SETTLING OF PARTICLES IN THE VICINITY OF VORTEX FLOWS

Abstract

A new mathematical analysis of the dynamics and settling distances of exhaled droplets and aerosols in the vicinity of vortical environments is presented. A dipolar vortex is considered self-propelling through a cloud of micron-sized droplets. This configuration may represent a vast number of indoor and outdoor environments in which similar unsteady vortical flow structures may interact with the exhaled respiratory droplet. We consider the steady two-dimensional Lamb-Chaplygin solution for the carried flow, coupled with unsteady Lagrangian particle equations for the droplet dynamics. We find that the vortex dipole effect may significantly enhance the droplet settling distances, which depend on the Stokes number, the vorticity, and the droplets' location relative to the vortex core. Our theoretical analysis reveals non-intuitive interactions between the vortex dipole, droplet relaxation time, and gravity, suggesting an optimal Stokes number for maximum displacement, which may reach up to an order of magnitude larger than the vortex core length-scale at moderate Stokes numbers. In terms of exhaled respiratory droplets, the results show that exhaled droplets in the vicinity of such vortical flow structures may be captured and transferred by self-propelling vortical structures and propagate much farther than previously reported for both quiescent and turbulent jets. Our theoretical study suggests a new mechanism for virus spread and proposes a simple model that may be used to controlling the spread of exhaled respiratory droplets in vortical environments.