Space and Physics
PUBLISHED

# Mystery Of Chocolate Fountain Shape Solved

Science has solved one of the world's tastiest mysteries: Why does melted chocolate draw inwards towards a chocolate fountain, rather than falling straight down? Knowing why chocolate behaves in this way may not make it any more delicious, but it could prove useful in the management of similar fluids.

As shown in the image above, melted chocolate falls inwards as it drops from the widest part of a chocolate fountain. For decades, puzzled partygoers have briefly wondered why they need to stretch a few centimeters further to coat their strawberries in a layer of deliciousness.

Adam Townsend, a mathematics student at University College London, set out to solve this mystery during his undergraduate degree; a study subject that no doubt forced him to spend painful hours consuming material left over from his inquiries, lest it go to waste. He has now published his findings in The European Journal of Physics

Townsend's supervisor Dr. Helen Wilson explained in a statement that the solution began with a study of how water behaves in similar circumstances, known as a water bell. "You can build a water bell really easily in your kitchen. Just fix a pen vertically under a tap with a 10p coin flat on top and you'll see a beautiful bell-shaped fountain of water."

A simple water bell produced with household equipment reveals the same tendency for fluids to draw inwards through surface tension. Adam Townsend/Helen Wilson

“When chocolate is running smoothly, it falls inwards around three centimeters [1.2 inches] for every 10 centimeters [3.9 inches] it falls,” Townsend and Wilson reported. Nevertheless, they also observed that the flow is not uniform, moving in and out, and that “holes appear and disappear at the bottom of the sheet.”

The comparison is complicated because water is a Newtonian fluid, with the same resistance to flow irrespective of the pressures placed upon it. Chocolate at 40°C (105°F) is non-Newtonian, specifically shear-thinning, so that it flows more easily when placed under stress. Familiar shear-thinning fluids include toothpaste and wall paint. Using mathematical modeling, the authors predicted a similar shape to what they observed, and concluded that “surface tension is the dominating factor in pulling the sheet inwards.”

"It's serious maths applied to a fun problem," said Townsend. "I've been talking about it at mathematics enrichment events around London for the last few years. If I can convince just one person that maths is more than Pythagoras' Theorem, I'll have succeeded.”

Townsend and Wilson also explored the way warm chocolate flows up through the pipe inside the fountain, rising at a constant speed in the middle and more slowly close to the walls.

The paper acknowledges that not all chocolates fall alike, since chocolate with less than 30 percent fat flows relatively easily for a while even after shearing stops, like the ketchup that can be poured for a short time after the bottle has been shaken. Measurements were conducted with 38 percent fat chocolate.

“The subject matter is intrinsically attractive (tasty, even!),” the authors noted. “We hope that others get the opportunity to learn about this area of mathematics with their own chocolate fountain.”

### ARTICLE POSTED IN

Space and Physics
• chocolate,

• fountain,

• non-Newtonian fluids,

• physics of food