The ambient conditions surrounding liquid droplets determine their growth or shrinkage. However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated by its surroundings and the puff itself has not yet been fully quantified. From the view of airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies are critical. Here we employ direct numerical simulations (DNS) of a turbulent respiratory vapour puff and account for the mass and temperature exchange with respiratory droplets and aerosols. In particular, we investigate how droplets respond to different ambient temperatures and relative humidity (RH) by tracking their Lagrangian statistics. We reveal and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical view by William F. Wells (1934). Indeed, cold and humid environments diminish the ability of air to hold water vapour, thus causing the respiratory vapour puff to super-saturate. Consequently, the super-saturated vapour field drives the growth of droplets that are caught and transported within the humid puff. To analytically predict the likelihood for droplet growth, we propose a model for the axial RH based on the assumption of a quasi-stationary jet. Our model correctly predicts super-saturated RH conditions and is in good quantitative agreement with our DNS. Our results culminate in a temperature-RH map that can be employed as an indicator for droplet growth or shrinkage.
To quantify the fate of respiratory droplets under different ambient relative humidities, direct numerical simulations of a typical respiratory event are performed. We found that, because small droplets (with initial diameter of 10um) are swept by turbulent eddies in the expelled humid puff, their lifetime gets extended by a factor of more than 30 times as compared to what is suggested by the classical picture by William F. Wells, for 50% relative humidity. With increasing ambient relative humidity the extension of the lifetimes of the small droplets further increases and goes up to around 150…
Pathogens contained in airborne respiratory droplets have been seen to remain infectious for periods of time that depend on the ambient temperature and humidity. In particular, regarding the humidity, the empirically least favorable conditions for the survival of viral pathogens are found at intermediate humidities. However, the precise physico-chemical mechanisms that generate such least-favorable conditions are not understood yet. In this work, we analyze the evaporation dynamics of respiratory-like droplets in air, semi-levitating them on superhydrophobic substrates with minimal solid-liqui…
A new mathematical analysis of exhaled respiratory droplet dynamics and settling distances in the vicinity of vortical environments is presented. Recent experimental and theoretical studies suggest that vortical flow structures may enhance the settling distances of exhaled respiratory droplets beyond the two-meter distancing rule recommended by health authorities lately. We propose a mathematical framework to study the underlying physical mechanism responsible for the entrapment and subsequently delayed settling times of evaporating droplets and solid particles. A dipolar vortex is considered …
One of the many unresolved questions that revolves around the Covid-19 pandemic is whether local outbreaks can depend on ambient conditions like temperature and relative humidity. In this paper, we develop a model that tries to explain and describe the temperature and relative humidity sensitivity of respiratory droplets and their possible connection in determining viral outbreaks. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism - the final equations of which are similar to the well-known SIR model. The advantage of modeling the…
Coronavirus disease 2019 (COVID-19) has become a global pandemic infectious respiratory disease with high mortality and infectiousness. This paper investigates respiratory droplet transmission, which is critical to understanding, modeling and controlling epidemics. In the present work, we implemented flow visualization, particle image velocimetry (PIV) and particle shadow tracking velocimetry (PSTV) to measure the velocity of the airflow and droplets involved in coughing and then constructed a physical model considering the evaporation effect to predict the motion of droplets under different w…
We formulate a model for the dynamics of respiratory droplets and use it to study their airborne lifetime in turbulent air representative of indoor settings. This lifetime is a common metric to assess the risk of respiratory transmission of infectious diseases, with longer lifetime correlating with higher risk. We consider a simple momentum balance to calculate the droplets spread, accounting for their size evolution as they undergo vaporization via mass and energy balances. The model shows how an increase in relative humidity leads to higher droplet settling velocity, which shortens the lifet…
In the unfortunate event of current ongoing pandemic COVID-19, where vaccination development is still at the initial stage, several preventive control measures such as social distancing, hand-hygiene, and personal protective equipment have been recommended by health professionals and organizations. Among them, the safe wearing of facemasks has played a vital role in reducing the likelihood and severity of infectious respiratory disease transmission. The reported research in facemasks has covered many of their material types, fabrication techniques, mechanism characterization, and application a…
Face covering, commonly known as facemask, is considered to be one of the most effective Personal Protective Equipments (PPEs) to reduce transmissions of pathogens through respiratory droplets - both large drops and liquid aerosol particles. Face masks, not only inhibit the expulsion of such respiratory droplets from the user, but also protects the user from inhaling pathogen-laden potentially harmful droplets or their dried nuclei. While the efficacies of various dry face masks have been explored in the recent past, a comprehensive investigation of a wet mask is lacking. Yet, users wear masks…
A comprehensive analysis of the effect of ventilation and climatic conditions on covid-19 transmission through respiratory droplet transport via both airborne and fomite mode inside an elevator
The efficacy of face masks, neck gaiters and face shields are predicted and contrasted. In particular, a Lattice Spring Model of a neck gaiter serves as the input to a Lattice Boltzmann simulation. The Lattice Boltzmann method is used to capture the fluid dynamics both through and around various face coverings. The evaporation and transport of respiratory droplets is simulated in this flow field, and the efficacy of the different face coverings at stopping the spread of respiratory droplets are elucidated and contrasted. In agreement with recent experimental studies, we predict that neck gaite…
We predict and analyze the drying time of respiratory droplets from a COVID-19 infected subject, which is a crucial time to infect another subject. The drying of the droplet is predicted by diffusion-limited evaporation model for a sessile droplet placed on a partially-wetted surface with a pinned contact line. The variation of droplet volume, contact angle, ambient temperature, and humidity are considered. We analyze the chances of the survival of the viruses present in the droplet, based on the lifetime of the droplets in several conditions, and find that the chances of survival of the virus…
We isolate a nano-colloidal droplet of surrogate mucosalivary fluid to gain fundamental insights into the infectivity of air borne nuclei during the Covid-19 pandemic. Evaporation experiments are performed with salt-water solutions seeded with a viral load of inactive nanoparticles in an acoustic levitator. We seek to emulate the drying, flow and precipitation dynamics of such air borne mucosalivary droplets. Observations with the surrogate fluid are validated by similar experiments with actual samples from a healthy subject. A unique feature emerges with regards to the final crystallite dimen…
An analysis of the projectile motion in stagnant air is presented for an evaporating respiratory micro-droplet which has been ejected from the mouth as an isolated droplet. It is assumed that the air resistance is a nonlinear function of the droplet's velocity and that the rate of decrease of the droplet's external surface area depends only on the relative humidity and the ambient temperature. The droplet's initial content is considered to be 98 wt% water, 1 wt% salt and 1 wt% protein. The change of the average density of the droplet due to water evaporation is determined, up to the instant wh…
Leidenfrost droplets: The roles of ambient humidity and internal droplet circulation
University of Twente（特温特大学）；Max-Planck Center Twente for Complex Fluid Dynamics（马普中心特温特复杂流体力学）；J.M. Burgers Centre for Fluid Dynamics（J.M. 伯格斯流体力学中心）；University of Houston（休斯顿大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Max-Planck Institute for Dynamics and Self-Organization（马普动力学与自组织研究所）
This study deals with the estimation of the trajectory of coronavirus COVID-19 adhering to respiratory droplets projected horizontally, considering the geographical altitude. The size of viruses and respiratory droplets is the factor that determines the trajectory of the microparticles in a viscous medium such as air; For this purpose, a graphical comparison of the diameters and masses of the microparticles produced in respiratory activity has been made. The estimation of the vertical movement of the microparticles through the air is based on Stokes' Law, it was determined that respiratory dro…
The utility of wearing simple cloth face masks is analyzed using computational fluid dynamics simulations. We simulate the aerodynamic flow through the mask and the spatial spread of droplet ejecta resulting from respiratory events such as coughing or sneezing. Without a mask, a turbulent jet forms, and droplets with a broad size distribution are ejected. Large droplets (greater than about 125 μm in diameter) fall to the ground within about 2 m, while turbulent clouds transport a mist of small aerosolized droplets over significant distances (~ 5 m), consistent with reported experimental findin…
Respiratory droplets exhaled during speaking, coughing or sneezing have been responsible for the spread of the ongoing Covid-19 pandemic. The droplet dynamics depend on the surrounding air velocity, temperature and relative humidity. Droplets evaporate to form aerosols which contain the disease spreading virus. In a confined space like an elevator, the risk of transmission becomes higher when there is an infected person inside the elevator with other individuals. In this work, a numerical study is carried out in a 3D domain resembling an elevator using OpenFoam. Different modes of air circulat…
Spreading of respiratory diseases, such as COVID-19, from contaminated surfaces is dependent on the drying time of the deposited droplets containing the virus. The evaporation rate depends on environmental conditions, such as ambient temperature and relative humidity and physical properties (e.g., droplet volume, contact angle and composition). The respiratory droplets contain salt (NaCl), protein (mucin), and surfactant (dipalmitoylphosphatidylcholine) in addition to water, which are expected to influence the evaporation in a big way. A diffusion-based theoretical model for estimating the dry…
A model that predicts the outcome of collisions between droplets and particles in terms of the distribution of the droplet volume post-collision is lacking, in contrast to the case for droplet-droplet interactions. Taking existing models that successfully predict the outcomes (coalescence, stretching or reflexive separation) and post-separation characteristics (sizes, numbers and velocities of the resulting droplets) of droplet-droplet collisions and adapting them to take into account an inextensible, non-deformable particle with varying wettability characteristics, a new model is presented fo…
The COVID-19 pandemic has inspired several studies on the fluid dynamics of respiratory events. Here, we propose a computational approach in which respiratory droplets are coarse-grained into an Eulerian liquid field advected by the fluid streamlines. A direct numerical simulation is carried out for a moist cough using a closure model for space-time dependence of the evaporation time scale. Estimates of the Stokes number are provided, for the initial droplet size of $10 μ$m, which are found to be <<1 thereby justifying the neglect of droplet inertia. Several of the important features of the mo…
The dispersion of respiratory saliva droplets by indoor wake structures may enhance the transmission of various infectious diseases, as the wake spreads virus-laden droplets across the room. Thus, this study analyses the interaction between vortical wake structures and exhaled multi-component saliva droplets. A self-propelling analytically-described dipolar vortex is chosen as a model wake flow, passing through a cloud of micron-sized evaporating saliva droplets. The droplets' spatial location, velocity, diameter, and temperature are traced and coupled to their local flow field. For the first …
Human respiratory events, such as coughing and sneezing, play an important role in the host-to-host airborne transmission of diseases. Thus, there has been a substantial effort in understanding these processes: various analytical or numerical models have been developed to describe them, but their validity has not been fully assessed due to the difficulty of a direct comparison with real human exhalations. In this study, we report a unique comparison between datasets that have both detailed measurements of a real human cough using spirometer and particle tracking velocimetry, and direct numeric…
The effect of evaporation on droplet sedimentation times is crucial for estimating the risk of infection from virus-containing airborne droplets. For droplet radii in the range 100 nm < R < 60 μm, evaporation can be described in the stagnant-flow approximation and is diffusion limited. Analytical equations are presented for the droplet evaporation rate, the time-dependent droplet size and the sedimentation time, including the significant effect of evaporation cooling. Evaporation makes the time for large droplets to sediment much longer and thus significantly increases the viral air load. Usin…
The spread of COVID19 through droplets ejected by infected individuals during sneezing and coughing has been considered as a matter of key concern. Therefore, a quantitative understanding of the propagation of droplets containing virus assumes immense importance. Here we investigate the evolution of droplets in space and time under varying external conditions of temperature, humidity and wind flow by using laws of statistical and fluid mechanics. The effects of drag, diffusion and the gravity on droplets of different sizes and ejection velocities have been considered during their motion in the…
The COVID19 infection is known to disseminate through droplets ejected by infected individuals during coughing, sneezing, speaking and breathing. The spread of the infection and hence its menace depend on how the virus-loaded droplets evolve in space and time with changing environmental conditions. In view of this, we investigate the evolution of the droplets within the purview of the Brownian motion of the evaporating droplets in the air with varying weather conditions under the action of gravity. We track the movement of the droplets till either they gravitationally settle on the ground or e…
The ongoing respiratory COVID-19 pandemic has heavily impacted the social and private lives of the majority of the global population. This infection is primarily transmitted via virus-laden fluid particles (i.e., droplets and aerosols) that are formed in the respiratory tract of infected individuals and expelled from the mouth in the course of breathing, talking, coughing, and sneezing. To mitigate the risk of virus transmission, in many places of the world, the public has been asked or even obliged to use face covers. It is plausible that in the years ahead we will see the use of face masks, …
Combined effects of evaporation, sedimentation and solute crystallization on the dynamics of aerosol size distributions on multiple length and time scales
