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Original Articles

Effect of coherent structures on particle transport and deposition from a cough

ORCID Icon & ORCID Icon
Pages 425-433 | Received 26 Oct 2021, Accepted 01 Feb 2022, Published online: 16 Mar 2022

Abstract

The transport of droplets expelled when coughing is of critical importance for understanding and preventing airborne disease transmission. However, the cough flow structure is complex, and numerous simplifications are often made to the initial flow condition in laboratory and numerical studies. We aim to challenge some of these assumptions, through particle transport experiments from a highly repeatable cough generator with a realistic oral cavity. In the present study the simultaneous transport and deposition of 22–27 μm, 45–53 μm, and 180–212 μm particles was investigated. Hot-wire measurements of the flow field showed the formation of two parallel jets on either side of the tongue, which produced a free shear layer downstream. Quantitative deposition measurements show that particle deposition patterns are strongly dependent on the formed shear layer for the smaller particles but not the largest size. The effect of circulation was characterized using a modified Stokes number of the form given by Davila and Hunt (Citation2001). The scaling analysis and quantitative data both support the conclusion that while the 180–212 μm particles are not strongly affected, the transport and deposition of the smaller particles are influenced by orifice geometry. These results demonstrate that particle transport from a cough, for which most released droplets are below 22 μm, is a strong function of coherent flow structures present in the 3D flow field.

1. Introduction

The transport of droplets expelled when coughing, sneezing, or talking is of critical importance for understanding and preventing airborne disease transmission (Bourouiba Citation2021). However, large uncertainties still exist regarding the distance that droplets may travel; in the case of the SARS-CoV-2 pandemic this created significant challenges in developing proper social distancing guidelines (Bahl et al. Citation2020). The variability in droplet travel distance can be caused by environmental factors and subject-to-subject variation. The present work targets the second of these factors, and challenges several prevalent assumptions on the nature of the flow field generated by a cough.

Previous studies of the human cough have noted significant subject-to-subject variation (J. W. Tang et al. Citation2009), as well as the dependence of the flow rate on body position (J. W. Tang et al. Citation2009) and number of sequential coughs (Hegland, Troche, and Davenport Citation2013; Gupta, Lin, and Chen Citation2009). Consequently, most studies consider cough transport in aggregate, for which initial droplet size distributions (Chao et al. Citation2009; Duguid Citation1946) and velocity of the gas phase in the centerline plane have been investigated. The velocity of the fluid has been studied using Schlieren imaging (Prasanna Simha and Mohan Rao Citation2020; J. W. Tang et al. Citation2009), particle image velocimetry (PIV) (Dudalski et al. Citation2020; Savory et al. Citation2014; VanSciver, Miller, and Hertzberg Citation2011; Zhu, Kato, and Yang Citation2006; Chao et al. Citation2009; Kwon et al. Citation2012), shadowgraph (J. W. Tang et al. Citation2012) and hot-wire measurements (Dudalski et al. Citation2020).

Experiments which attempt to quantify droplet transport using human subjects are limited (Zhu, Kato, and Yang Citation2006); instead, droplet or particle transport is typically studied numerically or using “analogue” experiments with simplified geometries. The stated resemblance of the vertical centerline velocity profile to a round jet (e.g., J. W. Tang et al. Citation2009) has led a round jet type profile to be frequently assumed in droplet transport studies (e.g., Wei and Li Citation2015; Liu and Novoselac Citation2014; Sun and Ji Citation2007; Redrow et al. Citation2011). Even when facial features are included, mannequins with a circular airway are commonly used (e.g., Berlanga, Olmedo, and Adana Citation2017; Feng et al. Citation2015; Qian et al. Citation2006). Similarly, while some numerical studies resolve outer features of human subjects such as the jaw (Zhu, Kato, and Yang Citation2006; Yang et al. Citation2018)), the inlet airflow is still commonly computed using an injection area and flow rate rather than resolving the complexities of the inlet jet. The assumption of a round jet continues to persist despite indications of vortex ring dynamics present in human coughs (Prasanna Simha and Mohan Rao Citation2020). In an effort to capture additional complexity of the cough flow structure, Bourouiba, Dehandschoewercker, and Bush (Citation2014) and Wei and Li (Citation2017) suggest that the cough may be best represented by a multiphase puff or an interrupted jet, respectively. While an improvement, Wei and Li (Citation2017) noted that the difference in spread angle of the analogue and human subject may be due to the missing complex oral cavity, including the effect of teeth.

While experimental studies occasionally use mannequins with oral features, the accuracy of these models varies significantly. The oral cavity ranges from simplified semi-elliptical mouths (Villafruela, Olmedo, and San José Citation2016; Xu et al. Citation2015) to 3D printed computed tomography (CT) scans including the lungs, bronchi, and internal passages (Berlanga et al. Citation2020; Duan et al. Citation2020). Focusing on the centerline plane, Berlanga et al. (Citation2020) demonstrate the dependence of the flow field on the airway geometry through PIV measurements of a simplified airway (straight circular tube ending in a semi-elliptical orifice) and a CT scanned realistic airway. Among other effects, it was noted that the simplified model has a longer and clearer core structure in the initial vortex when compared to the realistic geometry, which results in a longer distance before the origin of a secondary vortex downstream. While these differences are apparent in the centerline plane, further research work is still needed as out-of-plane studies on the cough flow field either do not quantify velocities (Gupta, Lin, and Chen Citation2009) or focus on a single horizontal plane (Han et al. Citation2021). To the authors’ knowledge, the 3D velocity distribution from a cough has not been experimentally studied. Consequently, it is not possible to glean insight on the effect of vorticity present in the cough on particle transport. This is a major limitation, given that it is well known that vorticity can significantly affect particle transport (Eaton and Fessler Citation1994).

Far from the exit of a single-phase jet the inlet geometry has a diminished effect. However, there is known dependence of self-similarity scaling on the initial conditions (George Citation1989; Boersma, Brethouwer, and Nieuwstadt Citation1998). In other words, the initial conditions are known to influence the development of coherent structures. These structures have a significant impact on particle transport. The effect of vortical flows on particle transport has been studied in a variety of canonical flows including: a vortex-ring (Hunt et al. Citation2007), Lamb-Oseen vortex (Yang, Thomas, and Guo Citation2000), Rankine vortex (Davila and Hunt Citation2001), spherical vortex (Eames and Gilbertson Citation2004), and free-shear flows (Wen et al. Citation1992; Yang, Thomas, and Guo Citation2000; Perkins, Ghosh, and Phillips Citation1991; L. Tang et al. Citation1992; Lazaro and Lasheras Citation1989). For each of these flows, particle transport was highly dependent on the details of the vortical nature of the flow, and dense particles preferentially accumulated or were ejected in specific regions of the flow.

In large part due to the well-established phenomenon of particle clustering, efforts to produce self-similar particle velocity profiles (Casciola et al. Citation2010) and particle fluxes (Picano et al. Citation2010) for particle-laden turbulent jets have not yielded universal scaling. These approaches depend on scaling with the local Stokes number and local particle spreading rate, respectively. The lack of a universal scaling is driven by the interaction between the particle response time and local structures in the carrier fluid, which is explained in Section 2. Hence, studies of the flow field produced during a cough should capture both the mean flow field, as well as the initial size and breakdown of the 3D flow structures downstream in order to accurately predict particle transport. Yet, much remains unclear about the characteristic structures in the flow and their influence on droplet transport.

To contribute to filling this knowledge gap, we study the 3D flow field produced using a repeatable cough generator with a realistic oral cavity. We then study the effect of the flow field on particle transport and deposition. The inclusion of teeth, tongue, and lips in the oral cavity provides a marked addition to the data available in literature. To focus the experiments on mouth geometry effects, the coughed air was at ambient temperature and solid particles were released instead of liquid droplets. These choices allow us to ignore the effects of buoyancy and evaporation on droplet transport. Measurements of the simultaneous transport and deposition of particles from 22 to 212 μm indicate that the 3D nature of the flow field has a significant effect on particle deposition.

2. Theory

The non-dimensional equation for motion of a spherical, solid particle in unsteady flow was derived by Davila and Hunt (Citation2001): (1) dv˜dt=1+CMγ+CMDu˜Dt+γ1γ+CM1St(u˜v˜+VT˜)(1)

Here CM is the added-mass coefficient, St=tPU2/Γ is the Stokes number, tP is the particle response time, U is the maximum flow velocity, Γ is the circulation of the flow, γ=ρp/ρ is the ratio of particle to fluid density, v˜=v/U is the non-dimensional particle velocity, u˜=u/U is the non-dimensional fluid velocity, g is the acceleration due to gravity and VT˜=tPg/U is the non-dimensional terminal velocity of the particle.

For the condition of γ1000 (i.e., γ1,CM) this equation simplifies to: (2) dv˜dt=1St(u˜v˜+VT˜)(2)

Clearly, equilibrium points in the particle motion are possible provided (v˜u˜)VT˜. Davila and Hunt (Citation2001) show that small particles with high density ratio preferentially accumulate in regions of high strain rate and low vorticity. The tendency of particles to cluster is scaled by what was defined as a modified Stokes number (Hunt et al. Citation2007): (3) St*=VT2tPΓ(3)

This follows from the particle Froude number defined in Davila and Hunt (Citation2001), FrP=VT3/gΓ. The two are seen to be equivalent when noting the terminal velocity to be V T = gtP. When St*1, we expect that particles have sufficiently low inertia to be affected by vortices present in the flow (Hunt et al. Citation2007). It remains to show that vortical flows with circulation on the order of VT2tP are present in a cough-type event. If so, particles are expected to be affected by circulation present in the flow, and it is important to ensure that the flow field near the mouth is prescribed accurately in modeling or experiments.

3. Experimental setup

Experiments were conducted in the Cal Covid Cube, a room that is 2.84 m × 3.76 m (× 2.32 m high), isothermal, isopotential, and quiescent (further described in Thacher et al. Citation2021). Repeatable cough-type events were produced from an intubation trainer doll with a realistic mouth geometry (3B Scientific, item 1005596). The height of the center of the doll mouth is at z = 160 ± 0.2 cm above the floor. An image of the mouth and coordinate system is given in , for which the x-axis is coming out of the page. Fluorescent polyethylene microspheres from Cospheric () were placed in a particle ‘trap’ and a controlled air release carried the trap contents in a multi-phase turbulent puff. The puff traveled through an artificial trachea and oral cavity, which included teeth, tongue, and lips. The nasal cavity was blocked off at the back of the throat between the oral and nasal pharynx. The controlled air release lasted 1.0 s, with a nominal peak flow rate of 150 slpm. The airflow was generated via a release from a 22.7 liter tank. The air released from each cough was < 2% of the stored air volume, and a regulator provided the gas at a constant pressure (380 kPa) to an Alicat mass flow controller (MCR-2000SLPM). The Alicat has a reported uncertainty of ± (0.8% of reading + 0.2% of full scale). The flow rate was recorded directly from the Alicat using a National Instruments myDAQ. The volume of air released during the cough was determined to be highly repeatable, with a volume of Q = 1.23 ± 0.09 liters, which is within the range of 0.4–1.6 liters for male subjects given by Gupta, Lin, and Chen (Citation2009). The repeatability of the air release volume was determined as an integral of the flow rate across 64 coughs. However, it is important to note that the absolute value of the released volume is subject to the finite accuracy of the flow meter as stated above. The mouth opening area is approximately an ellipse with a major axis of a = 2.25 cm ± 0.07 cm and a minor axis of b = 0.725 ± 0.07 cm. This corresponds to an equivalent diameter of De=2ab=2.55 cm, and an opening area of Aexit= 5.1 cm2, which is slightly larger than the average of 4.00 ± 0.95 cm2 reported in Gupta, Lin, and Chen Citation2009. The nominal Reynolds number of the turbulent puff computed using the average flow rate is Re=QDeAexitν4100, where ν is the kinematic viscosity of the air (taken to be 1.5 x 105 m2/s). The average cough velocity along the y = 0 plane is given in , for which a snapshot of the particle release at the inset location is given in . The cough trajectory is characterized by the two angles given in , which can be compared to the expected values of θ1 = 15° ± 5° and θ2 = 40° ± 4° reported in Gupta, Lin, and Chen (Citation2009). The angle is also shallower than the approximate mean angle of 30° reported by J. W. Tang et al. (Citation2009), however it is noted that the angle varies with each subject as well as their body positioning.

Figure 1. Velocity contours in x/De = 1 plane from (a) realistic geometry and (b) canonical rectangular slot with tabs (figure re-created based on Zaman Citation1996).

Figure 1. Velocity contours in x/De = 1 plane from (a) realistic geometry and (b) canonical rectangular slot with tabs (figure re-created based on Zaman Citation1996).

Figure 2. (a) Snapshot of particle release during cough with contours of average velocity in the y = 0 plane superimposed. (b) Average velocity contours in y = 0 plane with angle of cough boundaries indicated. The boundary is defined by points at which the velocity is below 0.5 m/s, or less than 10% of the maximum jet velocity of 5 m/s.

Figure 2. (a) Snapshot of particle release during cough with contours of average velocity in the y = 0 plane superimposed. (b) Average velocity contours in y = 0 plane with angle of cough boundaries indicated. The boundary is defined by points at which the velocity is below 0.5 m/s, or less than 10% of the maximum jet velocity of 5 m/s.

Table 1. Particle load (mass per size class) used for each experiment. The particles nominally had density of water ( saliva), ρ =1 ± 0.01 g/cm3.

While the repeatable cough generator doesn’t capture changes to the cavity shape during a cough event (Ge et al. Citation2021), it includes many of the salient geometrical features and exposes how these may result in a more complex flow field than what is typically assumed (such as the flow field from a round or elliptical pipe release). Subsequently we describe the effect of this flow field on particle transport. Solid fluorescent color-coded particles were released to enable the simultaneous deposition of three particle sizes spanning an order of magnitude and exhibiting no coalescence or ambiguity in the original droplet size. Additionally the co-flowing air was kept nominally at room temperature, so that buoyancy would not affect the flow. While buoyancy and evaporation are important for particle transport in a real cough, neglecting these influences allows the effect of the mouth geometry to be studied independently of conflating factors.

To measure deposition, 102 mm × 51 mm adhesive TriTech vinyl backed sampling strips were placed at 46 locations on the floor. The strips were charge-neutralized (using Simco-Ion 5225 AeroBar with the neutrality inspected using the Simco-Ion FMX-003 electrostatic fieldmeter) prior to each experiment. Thacher et al. (Citation2021) provides further detail of the experimental and data analysis technique. As described in Thacher et al. (Citation2021), the particle identification rate with this method is greater than 98%, with a false positive rate below 2%. Notably, this error is significantly lower than the test-to-test variation. The mean, standard deviation, and relative error due to test-to-test variation for each location is given in the supplemental material. Reported mean particle density (given in and in further detail in the supplemental material) is the average of eight repeated experiments.

Point-wise flow measurements were made using a single omnidirectional hot-wire (Dantec Dynamics 55P16). Calibration of the hot wire bound the uncertainty to 5.6% across a velocity range of 0–12.2 m/s. The hot wire was traversed in x, y and z to a total of 654 unique locations, for which a minimum of three repeated measurements spanning the cough duration were made. The velocity measurements were made at 5 kHz. Time-averaged velocities from 0.1 s t1 s of the 1.0 s cough were computed, and the average of these velocities across the repeated measurements are what is reported here. No particles were present during the hot-wire measurements. As the cough is generated from a static geometry and a highly repeatable gas delivery system, ensemble averages of the flow field could be reported. The volume of air ejected during each cough was highly consistent with a 1.23 ± 0.09 litre released volume. While velocity at a given location fluctuates in time due to both turbulence and large coherent structures in the flow, the time-averaged velocity measurements across all locations had a mean standard deviation of 0.06 m/s. For measurements in the z=b plane, the average standard deviation of the time-averaged measurements was only 12% of the mean velocity. While additional physics may be contained within time-resolved measurements, we choose to approach the problem from a Reynolds-averaged perspective as this aligns with typical modeling practice.

4. Results

Contrary to previous studies which report only the centerline (y=0) profile and normalize by the maximum velocity, examining the flow beyond the centerline plane reveals that the cough forms two jets (seen in ). The jets are centered on either side of the y = 0 plane and below the z = 0 centerline due to the downward cough trajectory, and hence would have been missed in studies where only the centerline plane was characterized (even with realistic oral geometries). The likely cause of formation of the two jets is the tongue structure within the mouth, leading to a split in the flow. Similar formation of two parallel jets due to a partial blockage was reported for a canonical rectangular outlet geometry in Zaman (Citation1996). The contours of mean velocity for flow through the rectangular opening with tabs is shown in . The similarity between the two flows in the x/De=1 plane is apparent. While the formation of two jets still needs to be verified with human subject experiments, the work of Zaman (Citation1996) shows that even an area blockage area of 1.8% is sufficient for two jets to form. Therefore, it seems likely that the two jets are present in at least a subset of human coughs. In these cases, a round jet would make a poor approximation of the true flow field.

Since the mouth is not perfectly symmetric, the strength of the jets are not equal and have time-averaged velocities of 5.0 m/s and 3.9 m/s at a distance of x/De = 1 from the mouth. The two-jet pattern leads to the formation of a shear layer downstream (see ). This velocity profile downstream, including the shear layer formation, appear qualitatively similar to those found in human-subject experiments in Han et al. (Citation2021). Again, this serves to illustrate the relevance of the present work to human coughs despite the use of an intubation trainer doll in these experiments.

Figure 3. Downstream velocity profiles along z/b = −1 plane.

Figure 3. Downstream velocity profiles along z/b = −1 plane.

To determine the effect of the shear layer on particle displacement, the modified Stokes number is computed according to EquationEquation (3) with the vortex strength estimated as Γ=ΔU(x)λ(x). The equation for vortex strength is computed using the definition of circulation in a plane shear layer (as in Jimenez Citation1983), but with a modified definition of ΔU(x). The characteristic velocity, ΔU(x), is defined as the difference in velocity evaluated at y = 0.5λ(x) and y = 0.5λ(x) (to either side of the y = 0 centerline). This is in contrast to the definition given by Jimenez (Citation1983), who define the characteristic velocity as the velocity difference between the free jet and surrounding quiescent fluid. This change in the characteristic velocity scale is due to the steeper velocity gradient in the primary shear layer of the present experiments (within the cough and contained near the centerline). We assume that this shear will dominate the formation of coherent structures, as opposed to the shear layer caused by the interaction with the quiescent fluid external to the cough structure. λ(x) is the large-structure wavelength computed according to λ/x=Cα, where the constant α=(U1U2)/(U1+U2). This constant is computed using the initial velocity to either side of the centerline, such that for U1=5 m/s and U2=3.9 m/s, α=0.12. The constant C defines the spreading rate of the large-scale streamwise wavelength, and was determined empirically (Jimenez Citation1983) to be C = 0.561. This value matches closely with that from Hernan and Jimenez (Citation1982) for a plane shear layer produced by a finite velocity difference, ΔU. The constant spreading rate likely arises from the constant ratio between the spanwise and streamwise wavelengths in a plane shear layer (Huang and Ho Citation1990). The spanwise wavelength is also linearly dependent on x, and grows 1–1.5 times faster than the vorticity thickness (Jimenez Citation1983). This approximation of the vortex strength enables an estimate of the order of magnitude of the modified Stokes number as a function of streamwise distance and particle diameter ().

Figure 4. Modified Stokes number, St*, along the horizontal z/b = −1 plane and centerline particle concentration, with standard deviation due to test-to-test variation given by shaded error bars.

Figure 4. Modified Stokes number, St*, along the horizontal z/b = −1 plane and centerline particle concentration, with standard deviation due to test-to-test variation given by shaded error bars.

For St*1 the particles have sufficiently low inertia to be affected by the vortices produced in the shear layer. This criteria is never satisfied for the largest 200μm particles, which are deposited as ballistic projectiles. While the estimate of circulation only provides a rough approximation of St*, the 2227 μm and 4553 μm particles are predicted to be affected up until at least a distance of 20 De downstream (). Still further downstream it is predicted that the 2227 μm particles will continue to be strongly affected by the shear layer. The locally high standard deviation of 2227 μm particle counts at x = 37.4 De gives some indication of where particle-vortex interaction led to high test-to-test variation.

The ‘eddying pattern’ seen in the deposition of 2227 μm particles from a single experiment shows the ‘frozen signature’ of the flow structure (). This false color image was created from a picture obtained using a 495 nm longpass filter while illuminating the fluorescent particles with UV light. The pattern seen in the image was corroborated with quantitative deposition data (). This data provides a strong indication that particles are affected by the free shear layer. The eddying is most apparent in the near field, up to x  50 De, after which particle deposition appears to be relatively uniform across the span. The effect of eddying is also clear in the particle deposition counts, for which the row at x = 27.6 De received high particle counts while the centerline strips at the x = 17.7 De and x = 37.4 De had particle counts that were an order of magnitude lower. This result demonstrates that the spanwise shift in particle deposition due to the particle-vortex interaction in the free shear layer has a first-order effect on the particle deposition location. This large scale pattern would not have been expected from a single round jet release.

Figure 5. Comparison of (a) false color image of 22–27 μm (red) and 180–212 μm (green) particle deposition with (b) measured 22–27 μm particle deposition during a single experiment with image view indicated by dashed line.

Figure 5. Comparison of (a) false color image of 22–27 μm (red) and 180–212 μm (green) particle deposition with (b) measured 22–27 μm particle deposition during a single experiment with image view indicated by dashed line.

5. Discussion

The data suggests a clear effect on particle deposition from the cough release geometry, which is in agreement with what is expected given the modified Stokes number of the released particles. The eddying pattern seen in was present in repeated experiments up until 50De downstream (approximately 1.3 m away from the mouth). As circulation decreases exponentially downstream, the pattern fading further downstream lends further support for the presented interpretation of the data. There will still be a ‘far field’ distance at which the effects of the oral cavity geometry can be neglected. As a first approximation this distance can be described as the point at which St*1, which indicates the dependence of the ‘far field’ criteria on the particle size. Beyond this distance the inlet boundary condition (i.e., complex oral cavity) no longer affects particle transport. In this ‘far field’ region, a more general approximation of the flow field is likely sufficient, especially if the initial preferential clustering of particles has been accounted for. Notably, the majority of droplets ejected during a real cough rapidly evaporate to an equilibrium diameter and are smaller than what was considered in the present study (Duguid Citation1946; Chao et al. Citation2009). Therefore, the majority of droplets ejected during a real cough could continue to be affected by the complex mouth geometry much further downstream than the particles in the present study.

Consequently, studies that are attempting to predict particle transport on the order of typical social distancing (recommended social distancing guideline is 1.8 m (6 ft) as given in Balachandar et al. Citation2020) between individuals should consider the oral cavity as something more complex than a plain round or elliptical orifice when predicting the flow field and resulting particle transport.

6. Conclusions

Particle transport from a human cough has often been studied using a flow field generated by a round jet. We used a repeatable cough generator with a realistic oral cavity to demonstrate that in an open mouth position two jets may be formed during a cough event; these jets are likely caused by the tongue within the oral cavity. Data indicates that a free shear layer forms downstream, which produces circulation that based on our analysis is strong enough to affect particle motion in the size range 4553 μm and below.

The effect of the shear layer led to 2227 μm particle deposition following an eddying pattern up to x50De downstream. Sufficiently high circulation to affect particles of 4553 μm was contained to the area immediately following particle release. 180212 μm particles were seen to deposit ballistically with little response to fluctuations in the cough velocity. These results demonstrate that droplet transport from a cough, which contains smaller droplets then those yet considered, is a strong function of coherent flow structures produced by the oral cavity. While artificial cough generators and numerical modelers must make necessary simplifications to a true human cough, there could be significant value in increasing the accuracy of the oral cavity. Importantly, the flow field of the multiphase jet is shown to depart significantly from a round jet away from the centerline plane. This challenges the validity of common simplifying assumptions made when creating initial conditions for cough transport and other similar multiphase flow studies.

Supplemental material

Supplemental Material

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Acknowledgments

The authors gratefully acknowledge the gift of the Lam Research Corporation, SEMI, Advanced Energy Industries, Applied Materials, ASM, Entegris, JSR, KLA, TEL, and Wonik.

Additional information

Funding

This work began with the support of the 2020 Seed Fund Award 2020-0000000139 from CITRIS, and has been partially supported also by AFRI Competitive Grant no. 2020-67021-32855/project accession no. 1024262 from the USDA National Institute of Food and Agriculture (grant administered through AIFS: the AI Institute for Next Generation Food Systems. https://aifs.ucdavis.edu.) Research was partly supported by the DOE Office of Science through the National Virtual Biotechnology Laboratory, a consortium of DOE national laboratories focused on response to COVID-19, with funding provided by the Coronavirus CARES Act and the Department of Energy under Contract No. DEAC02-05CH11231.

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