Physics in the COVID-19 World

                                                                                                                                              Jenna Borovinsky

Physics in the COVID-19 World: Reducing chances of COVID-19 infection by a cough cloud in a closed space

https://aip.scitation.org/doi/am-pdf/10.1063/5.0029186

Background:

The authors of this research article are Amit Agrawal and Rajneesh Bhardwaj. Amit Agrawal is a professor in the department of mechanical engineering at the Indian Institute of Technology in Bombay Powai, Mumbai 400076, India. He received his Ph.D. at the University of Delaware in 2002 and received his bachelors in technology at IIT Kanpur in 1996. His co-worker, Rajneesh Bhardwaj is an associate professor in the department of mechanical engineering at the Indian Institute of Technology in Bombay Powai, Mumbai 400076, India. He received his Ph.D. at Columbia University in 2009 and was a postdoctoral fellow at Johns Hopkins University from 2010-12. 

Blog:

While it is wide-spread knowledge that coughing does spread harmful respiratory droplets in an open air of space, and is spread airborne, it is not known the volume of air at which this bacteria spreads. This is particularly important for COVID-19, as this harmful virus is the cause of a worldwide pandemic in which a vaccine has yet to be finalized for. Without a vaccine, a limitation in how far it spreads is the only way to slow the spread of this virus. Further, the impacts on ventilation systems within closed spaces has been studied due to this, and the exact volume of air in which these respiratory droplets spread would be very beneficial in order to know what type of ventilation should be used for a certain sized space. Professor Agrawal and Professor Bhardwaj sought to study the volume of air a cough by someone infected with coronavirus spreads in a closed space, and how much a mask can limit this spread. They also looked at the temperature and relative humidity of the cloud emitted when coughing, which aids in the establishment of a ventilation system to adequately limit the spread. Using literature equations, they derived an equation:

This equation shows that the air’s volume contained in the cloud is only dependent on the spread rate and distance travelled by the cloud, and is independent of the cough’s initial volume and velocity. Utilizing this equation in their study they found that volume in the cloud ultimately increases quadratically with distance. In terms of finding the temperature of the water droplets they used the conservation of energy equation and the specific humidity and then derived the relative humidity form that equation, which resulted in:

In the equation Pa is the partial pressure of air and Pg is the partial pressure of water vapour in saturated mixture at the given temperature. Utilizing this equation they found that the cloud’s temperature lowers monotonically from the exit temperature at the origin to the room temperature. This aids in elucidating how the droplets distribute within the cough cloud. Further, in order to compare the lateral velocity to the front velocity they derived this equation: 

This equation compares lateral velocity as a function of radial coordinate. The data shows that the lateral velocity was not only smaller than the front velocity, but also shows a difference in time. They then compared the time at which the cloud from a cough with someone infected with coronavirus spreads with no mask, a surgical mask and an N95 mask, using the equation they derived:

Utilizing this equation they found that the first 5-8 s after the cough occurs is crucial to stop droplets in air that individuals breathe in. Further, the volume of air infected with virus particles is around 23 times more than that ejected by coughing during this time period. The presence of a mask, even more so with an N-93 mask, significantly decreases this volume and consequently, dramatically lowers the risk of the infection to the others in the room. 

Overall, I found this research article to be very interesting in terms of how prevalent it is to today and how this data will really aid the pandemic we are facing. The research further proves how important a mask is in stopping the spread of COVID-19. It also shows how a mask still does not fully stop the spread of COVID-19 particles emphasizing the need for social distancing along with wearing a mask. The exact quantification in the spread of respiratory droplets will be very beneficial to create suitable ventilation systems. This article shows the power of Physics in having the ability to really slow the spread of the coronavirus. 

Works Cited

Agrawal, Amit, and Rajneesh Bhardwaj. “Reducing Chances of COVID-19 Infection by a 

Cough Cloud in a Closed Space.” Physics of Fluids, vol. 32, no. 10, 2020, p. 101704., 

doi:10.1063/5.0029186.