The dispersion of spherical droplets in source–sink flows and their relevance to the COVID-19 pandemic

Abstract

In this paper, we investigate the dynamics of spherical droplets in the presence of a source–sink pair flow field. The dynamics of the droplets is governed by the Maxey–Riley equation with the Basset–Boussinesq history term neglected. We find that, in the absence of gravity, there are two distinct behaviors for the droplets: small droplets cannot go further than a specific distance, which we determine analytically, from the source before getting pulled into the sink. Larger droplets can travel further from the source before getting pulled into the sink by virtue of their larger inertia, and their maximum traveled distance is determined analytically. We investigate the effects of gravity, and we find that there are three distinct droplet behaviors categorized by their relative sizes: small, intermediate-sized, and large. Counterintuitively, we find that the droplets with a minimum horizontal range are neither small nor large, but of intermediate size. Furthermore, we show that in conditions of regular human respiration, these intermediate-sized droplets range in size from a few μ m to a few hundred μ m. The result that such droplets have a very short range could have important implications for the interpretation of existing data on droplet dispersion.

The perspective of fluid flow behavior of respiratory droplets and aerosols through the facemasks in context of SARS-CoV-2

“…Recently, several studies have attempted to understand the dynamics of droplet formation and transport. Cummins et al 55 investigated the dispersion of spherical droplets in the presence of a source–sink pair flow field. The Maxey–Riley equation was used to describe the finite-sized spherical particle motion in an ambient fluid flow.…”

A Systematic Approach to Predict the Behavior of Cough Droplets Using Feedforward Neural Networks Method

“…The model focuses more on the human factor, including age, gender, and height, with the produced droplets. Another simplified model related to the respiratory droplet is in [23] using the Maxey Riley equation that has successfully analyzed droplet behavior, especially in horizontal penetration. This model has limitations only for a specific case hence limited variables coverage.…”

COVID‐19: Facemasks, healthcare policies and risk factors in the crucial initial months of a global pandemic

“…These particles then rapidly shrink in size as they traverse the air via evaporation and thus behave as aerosols (Lemieux et al, 2007). As aerosols remain airborne, they can travel over large distances and have the potential to cause long‐range infection (Cummins et al, 2020; Tellier, 2006).…”