“Droplets can be used as microcontainers that encapsulate small amounts of fluid and other components,” said Prof. Corey O’Hern, who led the study. Because of that, he said, they can be used to deliver drugs to the body, or to find the genomic signatures of a single cell. 

“Another cool application involves microreactors. You can put different concentrations of chemical species into the droplet, allow them to mix, and determine how they react.”

“The main issue involves the small sizes of droplets,” said O’Hern, professor of mechanical engineering. “You have to create a particular distribution of droplet sizes for these applications, and you can’t just order your favorite droplet size distribution online.”

To get the right size, a droplet has to undergo a series of breakages. One possibility is that a large droplet is first cut in half, and those halves are each cut in half, and so on. But predicting the size ratios of the smaller droplets, or “daughter droplets,” is difficult.

“The droplets do not always break in half; the size ratios of the daughter droplets can potentially depend on many properties of the droplet and surrounding fluid.”

The researchers ran experiments in which a single drop — usually water, immersed in oil — passes through a microfluidics chamber designed with an internal array of tiny obstacles. By the time it’s completed the length of the chamber, the droplet has broken up into many smaller droplets. The researchers then analyzed why some droplets hit an obstacle and remain intact, while others broke up into smaller droplets and different sizes. 

The answer was found in a combination of the droplet’s surface tension and the angle of the collision between the droplet and obstacle. The surface tension quantifies how strongly a droplet seeks to maintain a spherical shape. The droplet’s capillary number describes the relative strength of the droplet’s surface tension to the viscous forces of the surrounding fluid. By controlling the speed of the background fluid, the researchers can tune the speed of the droplet and, in turn, the capillary number for the droplet.

And then there’s the matter of how the droplets collide with the obstacles. A head-on collision typically means that it would break in half, but a glancing blows produces uneven breakup events or no breakup at all.

“There's a clear dividing line in the parameter space of the angle of approach and the capillary number when the droplets break up and when they don't,” O’Hern said. “For example, if the collision is not head-on, larger capillary numbers will not result in a droplet breakup.”

The research team ran 5,000 of these experiments of single droplet breakup. In addition, the team ran computer simulations of droplet breakup to explore a wider range of the parameter space for the droplet and fluid. The results of the simulations matched those of the experiments quantitatively. The validated simulations can now be used to investigate multi-droplet breakup in larger obstacle arrays.  

Going forward, O’Hern said the research team will focus on the opposite effect — how separate drops come together and merge into one, since both coalescence and breakup determine the steady state droplet size distribution in these systems.