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Triangular taps produce the tiniest drips, according to new research by mathematicians from Harvard University.

Henry Chen and Michael Brenner say their tap could increase the resolution of ink-jet printers, shrink chip components, and make biochips more accurate. All these technologies need nozzles to squirt out minuscule droplets of liquid.

Smaller nozzles produce smaller drops, but because tighter, more curved drops have a greater surface tension, it takes a higher pressure to force them out. That costs energy and tests the mechanical strength of the pipelines. Drops of about 10 picolitres (10 billionths of a millilitre) are the smallest anyone has managed using round taps, at any rate.

鈥淚 don鈥檛 think it occurred to anyone to use anything other than a circular nozzle. Why would you? At first it wasn鈥檛 clear to us that the circle can be improved upon,鈥� Chen says.

But when he and Brenner did the maths to work out how different nozzles should perform, they found that changing the shape can cut the droplet size by 20 per cent, with no increase in pressure.

The optimum shape was a sort of sucked-in triangle, Chen says. Only a small drop can squeeze out through the central hole, while the spiky corners lessen the curvature of the liquid鈥檚 surface, so the pressure in the nozzle does not have to be so high.