What determines the droplet size in sprays?

A formula can predict the size of droplets formed by a nozzle’s spray.

This nozzle extrudes liquid as a sheet, which fractures into droplets whose size can be predicted by a new formula. Credit: S. Kooij et al./Phys. Rev. X
This nozzle extrudes liquid as a sheet, which fractures into droplets whose size can be predicted by a new formula. Credit: S. Kooij et al./Phys. Rev. X

A spray nozzle produces a range of droplet sizes that can often be summarized by a single number. Which single number is appropriate to use to compare the droplet spectrum of several sprays depends on the application.

Firstly there will be a spread of droplet sizes within a spray so some kind of average will need to be taken but which type of average is appropriate. Secondly, there are different methods for actually analyzing sprays and they will produce different results depending on the type of spray. It is important to understand which is being used and particularly to ensure that the same method is used when comparing the sprays produced by two different nozzles.

The size of droplets in a sprayed liquid is important for a range of applications. For example, pesticides must be delivered in droplets that are small enough to cover crops evenly but not so small that they drift away.

In order to measure the size of the droplet when liquid is sprayed from a nozzle, Daniel Bonn at the University of Amsterdam and his colleagues used lasers and high-speed photography.

Scientists varied both the spraying parameters, such as the pressure and geometry of the nozzle and the fluid parameters, such as viscosity and surface tension. The outcomes demonstrate that at the drop size is determined by a competition between fluid inertia and surface tension, which allows for the prediction of the drop size from the Weber number and geometry of the nozzle.

It suggests that increasing the liquid’s pressure led to smaller droplets, whereas increasing its surface tension and the nozzle’s width boosted droplet size.

For their work, scientists created a formula that uses these variables to predict droplet size. According to them, this could help them improve the design of sprays in applications ranging from printing to fire-fighting.

The work is described in a paper published in Phys. Rev. X (2018).