FRAGMENTATION OF WATER DROPS IN COLLISION WITH A SMALL OBSTACLE

Abstract

The study is dedicated to the general features of the processes of deformation and fragmentation of liquid drops have been studied when they collide with obstacles. Masks and filters, protecting against airborne infections, are among the possible obstacles. Coughing, sneezing, and talking cause the ejection of drops of saliva and bronchial mucus. A local drop-mask or drop-filter collision is modeled by the impact of a drop on a small obstacle as the simplest hydrodynamic case with a minimum number of influencing factors. For water-based oral and bronchial drops with a typical diameter <i>d<sub>i</sub></i> = 100 μm and impact velocity of the order of <i>v<sub>i</sub></i> = 10 m/s, the impact Weber number is about We<sub><i>i</i></sub> = ρ<i>v<sub>i</sub></i><sup>2</sup><i>d<sub>i</sub></i>/γ = 139. As a starting point in the problem of the drop breakup in a collision with a solid obstacle, we consider the coaxial impact of an inviscid liquid drop with a diameter of 2.8 mm on a disk with a diameter of 4.0 mm. In laboratory experiments, the similarity was provided by impact velocities of 1.88-3.57 m/s, which gives impact Weber numbers We<sub><i>i</i></sub> = 137-496. Such collisions are controlled only by inertia and capillarity, while the influence of all other factors is negligible. A round liquid lamella with a torus-shaped rim is formed upon the collision. The rim first expands and then retracts, forming radially directed liquid fingers in the rim. At low impact velocities, the fingers retained continuity, while at sufficiently high velocities, the fingers spattered into secondary droplets. Experiments have shown that the critical Weber number corresponding to the transition to spattering lies between 137 and 206. Approximately the same values of the Weber number occur when infected drops hit masks or filters.