Some friendly banter between a married couple making crepes in their kitchen could lead to cheaper electronics and more efficient paints.
As Mathieu Sellier pondered how to get his crepes perfectly smooth and even, his wife pointed out that as a fluid physics specialist, he should know the answer.
So Sellier, a physicist at the University of Canterbury in New Zealand, teamed up with Edouard Boujo, from the École Polytechnique in France, to explore the problem.
Their findings are published in journal Physical Review Fluids.
Although the conclusion, that you should put a dollop of batter in the middle of the pan, tilt it and then rotate it to get even coverage, is not surprising, the development of a sophisticated theory of how liquids coat a surface could be employed.
The manufacture of many materials used for electronics, for example printed circuit boards, involves applying thin, even layers. The use of liquids could offer a cheaper and more energy efficient way to create these coating than current methods that rely on deposition from hot vapours.
It sounds simple to spread batter around a pan, but the problem of finding the optimal method with a tilting, rotating pan and batter that is turning from a liquid into a solid as it cooks is surprisingly complex.
Sellier says the maths of the problem was laid out in a series of interwoven equations called partial differential equations (PDEs) that was not easy to solve.
“The theory we used was called the optimal control of PDEs – that’s the tricky bit,” he says.
“It’s an important contribution, I don’t think anybody’s done it like this before.”
The exact solution is as follows: right after placing the batter into the pan, incline the pan steeply in one direction so that the batter flows from the pan’s centre to its rim.
Next, rotate the inclined pan in a circle—this step ensures that the batter coats the pan’s full circumference. Finally, while continuing the circular motion, decrease the pan’s incline, filling in any holes, until the pan is horizontal and the batter is cooked.
While industry companies may be keen to employ the research to make paints that coat surfaces more efficiently, Sellier’s relatives are hoping he stays with the edible research.