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You’ve been stirring your coffee all wrong. According to a series of simulations, not only should your stirring implement be shaped like a weird pentagon but you should use two of them and move them in a jagged half circle before letting vortices generated in the fluid do the rest.

at University of Mainz Medical Center in Germany and at King Abdullah University of Science and Technology in Saudi Arabia used simulations and an algorithm to determine what shape is the most efficient for stirring two liquids together.

The simulation was of a cylindrical container filled with two fluids both with a consistency similar to water, stirred by two stirrers. The stirrers were initially cylindrical and set to move in smooth circles, one on the edge of the container and one close to its centre, as is often the case in large mixing processes in the food or pharmaceutical industry.

The researchers then set an optimisation algorithm to the task of iteratively improving the stirrers’ shape and motion so that they mixed the liquids faster and more thoroughly with each attempt.

The algorithm found that the best stirrer was shaped like an uneven, curvy pentagon. It also found that the stirring technique could be improved upon too, using a jagged, start-and-stop motion. The researchers used a standard measure of how mixed two liquids are to assess the different approaches. The algorithm’s preferred stirrers and stirring technique resulted in liquids that were up to 2.3 times more mixed than liquids combined using standard cylinder-shaped stirrers moving in a circular motion.

Schmid says that the new stirrer shape works well because when combined with the new mixing motion it creates lots of vortices – small whirlpools that form as the stirrer moves. Stirrers mainly influence what is happening to liquids right next to them, but vortices can move away from the stirrer and act as tiny swirling mixers themselves, he says.

He and Schmid say they have no intention of actually making coffee stirrers. Instead, they hope the findings will be useful for mixing liquids in industrial settings.

at the University of Wisconsin says that stirrers and motions that create many vortices improve mixing processes so even slightly more angular stirring implements could be a great help.

In the future, Eggl says, the researchers want to consider fluids that become thicker or thinner as they are being stirred like toothpaste and ketchup. Additionally, they want to incorporate shaking of the container into the simulations to see whether a combination of stirring and shaking could be more energy-efficient than stirring alone.