Tea drinkers know all too well that annoying dribble from the kettle spout that so often occurs as one pours a nice refreshing cuppa. It's even known as the "teapot effect," and it usually happens when the tea is poured too slowly. Potters usually design their pots—giving the spout a thin lip, for instance—to reduce the likelihood of dribbling, based on centuries of accrued knowledge derived from trial and error.

Now a group of Dutch physicists has come up with a quantitative model to accurately predict the precise flow rate for how much (or how little) a teapot will dribble as it pours, described in a recent paper in Physical Review Letters. The model accurately describes both the simple teapot effect and more complex behavior—notably, the formation of a helix as a water stream swirls around a cylinder. That should be a boon not just for teapot design, but for 3D printing and similar industrial applications, which are also plagued by inconvenient dribbling.

Physicists have long been fascinated by the phenomenon. The late Stanford engineer and mathematician Joseph B. Keller once recalled attending a lecture by an Israeli scientist who mentioned that he'd posed the question of why teapots dribble to 100 physicists. All opined that it must be due to surface tension, but when the Israeli scientist performed experiments to test that theory, this proved not to be the case.

Intrigued, Keller did his own investigation and concluded that the dripping was actually due to air pressure. He and a colleague, Jean-Marc Vanden‐Broeck, published a paper in 1986—work that earned them an Ig Nobel prize in 2012. "It is simply that at the pouring lip the pressure in the liquid is lower than the pressure in the surrounding air," Keller told the Etsy Journal in 2013 (he died in 2016). "So air pressure pushes the tea against the lip and against the outside of the spout."

In physics jargon, at higher flow rates, the layer of fluid that is closest to the teapot's spout detaches so it flows smoothly and doesn't drip. At lower flow rates, when flow separation occurs, it reattaches to the spout's surface, resulting in a dribbling flow.

The spout's diameter, curvature of the lip, and the "wettability" (the preference of a liquid to be in contact with a solid surrounded by another fluid) of whatever material the teapot is made of, are also factors that can affect whether or not the kettle drips. But they aren't the primary culprit. In a 2010 paper, a team of French physicists from the University of Lyon demonstrated that the actual cause of the dribbling is a kind of "hydro-capillary effect" that prevents (at slower pour speeds) the liquid from detaching from the spout for a smooth, clean flow. All the other factors play a role in determining how strong that hydro-capillary effect will be.

As is so often the case, this latest study grew out of a curious scientist noting something odd and trying to ferret out an explanation. Etienne Jambon-Puillet, a postdoc at the University of Amsterdam, was cleaning syringes with a squirt bottle in the lab one day and was fascinated by how the liquid wrapped around the cylindrical needle to form a kind of helix structure. "I was seeing [the ethanol stream] swirling around on the needle, and I was like, 'Oh wow, this is amazing'," he told Physics Buzz.

A quick perusal of the existing physics literature didn't yield any truly viable models to explain the phenomenon, so he decided to do "a proper experiment." And he recruited colleagues at the Universities of Amsterdam, Twente, and Saxion to help. They set up a series of vertical cylinders (one set made of glass, the other of Teflon) and shot jets of dyed water at them, videotaping how the liquid behaved at varying flow rates.

They found that the water jets kept to a straight path at high flow rates, and as that rate decreased, the water began to deflect a little. At even lower flow rates, the water started coiling and "clinging" to the cylindrical surface before spiraling around to form a helix—much like the ethanol around the needle that day in Jambon-Puillet's lab. Apparently, it's due to a coupling between hydrodynamic suction and wetting.

Per Physics Buzz:

Hydrodynamic suction is the same effect that keeps an airplane in the sky or a ball hovering above a leaf blower. [It] 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.

Their new model accurately predicts when this crucial transition to "sticking," rather than detaching, from a solid surface like the cylinder (or tea spout) will occur.

DOI: Physical Review Letters, 2019. 10.1103/PhysRevLett.122.184501 (About DOIs).