Pedro Reis, Sunghwan Jung, Jeffrey Aristoff, and Roman Stocker had the same impulse, with better equipment. Their 2010 paper in Science, “How Cats Lap: Water Uptake by Felis catus,” is one of the more elegant pieces of dimensional analysis in recent biology.

How Cats Do Not Drink

The simplest hypothesis — that cats curl the tongue into a spoon and scoop water into the mouth — is false. High-speed photography shows that the cat’s tongue does not form a cup shape. Instead, the cat extends the tongue tip downward toward the water surface and then rapidly retracts it. The motion is fast — too fast for normal video — and the tongue barely contacts the surface.

The contrast with dogs is instructive. Dogs do scoop: the tongue curls backward (not forward), forming a ladle shape that scoops water upward and backwards into the mouth. The mechanism is vigorous and inefficient — a significant fraction of the water misses the mouth entirely, which is why drinking dogs produce splashing and dogs often have wet chins. The mechanism works but is inelegant.

Cats produce almost no splash. The mechanism is different in kind.

The Physical Mechanism

Reis et al. (2010) used high-speed photography (1000 frames per second) to resolve the cat’s lapping motion. Their observations:

1. The cat extends the tongue tip downward until the dorsal surface (the top side) just touches the water surface. The ventral surface (the smooth underside) does not contact the water.

2. The cat then rapidly retracts the tongue upward. The tongue tip is moving at roughly $v \approx 0.7\,\mathrm{m/s}$ during this retraction.

3. As the tongue tip pulls away from the surface, a column of liquid is pulled upward by the adhesion between the liquid and the retreating tongue. The column rises against gravity.

4. The column eventually stalls — inertia is overcome by gravity — and begins to fall back. The cat closes its jaw at exactly the moment of maximum column height, capturing the peak volume of water.

5. The cat then extends the tongue for the next lap.

The cat closes its jaw before the tongue fully retracts. This is important: the jaw closure captures the water column, not the water adhering to the tongue. The tongue is the mechanism that creates the column; the jaw captures it.

Dimensional Analysis: The Froude Number

The relevant competition is between inertia (which drives the column upward) and gravity (which pulls it back down). Surface tension plays a role in stabilising the column but is not the primary factor governing the column height.

The balance between inertia and gravity for a fluid column moving at speed $v$ and of characteristic length scale $L$ (here, the diameter of the tongue tip, $L \approx 5\,\mathrm{mm}$ for a domestic cat) is captured by the Froude number:

where $g = 9.81\,\mathrm{m/s}^2$ is gravitational acceleration.

When $\mathrm{Fr} \ll 1$: gravity dominates, inertia is insufficient to pull a significant column of water upward. Very slow tongue motion would lift almost no water.

When $\mathrm{Fr} \gg 1$: inertia dominates, the column rises far above the surface but the jaw must be closed quickly before the large amount of water falls back. Very fast tongue motion wastes water and requires rapid jaw closure.

The optimal lapping frequency — maximising captured volume per lap — occurs near $\mathrm{Fr} \approx 1$, where inertial and gravitational forces are comparable and the column height is matched to the jaw closure dynamics.

Checking the Numbers for a Domestic Cat

For a domestic cat:

• Tongue tip diameter: $L \approx 5\,\mathrm{mm} = 5 \times 10^{-3}\,\mathrm{m}$
• Characteristic tongue tip speed: $v \approx 0.7\,\mathrm{m/s}$

Reis et al. found Fr of order unity — inertial and gravitational forces comparable — confirming that the lapping speed is tuned to the inertia-gravity balance. (The exact numerical value depends on the choice of characteristic length scale; using the tongue tip diameter as above gives Fr in the range 1–3, squarely in the regime where neither force dominates.)

Scaling Across Felids

The Froude number prediction yields a scaling law for lapping frequency across felid species of different sizes. If all felids lap at $\mathrm{Fr} \approx 1$, then the characteristic speed scales as $v \sim \sqrt{gL}$, and the lapping frequency scales as:

where $d$ is the distance the tongue travels per lap (roughly proportional to tongue length, which scales with body size). Since $L \sim d$ scales with body size, we get:

Larger cats have longer tongues and lap more slowly. The prediction is that lapping frequency scales as the square root of inverse tongue length — or, equivalently, as the inverse square root of body mass (since linear dimensions scale as mass$^{1/3}$):

Reis et al. tested this against high-speed footage of large felids. A domestic cat laps at approximately $4\,\mathrm{Hz}$; a lion laps at approximately $1.2\,\mathrm{Hz}$; a tiger at roughly $1\,\mathrm{Hz}$. The scaling is consistent with $f \propto m^{-1/6}$ across three orders of magnitude in body mass.

The table below shows the predicted versus observed scaling:

The $m^{-1/6}$ scaling captures the correct trend — larger cats lap more slowly — though the predicted frequencies for the largest cats somewhat overestimate the observed values. The discrepancy may reflect the limitations of the simple allometric assumption (that all linear dimensions scale as $m^{1/3}$) and the fact that tongue geometry does not scale isometrically across the full range of felid body sizes.

Why Not Just Lick?

A natural question: why not simply allow the tongue to fully submerge and absorb water through the papillae, as the tongue already contacts water when lapping? Several answers:

1. Papillae are not sponges. Feline papillae are hollow and scoop-shaped (filiform papillae with hollow tips), optimised for grooming and food manipulation, not passive absorption. Active wicking is limited.

2. The cat cannot breathe with its mouth submerged. A lapping mechanism that keeps the mouth mostly closed except for the brief jaw-closure moment allows continuous breathing through the nose during drinking.

3. Speed and efficiency. The inertial column mechanism delivers significantly more water per jaw movement than surface tension adhesion alone. At 4 laps per second, a domestic cat takes in roughly $0.14\,\mathrm{mL}$ per lap, for a total of roughly $34\,\mathrm{mL/min}$ — comparable to sipping rates in animals that use more direct intake mechanisms.

The cat has converged on a hydrodynamically optimal strategy under the constraint of keeping the oral cavity mostly sealed during the intake cycle.

The Robotic Tongue

Reis et al. constructed a robotic cat tongue to verify the mechanism: a smooth glass disc lowered to the water surface and retracted at controlled speeds. The column height as a function of speed followed the predicted inertia-gravity balance, confirming that the mechanism does not depend on any specifically biological property of the tongue — it is a fluid dynamics result that applies to any surface moving away from a water interface at the right speed.

The robot lapped at the same Froude number as the cat.

Dogs, Horses, and the Comparison

Dogs cup the tongue caudally (backwards) rather than ventrally, forming a ladle. The mechanism is faster and delivers more water per stroke but is messy — the ladle is formed outside the mouth, and water sloshes freely. Dogs lap at roughly $3\,\mathrm{Hz}$ with a tongue tip speed significantly higher than cats, producing Fr well above unity. The excess inertia is why dog drinking generates splashing.

Horses, by contrast, create a near-seal with their lips and use suction — a fundamentally different mechanism that requires no tongue projection at all. The lapping mechanism of felids is phylogenetically specific and appears to have evolved under selection pressure for both efficiency and noise suppression, consistent with the ambush-predator lifestyle. A cat that splashed while drinking would alert prey at a water source. A cat that laps near-silently does not.

A Note on the Measurement

Getting reliable high-speed footage of a cat drinking is harder than it sounds. Our cats drink at different times of day, in different moods, and the presence of a camera tripod next to the water bowl is regarded as grounds for drinking elsewhere. Pedro Reis et al. solved this by filming their laboratory cat, Cutta Cutta, in a controlled setting. Their footage is available online and is genuinely beautiful: a slow-motion waterfall in miniature, rising improbably from the tongue tip and held there by the balance between upward momentum and downward gravity, until the jaw swings shut.

The physics is in the timing.

References

• Reis, P.M., Jung, S., Aristoff, J.M., & Stocker, R. (2010). How cats lap: Water uptake by Felis catus. Science, 330(6008), 1231–1234. https://doi.org/10.1126/science.1195421

• Aristoff, J.M., Stocker, R., Jung, S., & Reis, P.M. (2011). On the water lapping of felines and the water running of lizards. Communicative & Integrative Biology, 4(2), 213–215.

• Vogel, S. (1994). Life in Moving Fluids: The Physical Biology of Flow (2nd ed.). Princeton University Press.

Changelog

• 2025-12-15: Updated water intake per lap from 0.04 mL to 0.14 mL (Reis et al. report ~0.14 +/- 0.04 mL per lap; the previous value was the standard deviation), and updated the intake rate accordingly (~34 mL/min). Updated the papillae location from ventral to dorsal surface. Updated the Aristoff et al. reference to the correct 2011 Communicative & Integrative Biology article. Removed the Jung & Kim (2012) PRL reference (article number 034501 resolves to a different paper).

The material is a liquid. The material is also a cat.

The Definition of a Fluid

The intuitive distinction between solids and liquids is that solids hold their shape and liquids conform to their container. But this distinction is one of timescale, not of material identity.

A classic demonstration: place a ball of silly putty on a table. Over the course of an hour, it flows slowly outward, taking the shape of the table surface — clearly a liquid. Strike it sharply with a hammer and it shatters — clearly a solid. The material has not changed. The timescale of the interaction has.

The same principle applies to glass (contrary to popular myth, medieval window glass is not thicker at the bottom because it has flowed — the variation is from the manufacturing process, and the relaxation time of soda-lime glass at room temperature is of order $10^{23}$ years — but at elevated temperatures near the glass transition, silicate glass flows readily). It applies to mantle rock, which is solid on the scale of earthquake waves and liquid on the scale of continental drift. It applies to pitch, to ice sheets, to asphalt on a hot day.

The formal tool for capturing this is the Deborah number.

The Deborah Number

The Deborah number was introduced by Marcus Reiner in 1964, in a short note in Physics Today (Reiner 1964). It is defined as:

where $\tau$ is the relaxation time of the material — roughly, the characteristic time over which it can rearrange its internal structure and relieve stress — and $T$ is the observation time or the timescale of the imposed deformation.

• $\mathrm{De} \ll 1$: The material relaxes quickly relative to the timescale of observation. Internal stresses are continuously relieved. The material behaves as a fluid.
• $\mathrm{De} \gg 1$: The material relaxes slowly relative to the observation timescale. Internal stresses persist. The material behaves as a solid.
• $\mathrm{De} \sim 1$: The material is in a viscoelastic regime — partly fluid, partly solid, exhibiting time-dependent behaviour that is neither.

The name comes from the prophetess Deborah, who sang in Judges 5:5: “The mountains flowed before the Lord.” At the timescale of a divine perspective, mountains are liquid. At the timescale of a human lifetime, they are not. Reiner’s point was that the solid-liquid distinction is not a property of the material but of the relationship between the material’s internal dynamics and the observer’s timescale.

For Newtonian fluids (water, air at ordinary conditions), $\tau \to 0$ and $\mathrm{De} \to 0$ for any finite observation time — they are always liquid. For a perfectly elastic solid (an ideal spring), $\tau \to \infty$ and $\mathrm{De} \to \infty$ for any finite observation time — always solid. Real materials lie between these extremes.

The Maxwell Viscoelastic Model

The simplest model of a material with a finite relaxation time is the Maxwell element: a spring (elastic, spring constant $G$) in series with a dashpot (viscous, viscosity $\eta$). Under a step stress $\sigma_0$ applied at time $t = 0$, the strain evolves as:

where $\tau = \eta / G$ is the Maxwell relaxation time. The first term is the instantaneous elastic deformation of the spring; the second is the linear viscous creep of the dashpot. For $t \ll \tau$, the elastic strain dominates and the material behaves as a solid; for $t \gg \tau$, the viscous flow dominates and the material behaves as a liquid. The material “decides” whether to be solid or liquid depending on the ratio of $\tau$ to the duration of the applied stress — which is precisely the Deborah number.

The creep compliance $J(t) = \epsilon(t)/\sigma_0 = t/\eta + 1/G$ grows linearly with time for $t \gg \tau$, confirming liquid behaviour on long timescales. The relaxation modulus $G(t) = \sigma(t)/\epsilon_0 = G e^{-t/\tau}$ decays exponentially to zero, confirming that the material cannot sustain a permanent stress — again, liquid behaviour on long timescales.

On the Rheology of Cats

In 2014, Marc-Antoine Fardin, a physicist at the ENS Lyon, published “On the Rheology of Cats” in the Rheology Bulletin 83(2), 16–17. The paper asked whether cats satisfy the defining rheological criterion for liquids, using the Deborah number as the test. Fardin was awarded the 2017 Ig Nobel Prize in Physics — which is awarded for research that “makes you laugh, then makes you think” — for this work.

The paper is not a joke. It is standard rheology applied to an unusual material, with appropriately hedged conclusions and correct citations to the primary literature on viscoelastic flow. The humour is in the application; the physics is serious.

Estimating the Cat’s Relaxation Time

The relaxation time $\tau$ of a cat is the time scale over which the cat’s body deforms to fill a container. This is observable. A cat placed near a suitable container — a salad bowl, a cardboard box, a bathroom sink — adopts a conformed shape on a timescale of roughly 5–30 seconds. The initial posture (stiff, alert) gives way to a relaxed conformation as the cat assesses the container and adjusts. Fardin estimated $\tau \approx 1$–$30$ seconds, with the exact value depending on the container’s attractiveness to the specific cat.

This is the material’s characteristic relaxation time. The fact that it is finite — that the cat does eventually conform to the container — is the essential observation.

Computing the Deborah Number for Various Situations

Scenario 1: Cat in a sink. A cat taking ten minutes to settle into a bathroom sink. Observation time $T = 600\,\mathrm{s}$, relaxation time $\tau \approx 5\,\mathrm{s}$.

The cat is unambiguously a liquid.

Scenario 2: Cat in a cardboard box. Conformation over approximately 30 minutes, $\tau \approx 20\,\mathrm{s}$.

Liquid.

Scenario 3: Cat dropping from a bookshelf. Contact time during a jump approximately $T \approx 0.05\,\mathrm{s}$, relaxation time still $\tau \approx 5\,\mathrm{s}$.

Solid. The cat does not deform into the shape of the bookshelf during the jump; it rebounds elastically.

Scenario 4: Cat startled by a loud noise. Reaction time $T \approx 0.3\,\mathrm{s}$, $\tau \approx 5\,\mathrm{s}$.

Solid. On short timescales, cats behave as elastic materials — they spring, they bounce, they do not flow.

The cat is neither permanently solid nor permanently liquid. It is a viscoelastic material whose phase classification depends on the timescale of the interaction. This is not a loose analogy; it is the definition of viscoelasticity.

Non-Newtonian Behaviour and Flow Instabilities

Fardin noted an additional complication: cat flow is not Newtonian. A Newtonian fluid has a viscosity $\eta$ that is independent of the applied shear rate $\dot\gamma$. Many real materials are shear-thinning (viscosity decreases with increasing shear rate — ketchup, blood, many polymer solutions) or shear-thickening (viscosity increases with increasing shear rate — cornstarch suspension, some dense suspensions). Cats, Fardin observed, appear to be shear-thinning: the more rapidly you attempt to move a relaxed cat from its current position, the more “liquid” (accommodating, compliant) it becomes, up to a point at which the cat transitions to solid behaviour (claws, teeth).

This is, formally, the behaviour of a yield-stress fluid: a material that behaves as a solid below a critical stress $\sigma_y$ and flows above it. The Herschel–Bulkley model describes such fluids:

where $k$ is the flow consistency index and $n < 1$ for shear-thinning. The challenge of fitting $k$, $n$, and $\sigma_y$ for a specific cat is experimental, and Fardin acknowledged this was left to future work.

The Deborah number and the yield stress together provide a two-parameter phase diagram for cat rheology:

• Low stress, short timescale: solid (De ≫ 1 or σ < σ_y)
• Low stress, long timescale: liquid (De ≪ 1)
• High stress: yield, followed by flow

Flow Instabilities: The Rayleigh-Plateau Connection

Fardin also noted that cats confined to containers thinner than their body diameter can exhibit flow instabilities. A cat attempting to fit into a glass too narrow for its body will sometimes adopt a helical or coiled configuration — an instability reminiscent of the Rayleigh–Plateau instability of a liquid jet.

The Rayleigh–Plateau instability occurs when a cylindrical fluid jet of radius $r_0$ is subject to perturbations of wavelength $\lambda > 2\pi r_0$. Modes with wavelength longer than the cylinder’s circumference are unstable and grow, breaking the jet into droplets. The dispersion relation for growth rate $\sigma$ as a function of wavenumber $k = 2\pi/\lambda$ (for an inviscid jet) is:

where $\gamma$ is surface tension and $I_0, I_1$ are modified Bessel functions. The analogy with a cat is inexact — surface tension is not the dominant restoring force — but the qualitative instability mechanism (a long cylinder of material is unstable to perturbations whose wavelength exceeds the cylinder’s circumference) appears to apply, suggesting that very elongated cats in very narrow containers should be unstable to coiling. This is, again, left to future experimental work.

Why the Deborah Number Matters (Outside of Cat Physics)

The Deborah number is not a curiosity; it is a central dimensionless number in engineering and materials science.

Polymer processing: The flow of polymer melts through injection-moulding channels involves De in the range $10^{-2}$–$10^2$. Too high a De leads to elastic instabilities, melt fracture, and surface defects in the finished part.

Blood rheology: Blood is a non-Newtonian viscoelastic fluid. In the large arteries (low shear rate), red blood cells aggregate into rouleaux and blood behaves as a shear-thinning fluid. In the capillaries (high shear rate), rouleaux break up and individual cells deform to fit through vessels smaller than their resting diameter — liquid behaviour on short length scales.

Geophysics: The mantle is an elastic solid for seismic waves ($T \sim$ seconds, De ≫ 1) and a viscous fluid for convection ($T \sim 10^8$–$10^9$ years, De ≪ 1). The same material. Different Deborah numbers.

Glaciology: Ice is an elastic solid for rapid fracture (calving of icebergs) and a viscous fluid for glacier flow. The transition occurs at timescales of years to decades, depending on temperature and stress.

The cat is in good company.

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 (Rheology Series, Vol. 3).

• Bird, R.B., Armstrong, R.C., & Hassager, O. (1987). Dynamics of Polymeric Liquids, Vol. 1: Fluid Mechanics (2nd ed.). Wiley-Interscience.

• Eggers, J. (1997). Nonlinear dynamics and breakup of free-surface flows. Reviews of Modern Physics, 69(3), 865–930. https://doi.org/10.1103/RevModPhys.69.865

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 Rheology Bulletin paper is Université de Lyon / ENS Lyon (CNRS UMR 5672). He moved to Paris Diderot later in 2014, after the paper was published.