The physics of falling water droplets with different Weber numbers

When a droplet falls on a liquid surface — like rain on a pond — the liquids splash and often create secondary central jets or droplets. Studying these dynamics, through experimental, theoretical and numerical models, is important to a wide range of applications such as oil spills, inkjet printing, fuel injection, and irrigation.

Ma et al. study the effects of droplets falling on water using numerical and experimental methods. The paper describes the effects of water droplets with different Weber numbers — a dimensionless number useful in analyzing fluid flows, which is dependent on the density, velocity and size of the droplet, as well as the surface tension of the liquid.

To study the effects experimentally, the authors set up a peristaltic pump to deliver water to a needle, whose height could be adjusted. From the needle, the droplets fell into a water tank, where their impact was recorded by two high-speed cameras taking images at 1,000 frames per second. The results were then analyzed using image-processing software. The same impact process was also numerically simulated using a mathematical model.

The paper considered the case where a central jet bounces up and pinches off to form a secondary droplet, as well as how the secondary droplet falls back onto the water, forming a secondary central jet. The results found the diameter of the secondary droplet and heights of central jets linearly increased with increasing Weber number within their experiment ranges. Their numerical and experimental results agreed well.

The researchers also found the depth and diameter of the cavity created upon impact increased linearly with increasing Weber number. Studying the energy conversion, their results showed the target liquid absorbed 70% of the total energy from the initial impact.

Source: “Deformation characteristics and energy conversion during droplet impact on a water surface,” by Huimin Ma, Changgen Liu, Xu Li, Hongbo Huang, and Jiaojiao Dong, Physics of Fluids (2019). The article can be accessed at https://doi.org/10.1063/1.5099228 .