On New Year’s Day about 15 years ago, we spent hours looking for our cat. The fireworks had frightened the poor animal so much that it had hidden somewhere. We searched all its favorite places without success. The feline seemed to have vanished. But at some point, we were amazed to see something black and fluffy crawl out of a long, narrow opening under our fireplace. Tigrou, our house cat, had hidden in a space seemingly too narrow for the creature to fit.
Many other people have made similar observations. Memes referring to cats as liquid have been circulating online for several years. And they caught the eye of physicist Marc-Antoine Fardin of the Jacques Monod Institute, now at Paris City University and the French National Center for Scientific Research. “I spend some time on the Internet,” he said in a 2019 TEDx talk, “for research purposes, of course.” In the spring of 2014, Fardin began to scientifically study the fluid behavior of cats—a pastime that allowed him to avoid his real work. “This procrastination actually led to some success,” he explained in his talk. “It won me the Ig Nobel Prize of Physics, which rewards research that makes you laugh as well as think.”
There is more than one way to think about states of matter, such as liquids and solids. For example, in school you may have learned that molecules within a solid are tightly packed together in fixed positions, whereas those in a liquid move more freely around one another.
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But Fardin’s research is based on the science of fluid dynamics, or rheology. In this field, objects that have a constant volume and a fixed shape are solids. By contrast, the volume of liquid substances remains the same, but their shape can change. The latter criterion seems to apply to cats: despite a constant volume, they can bend as they please to fill a container such as a cardboard box or a sink. This means that cats should be classified as liquids, right?
The question is not so easy to answer. “If we wait long enough, everything eventually flows. That’s the motto of rheology,” Fardin said during his TEDx talk. For example, the solid asphalt of a sloping road continues to flow very slowly, which can be observed after several years or decades. Solids can also be deformed if enough pressure is applied to them. On the other hand, liquids can also have solid properties. Ketchup, for instance, only flows out of an open glass bottle after it has been shaken several times.
What Is a Liquid?
The previously given definition of a liquid is therefore not entirely valid. What is liquid clearly depends on how long you observe something. Rheologists therefore use a value called the Deborah number (De), which depends in part on the observation time (T), to indicate how liquid an object is. In principle, the smaller the Deborah number, the more liquid the substance.
In addition to the observation time, the Deborah number also depends on the so-called relaxation time (τ), the time it takes for a fluid to adapt its shape. If you pour water into a glass, it fills it up very quickly, so the relaxation time is very short. With a viscous liquid such as honey, however, you have to wait longer. By setting the relaxation time and the observation time in the ratio τ⁄T, you get the Deborah number. For values less than 1, materials are considered liquid. If the Deborah number is greater than or equal to 1, however, they are said to be solid.
The longer you observe something, the smaller the Deborah number becomes and the more fluid it appears. Mountains are indisputably solid for us. During a human lifetime, no flow behavior can be detected. But over millions of years, this changes. In fact, the name of the Deborah number comes from a line in a section of the Old Testament known as the “Song of Deborah.” (Although translations vary, the King James Version is: “The mountains melted from before the Lord.”)
Big picture: the Deborah number reminds us that it’s not clear whether cats qualify as a liquid—or precisely what a liquid is—because that depends on how long you observe them.
Cats and Liquids Share Many Characteristics
Nevertheless, rheological studies can be carried out—and these reveal cats’ many liquid characteristics. To calculate the Deborah number of cats, you have to determine their relaxation time. This varies from animal to animal, depending on its breed, age, and so on. Young kittens, for instance, may have a longer relaxation time because they fidget a lot. It can take hours for them to settle down and adapt their shape to their environment.
Cats like to take up as much space as possible in small containers.
In his lecture, Fardin pointed out that the shape of the container or environment also matters. For example, cats may relax more quickly on their owner’s lap than in a carrier in which they are transported to the vet.
This variability hardly disqualified cats from liquid status. Many familiar fluids feature relaxation times that vary based on their environment. Water forms droplets on repellent surfaces such as Teflon, while it spreads easily on other surfaces.
In work published in the journal Rheology Bulletin in 2014, Fardin had proposed that the relaxation time of young adult cats is between one second and one minute. This estimate allows the Deborah number to be calculated: if, say, a cat squeezes itself into a small cardboard box within five seconds and is observed for one minute, then De = 0.0833…. That is significantly smaller than 1: the cat is clearly exhibiting fluid behavior.
As Fardin pointed out in his paper, cats share other properties with liquids. For example, they have a yield stress, meaning that a minimum amount of force must be applied before they flow out of a container. The same applies to ketchup in a plastic bottle, which must be squeezed out. In addition, cats, like a fluid, adapt their body to the vessel they enter so that they fill it completely. Another characteristic that cats share with some liquids is their high surface tension, which comes into play as they press in or out of a small container.
Fardin was also interested in other flow properties of cats, such as whether they could create turbulence. But cats, he noted in his paper, fall in a class of “biologically active materials” alongside bacteria, flocks and schools, which have “their own motive power,” and are therefore hard to assess in this way.
“In conclusion, much more work remains ahead, but cats are proving to be a rich model system for rheological research,” Fardin wrote.
Biology offers a different lens on this question. From a life science point of view, these animals resemble a liquid—much more so than other creatures such as humans—because of their movable (and sometimes missing) collarbone. Once their head fits through an opening, the rest of the body can easily follow. This is how Tigrou flowed into the narrow gap beneath our fireplace.
This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.
