In this work, researchers from University of Toronto, Indian Institute of Science and University of California, San Diego,have developed a first principles model that connects respiratory droplet physics with the evolution of a pandemic like the ongoing COVID-19.
The model has two parts. First, they modelled the growth rate of the infected population based on a reaction mechanism. The advantage of doing this is that the rate constants have sound physical interpretation. The infection rate constant is then derived using collision rate theory, based on the collisions between infectious respiratory droplet clouds and the susceptible population, to arrive at the pandemic evolution equations. The rate constant is shown to be a function of the respiratory droplet lifetime.
Schematic of the collision rate model for the infection. Infected person P carries cloud of infectious droplets D(small red dots) and PD system approaches healthy person H with relative velocity ~VDH to infect them. Figure also shows collision volume swept by droplet cloud D and H with respective effective diameters.
In the second part, they emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time while accounting for droplet cooling, heat and mass transfer and finally crystallization of the dissolved salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution respectively, thus ensuring the fidelity of the model.
Instantaneous droplet images taken by CCD camera (top left) and dark field micrograph of the final salt precipitate (top right). Comparison of experiments and simulations in the bottom left and right panels. Evolution of normalized droplet diameter as a function of time for pure water (bottom left) and salt-water solution droplet with 1% NaCl (bottom right).
The researchers find that droplet evaporation/desiccation time is indeed dependent on ambient temperature and is also a strong function of relative humidity. The multi-scale model thus developed and the firm theoretical underpinning that connects the two scales ‒ macro-scale pandemic dynamics and the micro-scale droplet physics ‒ could emerge as a powerful tool in elucidating the role of environmental factors such as temperature and relative humidity on infection spread through respiratory droplets.
Chaudhuri, S., Basu, S., Kabi, P., Unni, V. and Saha, A., 2020.Modeling the role of respiratory droplets in Covid-19 type pandemics.Physics of Fluids, 32(6), p.063309.