Answering the question that won me the Ig Nobel Prize: are cats liquid?

An earlier version of this article was published in 2017.

Traditionally a liquid is defined as a material that adapts its shape to fit a container. However, under certain conditions, it appears that cats fit this definition.

This paradoxical observation came up on the web a few years ago and joined the long list of internet memes related to our feline friends. The first time I saw this question it made me laugh, but then I pondered and decided to rephrase it to illustrate some of the basic problems of the rheology, the study of the deformation and flow of matter. My study on the rheology of cats won the Ig Nobel Prize of 2017 in the physics category.

The prizes are awarded annually by Improbable Research, an organization dedicated to science and humor that aims to highlight scientific studies that first make us laugh, but then make us reflect. Every year it takes place a ceremony awards ceremony at Harvard University.

Okay, but what is a liquid?

Action is an important part of the definition of liquid: a material must be able to modify its shape to fit a container and the action must also have a certain duration. In rheology this is known as the relaxation time and determining whether something is liquid will depend on whether the action takes place in a shorter or longer period of time than the relaxation time.

If we take cats as an example, the fact is that they can adapt their shape to that of a container if we give them enough time to do so. Therefore, cats are liquid if we give them enough time to become liquid. In the rheology, the state of a material is not a fixed characteristic: what must be taken into account is the relaxation time. What is its value and what does it depend on? For example, does a cat’s relaxation time vary with its age? (In rheology we talk about thixotropy).

Could the type of container be a factor? (In rheology this is studied in the problems of “humidification”) Or does it vary with the degree of stress of the cat? (We speak of “thickening of shear” if the relaxation time increases with stress or “dilution by shear” if the opposite occurs). Of course, we refer to stress in the mechanical sense and not the emotional meaning, although in some cases they may coincide.

What cats clearly show us is that to determine the state of a material it is necessary to compare two moments: the relaxation time and the experimental time (the time elapsed since the beginning of the deformation initiated by the container). For example, it could be the time that elapses since the cat gets into a sink. The normal thing would be to divide the relaxation time by the experimentation time and if the result is greater than 1, the material is relatively solid; whereas if the result is less than 1, the material is relatively liquid.

Measuring the speed of the pastry dough

This is known as eDeborah’s number, named for the biblical priestess who pointed out that on geologic time scales (“before God”) even mountains moved. On shorter timescales you can see glaciers moving down valleys.

Even if the relaxation time is very long (days or years), the behavior can be that of a liquid if the Deborah number is less than 1. On the contrary, even if the relaxation time is very small (milliseconds), the behavior can be that of a solid if the Deborah number is greater than 1. This phenomenon is what occurs when we observe a water balloon at the moment it explodes.

Deborah’s number is an example of a dimensionless number: when dividing one period of time by another, the relationship has no units. In rheology, and science in general, there are many numbers dimensionless that can be used to determine the state or qualities of a material or a system.

(Hannah Reding / Unsplash)

There is another dimensionless number for liquids that can be used to calculate if the movement will be turbulent, with vortices, or if it will calmly follow the design of the container (in this case we are talking about flow laminate). If the flow velocity is V and the vessel has a typical size h perpendicular to the flow, we can define the velocity gradient V / h. The inverse value of this velocity gradient will be the timescale.

Comparison of said duration and relaxation time produces the Reynolds number in the case of fluids dominated by inertia (such as water), or the Weissenberg number for those dominated by elasticity (like pastry dough). If the value of these dimensionless numbers is greater than 1, then the flow is likely to be turbulent, while if the value is less than 1, the flow is likely to be laminar.

The question of whether cats are liquid allowed me to use this example to illustrate the use of these dimensionless numbers in rheology. I hope people laugh first and then reflect on it.

Image: John Benson / Flickr

Author: Marc-Antoine Fardin, University of Paris-Diderot.

This article was originally published on The Conversation. You can read the original article here.

Translated by Silvestre Urbón.