2.1 Mechanisms of droplet formation

It is generally established that respiratory droplets are formed from the fluid lining of the respiratory tract (Edwards et al. Reference Edwards, Man, Brand, Katstra, Sommerer, Stone, Nardell and Scheuch2004; Morawska et al. Reference Morawska, Hofmann, Hitchins-Loveday, Swanson and Mengersen2005, Reference Morawska, Johnson, Ristovski, Hargreaves, Mengersen, Corbett, Chao, Li and Katoshevski2009; Johnson & Morawska Reference Johnson and Morawska2009; Almstrand et al. Reference Almstrand, Bake, Ljungström, Larsson, Bredberg, Mirgorodskaya and Olin2010). The mechanisms of formation are usually associated with distinct locations in the respiratory tract; this is important because both the characteristics of the respiratory tract (length scales, airway elasticity, mucus and saliva properties, etc.) as well as the viral load carried by the lining are functions of the location (Almstrand et al. Reference Almstrand, Bake, Ljungström, Larsson, Bredberg, Mirgorodskaya and Olin2010; Johnson et al. Reference Johnson, Morawska, Ristovski, Hargreaves, Mengersen, Chao, Wan, Li, Xie and Katoshevski2011).

One key mechanism for the generation of respiratory droplets is the instability (Moriarty & Grotberg Reference Moriarty and Grotberg1999) and eventual fragmentation of the mucus lining due to the shear stress induced by the airflow. Predicting the fragmentation and droplet size distribution resulting from this fragmentation is non-trivial because mucus is a viscoelastic shear-thinning fluid subject to surface tension. This enables multiple instabilities to bear on this problem (Malashenko, Tsuda & Haber Reference Malashenko, Tsuda and Haber2009), including surface-tension-driven Rayleigh–Plateau instability (Eggers Reference Eggers1997; Lin & Reitz Reference Lin and Reitz1998; Romanò et al. Reference Romanò, Fujioka, Muradoglu and Grotberg2019), shear-driven Kelvin–Helmholtz instability (Kataoka, Ishii & Mishima Reference Kataoka, Ishii and Mishima1983; Scardovelli & Zaleski Reference Scardovelli and Zaleski1999) and acceleration-driven Rayleigh–Taylor instability (Joseph, Beavers & Funada Reference Joseph, Beavers and Funada2002; Halpern & Grotberg Reference Halpern and Grotberg2003). The Rayleigh–Taylor instability is particularly important in spasmodic events such as coughing and sneezing.

The second mechanism for droplet formation is associated with the rupture of the fluid lining during the opening of a closed respiratory passage (Malashenko et al. Reference Malashenko, Tsuda and Haber2009). One important site for this mechanism is in the terminal bronchioles during breathing. These submillimetre-sized passages collapse during exhalation, and the subsequent reopening during inhalation ruptures the mucus meniscus, resulting in the generation of micrometre-sized droplets (Almstrand et al. Reference Almstrand, Bake, Ljungström, Larsson, Bredberg, Mirgorodskaya and Olin2010; Johnson et al. Reference Johnson, Morawska, Ristovski, Hargreaves, Mengersen, Chao, Wan, Li, Xie and Katoshevski2011). A similar mechanism probably occurs in the larynx during activities such as talking and coughing, which involve the opening and closing of the vocal folds (Mittal, Erath & Plesniak Reference Mittal, Erath and Plesniak2013). Finally, movement and contact of the tongue and lips, particularly during violent events such as sneezing, generate salivary droplets via this mechanism. The fluid dynamics of meniscus breakup associated with this mechanism is difficult to predict, especially given the non-Newtonian properties of the fluids involved, the dominant role of moving boundaries, and the large range of length and time scales implicated in this phenomenon.

2.2 Droplet characteristics

The number density, velocity and size distributions of droplets ejected by expiratory events have important implications for transmission, and numerous studies have attempted to measure these characteristics (Duguid Reference Duguid1946; Wells Reference Wells1955; Morawska et al. Reference Morawska, Johnson, Ristovski, Hargreaves, Mengersen, Corbett, Chao, Li and Katoshevski2009; Xie et al. Reference Xie, Li, Sun and Liu2009; Han, Weng & Huang Reference Han, Weng and Huang2013; Bourouiba, Dehandschoewercker & Bush Reference Bourouiba, Dehandschoewercker and Bush2014; Scharfman et al. Reference Scharfman, Techet, Bush and Bourouiba2016; Asadi et al. Reference Asadi, Wexler, Cappa, Barreda, Bouvier and Ristenpart2019). A single sneeze can generate $O(10^{4})$ or more droplets, with velocities upwards of $20~\text{m}~\text{s}^{-1}$ (Han et al. Reference Han, Weng and Huang2013). Coughing generates 10–100 times fewer droplets than sneezing, with velocities of approximately $10~\text{m}~\text{s}^{-1}$, but even talking can generate approximately 50 particles per second (Asadi et al. Reference Asadi, Wexler, Cappa, Barreda, Bouvier and Ristenpart2019). Measured droplet sizes range over four orders of magnitude, from $O(0.1)$ to $O(1000)~\unicode[STIX]{x03BC}\text{m}$. Recent studies have noted that, while breathing generates droplets at a much lower rate, it probably accounts for more expired bioaerosols over the course of a day than intermittent events such as coughing and sneezing (Fiegel, Clarke & Edwards Reference Fiegel, Clarke and Edwards2006; Atkinson & Wein Reference Atkinson and Wein2008). Consensus on all these droplet characteristics continues to be elusive due to the multifactorial nature of the phenomena as well as the difficulty of making such measurements (Chao et al. Reference Chao, Wan, Morawska, Johnson, Ristovski, Hargreaves, Mengersen, Corbett, Li, Xie and Katoshevski2009; Morawska et al. Reference Morawska, Johnson, Ristovski, Hargreaves, Mengersen, Corbett, Chao, Li and Katoshevski2009; Han et al. Reference Han, Weng and Huang2013).

2.3 The expiratory jet and droplet transmission

Droplets generated within the respiratory tract by the mechanisms described above are carried outwards by the respiratory airflow, and those droplets that are not reabsorbed by the fluid lining are expelled within a two-phase buoyant jet from the mouth and/or nose. Breathing and talking generate jet velocities that seldom exceed $5~\text{m}~\text{s}^{-1}$ (Tang et al. Reference Tang, Nicolle, Klettner, Pantelic, Wang, Suhaimi, Tan, Ong, Su and Sekhar2013) and mostly expel small droplets. Violent expiratory events like coughing and sneezing, on the other hand, generate turbulent jets with Reynolds numbers of $O(10^{4})$ and higher (Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014). Mucus and saliva that are expelled out of the nose and mouth can be stretched into ligaments and sheets, and eventually fragment into small droplets if the Weber number is large enough (Jain et al. Reference Jain, Prakash, Tomar and Ravikrishna2015). This breakup process probably contributes to the generation of large droplets that fall ballistically and contaminate nearby surfaces (Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014).

Wells’ simple but elegant analysis predicted that the critical size that differentiates large from small droplets is approximately $100~\unicode[STIX]{x03BC}\text{m}$ (Wells Reference Wells1934). Subsequent analysis has shown that typical temperature and humidity variations expand the critical size range from approximately $50$ to $150~\unicode[STIX]{x03BC}\text{m}$ (Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007). For the droplet transmission route, an important consideration is the horizontal distance travelled by the large droplets. Thus the 3–6 feet social distancing guidelines (CDC 2020b; WHO 2020) probably originate from Wells’ original work. However, studies indicate that, while this distance might be adequate for droplets expelled during breathing and coughing (Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007; Wei & Li Reference Wei and Li2015), large droplets expelled from sneezes may travel 20 feet or more (Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007; Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014). Studies also suggest that social distancing in indoor environments (Wong et al. Reference Wong, Lee, Tam, Lau, Yu, Lui, Chan, Li, Bresee and Sung2004) could be complicated by ventilation-system-induced air currents.

It has also been shown that the respiratory jet transforms into a turbulent cloud or puff (Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014). While large droplets are mostly not affected by the cloud dynamics, small and medium-sized droplets can be suspended in the turbulent cloud for a longer time by its circulatory flow, thereby extending the travel distance significantly (Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014). This also has important implications for transmission via indirect contact with contaminated surfaces, since SARS-CoV-2 is able to survive on many types of surfaces for hours (van Doremalen et al. Reference van Doremalen, Bushmaker, Morris, Holbrook, Gamble, Williamson, Tamin, Harcourt, Thornburg and Gerber2020). The turbulent cloud also moves upwards due to buoyancy (Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014), thereby enabling small droplets and droplet nuclei to reach heights where they can enter the ventilation system and accelerate airborne transmissions (see § 2.5). The notion of a critical droplet size that was introduced by Wells (Reference Wells1934) might need to be re-examined in the light of our rapidly evolving knowledge about these expiratory events (Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007; Bourouiba et al. Reference Bourouiba, Dehandschoewercker and Bush2014).

2.4 Droplet evaporation and droplet nuclei

Droplet evaporation plays a singularly important role in the eventual fate of a droplet (Wells Reference Wells1934). The rate of evaporation depends on the difference between the droplet surface saturation vapour pressure and the vapour pressure of the surrounding air, the latter being dependent on humidity. The evaporation rate also depends on the mass-diffusion coefficient, which is a strong function of surface-to-ambient temperature difference, as well as the relative velocity between the droplet and surrounding gas. Thus, Reynolds, Nusselt and Sherwood numbers for the droplets are just some of the non-dimensional parameters that determine this phenomenon (Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007). This dependence of evaporation rates on the ambient temperature and humidity has implications for the very important, and as yet unresolved, questions regarding seasonal and geographic variations in transmission rates (Tang Reference Tang2009; Ma et al. Reference Ma, Zhao, Liu, He, Wang, Fu, Yan, Niu, Zhou and Luo2020) as well as transmission in various indoor environments (Tang et al. Reference Tang, Li, Eames, Chan and Ridgway2006; Li et al. Reference Li, Leung, Tang, Yang, Chao, Lin, Lu, Nielsen, Niu and Qian2007).

Higher temperatures and lower relative humidities lead to larger evaporation rates that increase the critical droplet size (Wells Reference Wells1934; Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007). However, temperature changes are usually accompanied by changes in humidity, and the overall effect of environmental conditions on transmission rates has been difficult to ascertain. This is not only due to the fact that these factors modulate the relative importance of the droplet and airborne routes of transmission, but also because survivability of enveloped viruses such as SARS-CoV-2 seem to be linked to these factors in a complex, non-monotonic manner (Geller, Varbanov & Duval Reference Geller, Varbanov and Duval2012). Models that can combine droplet/aerosol fluid dynamics with virus microbiology and/or population dynamics could help unravel this complex effect of ambient conditions on transmission rates.

2.5 Airborne transmission

The airborne transmission route is associated with small droplets that are suspended and transported in air currents. Most of these droplets evaporate within a few seconds (Xie et al. Reference Xie, Li, Chwang, Ho and Seto2007) to form droplet nuclei, although the vapour-rich, buoyant turbulent expiratory jet can slow this evaporation process (Bourouiba Reference Bourouiba2020). The nuclei consist of virions and solid residue (Vejerano & Marr Reference Vejerano and Marr2018), but water may never be completely removed (Mezhericher, Levy & Borde Reference Mezhericher, Levy and Borde2010). These droplet nuclei are submicrometre to approximately $10~\unicode[STIX]{x03BC}\text{m}$ in size, and may remain suspended in the air for hours. Each droplet nucleus could contain multiple virions, and, given the approximately one hour viability half-life of the SARS-CoV-2 virus (van Doremalen et al. Reference van Doremalen, Bushmaker, Morris, Holbrook, Gamble, Williamson, Tamin, Harcourt, Thornburg and Gerber2020) and the fact that SARS-type infections in a host may potentially be caused by a single virus (Nicas, Nazaroff & Hubbard Reference Nicas, Nazaroff and Hubbard2005), droplet nuclei play a singularly important role in the transmission of COVID-19-type infections (Asadi et al. Reference Asadi, Bouvier, Wexler and Ristenpart2020). The evaporation process of virus-laden respiratory droplets and the composition of droplet nuclei require further analysis because these have implications for the viability and potency of the virus that is transported by these nuclei.

The transport of droplet nuclei over larger distances is primarily driven by ambient flows, and indoor environments such as homes, offices, malls, aircraft and public transport vehicles pose a particular challenge for disease transmission. The importance of ventilation in controlling airborne transmission of infections is well known (Tang et al. Reference Tang, Li, Eames, Chan and Ridgway2006; Li et al. Reference Li, Leung, Tang, Yang, Chao, Lin, Lu, Nielsen, Niu and Qian2007) and much of the recent work in this area has exploited the power of computational fluid dynamic (CFD) modelling (Thatiparti, Ghia & Mead Reference Thatiparti, Ghia and Mead2017; Yang et al. Reference Yang, Li, Yan and Tu2018; Yu, Mui & Wong Reference Yu, Mui and Wong2018). However, indoor spaces can have extremely complex flows, due not only to the presence of recirculatory flows driven by ventilation systems but also to anthropogenic thermally driven flow effects (Craven & Settles Reference Craven and Settles2006; Licina et al. Reference Licina, Pantelic, Melikov, Sekhar and Tham2014). COVID-19 transmission from asymptomatic hosts (Bai et al. Reference Bai, Yao, Wei, Tian, Jin, Chen and Wang2020; Ye et al. Reference Ye, Xu, Rong, Xu, Liu, Deng, Liu and Xu2020) makes it more critical than ever that we develop methods of analysis that provide better prediction of these effects.

4.1 Mucus property modification

The physical properties of the mucus play a key role in droplet formation within the respiratory tract. Transient modification of the physical properties of the mucus lining via material delivery to enhance mucus stability therefore provides a means for reducing infection rates. Fiegel et al. (Reference Fiegel, Clarke and Edwards2006) used isotonic saline to change the mucus lining properties via the induced ionic charge to reduce droplet formation, and Edwards et al. (Reference Edwards, Man, Brand, Katstra, Sommerer, Stone, Nardell and Scheuch2004) explored the use of surface-tension-enhancing inhalants to reduce droplet generation. These techniques involve complex multiphysics flow phenomena that could benefit from advanced experimental and computational techniques.

4.2 Fogging machines

Fogging machines provide an effective means for disinfecting large spaces, such as hospitals, nursing homes, grocery stores and airplanes. Fogging machines that rely on the dispersion of a fine mist of disinfectants in the air have proven their performance in the healthcare sector (Otter et al. Reference Otter, Yezli, Perl, Barbut and French2013) and the food industry (Oh et al. Reference Oh, Gray, Dougherty and Kang2005). Commercial fogging machines are also designed based on the same flow physics of aerosolization, and their droplet size is below $10~\unicode[STIX]{x03BC}\text{m}$ (Krishnan et al. Reference Krishnan, Fey, Stansfield, Landry, Nguy, Klassen and Robertson2012) in order to facilitate extended airborne duration. For this range of droplet sizes, it is likely that inertial effects are small, and the collision between these disinfectant aerosol droplets and virus-bearing droplet nuclei might be dominated by diffusion. It is unclear if the collision rate will be enhanced by the turbulence generated by heating, ventilation and air-conditioning systems. Given that fogging machines have been widely employed in particle image velocimetry (PIV), experiments would be particularly well poised to study these phenomena.

4.3 Hand washing

Transmission of infection from surfaces with virion-laden respiratory droplets usually occurs via hands (Nicas & Jones Reference Nicas and Jones2009), and hand washing with soap therefore remains the most effective strategy for mitigating this mode of transmission (Stock & Francis Reference Stock and Francis1940). Soap molecules have a polar ionic hydrophilic side and a non-polar hydrophobic side that bonds with oils and lipids. Hand washing therefore works by emulsifying the lipid content of the material adhering to the hand into the bulk fluid and convecting it away. For enveloped viruses such as SARS-CoV-2, soap molecules also dismantle the lipid envelope of the virus, thereby deactivating it (Kohn, Gitelman & Inbar Reference Kohn, Gitelman and Inbar1980). The detritus from this disintegration is then trapped by the soap molecules into micelles, which are washed away.

These molecular-level mechanisms are powered by macro-level flow phenomena associated with the movements of the hands. Amazingly, despite the $170+$ year history of hand washing in medical hygiene (Rotter Reference Rotter1997), we were unable to find a single published research article on the flow physics of hand washing. The relative movement of the hands generates complex shear-driven flows of the soapy water, which forms a foam-laden, multiphase emulsion. Soap bubbles, which trap micelles, segregate rapidly from the fluid phase, thereby further accelerating the removal process.

It is known that liquid foam exhibits elastic and plastic deformation under small and large stresses, respectively. With large enough deformation rates, the foam can rearrange its network and flow (Weaire & Hutzler Reference Weaire and Hutzler1999), which can be studied experimentally (Janiaud & Graner Reference Janiaud and Graner2005). Reynolds numbers for these soapy liquid layers could exceed $O(1000)$, suggesting that inertia, viscosity, surface tension and gravitational forces would all play an important role in this process. An improved understanding of hand-washing flow physics in the COVID-19 era could provide a science-based foundation for public guidelines/recommendations as well as new technologies that could improve the effectiveness of this practice.

4.4 Face masks

One issue that has generated significant controversy during the COVID-19 pandemic is the effectiveness of face masks (Dwyer & Aubrey Reference Dwyer and Aubrey2020; Elegant Reference Elegant2020; Feng et al. Reference Feng, Shen, Xia, Song, Fan and Cowling2020). Indeed, it is likely that the years ahead will see the use of face masks become a norm in our lives. Understanding the physics that underpins the effectiveness of face masks as a defence against airborne pathogens is, therefore, more important than ever.

Face masks provide ‘inward’ protection by filtering virus-laden aerosolized particles that would otherwise be inhaled by an uninfected person, and ‘outward’ protection by trapping virus-laden droplets expelled by an infected person (van der Sande, Teunis & Sabel Reference van der Sande, Teunis and Sabel2008). The effectiveness of a simple face mask such as the surgical, N95 or homemade cloth face mask is a function of the combined effect of the filtering properties of the face-mask material, the fit of the mask on the face and the related leaks from the perimeter of the face mask. Each of these features implicates complex flow phenomena, which are briefly addressed here.