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An-Ti-Ci-Pa-Tion: The Physics of Dripping Honey

The views expressed are those of the author and are not necessarily those of Scientific American.


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Forget Big Questions like dark matter, dark energy, supersymmetry, and the quest for a grand unified theory for a moment — what we really need physicists to focus on is the mystery of why strands of sweet, sticky honey can get so long and thin as they drip without actually breaking. Inquiring minds want to know! Although if you’re the sort who thinks all science has to have an application, it could help improve industrial processes like fabricating optical fibers, which involves pulling long strands of viscous fluids (like molten glass) into long thin strands. So there.

Seriously, it might seem trivial, but it’s a theoretical question that dates back to the late 19th century, when Lord Rayleigh and a Belgian physicist named Joseph Plateau studied the behavior of fluids, particularly how a column of water, for example, will fragment into discrete drops after just 10 centimeters. They attributed this to surface tension, which amplifies the effects of small fluctuations, or waves, that develop naturally in a column of liquid as gravity pulls it down, eventually forming drops. It’s called the Rayleigh-Plateau instability.

Honey forms long thin strands as it pours that resist breaking up into droplets. Photo: Sean Carroll.

But honey — also a kind of fluid — doesn’t behave like that; it is much more stable. The breaking up into droplets is delayed significantly, so much so that a single strand can stretch as much as 10 meters before it snaps.

Physicists have been puzzling over why this might be the case ever since. In fact, there have been several attempts at modeling the behavior of honey as it drips over the last eight years, and a team of French scientists think they may have finally cracked the case with a new paper in Physical Review Letters.

Honey is an example of a non-Newtonian fluid – a fluid that changes its behavior when under stress or strain. Let me borrow a few paragraphs from my 2012 post on “oobleck” for context. Isaac Newton first delineated the properties of what he deemed an “ideal liquid,” of which water is the best example. One of those properties is viscosity, loosely defined as how much friction/resistance there is to flow in a given substance.

The friction arises because a flowing liquid is essentially a series of layers sliding past one another. The faster one layer slides over another, the more resistance there is, and the slower one layer slides over another, the less resistance there is. Anyone who’s ever stuck their arm out of the window of a moving car can attest that there is more air resistance the faster the car is moving (air is technically a fluid).

That’s the basic principle.  But the world is not an ideal place. In a Newtonian fluid, the viscosity is largely dependent on temperature and pressure: water will continue to flow — i.e., act like water — 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 behavior.

A simulation of fluids with different viscosities. Source: Wikimedia Commons, User:Anynobody.

Stirring a cup of water produces a shearing force, and the water shears to move out of the way. The viscosity remains unchanged. But non-Newtonian fluids? Their viscosity changes when a shearing force is applied.

Blood, ketchup, yogurt, gravy, mud, pudding, custard, thickened pie fillings and, yes, honey, are all examples of non-Newtonian fluids. They aren’t all exactly alike in terms of their behavior, but none of them adhere to Newton’s definition of an ideal liquid.

Not all non-Newtonian fluids are created equal: they respond to stress or a shearing force in different ways. Some react as a result of the amount of stress applied, while others react as a result of the length of time that stress is applied, like cream (viscosity increases with stress over time, i.e., the longer you whip it, the thicker it gets).

Oobleck, or custard, becomes more solid — viscosity increases with increased stress– while others become more fluid, like honey, ketchup, or tomato sauce, and viscosity decreases with stress over time. (You can perform a DIY viscosity experiment at home testing various liquids; instructions here.)

What does viscosity have to do with why strands of honey resist breaking up into droplets, compared to a less viscous fluid like water? Prior research seemed to indicate that viscosity didn’t really play a role in this behavior — gravity was primarily responsible for forming strands as a liquid was poured. But that would mean that all fluids should break at the same point, regardless of viscosity — and that clearly wasn’t the case when it comes to a viscous fluid like honey.

Back in 2004, physicists at the Technical University of Denmark in Lyngby modeled “an infinitely long dribble” of honey to try to shed some light on the problem. They introduced a “wobble” — the aforementioned fluctuation or wave — into the strand, and monitored how that strand behaved over time. The honey proved very stable, and the researchers concluded this was the case because the honey dripped more quickly than the wobble grew.

It turns out that the point at which a strand of fluid breaks does depend on its viscosity. Specifically, the more viscous the fluid, the more it slows down the amplification of the little wobbles or waves that ultimately lead to the formation of drops and cause the strand to break.

The Danish work focused on pinpointing the exact point at which the effects of viscosity were no longer relevant. This latest paper sheds further light on this phenomenon, demonstrating that it also depends on where the wavy fluctuations develop along the dripping strand. Per Physics Focus:

“For perturbations that start at the nozzle, this influence of viscosity doesn’t count for much, because they get rapidly stretched out as the jet descends, before they can grow and create a pinch-off. But irregularities appearing further down the jet can grow in amplitude before they get stretched too much, so viscosity matters for them.”

The French scientists tested their model’s prediction by experimenting with dripping silicone oils, varying the viscosity, and those predictions held except in the case of the most viscous fluids. At that point, they hypothesize, “the jets become so thick before they break that they are more susceptible to perturbation than the theory can describe.”

SCIENCE! See? Honey might be commonplace, but from a physics standpoint, it’s fascinating stuff. Incidentally, it’s not just the way it forms long strands that’s interesting scientifically. There’s also a nifty rope coiling effect that occurs as the dripping honey hits the surface. I’ll let Dustin at Smarter Every Day fill you in on that little bit of fluid dynamics:

References:

Garcia, J.M., et al. (2005) “Viscosity Measurements of Nectar- and Honey-Thick Liquids: Product, Liquid, and Time Comparisons,” Dysphagia 20(4): 325-335.

Javadi, A. et al. (2013) “Delayed Capillary Breakup of Falling Viscous Jets,” Phys. Rev. Lett. 110, 144501.

Papageorgiou, D. T. (1995). “On the Breakup of Viscous Liquid Threads,” Physics of Fluids 7 (7): 1529–1521.

Senchenko, S. and Bohr, T. (2005) “Shape and Stability of a Viscous Thread,” Phys. Rev. E 71, 056301.

 

Jennifer Ouellette About the Author: Jennifer Ouellette is a science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large. Follow on Twitter @JenLucPiquant.

The views expressed are those of the author and are not necessarily those of Scientific American.





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