Safe Distance of Viruses - Quantitative Analysis the Trajectory of Pathogen Containing Droplets in Respiratory Airways

Student: Hanwen Miao
Table: MED6
Experimentation location: Reseach Institution, Home
Regulated Research (Form 1c): No
Project continuation (Form 7): Yes

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[1] B.E.Scharfman, A.H.Techet, J.W.M.Bush, and L.Bourouiba. “Visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets.” Exp Fluids (2016) 57:24. dois:10.1007/s00348-015-2078-4.

[2] Yidan Shang, Yao Tao, Jingliang Dong, Fajiang He, and Jiyuan Tu (9 January 2021). “Deposition features of inhaled viral droplets may lead to rapid secondary transmission of COVID-19”. Journal of Aerosol Science, 154(2021) 105745.

[3] Page J, Hinshaw D, McKay B (26 February 2021). “In Hunt for Covid-19 Origin, Patient Zero Points to Second Wuhan Market – The man with the first confirmed infection of the new coronavirus told the WHO team that his parents had shopped there”. The Wall Street Journal.

[4] Centers for Disease Control and Prevention (CDC). “Symptoms of COVID-19”, 22 February 2021.

[5] Centers for Disease Control and Prevention (CDC). “Frequent Asked Questions”, 21 October 2021. Coronavirus (COVID-19) frequently asked questions | CDC.

[6] Betsch, C., Korn, L., et al. (2020). “Social and behavioral consequences of mask policies during the COVID-19 pandemic”. Proceedings of the National Academy of Sciences, 117(36), pp. 21851–21853.

[7] World Health Organization. “Coronavirus disease (COVID-19): How is it transmitted?". Retrieved 6 December 2020.

[8] Centers for Disease Control and Prevention (CDC). “Coronavirus Disease 2019 (COVID-19)”. Retrieved 6 December 2020.

[9] Centers for Disease Control and Prevention (CDC). “Coronavirus Disease 2019 (COVID-19)”. 25 October 2020.

[10] New Youth Anesthesia Daily. “People’s Daily: Can Wearing Facemask prevents COVID-19”, 22 January 2020.

[11] National Aeronautics and Space Administration (NASA). “What is Drag”, Retrieved 6 December 2020.

[12] Symon, Keith R. Mechanics (3rd Edition), December 1971. Boston, MA: Addison-Wesley. ISBN 978-0-201-07392-8.

[13] Hirt, C., Claessens, S., Fecher, T., Kuhn, M.; Pail, R., Rexer, M (2013). “New ultrahighresolution picture of Earth's gravity field”. Geophysical Research Letters, 40 (16), pp. 4279–4283. doi:10.1002/grl.50838.

[14] Ball, Philip (2008). "Water: Water—an enduring mystery". Nature, 452 (7185), pp. 291–2. doi:10.1038/452291a.

[15] Our World Data. “Human Height”, May 2019.

[16] Detailed description of both methods is written in the “Appending” section.

[17] The codes responsible for generating these plots are recorded in the “Appending” section.

[18] Cunningham, E., “On the velocity of steady fall of spherical particles through fluid medium,” Proc. Roy. Soc. A 83(1910)357. doi:10.1098/rspa.1910.0024

[19] NCBI. Benjamin J. Delgado, Tushar Bajaj. “Physiology, Lung Capacity”, July 26, 2021.

[20] Cameron Tropea, Alexander Yarin, John Foss, eds. Springer Handbook of Experimental Fluid Mechanics, 9 October 2007. New York: Springer.

[21] Specific model and classification of different parts of the respiratory system can be found in the “Attachment” section.

[22] NCBI. Joshua J. Hurley, Jeremy L. Hensley, “Physiology, Airway Resistance”, 22 September 2021.

[23] CDC. “How to Protect Yourself & Others”, 13 August 2021.

[24] Hamed Mortazavi, Hamidreza Mortazavy Beni, Fatemeh Aghaei, Seyed Hossein Sajadiana (11 November 2020). “SARS-CoV-2 droplet deposition path and its effects on the human upper airway in the oral inhalation”. Computer Methods and Programs in Biomedicine 200(2021) 105843.


Additional Project Information

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Research Plan:


Droplets of mucosalivary ejecta emitted by sneezing or coughing are major carriers of numerous types of bacterial and viral diseases. This study develops anumerical model to estimate the spreading distance of inhalable droplets (1–50 µm) in the air, the inhalability of these droplets, and the trajectory and the velocity of these droplets in human respiratory airways. It assesses, in particular, the inhalability of droplets with diameters of 1µm, 5µm, 10 µm, and 50 µm and estimates their transmission velocities. Data utilized in the study are derived from previous studies, e.g., the paper by Scharfman et al. (on the visualization of sneeze ejecta) and the paper by Shang et al. (on the deposition features of inhaled ejecta drops). These data are used to set the parameters for this study’s predictive model.


Questions and Answers

1. What was the major objective of your project and what was your plan to achieve it? 

       a. Was that goal the result of any specific situation, experience, or problem you encountered?  


My goal is to calculate the safe distance for viruses (including COVID-19) that use sneeze ejecta droplets as carriers. While conducting this study, one question had special significance: how many different factors should be considered in building the model (some are very important, but some might not be significant)? Many possible factors come to mind, for example, the viscosity of sneeze ejecta, the air drag acting on the particle, and the change in particle size due to evaporation. But are all these factors equally significant? It is important to select only the most relevant factors and to weight them appropriately – lest the model be overly complicated and difficult to solve or altogether non-predictive and inaccurate.


       b. Were you trying to solve a problem, answer a question, or test a hypothesis?


I am trying to answer the following question: in infectious environments, what is the minimal distance people should maintain from one other in order to avoid infectious spread under a non-masked situation?



2. What were the major tasks you had to perform in order to complete your project?

       a. For teams, describe what each member worked on.


I worked alone on this study, gathering data from previous studies to calculate the initial velocity of sneeze/cough droplet ejecta, generating a mathematical and computational model of droplet transmission trajectories, estimating the inhalability of ejected particles, and, by calculating their Stoke’s number, determining whether such particles are able to enter deep enough into respiratory airways to pose an infection threat. If I had had access to human subjects and to the requisite laboratory resources, I would have gathered live data on the initial velocities of sneeze/cough ejecta directly and not relied on the less accurate borrowed data I used (which were generated by robots designed to mimic human sneezing).



3. What is new or novel about your project?

       a. Is there some aspect of your project's objective, or how you achieved it that you haven't done before?

       b. Is your project's objective, or the way you implemented it, different from anything you have seen?


My study combined mathematical modeling and computer simulation techniques to estimate the trajectories of sneeze ejecta. Such a combination is largely novel in this area of research. In addition, my study not only calculated the safe distance but also analyzed the impact of droplet radius on both droplet inhalability and Stoke’s number – two dimensions that determine how deeply particles can enter the lungs of a person breathing them in. In this way, I was able to assess the relative threat that different types of pathogen-containing sneeze ejecta pose. Similar assessments have only seldom appeared in previous studies. Finally, my study is generally applicable to all types of viruses, since it focuses on the role of droplets in transmitting any viruses, not on specific viruses themselves. This approach, too, is novel.


       c. If you believe your work to be unique in some way, what research have you done to confirm that it is?


I have read relevant peer-reviewed papers. Few of the studies I read involved computer-simulating the sneeze ejecta transmission process, and most prior studies focus on one type of specific virus or bacterial pathogen only. Also, few prior studies assessed the relative threat of the viruses they considered with reference to the very important parameter known as Stoke’s number of inhalability.


4. What was the most challenging part of completing your project?

      a. What problems did you encounter, and how did you overcome them?


When I began my study, I focused on the size of viruses themselves (as many other studies in this field do). This greatly limited the potential significance of my work.  Initially I only considered COVID 19 virus. Therefore, initial research was only narrowly applicable. In order for the research to be more generally applicable, I need to consider viruses of any potential size. After considering this size problem, I started over, shifting the focus of my model-designing work to the droplets that contain pathogens, thus ensuring that the results of my study can be applied to almost every type of virus or bacterium. In addition, as a high school student I was not able to access an advanced biochemical laboratory to conduct my research. Thus, I could not gather data through direct experimentation; instead, I relied on secondary data drawn from previous studies. This impacted the accuracy of my results. Finally, when I constructed my mathematical model of ejecta transmission, I did not take evaporation into consideration, since I initially thought it was not a significant factor. I was mistaken. Evaporation, in fact, reduces the size of ejected particles over short time spans; it is, thus, a very important parameter to consider. My initial failure to do this also negatively impacted my results. I went on to solve this problem, however, designing a computer simulation of the entire process of transmission which factored in the effects of evaporation. The results I obtained after making this adjustment matched well with the findings of other researchers.


      b. What did you learn from overcoming these problems?


By solving these problems, I learned to think creatively, to pivot my work as needed, and to make effective use of prior research. I learned to recognize my own faulty reasoning and to change my approach – for example, shifting the focus of my study from virus size to ejecta droplet size, and, after failing to do so initially, factoring in the effect of evaporation.  I also applied novel methods in my study (such as the inclusion of computer simulation).



5. If you were going to do this project again, are there any things you would you do differently the next time?


If I am going to do this study again, I would add more consider more factors under a much more verifying background. The first factor that I would additionally consider is to valuate the approximate amount of pathogen-containing droplets needed to be inhaled in order to generate diseases. Another potential future development is that I can investigate the situation of those people wearing masks, which is a more accurate simulation of the reality.



6. Did working on this project give you any ideas for other projects? 


Doing this project inspired my work on another completely different school project (which I am doing as part of my school’s research period). This project studies the relationship between music and emotion. Many of the challenges I dealt with on my sneeze ejecta project, I am also encountering on this project. For instance, my sneeze ejecta project made me think long and hard about how complex my model needed to be. If I made it too simple, it would be less accurate. For example, if I ignored the effect of drag force of air acting on ejected particles, my resulting safe-distance calculation would have been absurd: about two football fields in length. Yet, it would have been infeasible (and unnecessary) to try modeling all possible factors. Learning how to handle this sort of complexity was key to the success of my sneeze ejecta project. The same is true of my music project, which also requires careful consideration of which factors are or not important for me to model.



7. How did COVID-19 affect the completion of your project?


The COVID-19 epidemic was the worst of times; it was also the best of times. It was partly because of the pandemic that I was not able to include an experimental component in my research (which would have enabled me to produce first-hand data). However, it was also COVID-19 that generated my interest in the problem I studied. Seeing the virus spread through the world and have such a devastating impact on so many people’s lives inspired me to try to help. I would say, therefore, that I was trapped and troubled by the problems of the COVID era, but that I also benefited from the inspiration it gave me. I know I will carry this inspiration into my future career in research.