To Build a Better Teapot, Researchers Create Liquid Helix

It is a truth universally acknowledged that nothing—nothing—is more pointlessly irritating than a poorly designed water jug. You know—the kind that mindlessly dribbles all over the table every time you try to serve yourself? For centuries ceramicists and potters have slowly perfected ways to get around the so-called “teapot effect”, but scientists have long struggled to properly model the phenomenon.

Image credit: GettyImages

Well, until now. In a new article in Physical Review Letters, researchers provide a model for this frustrating process. Etienne Jambon-Puillet, of the University of Amsterdam, describes how he first became interested in the problem, saying “To be honest, it started very basic in the kitchen,” he says. The postdoctoral scholar was in the middle of cleaning a set of syringes using a squirt bottle when he became mesmerized by the way the jet of liquid wrapped around the cylindrical needle to form stunning helical structures. “I was seeing [the ethanol stream] swirling around on the needle and I was like oh wow, this looks amazing,” he says. Intrigued by the phenomenon, he started searching for an explanation in the literature—with limited success.

Granted, a smattering of papers did attempt to describe some of the underlying principles responsible for the attraction between liquid streams and solid surfaces, but none of the models accurately described what he was looking at under his laboratory sink. “So I decided, OK, let’s go for it and do a proper experiment,” he recalls.

Before starting on that experiment, though, he needed to garner some understanding of the research that was already out there. Although it didn’t occur to him initially, he soon came to realize that his helix was a variation on the teapot effect; his solid just happened to take the form of a cylinder rather than a spout. Fortunately, this phenomenon had enough research behind it that he could understand the basic mechanisms responsible: fluid dynamics and wetting.

Jambon-Puillet’s liquid helix. In this case, the structure is formed by dyed water wrapping around a glass cylinder. Image credit: Etienne Jambon-Puillet

The first, hydrodynamic suction, is the same effect that keeps an airplane in the sky or a ball hovering above a leaf blower. This fluid dynamics effect shows up where a fluid—which can be either a gas or a liquid—attempts to move past a curved surface in a laminar (straight-line) flow; the curvature of the solid interrupts the flow and creates a pressure drop that sucks the fluid in.

Wetting kicks in the moment the stream encounters the cylinder’s surface as the molecules on the outermost edges of the stream interact with the solid, similarly to how water forms a meniscus in a test tube. It’s the combination of this force and the hydrodynamic suction that keeps the liquid bound to the cylinder as it swirls downwards.
Of course, that isn’t the whole story. To begin with, a landmark 2010 paper revealed that the two effects work in tandem, making it impossible to tease out each one’s individual contribution. Additionally, Jambon-Puillet noticed that if he gave the ethanol a high speed the jet wouldn’t bend much at all, and that he had to hit the syringe at different angles for each speed in order to create a proper helix; indeed, the liquid’s momentum, which encapsulates the speed and angle of incidence, competes with the other effects to moderate the overall outcome.
This much was already known, but Jambon-Puillet still wasn’t satisfied. He discovered that if he went off of existing models, the liquid should always detach from the cylinder after a certain number of turns—and that just didn’t match with his casual observations. So he did what any reasonable engineer would do, and took the problem to his colleagues at the Universities of Amsterdam, Twente, and Saxion.

Experimental results overlain with their theoretical predictions (red dotted line) showing high accuracy for a wide variety of parameters. Image credit: Jambon-Puillet et al.

Initially, the team approached the problem from an analytical perspective, studying the change in momentum of a hypothetical liquid jet as it wrapped around a hypothetical cylinder. “If you want to do it properly, it is very complicated,” Jambon-Puillet says. This is partly due to the coupling of the hydrodynamic suction and wetting effects, and partly because studying wetting in fast-moving liquid is a relatively new field. In fact, it was only through a mathematical sleight-of-hand that reduced the problem to a 2-dimensional plane that they were able to solve the equations at all.
Once they finally constructed a physical counterpart to their hypothetical experiment, they were stunned by their model’s accuracy. Taking into account the liquid’s angle of incidence and initial speed as well as the solid’s dimensions, their equations predicted the shape of the helix remarkably well.

Even more exciting, their model was the first to accurately predict whether the cylinder would release the stream. Recall that existing models required the stream to eventually leave the cylinder, in contradiction with experimental observation. In fact, their research showed that once the stream had completed a half-turn (180 degrees) around the glass tube, it would not detach at all. “That’s one of the nicest things about our new model—it actually gets this. None of the other models got this before,” Jambon-Puillet says.
They were in for a bigger surprise when they inspected their model more closely. Just like Jambon-Puillet had noticed in his sink, at high liquid velocities the stream wouldn’t complete the requisite half-turn and would accordingly detach from the cylinder fairly quickly. They identified a critical velocity (for a given set of parameters) that was the highest speed to allow for a full helix. However, they soon realized that if they created a stable helix at or below this critical velocity before slowly increasing the stream’s speed, the helix would remain stable (up to a certain point, at least)—a phenomenon the team dubbed the “sticking transition”.

The left three images show the partial wrapping that occurs with relatively higher speeds. The fourth image 
was taken at a lower speed, the highest that allowed a full helix to develop. This helix pushes the system 
into the “sticking transition” where the flow rate can be moderately increased to 3.16 m/s without disrupting
the helix.

Although this model focuses only on liquid jets wrapping around a cylinder, it is the team’s hope that this will assist industry in the production of anti-drip containers and clean up extruders everywhere. Since there are three main factors that influence whether or not a liquid stream will stick to a nearby solid—momentum, fluid dynamics, and wetting—engineers and consumers can use three corresponding tactics to fight the drizzle, all of which are fairly intuitive. 
  1. You can increase the liquid’s momentum by simply pouring faster; in many instances, it’s only when you attempt a slow drizzle that the effect really shows itself. This generally falls to the consumer, but some receptacles are carefully designed with this concept in mind. Those elegant long-necked coffee pots? Their thin stems force the liquid to move faster for a given flow rate, increasing its momentum and decreasing its chances of adhering to the pot. Even in the case of a more traditional pitcher, the spout serves a double function as it both guides and speeds up the liquid
  2. The distortion of a liquid stream also scales with the curvature of a nearby solid; gentler curves cause greater distortion to the jet. Correspondingly, ceramicists typically try to create a sharper edge where they know people will want to pour from (this is how those “dribble-free” wine spouts work too).
  3. Finally, the wettability of the surface is critical. The liquid’s surface tension is the real culprit when it comes to actual adhesion, as the molecules’ interactions with each other and the glass pulls the entire stream of liquid in. Especially in a manufacturing setting, many surfaces are coated to be hyper fluid-repellent so these molecules can’t get a real foothold.

None of these techniques is novel; they have been used for centuries as potters improved their designs through trial and error. What is new is the glimpse at a quantitative model that tells manufacturers how their creations will perform, whereas this was previously understood only qualitatively. “You can actually start to put numbers on this kind of empirical world,” Jambon-Puillet says triumphantly.
After all, isn’t that what science is all about?
–Eleanor Hook

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