<![CDATA[Is a Cat a Liquid or a Solid?]]>

Cats are paradoxes. They are adorable and cuddly, yet they can abruptly become fierce and unapproachable. Perhaps their dual nature is what compelled Erwin Schrödinger in his famous thought experiment, in which he concluded that a cat in a box can be simultaneously dead and alive.

Cats have also inspired another scientist to investigate the paradoxical nature of felines, with comparable results. Because of this groundbreaking research, we now know the answer to the question, “Can a cat be classified as a liquid or a solid?” That answer is, “Both.”

We know cats have the amazing ability to fit themselves into whatever space seems comfy to them. That’s why it wasn’t too much of a stretch of the imagination to believe the Bonsai Kitten Hoax of which we wrote a couple of years ago.

This shape-conforming quality is one of the defining characteristics of a liquid — the ability to take the shape of its container while retaining its volume. Does that mean that a cat is an animated liquid substance?

Marc-Antoine Fardin, a researcher of rheology at Université Paris Diderot – USPC, found himself pondering this problem. He used it as the basis for illustrating some of the dilemmas in rheology, which is the study of deformations and flows of matter. His research was published as “On the Rheology of Cats” in the July 2, 2014, Rheology Bulletin. For his efforts, Fardin was awarded the 2017 Ig Nobel Prize in Physics.

For a substance to be classified as a liquid, it is not enough for it to adapt to the shape of its container. It must also do so in a requisite period of time. This period of adaptation is known as the relaxation time.

When applied to cats, they clearly have the ability to take the shape of their containers if given enough time. The issue is what that time is and whether anything causes that time to fluctuate. Does it differ, for example, according to the age, size, or furriness of the cat? The technical term for this is thixotropy — the property of becoming more or less viscous when outside forces are applied.

In addition to relaxation time, rheology looks at the experimental time. This refers to the time elapsed from the beginning of shape change initiated by the container until the end of the observed period.

The state of the substance in question is defined in terms of its Deborah number. It is named in honor of Deborah, a biblical priestess who said, “The mountains melted from before the LORD…” (Judges 5:5 King James Version).

*Photos and caption from Fardin’s study: FIG. 1: (a) A cat appears as a solid material with a consistent shape rotating and bouncing, like Silly Putty on short time scales. We have De* ≫ *1 because the time of observation is under a second. (b) At longer time scales, a cat flows and fills an empty wine glass. In this case, we have De* ≪ 1. In both cases, even if the samples are different, we can estimate the relaxation time to be in the range τ = 1 s to 1 min. (c-d) For older cats, we can also introduce a characteristic time of expansion and distinguish between liquid (c) and gaseous (d) feline states. [(a) Courtesy of http://cat-bounce.com, (b) http://www.dweebist.com/2009/07/kitten-in-wine-glass/, (c) http://imgur.com/gallery/UuNSR, (d) http://imgur.com/s7JtV ]

The Deborah number is the relaxation time divided by the experimental time. If the substance in question has a Deborah number of less than 1, that indicates it is a gas or a liquid. In other words, the substance noticeably begins changing shape while under observation. If the Deborah number is greater than 1, the substance is considered to be a solid. In other words, it appears, while under observation, to maintain its own shape.

As cats demonstrate, defining a material’s state is dependent upon the amount of time under observation. If talking about a cat that has just stepped into a comfy box, the experimental time is less than one second. The relaxation time is insignificant because the cat is still getting comfortable. In this scenario, the Deborah number is well above 1, so the cat is relatively solid.

If we extend the observation time to a minute or so, the cat has enough time to make itself comfortable and eases itself into its nap site. The relaxation time is less than one minute, so the Deborah number is less than 1, indicating the cat is relatively liquid.

The Deborah number helps explain why ice, which is generally classified as a solid, can be described as “flowing” when talking about glaciers and geological lengths of time. Conversely, if the observation time is minuscule, even water can appear to be a solid, such as the moment at which a water balloon is popped and the water still retains the balloon shape.

This is not to suggest that Commonplace Fun Facts condones filling water balloons with cats or transporting your favorite feline in a coffee thermos. We do, however, point out the utter scarcity of examples in science fiction of moody, narcissistic, demanding, shape-shifting entities who end up being on the side of humanity.