We now know a little bit more about the dynamics of chocolate fountains, thanks to the efforts of Adam Townsend, a graduate student at University College London. He decided to figure out why that "curtain" of molten chocolate always falls inwards and the ensuing paper appeared last month in the European Journal of Physics.
It all started with Townsend's advisor, Helen Wilson, who was hiking one day when her thoughts turned to that peculiar behaviour of a chocolate fountain. Her colleagues in the department of applied mathematics proffered some likely explanations, but nobody could agree.
So she added it to her list of possible projects for her students. That's when Townsend pounced on it. "There were some very technical words on that project list," he told the Washington Post. "And then I saw 'chocolate fountain,' and I said, 'Aha! That's the one.'"
From a physics standpoint, molten chocolate is a type of non-Newtonian fluid. In a traditional Newtonian fluid like water, the viscosity — loosely defined as how much friction/resistance there is to flow in a given substance — is largely dependent on temperature and pressure: water will continue to flow regardless of other forces acting upon it, such as being stirred or mixed. In a non-Newtonian fluid, the viscosity changes in response to an applied strain or shearing force, thereby straddling the boundary between liquid and solid behaviour.
Surely you've seen all those YouTube videos showing people walking across a mixture of water and cornstarch, which solidifies in response to stress.
Blood, ketchup, yoghurt, gravy, mud, pudding, custard, thickened pie fillings and honey are other examples of non-Newtonian fluids. Not all such fluids are created equal: they respond to stress or a shearing force in different ways. With cream, the viscosity increases with stress over time: the longer you whip it, the thicker it gets.
Custard also becomes more solid — viscosity increases with increased stress — while honey, ketchup, or tomato sauce become more fluid, as viscosity decreases with stress over time. The latter are known as shear-thinning non-Newtonian fluids.
Molten chocolate also becomes less viscous under stress. For their analysis, Townsend and Wilson divided the flow behaviour into three phases: one where the chocolate is travelling up through the pipe inside the fountain, a second where the chocolate forms a thin-flowing film over the dome, and finally, that lovely curtain of molten yumminess just waiting for you to dip all manner of delectable nibbles into it.
In the pipe flow phase, they found the chocolate's motion followed a standard parabolic curve, with a pretty fast flow as it travels up the pipe. The chocolate thins and slows down as it flows over the dome in the second phase. As for the third "curtain" phase, the primary force acting on the chocolate at that point is surface tension.
The dynamics are similar to a water bell, something Wilson pointed out could be easily built in one's 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."
Townsend has found this work makes for an excellent lecture demonstration geared toward the general public, perhaps because audience members are so keen to sample the chocolate afterwards. But it also serves as a great introduction to the basics of non-Newtonian fluids. "If I can convince just one person that maths is more than Pythagoras' Theorem, I'll have succeeded," he said in a UCL press release.
And the actual models could contribute to improved understanding of similar fluid behaviour, such as volcanic lava flows, tear films in the eye, and how plasmas are extracted from nuclear fusion reactors.
Mostly though, "Chocolate fountains are just cool, aren't they?" Townsend enthused. Yes. Yes, they really are.
Townsend, A.K. and Wilson, H.J. (2015) "The fluid dynamics of the chocolate fountain," European Journal of Physics 37: 1.
[Via Fuck Yeah Fluid Dynamics]
Images: A. Townsend and H. Wilson/UCL