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

• Published in: Physics of fluids (1994) 2020-08, Vol.32 (8)
• Main Authors: Ajayi, O J, Mehendale, F V, Gabl, R, Viola, I M
• Format: Article
• Language: English
• Subjects: Boussinesq equations; COVID-19; Dispersion; Droplets; Fluid dynamics; Gravitation; Gravitational effects; Physics
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0021427

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