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

TL;DR

This study models spherical droplet dynamics in source-sink flows, revealing size-dependent behaviors and implications for COVID-19 droplet dispersion, especially highlighting the short-range travel of intermediate-sized droplets during respiration.

Contribution

The paper provides analytical insights into droplet trajectories in source-sink flows, including effects of gravity and inertia, with relevance to respiratory droplet dispersion in pandemic contexts.

Findings

Small droplets are limited in travel distance before being pulled into the sink.

Large droplets can travel further due to inertia, with maximum distance analytically determined.

Intermediate-sized droplets have the shortest horizontal range, affecting disease transmission understanding.

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 Basset-Boussinesq history term neglected. We find that, in the absence of gravity, there are two distinct behaviours 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 travelled distance is determined analytically. We investigate the effects of gravity, and we find that there are three distinct droplet behaviours categorised by their relative sizes: small, intermediate-sized, and large. Counterintuitively, we find that the droplets with 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 $\mu$m to a few hundred $\mu$m. The result that such droplets have a very short range could have important implications for the interpretation of existing data on droplet dispersion.