Biological fluid dynamics of airborne COVID-19 infection

Abstract

Abstract: We review the state of knowledge on the bio-fluid dynamic mechanisms involved in the transmission of the infection from SARS-CoV-2. The relevance of the subject stems from the key role of airborne virus transmission by viral particles released by an infected person via coughing, sneezing, speaking or simply breathing. Speech droplets generated by asymptomatic disease carriers are also considered for their viral load and potential for infection. Proper understanding of the mechanics of the complex processes whereby the two-phase flow emitted by an infected individual disperses into the environment would allow us to infer from first principles the practical rules to be imposed on social distancing and on the use of facial and eye protection, which to date have been adopted on a rather empirical basis. These measures need compelling scientific validation. A deeper understanding of the relevant biological fluid dynamics would also allow us to evaluate the contrasting effects of natural or forced ventilation of environments on the transmission of contagion: the risk decreases as the viral load is diluted by mixing effects but contagion is potentially allowed to reach larger distances from the infected source. To that end, our survey supports the view that a formal assessment of a number of open problems is needed. They are outlined in the discussion.

Keywords: Clouds, jets, puffs; Coughing, sneezing, speaking; Distancing; Droplets; Non-pharmaceutical protection measures; Respiratory emissions.

Fig. 1

Upsurge in research on various aspects of the pandemic: cumulative number of research studies (in thousands) published from January to May 2020 (source: The Economist, May 7, 2020). https://www.economist.com/science-and-technology/2020/05/07/scientific-research-on-the-coronavirus-is-being-released-in-a-torrent

Fig. 2

Schematic illustration of the structure of SARS-CoV-2 virion

Fig. 3

Schematic of the mucociliary barrier providing the first defense against respiratory pathogens

Fig. 4

Schematic representation of the interaction between SARS-CoV-2 and the human cell membrane

Fig. 5

The sketch illustrates the results from the scientific literature on the persistence of different viruses on various surfaces (adapted from Fathizadeh et al. 2020)

Fig. 6

A plot of the sedimentation-evaporation of the droplets (Wells 1934), providing an estimate of the time scale of the two processes as a function of the droplet size (adapted from Xie et al. 2007)

Fig. 7

Horizontal distances reached by droplets of various sizes as the initial speed U₀ of the expiratory jet increases according to Xie et al. (2007) (adapted from Xie et al. 2007)

Fig. 8

Size distribution of the droplets emitted by cough (adapted from Zayas et al. 2012)

Fig. 9

Unimodal (left) and bimodal (right) distributions of the volumes of droplets recorded for sneeze emissions of 23 patients (adapted from Han et al. 2013)

Fig. 10

Comparison between the size distributions of the droplets emitted by sneeze and speech (left) or sneeze and cough (right) as measured by different authors (adapted from Han et al. 2013)

Fig. 11

Characteristic trend of the expiratory flow rate associated with a cough event. The original reference reports the measured values of the peak flow rate (CPFR), the total expired volume (CEV) and the peak velocity time (PVT). The measured CPFR ranges are 3–8.5 (l/s) for males, and 1.6–6 l/s for females. Analogously, the CEV ranges are 400–1600 ml for males and 250–1250 ml for females; PVT: 57–96 ms (males) and 57–110 ms (females) (adapted from Gupta et al. 2009)

Fig. 12

Images of the cloud released by a cough event recorded at a frequency of 1000 fps. a 0.006 s, b 0.01 s, c 0.029 s and d 0.106 s. e Ballistic trajectories of the largest droplets. f Smoke visualization of the motion of the gas phase recorded at 2000 fps. In e the instantaneous images of the trajectories of all the droplets recorded throughout the entire sequence are superimposed. Similarly for the smoke particles in Fig. 9f (adapted from Bourouiba et al. 2014)

Fig. 13

Images of the cloud expelled by sneezing, recorded at a frequency of 1000 fps a 0.007 s, b 0.03 s, c 0.107 s, d 0.162 s, e 0.251 s, f 0.34 s (adapted from Borouiba et al. 2014)

Fig. 14

Lateral (upper panel, 8000 fps) and top (lower panel, 2000 fps) views of the initial phase of the expiratory expulsion associated with a sneeze. Droplets (right column, t = 117 ms) form from the fragmentation of complex structures evolving from sheets and bags (left column, t = 8 ms) into elongated filaments (central column, t = 21 ms) (adapted from Scharfman et al. 2016)

Fig. 15

Panel A shows the number of flashes that were recorded in a single video frame. Sampling frequency was 60 fps. Green denotes the time when the person spoke. Note that, during the silent intervals (grey line), the number of flashes did not vanish immediately, presumably because a few droplets remained in the light sheet for a few seconds after speaking stopped (Anfinrud et al. 2020). b Shows a photogram corresponding to a peak in droplets emission (see arrow in a). The different brightness of individual flashes indicates the different droplet size (images provided by Adriaan Bax). Panel C shows a snapshot of saliva droplets, and Panel D an image of the experimental setup (photo credit: National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health)

Fig. 16

Sketch illustrating the double liquid layer coating the human airways (adapted from Grotberg 1994)

Fig. 17

Sketch illustrating the mechanism whereby the instability of the mucus layer lining an airway may lead to its occlusion (adapted from Malashenko et al. 2009)

Fig. 18

Results of experimental observations on the trajectory of the cloud of exhaled air and its characteristic size compared with the predictions of a simple theoretical model. Here, r is the characteristic radius of the cloud (cm), and s (cm) is the longitudinal coordinate of the cloud’s center of mass, defined along its trajectory. a Time evolution of s. The two asymptotic regimes are shown; b The entrainment is described by assuming that r = α s(t) with α being a suitable entrainment coefficient estimated from the experimental data. Clearly, the results from the theoretical model depend on the choice of α (adapted from Bourouiba et al. 2014)

Fig. 19

Surgical mask

Fig. 20

High protection masks devoid of (left) or equipped with (right) expiration valves

Fig. 21

Efficiency of surgical masks in reducing the number of respiratory viruses exhaled in droplets of different sizes by symptomatic patients suffering from coronavirus (a), influenza (b) or rhinovirus (c). The figure plots the number of virus copies for each sample. Samples were collected from nasal swabs (red), pharyngeal swabs (blue), exhaled droplets (d > 5 μm) collected for 30 min from patients that did not wear (dark green) or wore (light green) a surgical mask and smaller droplets (d < 5 μm) collected for 30 min (brown no mask, orange with mask) (adapted from Leung et al. (2020)

Fig. 22

Schlieren images of two volunteers. The roughness of the Schlieren image is related to the turbulence of the emission, and visualizes the fluid flow of the emitted aerosols. In one instance, a person coughs without any mask protection (top), wearing a surgical mask (middle) and finally a FFP2 mask (bottom). The flow direction is inclined 308° downward in the top image. It has both vertical components (downward and upward) and lateral components that bypass the surgical mask in the middle image. The best fit of a FFP2 mask reduces the bypass flow but it increases the flux released through the mask. However, its weak speed limits the region affected by exhalations to the immediate neighborhood of the volunteer (images provided by Gary S. Settles)

Fig. 23

Variation of the absolute risk of infection from SARS-CoV-2 and SARS-CoV with distance infected-susceptible for given reference risks (baseline risk). The shift from a condition of high risk (high baseline risk) to an intermediate one, corresponding to the use of N95 masks or equivalent ones (adapted from Chu et al. 2020)

Fig. 24

Prediction of the distance from the source reached by expiratory exhalations according to mathematical or numerical models, experimental observations or testing on patients. Note the large spread in the data, a possible consequence of the broad variability in the ambient conditions inside which the expiratory exhalations evolve (adapted from Bahl et al. 2020)

Fig. 25

Viral load detected in nasal swabs obtained from patients infected with SARS-CoV. This is an example of direct measurement of the viral load cycle, here expressed in units of measure specific of a test system using RT-PCR ($C_{\text{t}}$ value), immaterial to the evaluation of the cycle, days, that is of interest here (adapted from Zou et al. 2020)