These pathogens are predominantly carried within a spectrum of droplet sizes produced by the infected person during various respiratory actions such as breathing, speaking, coughing, and sneezing.^1,2 In the late 19th century, Flügge³ scrutinized droplet sprays employing culture plates, concluding that respiratory droplets are relatively large and tend to settle swiftly within a short range. By the early 20th century, Wells⁴ introduced a critical size threshold of $100 μm$ to differentiate between large and small droplets. The study concluded that larger droplets tend to settle within close proximity to the source. However, more recent investigations have challenged the simplistic classification of large vs small droplets.^5,6 Instead, these exhalations are referred to as turbulent puffs involving interactions between the fluid phase and the surrounding environment. Nevertheless, despite these advances, a comprehensive understanding of the underlying flow dynamics governing these flows remains limited due to a lack of experimental data for validation of mathematical models,^6,7 particularly those that can directly resolve the wide range of turbulent scales prevalent in these human-generated coughs. Hence, it is imperative to develop and refine experimental methods to further our understanding of the intricate transport mechanisms of respiratory droplets. Such an understanding is significant for evaluating risks and devising strategies for infection control. This understanding is also essential for guiding infection control measures through effective utilization of non-pharmaceutical interventions.^8–10 

The emergence of pandemics and epidemics has underscored the urgent need to study the dynamics of respiratory flows. The rapid global spread of viruses has highlighted the critical role of human exhalations in disease transmission.⁶ The need for effective infection control strategies to minimize respiratory infections has amplified the significance of comprehensive research in respiratory fluid dynamics. Several experimental methods have emerged over the past decade to understand the dynamics of droplets expelled during human exhalations. These methods include phase Doppler interferometry,¹¹ volume/back illumination,¹² shadowgraph imaging,¹³ schlieren,¹⁴ and particle image/tracking velocimetry (PIV/PTV).^15–17 Of these methods, PIV and PTV-based approaches have garnered significant interest due to their ability to provide detailed information on particle motion, ranging from planar measurements^15,17,18 to volumetric measurements.¹⁹ Typically, these experiments employ high-speed cameras coupled with a high-energy light source, often pulsed to illuminate the droplets in the flow. Recent studies have directly applied these methods to human exhalations to investigate expelled droplets.^{12,14–16,18} Some studies have also introduced artificial tracers^19,20 into the environment surrounding such sources, although mostly limited to artificially generated exhalations.

Additionally, investigations have explored the role of turbulent puffs released during violent exhalations in extending the spread of pathogen-laden droplets. For instance, Bourouiba et al.⁵ developed and validated a theoretical model through analogous experiments, highlighting the contribution of respiratory clouds in extending the reach of tiny droplets. More recently, Chong et al.²¹ examined the role of relative humidity in prolonging the lifetime of respiratory droplets suspended in turbulent puffs through direct numerical simulations.

However, previous studies have not experimentally investigated the flow characteristics of puffs released during human exhalations—a gap the framework presented in this study aims to fill. This work demonstrates the framework's capability to explore the flow and turbulence statistics of exhalation puffs, an area not previously examined. The experimental approach utilizes a neutrally buoyant helium-filled soap bubble (HFSB) system to visualize the turbulent puffs exhaled by humans. By introducing tracers into the environment noninvasively and illuminating them with LED-based light sources, this method allows for the observation and quantitative analysis of expelled puffs during respiratory events. In this study, we applied and validated this framework to actual human coughs to demonstrate its analytical capabilities.

The turbulent puff expelled during coughing was captured using helium-filled soap bubbles (HFSB) as flow tracers. Flow visualization was accomplished by employing a high-speed camera and light sheet illumination generated using an LED source. The experiments were performed in a controlled environment at the UNSW Aerosol Dynamics Laboratory (⁠ $5 ×5×4 m3$⁠), where a constant temperature of 22 °C and a relative humidity (RH) between 43% and 45% were maintained. The subject's head was positioned in front of a black backdrop for the experiments, and the room was then filled with HFSB for 5 min. After this period, a 2-min wait allowed the flow from the bubble nozzles to settle before the subject coughed. This procedure ensured that the environment was stable and that the bubbles could effectively act as tracers for visualizing the turbulence and flow characteristics of the cough. The light source, positioned on the ground and facing upward, allowed the generation of the light sheet for visualization (detailed further in Secs. II A and II B). Any convection currents within the field of view were quantified and only resulted in an average background airflow velocity of $0.24 ± 0.02 ms−1$⁠. The high-speed camera captured a sequence of images of the subject coughing. A series of operations were performed to isolate the puff expelled during the coughs from these frames (detailed further in Sec. II C).

Ethical approval for the experiments was obtained from the University of New South Wales Human Research Ethics Committee [iRECS4728].

In the current investigation, the flow was visualized using helium-filled soap bubbles (HFSBs) as tracers, a widely utilized technique for flow visualization since the 1970s and 80 s.^22–25 HFSBs offer several advantages for flow visualization, including their high light scattering efficiency, adjustable size, and neutral buoyancy. However, they also come with certain limitations, such as their limited lifespan and the restricted resolution for capturing smaller flow structures due to the dimensions of the HFSBs.

The HFSBs were generated using an HFSB generator from LaVision. The HFSB generator operates based on coaxial channels terminating with a small circular orifice. It receives a continuous flow of helium, air, and bubble fluid solution (BFS). The BFS is composed of water, glycerin, and soap. The size of the bubbles generated by HFSB generator was controlled using the air, helium, and BFS supply. For the experiments conducted in this study, we used the settings recommended by the manufacturer to generate HFSBs with an average diameter of approximately 0.2–0.3 mm.

Due to the relatively short duration of coughing, which lasts approximately $150−300$ ms,²⁶ it is imperative to employ high-speed motion capture to visualize and analyze the expelled puff's motion accurately. Consequently, a high-speed monochrome camera model (nac MEMRECAM HX-7s) was employed for capturing high-speed frames of coughs. The frames were captured at a resolution of $2560×1440$ pixels and a frame rate of 1000 Hz, ensuring the precise temporal resolution necessary for detailed analysis. A schematic of the experimental setup is shown in Fig. 1.

The flow was illuminated using a light sheet technique, where a specific section of the flow was selectively illuminated, as depicted in Fig. 1. To achieve this, two LED-based light sources (GSVitec MultiLED MX) with a power of 500 W and a luminous flux of 50 000 lumens were employed. The light source was used in pulsed mode and was synchronized with the high-speed camera using Rigol DG1000Z signal generator. For synchronization, a 5 V, 1000 Hz square wave signal was generated and used as an input for both the light sources and the camera. The light source emitted white light with a beam divergence angle of approximately 15°. A slit, measuring 1 mm in width and 60 mm in length, was created using LaVision variable aperture and positioned in front of the light source. Additionally, a glass rod with a diameter of 30 mm was situated 30 mm away from the slit to collimate the initially diverging light beam. This setup achieved a divergence angle of approximately $1.5°$⁠.

The high-speed image sequences underwent a series of processing steps using an in-house Python code that leverages the NumPy and OpenCV libraries. Various transformations and enhancements were applied during the processing, as further explained in Secs. II C 1 to II C 3. The outlined methodology to measure puff trajectory and radius can be directly applied to the images obtained from the camera or the velocity fields obtained from PIV. We note that the former provides a quicker means of determining puff trajectory and entrainment without the need to determine velocity fields through PIV initially.

To obtain a precise conversion from pixel coordinates to real coordinates, a calibration target with $27×29$ dots and a dot spacing of 5 mm was employed. Furthermore, this removed any perspective distortion in the images.

Background subtraction removed the background and sensor noise in the images. This was done by subtracting the background image captured before the experiments from all the images in the sequence. This removed any distortion due to creases in the backdrop, along with the static sensor noise.

Here, the window size in the image, represented by $2k+1$⁠, determined the size of the moving mean. By applying this process, noise pixels were effectively eliminated, enhancing the isolation of the air puff. Figure 2 illustrates the output obtained after this step.

A threshold was then applied to analyze the shape of the puff to convert the image obtained after Gaussian filtering [ $If(x,y)$] into a binary form. By binarizing the image, a clear distinction was made between the puff and its surroundings. To identify the boundary of the puff, the Canny Edge detection algorithm was utilized.²⁷ This algorithm effectively identifies the edges of objects within the image, thereby locating the boundary of the puff.

In order to determine the puff trajectory, a distance map of each binary image is generated. The distance map is generated for the velocity field when using PIV data as the source, enabling the labeling of individual puff pixels with their respective distances to the nearest boundary. The resulting output of this process is displayed in Fig. 3. By utilizing the distance map, a point within the puff that is equidistant from the leading edge can be identified. This point is then tracked throughout the entire sequence of images, enabling the determination of the puff trajectory (s), which was calculated by integrating the changes in the x and y coordinates of this point at each time step. The radius of the puff's leading edge (r) is measured by measuring the half-width of the puff at the location of the point equidistant from the leading edge.

Given the uniform seeding within the field of view, we conducted particle image velocimetry (PIV) on the calibrated image sequence to obtain the velocity fields for analysis. This analysis provides better insight into the flow statistics of the turbulent puff than previously possible and would enable us to examine the puff's turbulence statistically. LaVision Davis was employed to process the data, where a multi-pass PIV operation was performed on the image sequence to obtain the velocity field. The interrogation window used in this analysis started with an initial size of $128×128$ pixels and then reduced to a final size of $64×64$ pixels. The window overlap factor was set at 75%.

This section presents the results by analyzing fifteen distinct coughs performed by three male subjects in the age range of 25–35 years. All subjects were healthy and nonsmokers. The initiation of the cough was determined through visual observation, specifically by identifying the commencement of airflow from the mouth.

To visualize the instantaneous flow field, Fig. 4 depicts the temporal evolution of the flow field of the puff associated with a representative cough from subject 1. During this cough event, the leading edge of the puff traversed the field of view, which spans a distance of $0.8 m$ from the mouth, within a duration of $0.3 s$⁠. Subject 1's maximum and average velocities observed within the puff are approximately $10.3 ± 3.4$ and $1.9 ± 0.14 ms−1$⁠, respectively. For subject 2, these values are approximately $8.7 ± 3.4$ and $1.34 ± 0.28 ms−1$⁠, respectively. For subject 3, the maximum and average velocities observed within the puff are approximately $7.5 ± 1.2$ and $1.62 ± 0.31 ms−1$⁠, respectively. These values are consistent with the previous studies employing particle tracking velocimetry on the droplets expelled during respiratory exhalations.^12,16,17

An important phenomenon we observed in multiple coughs was the puff's tendency to branch. This branching initiates from the leading edge, as marked with dashed red circles in Fig. 4 at $t=0.2 s$⁠, and subsequently results in the detachment of smaller segments from the main puff as visible at the top right corner in $t=0.3 s$⁠. This observation implies the creation of multiple mini clouds of suspended droplets originating from the main puff, which can be advected by ambient air currents and potentially elevate the risk of infection throughout the indoor environment.

Figure 5 presents the mean velocity of the leading edge of the puffs from all the coughs for each subject, with the corresponding standard deviation shown as a shaded region. The figure reveals an initial peak in velocity at $0.01 s$⁠, reaching a magnitude of $10 ms−1$⁠. Subsequently, the velocity consistently decreases throughout the puff's traversal within the field of view. This decrease in velocity can be attributed to entrainment and drag forces. As the puff decelerates, its coherence is lost, and the subsequent dispersion of droplets becomes reliant on ambient air currents and turbulence. It is evident from Fig. 4 that the puff's coherence remains preserved for at least $0.5 s$⁠, suggesting the potential for the puff to cover a considerable distance propelled solely by the initial momentum of the exhalation.

The experiments from the present work also allow us to analyze the instantaneous transverse vorticity (⁠ $ωz$⁠) of the turbulent puff, which is not accessible from qualitative flow visualizations in previous works. To demonstrate this, Fig. 6 depicts the progressive evolution of the transverse vorticity distribution of a representative cough from subject 1, with the exhalation airflow still in progress. At the onset of the cough, the vorticity is symmetric about the centerline along the subject's mouth, a typical characteristic of a turbulent jet. In the later stage, once the air exhalation has stopped (⁠ $t=0.3 s$⁠), the vorticity transitions toward a more homogeneous distribution, a characteristic of a turbulent puff. Similar observations were present for the vorticity distribution among the coughs from all three subjects, hence, it is not presented here for brevity.

Figure 7(a) presents the puff trajectory for each subject's cough events, recorded over a time span of 0.4 s from the initiation of each cough. The mean trajectory (⁠ $s¯$⁠) and standard deviation (⁠ $σ$⁠) of all 15 coughs are shown in Fig. 7(b). Following the onset of a cough, the propagation of droplet-laden turbulent puff exhibits an initial proportional relationship to $t1/2$ for approximately 0.05 s, followed by a subsequent propagation that adheres to a $t1/4$⁠. These trends are similar to those predicted through water tank experiments based on the modeling of sneezes by Bourouiba et al.⁵ Notably, the results indicate that within a timeframe of 0.4 s, the puff of a single cough extends beyond a distance of 0.7 m. Considering the cumulative effect of successive cough events and an average advection speed of $2−3 ms−1$⁠, it is plausible for the droplet-laden puff to surpass a distance of 1 m within a second. Moreover, the presence of a moist puff is known to delay evaporation and prolong the lifespan of expelled droplets during respiratory events, thereby enabling the transportation of droplets smaller than 10  $μm$ to even greater distances.^5,21

Figure 8 presents a comparative analysis of three representative coughs, one for each subject, showing trajectory estimates directly from the image sequence and the velocity fields obtained after performing PIV.

Figure 8(a) presents a comparison between the puff trajectory determined using the images as the source (triangle markers) and the trajectory derived from the velocity fields obtained from PIV data (circle markers). Based on the background mean velocity, a velocity threshold of $0.25 ms−1$ was applied to the PIV data to isolate the background velocity from the puff's velocity field. Once the puff is isolated, the framework described in Sec. II C 3 is used to determine s. The difference in the measurements due to using images and velocity fields as the source is illustrated in Fig. 8(b), where the difference in trajectory estimates (⁠ $Δs$⁠) is presented. For all the coughs, the root mean square error (RMSE) in the estimate of s using images and velocity fields as sources is $0.011 ± 0.0028 m$⁠.

During the progression of the turbulent puff, the surrounding fluid is entrained into the puff.⁵ This phenomenon results in an expansion of the puff, leading to a deceleration, as evident in Fig. 5. Several models have been proposed, initially based on conserving volume, momentum, and buoyant fluxes, assuming a constant entrainment rate.²⁸ However, subsequent advancements have led to the development of more comprehensive models that incorporate additional parameters related to the source conditions to quantify the characteristics of plumes.²⁹ Experimental measurements supporting these models have demonstrated agreement, providing evidence that volume fluxes exhibit a linear change with respect to distance from the source.^5,30

The ambient fluid's entrainment influences the mass and volume of a puff, while its fundamental shape remains largely unchanged. Previous studies have revealed that the initial jet-like phase exhibits self-similar growth, as described by the relationship $r∼αs$⁠, where r represents the half-width of the puff's leading edge, s denotes the distance from the source, and $α$ is the entrainment coefficient.⁵ This relationship is visually presented in Fig. 9(a), showcasing the variations in half-width (r) across the observed coughs from different subjects, corresponding to their respective puff trajectories (s).

Figure 9(b) displays the relationship between the mean half-width and the mean trajectory of all 15 coughs. The puff evolution can be observed as a two-stage process, with an initial jet-like phase transitioning to a puff-like phase, as observed in analogous experiments conducted by Bourouiba et al.⁵ and Wei and Li.³¹ For the initial jet-like stage, we observed $α=0.2 ± 0.03$ for subject 1, $0.23 ± 0.04$ for subject 2, and $0.42 ± 0.06$ for subject 3. For the second stage, we observed $α=0.13 ± 0.02$ for subject 1, $0.16 ± 0.02$ for subject 2, and $0.18 ± 0.015$ for subject 3. These values of $α$ align closely with the values reported by Bourouiba et al.⁵ in human cough experiments (⁠ $0.24 ± 0.02$ for jet phase and $0.132 ± 0.06$ for puff phase) and the values we calculated for the initial jet phase based on data provided in Gupta et al.²⁶ (⁠ $0.21 ± 0.07$⁠). We note only a numerical value for the entrainment coefficients can be obtained by these studies for human cough experiments, making visual comparisons impossible. The presented experimental framework provides a quick way of calculating these parameters from images. These findings will be valuable in future works toward modeling these flows more precisely as they determine the evolution of the turbulent puff expelled during a cough.

This study presents an experimental framework that employs high-speed particle image velocimetry (PIV) with neutrally buoyant helium-filled soap bubbles (HFSBs) to visualize the turbulent puffs exhaled during respiratory events and quantify flow statistics within these puffs. This framework offers improved insight into the transport mechanisms of respiratory aerosols by enabling direct, noninvasive measurements of different flow parameters of turbulent puffs. Such quantitative analysis was not achievable with the qualitative flow visualizations used in previous studies on respiratory exhalations.

The framework is validated by applying it to 15 cough-induced puffs from three subjects. The maximum velocity within the puff we observed ranges from $7.5$ to $10.3 ms−1$⁠, and the mean velocity ranges from $1.34$ to $1.9 ms−1$⁠, consistent with previous studies on droplet flow statistics. We also observed a two-stage evolution of the puff, characterized by an initial jet-like phase where the trajectory, s follows $t1/2$ scaling, which is then followed by a second puff-like phase where s follows $t1/4$⁠. After an initial rise, the velocity of the puff consistently decreased as it traversed the field of view, mainly driven by entrainment and drag forces. These findings on puff evolution, along with the results on entrainment coefficients, also align with existing experimental studies on human coughs.

A limitation of this study is the variability in cough patterns across different subjects, along with potential errors introduced by 2D measurements. These issues will be addressed in future work on the dynamics of turbulent puffs, where a significantly larger and more diverse sample size will be used to explore the flow and turbulence statistics of these puffs. Additionally, multi-camera 3D measurements will be employed to enhance accuracy. Overall, this experimental framework establishes a foundation for a more precise understanding of turbulent puffs originating from real human exhalations, thereby enhancing our capacity to effectively address the challenges posed by infectious disease transmission.

This research was supported by the NHMRC Centre for Research Excellence (Grant No. APP2006595) (BREATHE), NHMRC MRFF grant (Grant No. APP2017048), and ARC LIEF funding (Grant No. LE200100042).

The authors have no conflicts to disclose.

Prateek Bahl: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Shovon Bhattacharjee: Data curation (supporting); Investigation (supporting); Writing – review & editing (supporting). C. Raina MacIntyre: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). Con J. Doolan: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). Charitha Mahesh de Silva: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

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