Some questions on dispersion of human exhaled droplets in ventilation room: answers from numerical investigation

Abstract This study employs a numerical model to investigate the dispersion characteristics of human exhaled droplets in ventilation rooms. The numerical model is validated by two different experiments prior to the application for the studied cases. Some typical questions on studying dispersion of human exhaled droplets indoors are reviewed and numerical study using the normalized evaporation time and normalized gravitational sedimentation time was performed to obtain the answers. It was found that modeling the transient process from a droplet to a droplet nucleus due to evaporation can be neglected when the normalized evaporation time is <0.051. When the normalized gravitational sedimentation time is <0.005, the influence of ventilation rate could be neglected. However, the influence of ventilation pattern and initial exhaled velocity on the exhaled droplets dispersion is dominant as the airflow decides the droplets dispersion significantly. Besides, the influence of temperature and relative humidity on the dispersion of droplets can be neglected for the droplet with initial diameter <200 μm; while droplet nuclei size plays an important role only for the droplets with initial diameter within the range of 10 μm–100 μm.

Practical Implications

Dispersion of human exhaled droplets indoor is a key issue when evaluating human exposure to infectious droplets. Results from detailed numerical studies in this study reveal how the evaporation of droplets, ventilation rate, airflow pattern, initial exhaled velocity, and particle component decide the droplet dispersion indoor. The detailed analysis of these main influencing factors on droplet dispersion in ventilation rooms may help to guide (1) the selection of numerical approach, e.g., if the transient process from a droplet to a droplet nucleus due to evaporation should be incorporated to study droplet dispersion, and (2) the selection of ventilation system to minimize the spread of pathogen‐laden droplets in an indoor environment.     

Dispersion and settling characteristics of evaporating droplets in ventilated room

Movement and evaporation of small droplets in the room air are investigated in this paper through CFD simulations. A modified drift-flux model is presented with the droplet evaporation rate and the drift velocity expressed as simple algebra functions of droplet diameter, which is integrated in the transport equations of droplet number density and droplet bulk density. Evaporating droplets are treated as a continuum phase with one way coupling with the carrier phase, i.e. air. Our numerical simulations reveal that the distribution of the large evaporating droplets in the ventilated room air is characterized by a combination of the settling feature when droplets are first generated and released and the dispersion feature after the droplets are evaporated to be either very fine or become droplet nuclei. For droplets less than 50 μm in diameter, the dispersion feature is dominant in the test room that we simulated, while for droplets larger than 100 μm in diameter, the settling feature dominates. For evaporating droplets between these two sizes, the spatial distribution of droplets tends to be located at the lower part of the test room than that of small neutral aerosol particles. Within this size range, a lower initial position of the droplets in the room results in a higher deposition rate of the droplets on the floor.     

Short‐range airborne transmission of expiratory droplets between two people

The occurrence of close proximity infection for many respiratory diseases is often cited as evidence of large droplet and/or close contact transmission. We explored interpersonal exposure of exhaled droplets and droplet nuclei of two standing thermal manikins as affected by distance, humidity, ventilation, and breathing mode. Under the specific set of conditions studied, we found a substantial increase in airborne exposure to droplet nuclei exhaled by the source manikin when a susceptible manikin is within about 1.5 m of the source manikin, referred to as the proximity effect. The threshold distance of about 1.5 m distinguishes the two basic transmission processes of droplets and droplet nuclei, that is, short‐range modes and the long‐range airborne route. The short‐range modes include both the conventional large droplet route and the newly defined short‐range airborne transmission. We thus reveal that transmission occurring in close proximity to the source patient includes both droplet‐borne (large droplet) and short‐range airborne routes, in addition to the direct deposition of large droplets on other body surfaces. The mechanisms of the droplet‐borne and short‐range airborne routes are different; their effective control methods also differ. Neither the current droplet precautions nor dilution ventilation prevents short‐range airborne transmission, so new control methods are needed.     

The impact of indoor thermal stratification on the dispersion of human speech droplets

Exhaled jets from an infected person are found to be locked at a certain height when thermal stratification exists in rooms, causing a potential high risk of disease transmission. This work is focused on the theoretical analysis of the dynamic characteristics of human speech droplets and the residual droplet nuclei in both thermally uniform and stratified environments. Results show that most droplets generated from human speaking can totally evaporate or deposit to the ground within 1.5-2 m. For small droplets of < 80μm, thermal stratification shows a more significant impact on their residues. The lock-up height of the droplet nuclei is a function of droplet size and the temperature gradient, and within this lock-up layer, these droplet nuclei can travel a long distance, much more than 2m. For medium droplets of 80-180 μm, thermal stratification can weaken the evaporation and accelerate the deposition processes, equivalent to a higher relative humidity (RH). Accordingly, more droplets can deposit to the ground, reducing the exposure to large droplets in close proximity to the source. Large droplets of > 180μm show no dependence on stratification and RH. These findings can have implications for developing effective engineering methods to limit the spread of infectious disease.     

Movement and control of evaporating droplets released from an open surface tank in the push–pull ventilation system

Push–pull ventilation systems are effective local ventilation methods to control airborne contaminants generated in industrial buildings, among which droplets are typical. In this paper, the numerical simulations of water droplets released from an open surface tank into the push–pull flow field are carried out and the effects of ambient relative humidity and the pull-flow velocity on the ventilation system performance are discussed based on the droplet evaporation and movement. It was found that the movement and evaporation of droplets were closely related to the push–pull flow mechanism and the droplet initial diameter. When the control effect was good due to the presence of air closure in the flow field (pull-flow velocity ranging from 1.5 m/s to 3.0 m/s), droplets were unlikely to move away from the closure and the evaporation of droplets smaller than 40 μm was obvious. Whereas when the control effect was poor (pull-flow velocity equaling 1.0 m/s), large droplets still moved around the tank surface but small droplets were subject to dispersing, and in such a case droplets smaller than 60 μm evaporated obviously. Moreover, the effect of ambient relative humidity (ranging from 0 to 80%) on controlling droplets was rather limited and no more than ±6%. In addition, the system could save airflow rate and energy consumption by reducing the pull-flow velocity which was excessive originally in ventilation design. Finally, the paper put forward a new index to evaluate the control effect from another standpoint based on whether the droplets did harm to the environment.     

Evaporation and dispersion of respiratory droplets from coughing

Understanding how respiratory droplets become droplet nuclei and their dispersion is essential for understanding the mechanisms and control of disease transmission via droplet‐borne and airborne routes. A theoretical model was developed to estimate the size of droplet nuclei and their dispersion as a function of the ambient humidity and droplet composition. The model‐predicted dried droplet nuclei size was 32% of the original diameter, which agrees with the maximum residue size in the classic study by Duguid, 1946, Edinburg Med. J., 52 , 335 and the validation experiment in this study, but is smaller than the 50% size predicted by Nicas et al., 2005, J. Occup. Environ. Hyg., 2 , 143. The droplet nuclei size at a relative humidity of 90% (25°C) could be 30% larger than the size of the same droplet at a relative humidity of less than 67.3% (25°C). The trajectories of respiratory droplets in a cough jet are significantly affected by turbulence, which promotes the wide dispersion of droplets. We found that medium‐sized droplets (e.g., 60 μm) are more influenced by humidity than are smaller and larger droplets, while large droplets (≥100 μm), whose travel is less influenced by humidity, quickly settle out of the jet.     

Distribution of respiratory droplets in enclosed environments under different air distribution methods

The dispersion characteristics of respiratory droplets are important in controlling transmission of airborne diseases indoors. This study investigates the spatial concentration distribution and temporal evolution of exhaled and sneezed/coughed droplets within the range of 1.0 − 10.0μm in an office room with three air distribution methods, specifically mixing ventilation (MV), displacement ventilation (DV), and under-floor air distribution (UFAD). The diffusion, gravitational settling and deposition mechanism of particulate matter were accounted by using an Eulerian modeling approach with one-way coupling. The simulation results indicate that exhaled droplets up to 10μm in diameter from normal human respiration are uniformly distributed in MV. However, they become trapped in the breathing zone by thermal stratifications in DV and UFAD, resulting in a higher droplet concentration and an increased exposure risk to other room occupants. Sneezed/coughed droplets are more slowly diluted in DV/UFAD than in MV. Low air speed in the breathing zone in DV/UFAD can lead to prolonged human exposure to droplets in the breathing zone.     

Dispersion of exhaled droplet nuclei in a two-bed hospital ward with three different ventilation systems

Effective ventilation in general hospital wards is important for controlling the airborne transmission of infectious respiratory diseases. Experiments have been carried out to increase our understanding of the interaction of the breathing flows of two individuals in a full-scale experimental hospital ward with three ventilation systems, i.e. mixing, downward and displacement ventilation. Two life-size breathing thermal manikins were used to simulate a source patient and a receiving patient. The exhalation jet from a bed-lying manikin was visualized using smoke. N2O was used as tracer gas to simulate the droplet nuclei exhaled by patients; and the spatial distribution of its concentrations was measured. Our experimental results show that for both mixing and downward ventilation, the exhaled jet penetrates a short distance and is diluted quickly by ventilation air. The exhaled droplet nuclei are well mixed in the ward. Bed distance does not affect the personal exposure of the receiving patient. For displacement ventilation, the exhaled jet can penetrate a long distance. A high concentration layer of exhaled droplet nuclei because of thermal stratification locking has also been observed with displacement ventilation. This work is useful for identifying an appropriate ventilation method that can remove droplet nuclei more effectively and minimize the risk of cross-infections in a hospital ward environment. PRACTICAL IMPLICATIONS: As one of the major potential sources for infectious droplet nuclei in a hospital environment, exhalation flows of an infected patient can interact with the respiratory activities of other close individuals and with the room ventilation systems. Our latest results provide information on the penetration of exhalation jets into the ambient environment in different ventilation systems. This work is useful in identifying an appropriate and effective ventilation method for removing droplet nuclei more effectively, and thus minimizing the risk of cross-infections in hospital wards with multiple beds.     

A review on the applied techniques of exhaled airflow and droplets characterization

In the last two decades, multidisciplinary research teams worked on developing a comprehensive understanding of the transmission mechanisms of airborne diseases. This article reviews the experimental studies on the characterization of the exhaled airflow and the droplets, comparing the measured parameters, the advantages, and the limitations of each technique. To characterize the airflow field, the global flow-field techniques—high-speed photography, schlieren photography, and PIV—are applied to visualize the shape and propagation of the exhaled airflow and its interaction with the ambient air, while the pointwise measurements provide quantitative measurements of the velocity, flow rate, humidity and temperature at a single point in the flow field. For the exhaled droplets, intrusive techniques are used to characterize the size distribution and concentration of the droplets' dry residues while non-intrusive techniques can measure the droplet size and velocity at different locations in the flow field. The evolution of droplets' size and velocity away from the source has not yet been thoroughly experimentally investigated. Besides, there is a lack of information about the temperature and humidity fields composed by the interaction of the exhaled airflow and the ambient air.     

Transport of expiratory droplets in an aircraft cabin

The droplets exhaled by an index patient with infectious disease such as influenza or tuberculosis may be the carriers of contagious agents. Indoor environments such as the airliner cabins may be susceptible to infection from such airborne contagious agents. The present investigation computed the transport of the droplets exhaled by the index patient seated in the middle of a seven-row, twin-aisle, fully occupied cabin using the CFD simulations. The droplets exhaled were from a single cough, a single breath, and a 15-s talk of the index patient. The expiratory droplets were tracked by using Lagrangian method, and their evaporation was modeled. It was found that the bulk airflow pattern in the cabin played the most important role on the droplet transport. The droplets were contained in the row before, at, and after the index patient within 30 s and dispersed uniformly to all the seven rows in 4 minutes. The total airborne droplet fraction reduced to 48, 32, 20, and 12% after they entered the cabin for 1, 2, 3, and 4 min, respectively, because of the ventilation from the environmental control system. PRACTICAL IMPLICATIONS: It is critical to predict the risk of airborne infection to take appropriate measures to control and mitigate the risk. Most of the studies in past either assume a homogenous distribution of contaminants or use steady-state conditions. The present study instead provides information on the transient movement of the droplets exhaled by an index passenger in an aircraft cabin. These droplets may contain active contagious agents and can be potent enough to cause infection. The findings can be used by medical professionals to estimate the spatial and temporal distribution of risk of infection to various passengers in the cabin.     

Quantifying the size‐resolved dynamics of indoor bioaerosol transport and control

Understanding the bioaerosol dynamics of droplets and droplet nuclei emitted during respiratory activities is important for understanding how infectious diseases are transmitted and potentially controlled. To this end, we conducted experiments to quantify the size‐resolved dynamics of indoor bioaerosol transport and control in an unoccupied apartment unit operating under four different HVAC particle filtration conditions. Two model organisms (Escherichia coli K12 and bacteriophage T4) were aerosolized under alternating low and high flow rates to roughly represent constant breathing and periodic coughing. Size‐resolved aerosol sampling and settle plate swabbing were conducted in multiple locations. Samples were analyzed by DNA extraction and quantitative polymerase chain reaction (qPCR). DNA from both organisms was detected during all test conditions in all air samples up to 7 m away from the source, but decreased in magnitude with the distance from the source. A greater fraction of T4 DNA was recovered from the aerosol size fractions smaller than 1 μm than E. coli K12 at all air sampling locations. Higher efficiency HVAC filtration also reduced the amount of DNA recovered in air samples and on settle plates located 3‐7 m from the source.     

Modeling the evaporation and dispersion of airborne sputum droplets expelled from a human cough

This study contributes a new model to simulate the evaporation and dispersion of sputum droplets from human coughs or sneezes. It is the first time different chemical components have been included in order to estimate the transport of sputum or similar biological droplets. This modified model demonstrates the ability to describe real-world phenomena that the widely used single droplet model lacks. Evaporation and dispersion of airborne sputum droplets originating from a human cough are simulated using this model combined with an initially buoyant turbulent jet. Constituents of sputum droplets such as NaCl, amino acids, carbohydrates, and lipids are included. Effects of these chemical components on evaporation rate, velocity, and temperature of droplets are investigated in detail. The results obtained for sputum droplets will provide a perspective of what conditions the viruses within a droplet might face upon being ejected from the mouth during a cough. Finally, computational fluid dynamics (CFD) and probability density function (PDF) techniques were used to complement the new model with a simulation of a cough jet and the dynamics of droplet nuclei in confined spaces. Numerical results indicate that a 10 microns sputum droplet will evaporate to become a droplet nucleus (3.5 microns) in 0.55 s at 0.8 or 80% RH, in 0.3 s at 0.5 or 50% RH, and in 0.25 s at 0.2 or 20% RH. The droplet temperature decreases rapidly from human body temperature to room temperature, which may affect the viability of any carried virus.     

Effects of Fine Water Mist on a Confined Blast

A computational, multi-phase, model has been developed to study the interactions between water droplets and radial expansion of a gas cloud in a spherical chamber. Initial conditions for the gas cloud are specified based on chemical equilibrium calculations for the detonation of a high explosive (RDX). Mono-dispersed water droplets are injected at uniform concentration into the chamber prior to the expansion. A Lagrangian model is used to track the breakup of the parent drops near the shock front to form child drops, which are extremely small. The Navier–Stokes solutions show that the child droplets accumulate near the shock front and evaporate at 100 times higher rate than the parent droplets. Latent heat absorption is the dominant mechanism followed by the sensible heat absorption by the water vapor (and droplets), and momentum absorption from the high velocity gases by the child droplets. The simulations also show that the water vapor formed by the evaporation increases the gas density at the shock front. The increased density and reduced gas temperature (cooling) have opposite effects on the pressure at the shock front. This leads to only a modest suppression in the pressure. At realistic droplet concentrations (0.08 kg droplets/m³ of air), the water mist is shown to evaporate completely in a short time (2.42 ms) prior to shock reflection at the chamber wall mainly due to the breakup at the shock front. High concentrations of mist may be desirable, but are difficult to achieve in practice at the total flooding conditions.     

Development and evaluation of two new droplet evaporation schemes for fire dynamics simulations

The evaporation of sprinkler droplets is an important phenomenon in fire simulations both for heat removal from the gas and for heat removal from surfaces. In this paper, we address the problems of potential numerical instability and super-saturation that may occur in explicit time integration of the droplet equations. Two novel numerical approaches are developed and evaluated. The first is based on an analytical solution that relaxes the cell composition and temperature toward the equilibrium values. The second method is an implicit solution to the droplet equations. The two approaches are implemented in the Fire Dynamics Simulator (FDS) and verified and validated using both single droplet and practical sprinkler calculations. Ultimately, the implicit approach is deemed the most cost effective for practical fire simulations.     

Simulation of water mist suppression of small scale methanol liquid pool fires

The focus of this paper is on numerical modeling of methanol liquid pool fires and the suppression of these fires using water mist. A mathematical model is first developed to describe the evaporation and burning of liquid methanol. The complete set of unsteady, compressible Navier–Stokes equations are solved along with an Eulerian sectional water mist model. Heat transfer into the liquid pool and the metal container through conduction, convection and radiation are modeled by solving a modified form of the energy equation. Clausius–Clapeyron relationships are invoked to model the evaporation rate of a two-dimensional pool of pure liquid methanol.The interaction of water mist with pulsating fires stabilized above a liquid methanol pool and steady fires stabilized by a strong co-flowing air jet are simulated. Time-dependent heat release/absorption profiles indicate the location where the water droplets evaporate and absorb energy. The relative contribution of the various suppression mechanisms such as oxygen dilution, radiation and thermal cooling is investigated. Parametric studies are performed to determine the effect of mist density, injection velocity and droplet diameter on entrainment and suppression of pool fires. These results are reported in terms of reduction in peak temperature, effect on burning rate and changes in overall heat release rate. Numerical simulations indicate that small droplet diameters exhibit smaller characteristic time for decrease of relative velocity with respect to the gas phase, and therefore entrain more rapidly into the diffusion flame than larger droplet. Hence for the co-flow injection case, smaller diameter droplets produce maximum flame suppression for a fixed amount of water mist.     

Numerical study of the lock-up phenomenon of human exhaled droplets under a displacement ventilated room

This paper adopts an Eulerian-Lagrangian approach to investigate the lock-up phenomenon (or trap phenomenon) of human exhaled droplets in a typical office room under displacement ventilation (DV). A particle-source-in-cell (PSI-C) scheme is used to correlate the concentration with the Lagrangian particle trajectories in computational cells. Respiratory droplets with sizes of 0.8 μm, 5 μm and 16 μm are released from a numerical thermal manikin (NTM). The influence factors including indoor temperature gradient, heat source configuration and exhalation modes are studied. It is found that large temperature gradient would result in trap phenomenon of small exhaled droplets (smaller than 5 μm). The intensive heat source near the NTM could help to transport the small droplets to the upper zone and decrease the concentration level in the trapped zone. Both nose-exhaled and mouth-exhaled small droplets would be trapped at the breathing height when temperature gradient is sufficiently high. However, the trap height of the droplets from mouth is a little bit higher. Because of large gravitational force, it is difficult for the thermal plume to carry 16 μm respiratory droplets to the upper zone.     

Direct or indirect exposure of exhaled contaminants in stratified environments using an integral model of an expiratory jet

The risk of cross‐infection is high when the susceptible persons are exposed to the pathogen‐laden droplets or droplet nuclei exhaled by infectors. This study proposes a jet integral model to predict the dispersion of exhaled contaminants, evaluating the exposure risk and determining a threshold distance to identify the direct and indirect exposures in both thermally uniform and stratified environments. The results show that the maximum concentration of contaminants exhaled by a bed‐lying infector clearly decreases in a short distance (<1.8 m) in a uniform environment, while it maintains high values in a long distance in a stratified environment. The lock‐up phenomenon largely weakens the decay of the concentration. The direct exposure of the receiver is determined primarily by the impact scope of the exhaled airflow, while the indirect exposure is mainly related to the ventilation rate and air distribution in the room. In particular, the distance of direct exposure is the longest (approximately 2 m) when the receiver's breathing height is at the lock‐up layer in a stratified environment. Our study could be useful for developing effective prevention measures to control cross‐infection in the initial stage of design of indoor layouts and ventilation systems.     

Role of air distribution in SARS transmission during the largest nosocomial outbreak in Hong Kong

Severe acute respiratory syndrome (SARS) is primarily transmitted by bio-aerosol droplets or direct personal contacts. This paper presents a detailed study of environmental evidence of possible airborne transmission in a hospital ward during the largest nosocomial SARS outbreak in Hong Kong in March 2003. Retrospective on-site inspections and measurements of the ventilation design and air distribution system were carried out on July 17, 2003. Limited on-site measurements of bio-aerosol dispersion were also carried out on July 22. Computational fluid dynamics simulations were performed to analyze the bio-aerosol dispersion in the hospital ward. We attempted to predict the air distribution during the time of measurement in July 2003 and the time of exposure in March 2003. The predicted bio-aerosol concentration distribution in the ward seemed to agree fairly well with the spatial infection pattern of SARS cases. Possible improvement to air distribution in the hospital ward was also considered. PRACTICAL IMPLICATIONS: Our study revealed the need for the development of improved ventilation and air-conditioning systems in an isolation ward or a general hospital ward for infectious respiratory diseases. The outbreak in Ward 8A, which was in a general hospital and could house nearly 40 patients, demonstrated the cross-infection risks of respiratory infectious diseases in hospitals if a potential highly infectious patient was not identified and isolated. Our example simulation, which extended the SARS Busters' design for an isolation room to Ward 8A, demonstrated that there was room for improvement to minimize cross-infection in large general hospital wards.     

Inhalation of expiratory droplets in aircraft cabins

Airliner cabins have high occupant density and long exposure time, so the risk of airborne infection transmission could be high if one or more passengers are infected with an airborne infectious disease. The droplets exhaled by an infected passenger may contain infectious agents. This study developed a method to predict the amount of expiratory droplets inhaled by the passengers in an airliner cabin for any flight duration. The spatial and temporal distribution of expiratory droplets for the first 3 min after the exhalation from the index passenger was obtained using the computational fluid dynamics simulations. The perfectly mixed model was used for beyond 3 min after the exhalation. For multiple exhalations, the droplet concentration in a zone can be obtained by adding the droplet concentrations for all the exhalations until the current time with a time shift via the superposition method. These methods were used to determine the amount of droplets inhaled by the susceptible passengers over a 4-h flight under three common scenarios. The method, if coupled with information on the viability and the amount of infectious agent in the droplet, can aid in evaluating the infection risk. PRACTICAL IMPLICATIONS: The distribution of the infectious agents contained in the expiratory droplets of an infected occupant in an indoor environment is transient and non-uniform. The risk of infection can thus vary with time and space. The investigations developed methods to predict the spatial and temporal distribution of expiratory droplets, and the inhalation of these droplets in an aircraft cabin. The methods can be used in other indoor environments to assess the relative risk of infection in different zones, and suitable measures to control the spread of infection can be adopted. Appropriate treatment can be implemented for the zone identified as high-risk zones.     

Study of Water Droplet Behavior in Hot Air Layer in Fire Extinguishment

Evaporation of water droplets while traveling in hot air layer will be studied. The air-droplet system is analyzed by solving the mass, momentum and energy conservation equations for each phase. The droplet phase is described by the Lagrangian approach. Two conditions of air flow in the smoke layer are assumed. Firstly, as commonly used in modeling fire suppression by water spray, the smoke layer is assumed to be quiescent. Secondly, both gas cooling effect and air entrainment in the water spray cone are included. The properties of gas phase related to evaporation are specific heat capacity, thermal conductivity and dynamic viscosity. All these are evaluated by the one-third rule. The Runge–Kutta algorithm is used to solve the ordinary differential equation group for the droplet motion with heat transfer. Droplet positions, velocities, temperatures and diameters are calculated while traveling in the hot air reservoir. The effects of air temperature, water vapor mass fraction, thickness of hot air reservoir, and initial diameter on the droplet behavior are analyzed. The quantity of heat absorbed by a single droplet is calculated. Results are then calculated for a water spray by taking it has many droplets. The cooling effect of the water vapor produced is considered. Water spray consisting of small droplets should absorb more heat while acting on the hot air layer. The ratio of the heat for vaporization to the total heat absorbed by water can go up to 0.9 when all the droplets are evaporated. Limited experimental data are selected to verify the mathematical model. Predicted results are useful for studying fire suppression by water mist system.