# The Least Little Drop

A triangular nozzle squeezes out smaller droplets than a circular one does, a physicist and a mathematician have calculated. Such odd-shaped orifices might improve fluid control in ink-jet printers and high-tech drug dispensers.

Force fluid through a small, circular nozzle, and out will flow a stream of equal-size drops. Here's why: If the nozzle is small enough, then the weight of the fluid plays no role, and the fluid bulges from the nozzle in a spherical dome. As the pressure in the fluid increases, the dome's curvature increases. Eventually, the curvature grows so great that the emerging droplet can no longer maintain contact with the edge of the nozzle all the way around. At that critical pressure, the droplet becomes unstable and detaches. And as long as everything stays round, creating smaller droplets requires smaller nozzles and higher pressures.

But a noncircular nozzle can produce smaller droplets at a given pressure, report physicist Henry Chen and applied mathematician Michael Brenner of Harvard University in Cambridge, Massachusetts. With the aid of a computer, the two analyzed the stability of the droplets bulging from nozzles of various shapes with the same area. They tracked the critical pressure as the shape of the nozzle deviated further from a circle. At a given critical pressure, a triangular nozzle with stretched corners produces drops 20% smaller than those squirting from a circular nozzle, they report in the 23 April issue of *Physical Review Letters*. Other starlike shapes may yield even smaller drops.

The 20% reduction in volume may seem modest, but it could prove useful in devices that control and dispense tiny amounts of fluid, such as ink-jet printers and "microfluidic" drug dispensers that continuously pump medicine into a patient's body, says Edward Furlani, a physicist with Eastman Kodak in Rochester, New York. Jens Eggers, an applied mathematician at the University of Bristol in the United Kingdom, says the from-scratch calculation exemplifies an emerging approach to engineering, which has generally relied on trial and error to find optimal designs.

**Related site**

The abstract for Chen and Brenner's paper