Mathematical models of Physical distancing
Respiratory droplets travel between eight to 13 feet before they evaporate or escape, without wind and depending on the ambient condition, according to Indian researchers who suggest that physical distancing greater than six feet may be essential to avoid COVID-19 transmission. The researchers, including those from the Indian Institute of Science (IISc), Bengaluru, Karnataka, noted that it is well established that the SARS-CoV-2 virus that causes COVID-19 disease is transmitted via respiratory droplets that infected people eject when they cough, sneeze or talk.
- The team developed a mathematical model for the early phases of a COVID-19-like pandemic using the aerodynamics and evaporation characteristics of respiratory droplets.
- The research, published in the journal Physics of Fluids, modelled the pandemic dynamics with a reaction mechanism, wherein each reaction has a rate constant obtained by calculating the droplet collision frequency.
- The researchers then compared the droplet cloud ejected by an infected person to the one by a healthy person.
- The size of the droplet cloud, the distance it travels, and the droplet lifetimes are, therefore, all important factors that we calculated using conservation of mass, momentum, energy and species.
- The model could be used to estimate approximately how long droplets can survive, how far they can travel, and which size of droplet survives for how long. The actual situation could be complicated by wind, turbulence, air-recirculation or many other effects.
- Without wind and depending on the ambient condition, we found droplets travel between 8 to 13 feet before they evaporate or escape, said Researcher.
- This finding implies that social distancing at perhaps greater than six feet is essential, according to the researchers.
- The initial size of the longest surviving droplets is in the range of 18-50 microns, meaning masks can indeed help.
- These findings, the researchers said, could help inform reopening measures for schools and offices looking at student or employee density.
- The researchers noted that their model and the firm theoretical underpinning that connects the two scales — macroscale pandemic dynamics and the microscale droplet physics — could emerge as a powerful tool in clarifying the role of environment on infection spread through respiratory droplets.