Modeling the role of respiratory droplets in Covid-19 type pandemics

Abstract

In this paper, we develop a first principles model that connects respiratory droplet physics with the evolution of a pandemic such as the ongoing Covid-19. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time, 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, ensuring fidelity of the model. The 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 micro-scale droplet physics-thus could emerge as a powerful tool in elucidating the role of environmental factors on infection spread through respiratory droplets.

Falling Dynamics of SARS-CoV-2 as a Function of Respiratory Droplet Size and Human Height

“…3). Large droplets > 100 µm, as was classified by Chaudhuri et al [7], reached the ground from 1.7 m in a relatively short period of time < 1.6 s. The droplets ≥ 30 µm fell within 4.42 s regardless of the human height (Fig. 3).…”

Aerosol filtration efficiency of household materials for homemade face masks: Influence of material properties, particle size, particle electrical charge, face velocity, and leaks

“…The fate and hazardousness of potentially viruscontaining droplets after exhalation strongly depends on their size. Small droplets, smaller than several tens of mm, evaporate within seconds (Morawska et al 2009;Gralton et al 2011;Parienta et al 2011;Chaudhuri et al 2020), leaving droplet nuclei of 30-50% of their initial diameter, depending on the amount of dissolved material. Droplet nuclei with d p < 10 mm can remain airborne over extended periods of time and can be inhaled, with smaller particles reaching deeper regions of the respiratory system (Oberd€ orster, Oberd€ orster, and Oberd€ orster 2005).…”

“…Droplet nuclei with d p < 10 mm can remain airborne over extended periods of time and can be inhaled, with smaller particles reaching deeper regions of the respiratory system (Oberd€ orster, Oberd€ orster, and Oberd€ orster 2005). Very large droplets, d p > 100 mm, sediment quickly and are mostly deposited on a surface before they evaporate (Chaudhuri et al 2020). The number of virions within a single respiratory particle depends on the virus titer in the source region and increases with the cube of the particle diameter.…”

Transport and deposition of dilute microparticles in turbulent thermal convection

“…For example, suspended atmospheric pollutant particles (PM10 and PM2.5) that originated from dust and smoke will severely influence the air quality 5,6 . Another example is pathogen laden droplets in confined indoors, which will cause viral and bacterial infectious diseases to spread in hospitals, schools, and airplanes [7][8][9][10] . In such a dispersed multiphase flow, the evolution of the phase interface may not be a primary concern 11 .…”