Physics Around the Clock

2

BREAKFAST WITH EINSTEIN

WHILE THE UK HAS a growing love for coffee, it might not be the first drink you consume in the morning. A cup of tea is my first hot beverage of the day (well, I am English) and, thankfully for this book, there is also a lot of interesting physics at play here, too. All tea comes from the tropical plant known as Camellia sinensis, which grows best in a warm climate with long days, cool nights and an abundance of rainfall. The varying types of tea such as green, black and oolong are due to how the leaves are processed after harvest - black tea being fermented while green tea isn't, for example. According to legend, tea has been brewed for centuries, beginning in China in around 2,700 BC, but it took thousands of years before it became a popular drink in the country. To make tea, 'kettles', typically made from bronze or iron, were used to boil water. Then in the nineteenth century, copper became more prevalent, given that it conducts heat more efficiently. Later that century the copper teapot, similar to how it looks today, made its way into homes.

In this speed read of tea-making history, the first electric kettle was also being developed around the end of the nineteenth century. In 1891, the US-based Carpenter Electrical Company released an electric teapot with a heating element separate from the water compartment, meaning it took some ten minutes to boil water. Improvements to electric kettles came in subsequent decades, which included the commonsense idea of placing the immersion heating element into the actual water container. Yet traditional steam kettles continued to be popular, especially with the advent of gas-cooker tops in the early twentieth century. While electric kettles are now commonplace in Europe, in the US the steam kettle is still widely used. This is due to cultural preference as well as the fact that the mains voltage in the US is 110-120 volts (compared to 230-240 volts in the UK), meaning it can take just as long to boil water in an electric kettle as it can in a traditional steam one. Once the water is boiled, an electric kettle automatically switches off thanks to a channel within the kettle, typically inside the handle, that carries steam to a thermostat near the base, which when heated to near 100°C will trip the power off. Those using a steam kettle, on the other hand, will be made aware that the water has boiled due to the characteristic noise of a kettle whistle. This is a cylindrical duct placed at the end of the spout, which includes two circular plates that are closely spaced apart inside (see figure on page 30). Both plates have a hole in the middle that allows the steam to pass through.

Despite this whistling noise having been heard for well over a century, nobody fully understood the physical mechanism behind it until 2013 when acoustic engineers Anurag Agarwal and Ross Henrywood, from Cambridge University in the UK, tackled the problem. Agarwal first became interested in the whistling kettle when doing a PhD in acoustics in the US. He discovered that the phenomenon was first tackled by the nineteenth-century British physicist and mathematician John William Strutt (known more widely as Lord Rayleigh).* In Rayleigh's 1877 book The Theory of Sound, he compared the mechanism to how birds produce birdsong. But even the great physicist admitted that 'much remains obscure' when it came to how the sound is produced. 'Lord Rayleigh didn't have microphones and similar equipment back then, which would have made it difficult to study, so we thought we would make the measurements and validate his theory,' Agarwal told me.

They found that Rayleigh's theory didn't quite apply to whistling kettles. To investigate further, Agarwal and Henrywood tested a series of whistles of different lengths by forcing air through them at various speeds.1 The pair found that once the water is near boiling, the steam going through the kettle's spout produces sound at a single, fixed frequency.┼ When they investigated this surprising result, they discovered that the noise is generated in the same way as when you gently blow over the open neck of a wine bottle. This creates something called a Helmholtz resonator, which in the case of a wine bottle causes sound to radiate from the neck of the bottle at a fixed frequency. In a similar way, the air inside the whistle reverberates like the air in the neck of a wine bottle, producing a characteristic hum at a constant, single frequency.

A kettle whistle features two plates that each have a small hole. The fast-moving steam entering the whistle's first hole forms a jet, while the second hole acts to produce mini vortices that are responsible for the characteristic whistling noise.

Once the water in the kettle is on a rolling boil, however, steam is pumping out and travelling much faster. This is when another sound - the whistling we are all accustomed to - kicks in. As the steam in the spout enters the first hole of the whistle, it contracts into a fast-flowing stream of steam. This jet of steam is unstable and starts to break up as it makes its way through the whistle's cavity to the next plate, producing sound waves in the duct between the plates. By the time it gets to the second plate the steam jet hits the hole and produces vortices outside the spout. These mini whirlwinds just happen to produce sound at the same frequency as the sound waves in the duct; the note produced being determined by the size and shape of the hole openings and the length of the spout - a bit like a flute. Agarwal found that it is exactly these vortices - a phenomenon called vortex shedding - that causes the sound. The frequency of the sound also increases with the flow rate of the steam, which is why you may hear the sound change the more the water boils. This vortex shedding is the same effect that happens when wind blows over telephone wires, or when the air travels over roof bars on top of your car. Both produce a whistling noise that is not so dissimilar to the physics of the whistling kettle.

Once the kettle is boiled, if you are not in a frantic race to get the kids off to school or head off to work, then you may instead prefer to sit down with a pot of tea. How civilised. The issue for teapot aficionados is pouring the tea while avoiding liquid trickling down the underside of the spout and on to the table. This is known as the 'teapot effect', a term first coined in 1956 by the Israeli physicist Markus Reiner.2 The phenomenon occurs when the liquid coming out of the spout 'sticks' to the tip and does not flow out cleanly, resulting in some of it trickling down the underside of the spout. It was thought that surface tension and adhesion of the liquid to the surface was behind the effect. Surface tension is the effect you can see on the surface of water that results in a 'film', which allows some insects to walk on water. Deep in a liquid, water molecules are surrounded by other water molecules on all sides, which results in the interactions between the molecules balancing out - giving no net tension. In other words, the molecule pulling above is balanced out by the molecule pulling below, and so on. However, molecules at the very top of the surface do not have neighbours above them - only at the sides or below. This results in the molecules bonding more strongly with their neighbouring molecules along the surface, creating a sticky 'surface film', much like the stretchy elastic sheet that pond skater insects use to literally walk on water.

In 1956, however, Reiner discovered that surface tension and adhesion alone were not enough to describe what was going on. Instead, he proposed that when a fluid flows against a surface, it shears. In other words, the part of the liquid that is away from the surface travels faster than the part that is at or near the surface, which is affected more by friction, and that makes it stick to the spout. Pouring quickly, however, helps to avoid this, as the liquid 'detaches' from the surface and flows freely out.

Thirty years later, in 1986, the physicist Joseph Keller, at Stanford University, proposed that the main culprit behind the teapot effect is actually pressure. As the liquid begins to turn out of the teapot, the pressure in the liquid at the pouring lip is lower than atmospheric pressure, since a pressure drop is required to balance the centrifugal forces.╬ This means that the air 'pushes' the tea against the lip and the outside of the spout, which causes the drip to pour down the underside of the spout. No need for surface tension. In 1989, Keller improved his model to include gravity to explain the point at which it starts to trickle down the underside of the teapot and on to the tablecloth.§

Case closed? Not quite. But the end of the dribbling teapot trauma finally came closer than ever in 2021 when researchers led by Bernhard Scheichl from the Vienna University of Technology in Austria declared to the world that they had formulated a 'complete - even though quite technical - theory' of the teapot effect. 'I hadn't actually heard of the teapot effect before,' Scheichl told me. 'But when we looked into it, we realised that no one had really fully explained what was going on.' By filming teapots as they poured water, the researchers discovered that a small liquid drop formed just under the sharp edge of the spout so that the area always remained wet. The size of this drop, however, depends on the speed that the liquid is flowing: if too slow then the drop acts to direct the...