One of our strays discovered, sometime in her first winter indoors — they are strictly indoor cats now, on our vet’s recommendation — that she could fit into a salad bowl. Not sit beside it, not rest her head on its rim: fit into it, curled into a precise sphere with her tail tucked under her chin and her ears folded flat. The resemblance to a liquid filling a container was excellent.

The resemblance is also where the literal claim ends. A cat is an active, articulated animal, not a passive sample whose constitutive equation has been measured. Fortunately, the joke still contains real rheology.

The Timescale in the Joke

The intuitive distinction between solids and liquids is that solids retain a shape while liquids flow. Viscoelastic materials complicate this distinction: their response depends on how quickly they are deformed and how long they are observed. Silly putty can creep on a table and fracture under a rapid impact. Mantle rock transmits seismic shear waves on a timescale of seconds yet flows over geological time.

The standard dimensionless ratio used to express this competition is the Deborah number,

$$\mathrm{De}=\frac{\tau}{T},$$

where $\tau$ is a characteristic material relaxation time and $T$ is the timescale of the process or observation. Marcus Reiner introduced the name in a 1964 Physics Today note, invoking the line “the mountains flowed before the Lord”: even mountains can flow if the observer waits on an appropriately long timescale.

For a material and deformation with a well-defined relaxation time, $\mathrm{De}\ll1$ means stresses relax within the process time and fluid-like behaviour can dominate. At $\mathrm{De}\gg1$, stress persists over the process time and the response can look elastic or solid-like. Near unity, neither limit can be ignored. This is not a universal phase test. Real materials may have several relaxation times, and Deborah number alone does not specify the constitutive law, strain amplitude, or flow geometry.

A Model Where the Ratio Is Exact

The Maxwell model puts a linear spring of modulus $G$ in series with a viscous dashpot of viscosity $\eta$. Its single relaxation time is

$$\tau=\frac{\eta}{G}.$$

Under a constant applied stress $\sigma_0$, its strain is

$$\epsilon(t)=\frac{\sigma_0}{G}+\frac{\sigma_0}{\eta}t.$$

The first term is an immediate elastic deformation; the second is unbounded viscous creep. In a stress-relaxation experiment at fixed strain, the model instead predicts

$$G(t)=G e^{-t/\tau}.$$

For this deliberately simple material, comparing $T$ with $\tau$ cleanly separates a short-time elastic response from long-time flow. Polymer melts, glacier ice, and geological materials require richer models, but the same discipline remains useful: state the material, deformation, and timescale before calling a response solid-like or fluid-like.

What Fardin Actually Did

Marc-Antoine Fardin’s two-page “On the Rheology of Cats,” published in the Rheology Bulletin in 2014, applies this vocabulary to photographs of cats in containers. It discusses Deborah number, wetting, yield stress, and related ideas in the register of a technical paper. The application is intentionally comic. It earned the 2017 Ig Nobel Prize in Physics.

The paper did not report a programme of cat rheometry. It did not measure a feline relaxation spectrum, viscosity, elastic modulus, yield stress, or surface tension. Nor did it establish that an animal voluntarily changing its posture obeys the passive constitutive law of a fluid. A cat settles into a bowl through muscles, joints, perception, and choice. Those mechanisms are exactly what a rheological material model leaves out.

That boundary matters because it preserves the useful part of the joke. A cat can illustrate how an observer’s timescale changes a description without becoming a Maxwell element.

An Arithmetic Illustration, Not a Measurement

Suppose, only for illustration, that I assign the bowl-settling performance a characteristic time of $\tau=5\,\mathrm{s}$ and watch for $T=600\,\mathrm{s}$. The ratio is

$$\mathrm{De}_\mathrm{illustration}=\frac{5}{600}\approx0.0083.$$

The arithmetic is correct. Its interpretation is conditional on an invented parameter: no experiment here shows that five seconds is an intrinsic relaxation time of this cat, independent of the bowl, temperature, mood, stimulus, or task. Changing the assigned timescale changes the answer without revealing a feline material property.

Likewise, dividing five seconds by a short contact time would produce a number much larger than one. That does not show that the cat undergoes a rheological phase transition during a jump. It shows that a dimensionless ratio inherits the quality of the quantities placed into it.

The earlier version of this article supplied several such cat times as though they were measured material constants. They were not. I have kept one worked ratio because it exposes both the idea and the failure mode.

Where the Analogy Stops

The other rheological labels in Fardin’s paper work the same way. A Herschel–Bulkley yield-stress fluid is described, above yield, by

$$\sigma=\sigma_y+k\dot\gamma^n,$$

with parameters obtained from stress–rate measurements under defined conditions. A cat resisting relocation has not thereby supplied $\sigma_y$, $k$, or $n$. Calling claws a yield transition is a punchline, not a fitted flow curve.

The Rayleigh–Plateau instability is even more specific. It concerns the surface-tension-driven breakup of a liquid cylinder. A cat coiling in a narrow container has bones, skin, active control, and contact forces; it is not a free liquid jet. Writing the jet’s dispersion relation beside the photograph adds formalism without establishing a shared instability mechanism.

No animal handling is needed to make either point. The photographs are enough.

Why the Deborah Number Still Matters

Outside cat physics, the ratio is useful precisely because researchers can define and measure the relevant material response. In polymer processing it helps compare molecular relaxation with a deformation time. In glaciology it helps distinguish rapid elastic or brittle response from long-term creep. In geophysics it helps explain why the mantle can transmit shear waves yet deform over millions of years. The numerical value remains model- and process-specific; “the Deborah number of this material” is incomplete unless the timescale and relaxation mode are identified.

The cat in the salad bowl therefore teaches two lessons. The first is Reiner’s: solid-like and fluid-like behaviour can depend on the clock. The second is more editorial: a dimensionless number does not turn an analogy into a measurement.

The material in the bowl is a cat.

Literature checked through 2026-07-11.

References

  • Fardin, M.-A. (2014). On the rheology of cats. Rheology Bulletin, 83(2), 16–17.

  • Reiner, M. (1964). The Deborah number. Physics Today, 17(1), 62. https://doi.org/10.1063/1.3051374

  • Barnes, H. A., Hutton, J. F., & Walters, K. (1989). An Introduction to Rheology. Elsevier.

Changelog

  • 2025-12-15: Fixed Deborah number in summary from 0.08 to 0.008 (matching the body calculation: 5/600 = 0.00833).
  • 2025-12-15: Corrected Fardin’s institutional affiliation from “Paris Diderot University” to “ENS Lyon”; his affiliation on the 2014 paper is Université de Lyon / ENS Lyon.
  • 2026-07-11: Reframed cat rheology as Fardin’s deliberate analogy, removed invented feline material parameters and inapplicable instability claims, and retained one explicitly hypothetical Deborah-number calculation.