The experiments were performed at the National Aquarium in Baltimore by training four female and two male bottlenose dolphins to swim just under the field-of-view (FOV) of a custom-made high-speed holography system. A 3D sketch of the experimental setup is presented in Figure 1A, and a top view is shown in Figure 1B. The imaging system was designed and built with input from the aquarium personnel and subsequently reviewed, with the dolphins’ health and welfare being of utmost importance. The animals were desensitized to the holography rig for four months prior to the experiments. The data acquisition experiments took place between October 2021 and January 2022. Marine Mammal and Animal Health staff maintained routine medical evaluations, including preventative diagnostics, behavioral observations, and daily communication with Veterinarians. There were no significant concerns impacting the data collection for the duration of this study. During data acquisition, the dolphins remained stationary within the experimental system, and executed, on cue from the trainer, different breath types, referred to as ‘normal’, ‘chuff (forced exhale)’, and ‘post-exercise’ (Table 1). The normal breath was characterized by the trainers as a short, soft exhalation, quiet to medium in sound volume. The chuff was a loud, forceful exhalation that could be described as chuffing, or cough-like. The post-exercise breath was defined by having the animals take normal breaths immediately after performing a series of high intensity/energy exercises in rapid succession for a minimum period of two minutes. Examples of such exercises included various weight-bearing styles of leap (Kramer et al., 2024), as well as cardio exercises, consisting of several types of speed swimming for a minimum of two laps. Table 1 provides the size, age, sex, body mass index (BMI), and average diameter of a fully open blowhole of these dolphins and assigns them identifiers used throughout this study. BMI is defined as the ratio of the mass of the dolphin in kilograms to its length in centimeters (Karns et al., 2019). The BMIs vary from 0.61 to 0.78 kgcm^-1, which falls near the average of values (0.37-1.11 kgcm^-1) measured for dolphins in the wild (Fahlman et al., 2018a).

Application of in-line holography (Figure 1B) consisted of illuminating a volume, hereafter called ‘sample volume’, where droplet motions and statistics were recorded with a collimated pulsed laser beam. Part of the light was scattered by the particles and interfered with the rest of the beam, and the interference pattern, the hologram, was recorded by a high-speed imaging system (Katz and Sheng, 2010). As the setup involved a large distance between the sample volume and the camera, to maximize the hologram quality, imaging lenses were used for recording the interference pattern in a plane located just outside of the sample volume, varying between 1 m and 2.2 m from the camera (Sheng et al., 2006). These lenses were also used for varying the magnification, i.e., the FOV. The light source was an Nd-YAG laser (532 nm) generated by a CrystaLaser QL532-500 (CrystaLaser, 4750 Longley Lane, Suite 205, Reno, NV 89502, USA) Q-switched pulsed laser. The beam was spatially filtered, collimated, and aligned parallel to the ledge, approximately 50 mm above the water surface. Owing to the forward-scattered light, in-line holography required a very low light intensity, a few μJ per pulse; therefore, an ND filter was used for attenuating the laser beam, ensuring that occasional exposure did not pose any risk to the dolphins. The final setup, including laser beam intensity and path, was evaluated and approved by the aquarium veterinarian.

The holograms were recorded by a Phantom v2640 high-speed CMOS camera (Vision Research Inc., 100 Dey Road, Wayne, NJ 07470, USA) using the full sensor resolution of 2048x1952 pixels, with a pixel size of 13.5 μm. Data were recorded at two magnifications. Holograms with a 68 mm diameter FOV and a pixel resolution of 33 μm were recorded using a 500 mm lens (Nikon AF-S NIKKOR 200-500mm f/5.6E ED VR, Nikon Inc., 1300 Walt Whitman Road, Melville, NY 11747, USA) and a 2X teleconverter (Nikon TC-201, Nikon Inc.). A 41 mm diameter FOV with a pixel resolution of 20 μm was obtained using a 300 mm focal length lens (Tamron 70-300mm f/4-5.6 Di LD Macro, Tamron Americas, 10 Austin Blvd., Commack, NY 11725, USA), also with the same teleconverter. In both cases, the FOV was dictated by the aperture size (f/5.6) and the teleconverter. The larger FOV was aimed at covering almost the entire jet generated by the dolphins’ exhalation, allowing better estimates of the ejected fluid volume, and the smaller field of view allowed us to detect smaller droplets. Most of the holograms were recorded at 2000 frames per second (fps), but in some cases, the acquisition rate was increased to 4000 fps to reduce the displacement between exposures, allowing easier tracking.

Since the exact surfacing location of the dolphins within the rig varied during each breathing event, two GoPro Hero9 Black cameras (GoPro Inc., 3025 Clearview Way, San Mateo, CA 94402, USA) aligned at two different angles were used for continuously recording stereo images of the vicinity of the sample area at 120 fps and 1920x1080 pixel resolution. Stereoscopic analysis, assuming pin-hole imaging (Faugeras, 1993; Hartley and Zisserman, 2000), was used to determine the location of the blowhole relative to the holographic sample volume. Only cases for which the blowhole was located just below the sample volume and recorded at 2000 fps or faster, 26 cases out of 94, were analyzed and included in the statistics. The resulting 26 datasets (Table 1) also enabled us to evaluate the variability for the same type of breath, sex, body mass, and repeatability for the same dolphin and breath type. Supplementary Table S1 in the supplemental information provides additional details on the experimental parameters. The droplet tracks were used for: (a) characterizing the droplet statistics exhaled and inhaled by the dolphins, (b) for crudely assessing the airflow out and into the blowhole while accounting for effects of gravity and acceleration (details follow), and (c) assessing the time evolution of airflow as well as duration of inhalation and exhalation. For most of the data (21 out of 26), the airborne droplets were generated solely by the dolphins during exhalation. As a result, the droplet distribution was non-uniform and varied in time. To improve the measurements of air speeds, for five of the tests, we used a mister to seed the air around the blowhole with 60-200 μm droplets. The resulting homogenized concentration of clean water droplets was used for obtaining a more complete distribution of the airflow around the blowhole. As described later, these droplets were not accounted for during analysis of the aerosol size and spatial distribution. The misting device, consisting of a low-noise 4.5-gallon Stealth air compressor (Alton Industry Ltd. Group, 1031 N Raddant Rd., Batavia, IL 60510, USA), and a spray generator (McMaster Carr, 200 New Canton Way, Robbinsville, NJ 08691, USA), was deployed on the ledge of the pool, away from the dolphin’s line of sight, and with the nozzle exit far from the sample volume to prevent any effect on the airflow. In some of the cases listed in Table 1, the dolphin partially or entirely blocked the FOV during parts of inhalation. In the case of partial blockage, the visible parts of the reconstructed holograms were used to obtain droplet statistics, but were not used for total liquid volume calculations to avoid underestimation. In the case of substantial or full blockage, the droplet statistics and volume fractions were measured until the time of blockage.

The holograms were enhanced by background subtraction, i.e., by removing the time-averaged image, rescaling, and then digitally reconstructed plane by plane using an in-house written Fast Fourier Transform (FFT) based Kirchhoff-Fresnel kernel. Detailed descriptions of the reconstruction procedures can be found in Sheng et al. (2006) and Katz and Sheng (2010). The reconstruction was performed in a series of parallel planes separated by 100 μm, covering a depth of 20 cm centered around the blowholes. To accelerate the subsequent data processing, each group of 100 nearby reconstructions was then projected onto a single plane by assigning the minimum intensity across the depth to each pixel. This procedure created a series of compressed images showing all the droplets in 10 mm thick slabs, which reduced the number of analyzed planes by two orders of magnitude. Owing to the inherent depth of focus problem of inline holography (Sheng et al., 2006), i.e., that reconstructed droplets appear elongated in the direction of the laser beam axis with a typical length of a few mm at the present FOV, there was no reason to make the slabs thinner.

Figure 2A presents sample reconstructed central planes showing the initial liquid blob and ligaments surrounded by a cloud of droplets 40 ms after the first droplet appeared, which is denoted by t=0. Figure 2B shows that after 120 ms, the same sample area contained only isolated droplets of varying sizes. The in-focus droplets within each slab were detected using the machine-learning software ilastik™, version 1.3.3post3, based on a ‘random forest’ training method (https://www.ilastik.org/). This software became popular in recent years for the characterization of complex multi-component images (Berg et al., 2019; Muriel and Katz, 2021, Muriel and Katz, 2023). The training and analyses were performed in two stages. The first focused on droplets smaller than 10 pixels (<200 μm and 330 μm for the small and large FOVs, respectively), out of which droplets smaller than 100 μm were used for the airflow assessment. The second phase included all the droplets and focused on measurements of droplet sizes and volume fractions. The ilastik data consisted of reconstructed holograms recorded in the aquarium, some of them marked for training, and others unmarked for validation. The training data consisted of 4x20 slabs originating from four holograms belonging to different datasets, with the droplets identified manually in each slab. The features (Laplacian of Gaussian, structure tensor eigenvalues, etc.) and the standard deviation, σ, of Gaussian smoothing were based on training involving several iterative loops of selection and verification. The ability of the trained system to detect the droplets in the rest of the reconstructed slabs was validated by careful examination of four different holographic fields, followed by modifications to the features, and by re-validations. Redundant features which did not cause detectable changes to the output were removed to reduce the likelihood of overfitting. These iterations (typically eight) were stopped when the maximum error in droplet diameter fell below 2 pixels (66 μm for the large FOV). To ensure that the detection was affected minimally by the limited resolution or noise, the detection was restricted to traces consisting of at least 3 congruent pixels. These constraints set the lower limit of the detected droplet size to 45 μm for the large FOV and 30 μm for the small FOV. In addition, once the parameters were selected, we manually checked samples of (previously) unseen data, typically 20 holograms, to ensure that we did not identify noise as droplets or had errors beyond two pixels in the droplet diameter. The resulting uncertainty in droplet diameter is about a pixel, corresponding to 20 and 33 μm for the small and large FOVs, respectively. Mean statistics reduce random errors by the square-root of the number of measurements, i.e., by 3 to 30, depending on the size of data bins. Owing to the sparse droplet concentrations, ilastik™ had little difficulty to detect all the droplets.

The droplet velocities were measured directly from the displacement of the droplets. The trajectories consisted of at least four consecutive detections in time to reduce the likelihood of detecting noise (Figure 2C). The Kalman filter based tracking procedure was performed using the in-house algorithm described in Zhang et al. (2022, 2024). The tracking criteria included the droplet diameter, maximum velocity, as well as the velocity magnitude and direction in the previous frame. The ‘maximum velocity’ for each case was selected as twice the manually measured typical droplet speed during exhalation. The tracking was restricted to droplets with the same diameter, allowing for 10% variation between frames. The changes in magnitude and direction were also restricted to 10% and 5⁰, respectively. For each droplet in one frame, a tracking score was assigned to all the droplets in the next frame based on the above criteria, and the droplet with the highest score was selected as the next exposure. The validity of these procedures and selection criteria was evaluated manually for selected droplets in each set. Cases with overlapping or merging trajectories were terminated. However, since the holographic field was separated into 1 cm thick slabs, and owing to low droplet concentrations, very few overlapping tracks were detected. Finally, the tracks were terminated when the tracked droplet fully or partially left the field of view (FOV). For each dataset, this process was performed for the slab aligned with the centerline of the blowhole, as determined from the GoPro stereo imaging, and two additional ones on each side of the centerline, for a total of 5 slabs. A quadratic curve was least-squares fitted to the droplet positions in each trajectory segment consisting of 4–5 consecutive exposures. Longer tracks were used to obtain multiple measurements. The horizontal and vertical velocity components, denoted as u_p and v_p, respectively, were calculated from the time derivative of the displacement in each fitted curve segment. As discussed in Zhang et al. (2022), the uncertainty in tracked droplet velocity fell in the 5-7% range. Assuming random errors, temporal and spatial averaging reduced this uncertainty by 3–10 times, depending on the number of average particle tracks.

The velocities of droplets, smaller than 100 μm, were also used for assessing the surrounding air speed and for estimating the air flow rate. Such applications raised the question of how well the droplets followed the flow, and what the resulting uncertainty was. The ability of airborne particles to follow the surrounding flow is typically assessed using the non-dimensional Stokes number, representing the ratio of the particle response time scale to that of the surrounding flow. Following Crowe (2005) and Nicolaou and Zaki (2016) the particle time scale ( τp)  was estimated from the time required for a settling droplet subjected to viscous drag and gravity in a quiescent domain to reach its terminal velocity. For small droplets, τp=ρpdp2/18µa, where ρ_p and d_p are the droplet density and diameter, respectively, and μ_a is the dynamic viscosity of air. The blowhole jet integral time scale ( τf)  was estimated from τf=D/U,  where D is the average blowhole diameter, the integral length scale of the flow, and U is the spatially averaged flow velocity at the exit from the blowhole. The highest Stokes number was 3.49 for droplets with diameters smaller than 100 μm with an integral velocity scale of 5 ms^-1 (the typical speed, results follow), implying the need to account for the particle dynamics, acceleration, and relative motion while assessing the airspeed from the droplet trajectories. The equation of motion for a liquid particle accelerating vertically in air under the influence of gravity and aerodynamic drag (Crowe, 2005) can be estimated as

where m_p, a_p, and F_d, are the mass, acceleration, and drag force of the particle, respectively, and g is the gravitational acceleration. For Reynolds numbers less than unity, namely Stokes flows, Fd=3πμadp(va−vp), where v_a and v_p are the air and particle velocities, respectively. Hence, the relative velocity between the air and the particle could be estimated by rearranging Equation 1 to form

All the parameters on the right-hand side of Equation 2 could be measured from the droplet trajectories, enabling us to estimate the relative velocity. As the Reynolds number (Re=ρa(va−vp)dp/μa,  where ρ_a is the air density), exceeded 1.0 (its maximum value reached 2.5 in the present data), the Stokes drag was no longer valid, and needed to be replaced with Fd=0.125πρpdp2Cd(va−vp)2, where Cd is the dimensionless drag coefficient. An empirical relationship for C_d relevant for the present range of Reynolds numbers, 0.01≤Re ≤ 20 (Brown and Lawler, 2003, Clift et al., 1978), was Cd=24Re(1+0.1315Re(0.82−0.05log10Re)), resulting in

To solve Equation 3, it was necessary to perform a numerical iteration since C_d depended on v_a-v_p. During analysis, the equation used for estimating the relative velocity (Equation 2 or 3) was selected based on the Reynolds number. However, calculations of droplet acceleration from individual tracks resulted in considerable errors since v_p(t+dt)-v_p(t) in typical tracks corresponded to a small fraction of a pixel. Consequently, the analysis was based on the spatially averaged acceleration of all the droplets within a fraction of the sample volume, i.e., from the time variation of the spatially averaged instantaneous velocity of all the tracks. A sample time series (normal breath of dolphin C, experiment #4) of the spatially averaged droplet velocity v_p, v_a-v_p (Equations 2, 3), and the estimated v_a is presented in Supplementary Figure S1A (in supplemental information). The time evolution of the corresponding spatially averaged a_p is compared to v_a-v_p in Supplementary Figure S1B. The latter shows that the acceleration varies between -7 and +8 ms^-2, and the associated relative velocity, between 0.2 and 0.5 ms^-1. Note that when a_p<-g, the estimated air speed was slower than the droplet velocity, and the drag force became negative, opposing the particle motion. When a_p>-g, the air speed was higher than the droplet velocity, hence the drag accelerated the particles. For the most part, the relative velocity was much smaller than the droplet velocity, but it was not negligible. Its characteristic magnitude fluctuated around the particle terminal settling velocity, around 0.3 ms^-1, when gravity was balanced by drag, i.e. a_p=0 in Equations 2 and 3. Consequently, the spatially averaged air velocity calculated using these equations was used for estimating the spatially averaged air speed, and then the volumetric flow rate of exhaled and inhaled airflows by the dolphins.

We restricted the droplet sizes used for air flow calculations to 100 μm to reduce the uncertainty in air speed estimations. Supplementary Figure S1C shows the variations of relative motion and acceleration as a function of droplet diameter, assuming Stokes flow (Equation 2). If the air flow calculations were based on droplets up to 200 μm in diameter, v_a-v_p would have been, at certain times, of the same order as the droplet velocity, causing considerable uncertainty in the calculations. Restricting ourselves to droplet diameters smaller than 100 μm enabled us to determine C_d from a published semi-empirical model for spheres at the limited Reynolds number range of 0.01≤Re ≤ 20 (Brown and Lawler, 2003; Clift et al., 1978). Assuming near-field turbulent velocity fluctuations of 10-25% of the mean velocity (Wygnanski and Fiedler, 1970, Zhou et al., 2018), there is ample literature showing that turbulence does not have a significant impact on C_d in the applicable range of Re (Warnica et al., 1995; Friedman and Katz, 2002). Nonetheless, a calculation of how a 20% change in C_d would affect the results shows a ~12% change in the difference between droplet and air speed, and a ~3% on the airflow data. As for turbulence affecting the droplet acceleration, there is literature showing that turbulence enhances the settling velocity of heavy particles (e.g., Wang and Maxey, 1993, Nielsen, 1993). The typical effect for the present range of Reynolds numbers is in the order of 10%. This effect would result in ~3% uncertainty in the estimates for air speed. Finally, by restricting the basis for estimating the air velocity to droplets smaller than 100 μm, the Reynolds number based on the relative velocity, even accounting for turbulence effects, was smaller than 20. In this range, the deformation of liquid droplets in air was minimal, and they were expected to remain nearly spherical (Grace et al., 1976; Clift et al., 1978). Furthermore, as part of another ongoing project, we have been performing experiments in a laboratory facility mimicking the breathing characteristics (blowhole size, air speeds, airborne droplet concentration, and size distribution) of the dolphins. The laboratory measurements enabled us to measure the air speed directly using Particle Image Velocimetry (PIV) as well as the droplet characteristics using holography. The velocity of tracked droplets smaller than 100 μm was used for estimating the air speed, following the same procedures as those used for processing the aquarium data, and results were compared to the direct PIV measurements. The differences ranged between 1% to 11%, providing us with a direct assessment of the uncertainty in the analysis performed in the present paper.

However, one should keep in mind that droplets of up to 100 μm in diameter are still unsuitable for assessing turbulent structures and secondary motions (vortices, etc.). To evaluate the response of the droplets to turbulence, we needed to choose a different τ_f, e.g., the Kolmogorov time scale (Tennekes and Lumley, 1972), τf=(µa/(ρaϵ)) 12, where ϵ is the average turbulent energy dissipation rate per unit mass. In this case, the Stokes number would have increased to several hundred, implying that the 100 μm droplets could not follow the turbulence in the air jet. Such measurements would require droplets in the order of 1 μm or smaller, the typical size used in PIV measurements in air. Considering that the spatial variations in small droplets’ velocity were small compared to the instantaneous average values, most of the droplet speed measurements were performed in the relatively uniform “potential core” of the jet, from about 0.4D to 2.4D.

While the velocities of over 99% of the droplets fell in the 3–7 ms^-1 range, a small fraction (less than 1%) travelled much faster than the surrounding droplets, with speeds that were three to five times higher than those of their neighbors. The higher speed droplets are referred to as ‘ejecta’, similar to those found during human sneezing (Scharfman et al., 2016). We measured the speed and fraction of these droplets separately and did not use them for estimating the air speeds. To the best of our knowledge, the existence of such ejecta has never been reported before for dolphins.

The exhaled air volumes during breathing events were estimated as the product of the temporal median vertical velocity component (v_a) during exhalation, the duration of exhalation, and the cross-sectional area of the air jet. The typical pattern of an oscillating jet, referred to as ‘zero-net-mass-flux jets’ (e.g., Cater and Soria, 2002; Mohseni and Mittal, 2014), is of a jet-like outflow and a hemispherical inflow (sink flow). These findings supported our choice of jet-like outflow and hemispherical radial inflow to describe the exhalation and inhalation processes, respectively. Consistent with the data, the exhalation was modeled as a conical jet with circular cross sections. The jet emerged from the blowhole that had a mean diameter of 3.6 cm. Based on the out-of-plane extent (z-direction) of the jet, by the time it reached the center horizontal plane of the FOV, the reconstructed 3D jet expanded to about 10 cm. This expansion corresponded to a half cone angle of 30°, matching the (directly measured) maximum angle of the droplet trajectories (28°). As for the inhalation, the presumed hemispherical sink flow based on the literature was consistent with the observed converging radial inflow from all directions towards the blowhole (Figure 2D). Furthermore, after accounting for drag, inertia, and gravity of the droplets, the air velocity magnitudes increased with decreasing distance from the center of the blowhole (Figure 2E), also consistent with a sink flow. Further confirmation was obtained from sample plots (see Supplementary Figure S13) showing that the radial air speed was inversely proportional to the distance from the blowhole. Hence, our choice of a sink flow was consistent with both the data and the published literature. To estimate the inflow volume, the inhaled air speed was multiplied by the duration and the surface area of a hemisphere (=2πR²) with radius R corresponding to the distance from the blowhole, where the velocity was estimated. It should be noted that this approach provided only an estimate since the size of the blowhole was comparable to the sample area, hence the flow was not radially symmetric. The maximum air flow rate was estimated by multiplying the peak spatially averaged air velocity with the cross-sectional area of the plume for exhalation, and with the surface area of the hemisphere for inhalation, in accordance with the volume estimates.

The concentration and size distributions of droplets were obtained using all the detected objects. The total number of droplets and their equivalent diameters (based on droplet area and perimeter) were calculated for each frame by projecting all the droplet traces in the 11 cm deep volume to a single plane. For the five cases where a mister was used to seed the sample volume, the number and size of the seeding particles were obtained from the reconstructed images before the dolphins exhaled. The size-dependent seed droplet statistics were then subtracted from the overall (40 μm wide) size bins, assuming that the external seed concentration remained steady over the data acquisition time. For droplets with circular projections, their shape was assumed to be spherical. For large droplets and liquid ligaments with irregular shapes, the out-of-plane dimensions were unknown. Hence, we used an equivalent diameter, defined as De=4Ap/pp, where A_p was the in-plane area and p_p their perimeter, for estimating the irregular-shaped droplet volume (=πDe3/6). The liquid volume fraction was defined as the ratio of the total volume of detected liquid to the volume of air within the FOV. To calculate it, the ejected or inhaled water volume, estimated by summing the equivalent volumes of all the detected droplets, was divided by the volume of the cylindrical FOV. To estimate the total volume of exhaled or inhaled liquid, we had to avoid counting the same droplets multiple times in different frames. Hence, we used instantaneous velocity in each frame to estimate the time required for droplets to clear the FOV and then skipped the appropriate number of frames. After skipping frames, the total volume was calculated by summing all the volumes of the observed droplets. The instantaneous Sauter Mean Diameter, defined as D32=Σinidi3Σinidi2, where n_i is the number of droplets falling within equivalent diameter bin i centered around d_i, was also obtained for each frame. For comparison among different datasets, we used the time-averaged value, denoted by <D₃₂>, weighted by the number of droplets in each frame. For exhalation, the time averaging was restricted to the period where the jet velocity magnitude was greater than 50% of its maximum value, and during inhalation, the magnitude of the (negative) velocity was higher than 25% of the maximum value.

Three-way Analysis of Variance (ANOVA) without interactions between groups were performed to assess the effects of the independent variables, e.g., type of breath, sex, and BMI, on the dependent variables, e.g., maximum air speed, tidal volumes, etc. Key comparisons are provided with the F- and p-values, with p < 0.05 considered statistically significant in this study. In addition, for significant results, the values of Cohen’s d (Cohen, 1988), namely the difference between the means divided by the pooled standard deviation, are also provided. Typically, size effects are considered large for d>0.8 and small for d < 0.2 We also provide the 95% confidence interval (CI) for d.

A sample movie containing the original holograms of the droplets ejected and inhaled by dolphin C (experiment #6) is provided as movie 1 in the supplemental information. It contains discernible droplets ranging in size between 45 μm to several mm. The exhalation phase, when the droplets are pushed upward, lasts about 170 ms, followed by the 730 ms long inhalation phase, when most of the droplets travel downward at a lower speed towards the blowhole, which is located about 20 mm below the field of view. This section starts with the evolution of air velocity calculated from the small droplet trajectories. Each time series starts at the beginning of exhalation, i.e., when the first droplets appear in the holograms (t=0), and is followed by inhalation. For some of the cases, we compare the plume velocities in parallel slabs and draw conclusions on the shape of the plume. A sample time evolution of the air velocity estimated from the small droplet tracks at the centerline slab, for a normal breath of dolphin C (experiment #4 in Table 1), is plotted in Figure 3. It also provides the corresponding number of instantaneous small droplet tracks used in the analysis. Similar plots for all the other cases are provided in Supplementary Figures S2, S3.

The air velocity is initially positive when the dolphins exhale and then becomes negative during inhalation. With a maximum of 4.5 ms^-1, the magnitude of the exhalation air speed is significantly higher than that of the inhalation, which remains at about 1 ms^-1. For this case, the duration of exhalation is 190 ms, while the inhalation, when v_a <0, exceeds the total data acquisition time of 1000 ms. The exhalation jet has a primary velocity peak at 50 ms and a secondary peak at 100 ms. The existence of more than one exhalation peak with varying delays is observed in more than 50% of the present cases. In contrast, the variations in inhalation speed are small for all the cases. Another observation is that the number of instantaneous small droplet tracks varies throughout the breathing period. It increases when the exhalation velocity is high and diminishes at the end of the inhalation period (Figure 3). The plausible reason for this trend is the increase in droplet fragmentation with increasing speed, which would inherently result in a larger number of small droplets as the exhalation speed becomes higher. Similar trends with variations in numbers have been observed in most cases.

The following paragraph describes the statistics of air speed based on the entire dataset. Figure 4A compares the maximum air velocity during exhalation and inhalation, plotted against the dolphin body mass. Results are also classified based on the type of breath (normal, chuff, and post-exercise), sex, and BMI, where we compare trends observed for dolphins with a BMI less than 0.70 kgcm^-1 (mean of values for animals in this study) to those with higher BMI. Data obtained for repeated tests for the same dolphin and conditions are presented separately to demonstrate the variability between experiments. Because of the overlap in data, results for inhalation and exhalation are shifted slightly from each other. Combined statistics characterizing the median, interquartile range, and extreme values are plotted in Figure 4B to show the effects of breath types, sex, and BMI on the maximum air velocity during exhalation and inhalation. Figure 4A shows that the maximum exhalation air speeds vary between 3.1 and 7.1 ms^-1, and that of inhalation is in the 0.3 to 1.2 ms^-1 range. The normal and chuff exhalation speeds seem to fall in the same range, 4.1-6.4 ms^-1, but the post-exercise speeds are higher, extending to 7.1 ms^-1. ANOVA results reveal that there is a significant effect of breath type, F(2, 21)=4.76, p = 0.019, but not of sex, F(1, 21)=1.66, p = 0.212, or BMI, F(1, 21)=0.01, p = 0.917. As is evident from Figure 4B, post-exercise breaths have a significantly higher average speed than that of normal breath, with d = 1.60, CI [0.34, 2.82], or chuff, with d = 1.75, CI [0.46, 2.99]. The post-exercise exhalation speeds appear to decrease with increasing body mass.

The maximum inhalation air speeds remain around 0.7 ms^-1 for all cases and are significantly different than the exhalation speeds (p < 0.01). However, they show less variability in magnitude in all classifications (breath type: F(2, 21)=0.16, p = 0.856, sex: F(1, 21)=0.01, p = 0.908, BMI: F(1, 21)=0.01, p = 0.929). Corresponding statistics on durations of exhalation and inhalation are provided in Figures 4C, D. Overall, the exhalation times vary between 150 and 400 ms with an average of 250.6 ± 61.4 ms (mean ± SD), whereas the inhalation phase lasts from about 550 ms to more than 900 ms with a mean of 751.3 ± 107.4 ms. The exhalation duration is dependent on the breath type, F(2, 21)=3.96, p = 0.035, but not on sex, F(1, 21)=0.07, p = 0.787 or BMI, F(1, 21)=1.48, p = 0.237. The mean duration for normal breaths is longer than that of the chuff (d = 1.11, CI [0.23, 1.97]) and post-exercise breaths (d = 0.85, CI [-0.28, 1.97]). Our findings are compared to previously published results by Fahlman et al. (2018a, 2018b, 2019) and Cauture et al. (2024) in the discussion.

Figures 5A, B show the present exhaled and inhaled air volumes per breath (tidal volume) and maximum (peak) air flow rate, respectively, and compare them to prior data. Combined statistics of the inhaled and exhaled tidal volumes per breath are plotted in Figure 5C, and those of the maximum flow rates, in Figure 5D. The present overall average exhaled tidal volume, 5.1 ± 1.9 L, and inhaled air volume, 5.1 ± 2.0 L, are almost equal (p>0.1), as expected, and do not show a significant dependence on body mass. However, the average peak exhalation air flow rate (Figure 5B), 40.6 ± 7.4 Ls^-1, is much higher than that of inhalation air flow, 10.5 ± 4.0 Ls^-1 (p < 0.01), again without variations with body mass. Other notable trends are as follows. (i) Figure 5B shows that the maximum exhalation flow rates of post-exercise breaths decrease with increasing body mass and tend to be higher than those of the other types of breaths. (ii) The inhaled tidal volume is higher for normal breaths, followed by post-exercise breaths, and by chuffs. (iii) The maximum flow rates do not vary significantly among groups (p>0.1) except for the notably higher exhaled flow rates for post-exercise breaths (p < 0.01), in accordance with the higher speeds measured for these cases.

Sample time evolutions of the total number of droplets, the liquid volume fraction, and the Sauter mean diameter (D₃₂) of droplets for a post-exercise breath of Dolphin C (experiment #6) are plotted in Figures 6A-C, respectively. Owing to the large variations in magnitudes, the data are presented in logarithmic scales. Similar data for the rest of the datasets are provided as supplemental Figures S4-S9. To help in correlating the droplet statistics to the timing of exhalation and inhalation, these Figures also include the spatially averaged velocity time history of small droplets. Samples of total droplet number densities, the first for t=38 ms, the timing with the maximum number of droplets during exhalation, and t=586 ms, the timing of peak inhalation velocity, are presented in Figures 6D, E, respectively. Similar distributions for other cases are provided as Supplementary Figures S10, S11.

As dolphin C exhales, the total number of droplets in the sample volume, and the corresponding liquid volume fraction increase rapidly, peaking at t=38 ms and 38.5 ms, respectively, and then decrease more gradually (Figures 6A, B). For the present cases, the maximum droplet number varies between 1000 and 8000 (3000 in Figure 6A), and the maximum volume fraction, between 0.04% and 2% (0.05% in Figure 6B). For the sample shown, the D₃₂ (Figure 6C) fluctuates in the 1500 to 2300 μm range but remains in what appears to be a plateau with a few peaks for the entire duration of exhalation. The tendency to form a plateau persists in other cases, but the D₃₂ varies between 300 and 14000 μm. During inhalation, for most cases, the total number of droplets decreases to a few hundred, the volume fraction decreases by an order of magnitude, and the D₃₂ decreases and typically plateaus in the 100 to 1200 μm range. A comparison between the two sample number density plots indicates that the decrease in the number of droplets during inhalation occurs across the entire size range, a trend that also persists for the entire dataset (p < 0.01). These trends indicate that only a small fraction of the droplets generated during exhalation are inhaled back by the same animal.

The time-averaged Sauter Mean Diameters, <D₃₂>, during exhalation and inhalation, are plotted in Figure 7A. The same data are combined in Figure 7B to obtain statistics based on the types of breath, sex, and BMI. There are variations in the exhalation <D₃₂>, with values ranging from 400 to 14000 μm, among the different dolphins, and even for the same animal. The cases with <D₃₂> larger than 6000 μm correspond to events where 1–2 large, oddly shaped liquid blobs form shortly after the beginning of exhalation, presumably originating from the liquid trapped on top of the blowhole. There are no noticeable trends with body mass, F(1, 21)=0.71, p = 0.410, but sex, F(1, 21)=6.80, p = 0.016 and breath type, F(2, 21)=3.01, p = 0.071, have some effect on the characteristic droplet size. The mean <D₃₂> for females is higher than that of the males (d = 1.10, CI [0.22, 1.95]). Also, post-exercise breaths have a higher average <D₃₂> than normal (d = 1.12, CI [-0.05, 2.26]) or chuff (d = 0.91, CI [-0.23, 2.03]) breaths. The scatter is lower for the inhalation data, where <D₃₂> varies between 100 μm and 1400 μm, without a clear trend with body mass, F(1, 21)=0.34, p = 0.566, or breath type, F(2, 21)=0.50, p = 0.613. As noted above, the droplets generated by females are larger and more variable than those of their male counterparts. Subsequently, during inhalation, the mean <D₃₂> for female dolphins are higher than those of the males (d = 1.05, CI [0.08, 1.98]).

The GoPro images show that liquid is trapped in the dimple above the blowhole after the dolphin surfaces from a dive. Hence, part of the aerosolized liquid originates from the dimple, and the rest, from the respiratory tract. While it is not possible to identify the origin of each droplet from the holograms, the initial part of the plume appears to have originated from the dimple. Except for one case, all the large blobs are part of the early jet, suggesting that they originate from the dimple. A comparison between values of <D₃₂> generated by the initial plume and those of the rest of the exhalation period for 20 of the present cases is provided as Supplementary Figure S12. There was no well-defined initial plume for the rest of the 6 cases, hence they are not being used for this comparison. In half (10) of the cases, the droplets generated at later times are significantly smaller than the initial ones. In nine other cases, the sizes are comparable, and only one case with a short-duration 1st plume has smaller initial droplets. Still, the inhaled droplets are always smaller than those generated during late exhalation phases by as much as 70%. Also, beyond the initial fragmentation phase, the droplet concentrations are typically sparse, and we have not seen coalescence events.

The total liquid volumes per breath during exhalation and inhalation are plotted in Figure 7C, and the corresponding combined statistics, in Figure 7D. During exhalation, the volume varies between 0.1 and 16 mL, with considerable scatter, and without a clear trend with body mass, F(1, 21)=0.00, p = 0.972, or breath type F(2, 21)=1.01, p = 0.382. Also, the current female dolphins eject more liquid than males (d = 1.01, CI [0.15, 1.86]). The inhaled liquid volumes are much smaller (p < 0.01) compared to the exhaled ones, with the median being around 0.1 mL irrespective of the type of breath, F(2, 21)=0.01, p = 0.989, sex, F(1, 21)=1.07, p = 0.312, or BMI, F(1, 21)=0.00, p = 0.967. In most cases, the inhaled liquid consists mostly of small droplets and a volume varying between 0.02 and 0.5 mL. Only one chuff breath of Dolphin S involves entrainment of droplets with <D₃₂> larger than 900 μm, and the inhaled liquid volume is as high as 1 mL.

As demonstrated in Figure 8A, the exhaled liquid occasionally contains ejecta, consisting of droplets or odd-shaped blobs that have significantly higher speeds than the surrounding droplets. In this sample, the displacement of the ejecta blob, indicated in orange, during the 500 μs interval, is five times higher than that of the surrounding droplets, whose characteristic displacement is indicated in yellow. The time evolution of ejecta velocity for two sample datasets, a normal breath of Dolphin J and a chuff of Dolphin B, are compared to the evolution of the small droplet velocities in Figures 8B, C, respectively. Here, each data point corresponds to a specific ejecta droplet entering the FOV. As is evident, the high-speed ejecta, with speeds ranging between 2 to 5 times that of bulk droplet velocity, peaking at 11.5 and 15 ms^-1, respectively, are present during most of the exhalation phase. Some peaks appear to co-occur with the bulk velocity peaks, but others do not. The ejecta does not appear during the earliest bulk velocity peak, which has been attributed to liquid trapped in the dimple on top of the blowhole, suggesting that the ejecta originates from deep within the respiratory tract.

For each case, we calculate the time-averaged ratio of the ejecta velocity to that of the small droplets surrounding it at the same time. The results are presented in Figure 9A, and the combined statistics are plotted in Figure 9B. As is evident, the ratio varies from 1.5 to 5, without a clear trend with body mass. The median ratio for post-exercise and normal breaths is about 3.5, and marginally lower (~2.5) for chuff breaths. Female dolphins have slightly higher ratios than males, and there is no dependence on BMI. The total volume of the ejecta is calculated by summing the volumes of all the detected ejecta droplets throughout the breathing event. Results for specific cases are plotted in Figure 9C and statistics in Figure 9D. The ejecta volumes vary between 0.001 and 0.06 mL across all the processed cases, but most values are smaller than 0.02 mL. These volumes are nearly two orders of magnitude smaller (0.5% on average) than the total volume of liquid ejected during exhalation. Post-exercise breaths generate the highest median ejecta volumes (0.023 mL) while values for normal or chuff breaths (0.005 mL) are substantially smaller (d = 1.62, CI [0.36, 2.84] and d = 0.70, CI [-0.42, 1.80], respectively). Female dolphins generate more ejecta than males (d = 0.81, CI [-0.03, 1.65]), similar to the trends of <D₃₂>, exhaled liquid volumes, and ejecta velocity. The high BMI dolphins generate more ejecta than the low BMI ones. The difference between them would have been much higher if not for one chuff breath of Dolphin B that generates a very high volume (0.058 mL).