How assessing if a cat is a liquid advanced science.

# Is a Cat a Liquid? Have You Seen How They Fit in Weird Containers?

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The state of the universe.
Nov. 9 2017 3:46 PM

# Is a Cat a Liquid?

## A liquid is traditionally defined as a material that adapts its shape to fit a container. Cats do that. Sort of.

This story was originally published on the Conversation and was republished here with permission.

A liquid is traditionally defined as a material that adapts its shape to fit a container. Yet under certain conditions, cats seem to fit this definition.

This somewhat paradoxical observation emerged on the web a few years ago and joined the long list of internet memes involving our feline friends. When I first saw this question it made me laugh and then think. I decided to reformulate it to illustrate some problems at the heart of rheology, the study of the deformations and flows of matter. My study on the rheology of cats won the 2017 Ig Nobel prize in physics.

The prizes are awarded every year by Improbable Research, an organization devoted to science and humor. The goal is to highlight scientific studies that first make people laugh, then think. A ceremony is held every year at Harvard University.

At the center of the definition of a liquid is an action: A material must be able to modify its form to fit within a container. The action must also have a characteristic duration. In rheology, this is called the relaxation time. Determining if something is liquid depends on whether it’s observed over a time period that’s shorter or longer than the relaxation time.

If we take cats as our example, the fact is that they can adapt their shape to their containers if we give them enough time. Cats are thus liquid if we give them the time to become liquid. In rheology, the state of a material is not really a fixed property—what must be measured is the relaxation time. What is its value, and on what does it depend? For example, does the relaxation time of a cat vary with its age? (In rheology, we speak of thixotropy.)

Could the type of container be a factor? (In rheology, this is studied in “wetting” problems.) Or does it vary with the cat’s degree of stress? (One speaks of “shear thickening” if the relaxation time increases with stress or “shear thinning” if the opposite is true.) Of course, we mean stress in the mechanical sense rather than emotional, but the two meanings may overlap in some cases.

What cats show clearly is that determining the state of a material requires comparing two time periods: the relaxation time and the experimental time, which is the time elapsed since the onset of deformation initiated by the container. For instance, it may be the time elapsed since the cat stepped into a sink. Conventionally, one divides the relaxation time by the experimental time, and if the result is more than 1, the material is relatively solid; if the result is lower than 1, the material is relatively liquid.

This is referred to as the Deborah number, after the biblical priestess who remarked that on geological time scales (“before God”) even mountains flowed. On shorter time scales, one can see glaciers progressively flowing down valleys.

Even if the relaxation time is very large (days, years), the behavior can be that of a liquid if the Deborah number is small (compared to 1). Conversely, even if the relaxation time is very small (milliseconds), the behavior can be that of a solid if the Deborah number is large (compared to 1). This is the case if one observes a water balloon at the instant when it’s popped.