Numerical study of cough droplets dispersion in indoor and quiescent environment: influence of droplet size and air humidity
DOI:
https://doi.org/10.18265/2447-9187a2025id8833Palavras-chave:
modelo Euleriano-Lagrangiano, dispersão de gotas respiratórias; , dinâmica de fluidos computacional;, acoplamento de fase;Resumo
A transmissão de doenças respiratórias infecciosas (DRIs) tem sido amplamente estudada em vários campos, usando diferentes métodos. O surgimento do SARS-CoV-2 (COVID-19) no final de 2019 aumentou a importância dessa pesquisa. Embora muitos estudos quantitativos tenham examinado como o acoplamento de fase, o tamanho da gota e a umidade relativa afetam o comportamento das gotas respiratórias, este estudo analisa especificamente como esses fatores influenciam as distâncias de dispersão horizontal e vertical. Ele também avalia o impacto do acoplamento de fase entre as fases contínua e discreta. Uma abordagem Euleriana-
Lagrangiana foi usada para simular a dispersão de gotas em um ambiente interno calmo sob diferentes condições de umidade. Os resultados mostram que tanto o tamanho da gota quanto a umidade relativa afetam significativamente as distâncias de dispersão. Notavelmente, gotas menores (1 μm de diâmetro) evaporaram quase instantaneamente após serem liberadas. Gotas medindo 10 μm percorreram distâncias horizontais e verticais mais curtas sob baixa umidade em comparação com ambientes de alta umidade, onde evaporaram rapidamente. Gotas maiores (100 μm) formaram nuvens de partículas mais compactas e percorreram distâncias totais mais curtas. Entre os tamanhos testados, gotículas intermediárias (50 μm) criaram as nuvens mais dispersas, resultando nas maiores distâncias de viagem. A 80% de umidade relativa, essas gotículas atingiram uma distância horizontal máxima de cerca de 1,40 metro, a
maior distância observada neste estudo, constituindo uma condição crítica potencial para a transmissão de DRIs pelo ar. Gotículas maiores tendem a contribuir mais para a contaminação de superfícies porque caem rapidamente, enquanto as gotículas menores representam menos risco de transmissão pelo ar devido à sua rápida evaporação. Os efeitos do acoplamento de fase na dispersão horizontal e vertical foram mínimos. Em conclusão, este estudo aumenta a compreensão dos fatores ambientais que influenciam a transmissão de DRIs em ambientes fechados e com ar parado. Com base nessas descobertas, recomenda-se que os ambientes internos mantenham baixa umidade relativa e espaçamento adequado entre os ocupantes para reduzir a propagação de gotículas produzidas pela tosse.
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ALIABADI, A. A.; ROGAK, S. N.; GREEN, S. I.; BARTLETT, K. H. CFD simulation of human coughs and sneezes: a study in droplet dispersion, heat, and mass transfer. In: ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2010, Vancouver. Proceedings [...]. Vancouver: ASME, 2010. p. 1051-1060. DOI: https://doi.org/10.1115/IMECE2010-37331.
ANSYS. ANSYS meshing user’s guide. Canonsburg: ANSYS, 2012.
AULER, A. C.; CÁSSARO, F. A. M.; SILVA, V. O.; PIRES, L. F. Evidence that high temperatures and intermediate relative humidity might favor the spread of COVID-1 in tropical climate: a case study for the most affected Brazilian cities. Science of the Total Environment, v. 729, 139090, 2020. DOI: https://doi.org/10.1016/j.scitotenv.2020.139090.
AYTOGAN, H; AYINTAP, E.; YILMAZ, N. Ö. Detection of coronavirus disease 2019 viral material on environmental surfaces of an ophthalmology examination room. JAMA Ophthalmology, v. 138, n. 9, p. 990-993, 2020. DOI: http://dx.doi.org/10.1001/jamaophthalmol.2020.3154.
AYUBA, N.; JUSTI, G. H.; LOPES, G. C. Numerical study of coughing in indoor environments: comparison between tetrahedral and hexahedral meshes. Computational and Applied Mathematics, v. 44, 222, 2025. DOI: https://doi.org/10.1007/s40314-025-03184-0.
AYUBA, N.; LOPES, G. C. Investigation of the influence of turbulence models on cough droplet evaporation: comparing (SST) k-Ω, k-ε, and Reynolds stress (RSM) turbulence models. In: BRAZILIAN TECHNOLOGY SYMPOSIUM, 7., 2021, Campinas. Proceedings […]. Cham: Springer International Publishing, 2023. p. 151-162. (Smart Innovation, Systems and Technologies, v. 207). DOI: https://doi.org/10.1007/978-3-031-04435-9_15.
BAHRAMIAN, A.; MOHAMMADI, M.; AHMADI, G. Effect of indoor temperature on the velocity fields and airborne transmission of sneeze droplets: an experimental study and transient CFD modeling. Science of The Total Environment, v. 858, Part 2, 159444, 2023. DOI: https://doi.org/10.1016/j.scitotenv.2022.159444.
BAZANT, M. Z.; BUSH, J. W. M. A guideline to limit indoor airborne transmission of COVID-19. Proceedings of the National Academy of Sciences, v. 118, n. 17, e2018995118, 2021. DOI: https://doi.org/10.1073/pnas.2018995118.
BHATTACHARJEE, S.; TOM, J.; CARBONE, M.; BRAGG, A. D. Investigating the parametric dependence of the impact of two-way coupling on inertial particle settling in turbulence. Journal of Fluid Mechanics, v. 987, A17, 2024. DOI: http://doi.org/10.1017/jfm.2024.322.
BRANCHE, A. R.; FALSEY, A. R. Respiratory syncytial virus infection in older adults: an under-recognized problem. Drugs & Aging, v. 32, p. 261-269, 2015. DOI: https://doi.org/10.1007/s40266-015-0258-9.
CAO, Q.; LIU, M.; LI, X.; LIN, C.-H.; WEI, D.; JI, S.; ZHANG, T.; CHEN, Q. Influencing factors in the simulation of airflow and particle transportation in aircraft cabins by CFD. Building and Environment, v. 207, 108413, 2022. DOI: https://doi.org/10.1016/j.buildenv.2021.108413.
CENGEL, Y. A.; BOLES, M. A. Thermodynamics: an Engineering approach. 8. ed. New York: McGraw-Hill, 2015.
CHAO, C. Y. H.; WAN, M. P.; MORAWSKA, L.; JOHNSON, G. R.; RISTOVSKI, Z. D.; HARGREAVES, M.; MENGERSEN, K.; CORBETT, S.; LI, Y.;
XIE, X.; KATOSHEVSKI, D. Characterization of expiration air jets and droplet size distributions immediately at the mouth opening. Journal of Aerosol Science, v. 40, n. 2, p. 122-133, 2009. DOI: https://doi.org/10.1016/j.jaerosci.2008.10.003.
CHILLÓN, S. A.; FERNANDEZ-GAMIZ, U.; ZULUETA, E.; UGARTE-ANERO, A.; BLANCO, J. M. Numerical performance of CO2 accumulation and droplet dispersion from a cough inside a hospital lift under different ventilation strategies. Scientific Reports, v. 14, 6843, 2024. DOI: https://doi.org/10.1038/s41598-024-57425-z.
COLE, E. C.; COOK, C. E. Characterization of infectious aerosols in health care facilities: an aid to effective engineering controls and preventive strategies. American Journal of Infection Control, v. 26, n. 4, p. 453-464, 1998. DOI: https://doi.org/10.1016/S0196-6553(98)70046-X.
D’ALESSANDRO, V.; FALONE, M.; GIAMMICHELE, L.; RICCI, R. Eulerian- Lagrangian modeling of cough droplets irradiated by ultraviolet-C light in relation to SARS-CoV-2 transmission. Physics of Fluids, v. 33, n. 3, 031905, 2021. DOI: https://doi.org/10.1063/5.0039224.
DBOUK, T.; DRIKAKIS, D. On coughing and airborne droplet transmission to humans. Physics of Fluids, v. 32, n. 5, 053310, 2020. DOI: https://doi.org/10.1063/5.0011960.
DHAND, R.; LI, J. Coughs and sneezes: their role in transmission of respiratory viral infections, including SARS-CoV-2. American Journal of Respiratory and Critical Care Medicine, v. 202, n. 5, p. 651-659, 2020. DOI: https://doi.org/10.1164/rccm.202004-1263PP.
ELGHANNAY, H. A.; TAFTI, D. K. Revised partial coupling in fluid-particulate systems. The Journal of Computational Multiphase Flows, v. 10, n. 4, p. 215-227, 2018. DOI: https://doi.org/10.1177/1757482X18791885.
FENG, Y.; LI, D.; MARCHISIO, D.; VANNI, M.; BUFFO, A. A computational fluid dynamics: population balance equation approach for evaporating cough droplets transport. International Journal of Multiphase Flow, v. 165, 104500, 2023. DOI: https://doi.org/10.1016/j.ijmultiphaseflow.2023.104500.
GE, H.; ZHAO, P.; CHOI, S.; DENG, T.; FENG, Y.; CUI, X. Effects of face shield on an emitter during a cough process: a large-eddy simulation study. Science of The Total Environment, v. 831, 154856, 2022. DOI: https://doi.org/10.1016/j.
scitotenv.2022.154856.
GRALTON, J.; TOVEY, E.; MCLAWS, M.-L.; RAWLINSON, W. D. The role of particle size in aerosolised pathogen transmission: a review. Journal of Infection, v. 62, n. 1, p. 1-13, 2011. DOI: https://doi.org/10.1016/j.jinf.2010.11.010.
GUERRA, V. G.; ACHILES, A. E.; BÉTTEGA, R. Influence of droplet size distribution on liquid dispersion in a Venturi scrubber: experimental measurements and CFD simulation. Industrial & Engineering Chemistry Research, v. 56, n. 8, p. 2177-2187, 2017.
DOI: https://doi.org/10.1021/acs.iecr.6b03761.
GUPTA, J. K.; LIN, C.-H.; CHEN, Q. Flow dynamics and characterization of a cough. Indoor Air – International Journal of Indoor Environment and Health, v. 19, n. 6, p. 517-525, 2009. DOI: https://doi.org/10.1111/j.1600-0668.2009.00619.x.
HAN, Z. Y.; WENG, W. G.; HUANG, Q. Y. Characterizations of particle size distribution of the droplets exhaled by sneeze. Journal of the Royal Society Interface, v. 10, n. 88, 20130560, 2013. DOI: https://doi.org/10.1098/rsif.2013.0560.
HINDS, W. C.; ZHU, Y. Aerosol technology: properties, behavior, and measurement of airborne particles. 3. ed. Hoboken, NJ: Wiley, 2022.
HONKINEN, M.; LAHTI, E.; ÖSTERBACK, R.; RUUSKANEN, O.; WARIS, M. Viruses and bacteria in sputum samples of children with communityacquired pneumonia. Clinical Microbiology and Infection, v. 18, n. 3, p. 300-307, 2012. DOI: https://doi.org/10.1111/j.1469-0691.2011.03603.x.
HÖPPE, P. Temperatures of expired air under varying climatic conditions. International Journal of Biometeorology, v. 25, p. 127-132, 1981. DOI: https://doi.org/10.1007/BF02184460.
KAMPF, G.; TODT, D.; PFAENDER, S.; STEINMANN, E. Persistence of coronaviruses on inanimate surfaces and their inactivation with biocidal agents. Journal of Hospital Infection, v. 104, n. 3, p. 246-251, 2020. DOI: https://doi.org/10.1016/j.jhin.2020.01.022.
KUCHARSKI, A. J.; KLEPAC, P.; CONLAN, A. J.; KISSLER, S. M.; TANG, M. L.; FRY, H.; GOG, J. R.; EDMUNDS, W. H. Effectiveness of isolation, testing, contact tracing, and physical distancing on reducing transmission of SARS-CoV-2 in different settings: a mathematical modelling study. The Lancet Infectious Diseases, v. 20, n. 10, p. 1151-1160, 2020. DOI: https://doi.org/10.1016/s1473-3099(20)30457-6.
LANCMANOVÁ, A.; BODNÁR, T. Numerical simulations of human respiratory flows: a review. Discover Applied Sciences, v. 7, 242, 2025. DOI: https://doi.org/10.1007/s42452-025-06617-x.
LEE, J.; YOO, D.; RYU, S.; HAM, S.; LEE, K.; YEO, M.; MIN, K.; YOON, C. Quantity, size distribution, and characteristics of cough-generated aerosol produced by patients with an upper respiratory tract infection. Aerosol and Air Quality Research, v. 19, n. 4,
p. 840-853, 2019. DOI: https://doi.org/10.4209/aaqr.2018.01.0031.
LI, H.; LEONG, F. Y.; XU, G.; GE, Z.; KANG, C. W.; LIM, K. H. Dispersion of evaporating cough droplets in tropical outdoor environment. Physics of Fluids, v. 32, n. 11, 113301, 2020. DOI: https://doi.org/10.1063/5.0026360.
LI, X.; SHANG, Y.; YAN, Y.; YANG, L.; TU, J. Modelling of evaporation of cough droplets in inhomogeneous humidity fields using the multi-component Eulerian-Lagrangian approach. Building and Environment, v. 128, p. 68-76, 2018. DOI: https://doi.org/10.1016/j.buildenv.2017.11.025.
MAGAR, A. M.; JOSHI, M.; RAJAGOPAL, P. S.; KHAN, A.; RAO, M. M.; SAPRA, B. K. CFD simulation of the airborne transmission of COVID-19 vectors emitted during respiratory mechanisms: revisiting the concept of safe distance. ACS Omega, v. 6, n. 26, p. 16876-16889, 2021. DOI: https://doi.org/10.1021/acsomega.1c01489.
MENTER, F. R.; KUNTZ, M.; LANGTRY, R. Ten years of industrial experience with the SST turbulence model. Turbulence, Heat and Mass Transfer, v. 4, n. 1, p. 625-632, 2003. Available at: https://www.researchgate.net/profile/Florian-Menter/publication/228742295_Ten_years_of_industrial_experience_with_the_SST_turbulence_model/links/0046353c6330b1c0a4000000/Ten-years-of-industrial-experience-with-the-SST-turbulence-model.pdf. Accessed on: 26 Jan. 2025.
MISHRA, N. P.; DAS, S. S.; YADAV, S.; KHAN, W.; AFZAL, M.; ALARIFI, A.; KENAWY, E.-R.; ANSARI, M. T.; HASNAIN, M. S.; NAYAK, A. K. Global impacts of pre- and post-COVID-19 pandemic: focus on socio-economic consequences. Sensors International, v. 1, 100042, 2020. DOI: https://doi.org/10.1016/j.sintl.2020.100042.
MORAWSKA, L. Droplet fate in indoor environments, or can we prevent the spread of infection? Indoor Air – International Journal of Indoor Environment and Health, v. 16, p. 335-347, 2006. DOI: https://doi.org/10.1111/j.1600-0668.2006.00432.x.
NICAS, M.; NAZAROFF, W. W.; HUBBARD, A. Toward understanding the risk of secondary airborne infection: emission of respirable pathogens. Journal of Occupational and Environmental Hygiene, v. 2, n. 3, p. 143-154, 2005. DOI: https://doi.org/10.1080/15459620590918466.
NINGTHOUJAM, R. COVID 19 can spread through breathing, talking, study estimates. Current Medicine Research and Practice, v. 10, n. 3, p. 132-133, 2020. DOI: https://doi.org/10.1016/j.cmrp.2020.05.003.
NORVIHOHO, L. K.; YIN, J.; ZHOU, Z.-F.; HAN, J.; CHEN, B.; FAN, L.-H.; LICHTFOUSE, E. Mechanisms controlling the transport and evaporation of human exhaled respiratory droplets containing the severe acute respiratory syndrome coronavirus: a review. Environmental Chemistry Letters, v. 21, p. 1701-1727, 2023. DOI: https://doi.org/10.1007/s10311-023-01579-1.
OH, W.; OOKA, R.; KIKUMOTO, H.; HAN, M. Numerical modeling of cough airflow: Establishment of spatial-temporal experimental dataset and CFD simulation method. Building and Environment, v. 207, Part b, 108531, 2022. DOI: https://doi.org/10.1016/j.
buildenv.2021.108531.
PAN, Y.; ZHANG, H.; NIU, Z.; AN, Y.; CHEN, C. Boundary conditions for exhaled airflow from a cough with a surgical or N95 mask. Indoor Air, v. 32, n. 8, e13088, 2022. DOI: https://doi.org/10.1111/ina.13088.
PATANKAR, S. V. Numerical heat transfer and fluid flow. Boca Raton: CRC Press, 1980. DOI: https://doi.org/10.1201/9781482234213.
PERELLA, P.; TABARRA, M.; HATAYSAL, E.; POURNASR, A.; RENFREW, I. Minimising exposure to droplet and aerosolised pathogens: a computational fluid dynamics study. British Journal of Anaesthesia, v. 126, n. 2, p. 544-549, 2021. DOI: https://doi.org/10.1016/j.bja.2020.09.047.
POKHAREL, A.; AKKERMAN, V.; CELIK, I. B.; AXELBAUM, R. L.; ISLAS, A.; YANG, Z. Impact of particle loading and phase coupling on gas–solid flow dynamics: a case study of a two-phase, gas-solid flow in an annular pipe. Physics of Fluids, v. 33, n. 7, 073308, 2021. DOI: https://doi.org/10.1063/5.0054906.
REDROW, J.; MAO, S.; CELIK, I.; POSADA, J. A.; FENG, Z.-G. Modeling the evaporation and dispersion of airborne sputum droplets expelled from a human cough. Building and Environment, v. 46, n. 10, p. 2042-2051, 2011.DOI: https://doi.org/10.1016/j.buildenv.2011.04.011.
ROACHE, P. J. Verification and validation in computational science and engineering. Albuquerque: Hermosa, 1998.
SANTANA, H. S.; SILVA, A. G. P.; LOPES, M. G. M.; RODRIGUES, A. C.; TARANTO, O. P.; SILVA JUNIOR, J. L. Computational methodology for the development of microdevices and microreactors with ANSYS CFX. MethodsX, v. 7, 100765, 2020. DOI: https://doi.org/10.1016/j.mex.2019.12.006.
SCHARFMAN, B. E.; TECHET, A. H.; BUSH, J. W. M.; BOUROUIBA, L. Visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets. Experiments in Fluids, v. 57, 24, 2016. DOI: https://doi.org/10.1007/s00348-015-2078-4.
SCHILLER, L.; NAUMANN, A. A drag coefficient correlation. Zeitschrift des Vereins Deutscher Ingenieure, v. 77, p. 318-320, 1935.
SHYY, W.; THAKUR, S.; WRIGHT, J. Second-order upwind and central difference schemes for recirculating flow computation. AIAA Journal, v. 30, n. 4, p. 923-932, 1992. DOI: https://doi.org/10.2514/3.11010.
SIRIGNANO, W. A. Fluid dynamics and transport of droplets and sprays. Cambridge, UK: Cambridge University Press, 2009. DOI: https://doi.org/10.1017/CBO9780511529566.
SONNTAG, D.; FOKEN, T.; VÖMEL, H.; HELLMUTH, O. Humidity sensors. In: FOKEN, T. (ed.). Springer handbook of atmospheric
measurements. Cham: Springer International Publishing, 2021. p. 209-241. DOI: https://doi.org/10.1007/978-3-030-52171-4_8.
TAKII, A.; YAMAKAWA, M.; KITAGAWA, A.; WATAMURA, T.; CHUNG, Y. M.; KIM, M. Numerical model for cough‐generated droplet dispersion on moving escalator with multiple passengers. Indoor Air, v. 32, n. 11, e13131, 2022. DOI: https://doi.org/10.1111/ina.13131.
THAKUR, N.; MURTHY, H. Simulation study of droplet formation in inkjet printing using ANSYS FLUENT. Journal of Physics: Conference Series, v. 2161, 012026, 2022. DOI: https://doi.org/10.1088/1742-6596/2161/1/012026.
TOM, J.; CARBONE, M.; BRAGG, A. D. How does two-way coupling modify particle settling and the role of multiscale preferential sweeping? Journal of Fluid Mechanics, v. 947, A7, 2022. DOI: https://doi.org/10.1017/jfm.2022.615.
TRIVEDI, S.; GKANTONAS, S.; MESQUITA, L. C. C.; IAVARONE, S.; OLIVEIRA, P. M.; MASTORAKOS, E. Estimates of the stochasticity of
droplet dispersion by a cough. Physics of Fluids, v. 33, n. 11, 115130, 2021. DOI: https://doi.org/10.1063/5.0070528.
VAN DER REIJDEN, W. A.; VEERMAN, E. C. I.; AMERONGEN, A. V. N. Shear rate dependent viscoelastic behavior of human glandular salivas. Biorheology, v. 30, n. 2, p. 141-152, 1993. DOI: https://doi.org/10.3233/BIR-1993-30205.
VEJERANO, E. P.; MARR, L. C. Physico-chemical characteristics of evaporating respiratory fluid droplets. Journal of The Royal Society Interface, v. 15, n. 139, 20170939, 2018. DOI: https://doi.org/10.1098/rsif.2017.0939.
VERSTEEG, H. K.; MALALASEKERA, W. An introduction to computational fluid dynamics: The Finite Volume Method. 2nd ed. Harlow: Pearson Education, 2007.
WAI, K.-M.; YUAN, C.; LAI, A.; YU, P. K. N. Relationship between pedestrian-level outdoor thermal comfort and building morphology in a high-density city. Science of the Total Environment, v. 708, 134516, 2020. DOI: https://doi.org/10.1016/j.scitotenv.2019.134516.
WANG, F.; ZENG, Y.; YAN, H. CFD-DEM study of impacts of the porous distributor medium on fluidization characteristics of a 2D-fluidized bed. Particuology, v. 87, p. 54-73, 2024. DOI: https://doi.org/10.1016/j.partic.2023.07.017.
WEBER, T. P.; STILIANAKIS, N. I. Inactivation of influenza A viruses in the environment and modes of transmission: a critical review. Journal of Infection, v. 57, n. 5, p. 361-373, 2008. DOI: https://doi.org/10.1016/j.jinf.2008.08.013.
WEI, J.; LI, Y. Enhanced spread of expiratory droplets by turbulence in a cough jet. Building and Environment, v. 93, Part 2, p. 86-96, 2015. DOI: https://doi.org/10.1016/j.buildenv.2015.06.018.
WEXLER, A; BROMBACHER, W. G. Methods of Measuring Humidity and Testing Hygrometers. Washington, D.C.: National Bureau of Standards, 1951. (NBS Circular, 512). Available at: https://www.govinfo.gov/content/pkg/GOVPUB-C13-b587954bfd21b3fddc15dcdfd4256f25/pdf/GOVPUB-C13-b587954bfd21b3fddc15dcdfd4256f25.pdf. Accessed on: 25 Feb. 2026.
WHO – WORLD HEALTH ORGANIZATION. COVID-19 Cases, World. WHO COVID-19 dashboard. 2025. Available at: https://data.who.int/dashboards/covid19/cases?n=o.Accessed on: 2 June 2025.
WHO – WORLD HEALTH ORGANIZATION. Tuberculosis control and research strategies for the 1990s: memorandum from a WHO meeting. Bulletin of the World Health Organization (WHO), v. 70, n. 1, p. 17-21, 1992. Available at: https://europepmc.org/article/pmc/2393335. Accessed on: 2 June 2025.
WÖLFEL, R.; CORMAN, V. M.; GUGGEMOS, W.; SEILMAIER, M.; ZANGE, S.; MÜLLER, M. A.; NIEMEYER, D.; JONES, T. C.; VOLLMAR, P.;
ROTHE, C.; HOELSCHER, M.; BLEICKER, T.; BRÜNINK, S.; SCHNEIDER, J.; EHMANN, R.; ZWIRGLMAIER, K.; DROSTEN, C.; WENDTNER, C. Virological assessment of hospitalized patients with COVID-2019. Nature, v. 581, p. 465-469, 2020. DOI: https://doi.org/10.1038/s41586-020-2196-x.
WU, J.; HE, F.; XIE, Z.; FU, M.; LI, Y.; WANG, J.; PAN, Y.; WENG, W. Review on respiratory infectious disease transmission mechanism: effects of human movement and facemask use. Emergency Management Science and Technology, v. 4, e004, 2024. DOI: https://doi.org/10.48130/emst-0024-0006.
YAN, Y.; LI, X.; TU, J. Thermal effect of human body on cough droplets evaporation and dispersion in an enclosed space. Building and Environment, v. 148, p. 96-106, 2019. DOI: https://doi.org/10.1016/j.buildenv.2018.10.039.
YANG, S.; LEE, G. W. M.; CHEN, C.-M.; WU, C.-C.; YU, K.-P. The size and concentration of droplets generated by coughing in human subjects. Journal of Aerosol Medicine and Pulmonary Drug Delivery, v. 20, n. 4, p. 484-494, 2007. DOI: https://doi.org/10.1089/jam.2007.0610.
ZAHARI, N. M.; ZAWAWI, M. H.; SIDEK, L. M.; MOHAMAD, D.; ITAM, Z.; RAMLI, M. Z.; SYAMSIR, A.; ABAS, A.; RASHID, M. Introduction of discrete phase model (DPM) in fluid flow: a review. AIP Conference Proceedings, v. 2030, n. 1, 020234, 2018. DOI: https://doi.org/10.1063/1.5066875.
ZHAO, Y.; CHENG, Y.; WU, C.; DING, Y.; JIN, Y. Eulerian-Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer. Particuology, v. 8, n. 1, p. 44-50, 2010. DOI: https://doi.org/10.1016/j.partic.2009.11.002.
ZODO, G.; KONKA, H.; STEVANOVIC, S.; SCHLUTER, J. Simulation of the transition of respiratory droplets to aerosol states: Implications for pathogen spread. Physics of Fluids, v. 37, n. 1, 015188, 2025. DOI: https://doi.org/10.1063/5.0246654.
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