When water droplets are subjected to strong electrical fields, like raindrops through a thundercloud, they tend to burst into fine electrified mists.

The stronger the electrical field, the more likely that a water droplet would break apart.

Researchers from MIT have presented a simple formula that they claim can predict the exact strength an electric field must be to burst a certain water droplet. This, they believe, can benefit technologies that rely on electrifying water droplets, including air or water purification, space propulsion, and others.

"Before our result, engineers and scientists had to perform computationally intensive simulations to assess the stability of an electrified droplet," stated Justin Beroz, a graduate student at MIT and the lead author of the study. "With our equation, one can predict this behavior immediately, with a simple paper-and-pencil calculation."

Before A Water Droplet Bursts

Droplets form little spheres due to surface tension. However, in the presence of other forces, like an electric field, it tends to lose its shape. While surface tension pulls water molecules inward, other forces pull outward.

If the electric field is strong enough, the water droplet will not be able to find a shape that can balance both forces. It becomes unstable and breaks apart.

The researchers were interested in the moment before the water droplet bursts. To investigate, they conducted an experiment in which water droplets are dispensed onto an electrified metal plate. They used a high-speed camera to observe water droplets change their shapes before they burst.

Beroz studied various sizes of water droplets under various electric field strengths. He outlined the critically stable shape of each water droplet before they burst and calculated parameters like volume, height, and radius.

He plotted each water droplet's data and found that it all fell into one straight line.

Volume, Not Height, Matters

The researchers formulated the equation using only "fixed" parameters, which meant that they disregarded a water droplet's height.

"For the last 100 years, the convention was to choose height," Beroz explained. "But as a droplet deforms, its height changes, and therefore the mathematical complexity of the problem is inherent in the height. On the other hand, a droplet's volume remains fixed regardless of how it deforms in the electric field."

The new formula derived by the team uses five parameters: the water droplet's radius, volume, surface tension, electric field strength, and electric permittivity of the surrounding air.

The team envisions the formula being adopted to develop techniques like electrospraying, which is commonly used to aerosolize biomolecules from a solution and even propel satellites in space.

The study was published in the Physical Review Letters.