The Kaye Effect: Why Shampoo Leaps Off the Pile

What you actually see

Take a bottle of ordinary shampoo and pour a thin, steady stream from about 10–30 cm onto a flat plate. At first the stream just piles up into a glistening mound. Then, seemingly at random, a slender jet of shampoo darts out of the heap, arcing several millimetres to a few centimetres up and sideways before falling back and rejoining the puddle. Left alone the leaping starts and stops — it is intermittent. Speed it up with a slow, controlled pour and you can coax it into repeating many times a second.

The British engineer Alan Kaye published the first account in a one-paragraph note, "A Bouncing Liquid Stream," in Nature in 1963. For decades it stayed a party trick, occasionally re-examined (Collyer and Fisher revisited it in Nature in 1976 and pinned it on shear-thinning). The full mechanism had to wait for fast cameras.

The mechanism: an air-lubricated ski jump

In 2006 Michel Versluis, Detlef Lohse and colleagues at the University of Twente filmed the effect at thousands of frames per second ("Leaping shampoo and the stable Kaye effect"). The causal chain they revealed is beautifully mechanical:

1. The falling jet presses a small dimple into the heap. Because the shampoo is stiff at low shear, the dimple holds its shape — it becomes a curved ramp.
2. As the jet dives into the dimple it drags a whisker-thin layer of air along with it. This entrained film (of order a micrometre thick) sits between the incoming jet and the pool.
3. That air film prevents coalescence: the jet cannot merge into the heap because they never actually touch.
4. Where the jet bends against the ramp it is sheared very hard, so its viscosity locally collapses and the near-surface liquid slides freely.
5. The curved dimple wall redirects the jet's momentum — a ski jump — and it launches back out, thinner and faster than it came in.

No elasticity, no rebound energy stored in a spring. Just lubricated redirection of momentum.

Why it must be shear-thinning

The secret ingredient is that shampoo, shower gel and liquid soap are shear-thinning (pseudoplastic): their viscosity falls as the shear rate γ̇ rises. A simple power-law captures it:

η(γ̇) = K · γ̇ⁿ⁻¹, with n < 1 (roughly n ≈ 0.2–0.5 for shampoo).

This dual personality is exactly what the effect needs. At the low shear inside the heap the liquid is stiff (η₀ ≈ 1–10 Pa·s), so the dimple ramp stays firm instead of slumping. At the high shear where the jet skids along the air film the viscosity plummets — by one to three orders of magnitude, to ~0.01–0.1 Pa·s — so the streamer flows like something far runnier and leaves cleanly. A Newtonian fluid can never do both at once: honey holds a ramp but is too gummy to leap, and water leaps off nothing because its air film instantly ruptures. Shear-thinning gives you stiff-where-you-need-it and slippery-where-you-need-it in a single liquid.

Running the numbers

Pour from a height h ≈ 0.15 m. The jet arrives at v = √(2gh) = √(2·9.81·0.15) ≈ 1.7 m/s, in a stream about 1–3 mm across. Where it bends against the ramp over a contact length of order a millimetre, the shear rate is roughly γ̇ ≈ v / δ ≈ 1.7 / (5×10⁻⁴) ≈ 3×10³ s⁻¹ — comfortably in the 10³–10⁴ s⁻¹ band where shampoo has already thinned dramatically.

That flips the flow regime. Using the bulk viscosity (~5 Pa·s), the Reynolds number Re = ρvd/η ≈ 1030·1.7·0.002 / 5 ≈ 0.7 — deeply viscous. But in the sheared streamer, with η ≈ 0.05 Pa·s, Re ≈ 70: now inertia can carry the jet up and out. The entrained air film that makes it all possible is only ~1–10 µm thick (an order-of-magnitude estimate — it is hard to measure directly), and the whole leap plays out over just a few milliseconds, which is why you need a high-speed camera to see the ramp at all.

Stable versus intermittent — the inclined-plane trick

On a flat plate the Kaye effect flickers on and off, and there is a tidy reason. The leaping streamer lands nearby and builds up a little secondary pile. Sooner or later that pile grows tall enough to intercept the incoming jet, spoiling the delicate dimple geometry, and the leaping stops until the heap redistributes. It is a self-limiting, self-restarting instability.

The Twente group's clever fix — the "stable Kaye effect" — was to pour onto a gently inclined surface. Now the leaping streamer flows away downhill instead of piling up under the incoming jet, so nothing ever interrupts the geometry and the shampoo leaps continuously, sometimes for many seconds. That experiment was the clincher: it showed the effect is a steady-state fluid-mechanical process, not a random hiccup, and let them study the ramp angle and streamer thickness at leisure.

The misconception, and where the physics really lives

The tempting wrong answer is that the shampoo bounces elastically — that it stores energy like a rubber ball or recoils via polymer elasticity (a Weissenberg-style normal-stress effect). It reads that way to the eye, and shampoo does contain long surfactant and polymer chains that give it some elasticity. But the leap survives in essentially inelastic shear-thinning liquids, and the high-speed footage shows a lubricated redirection, not a stored-and-returned rebound. Elasticity and surface tension help hold the streamer together; they are not the engine.

The same air-entrainment physics is a headache in industry: in high-speed dip-coating and curtain coating, a plunging sheet or jet drags in air films that cause coating defects and non-uniform wetting — the very lubrication that delights you in the shower is a manufacturing enemy. And it is a clean lab example of jet non-coalescence, the cousin of bouncing droplets kept apart by trapped air. Next time your shampoo jumps at you, you are watching micrometre-scale air lubrication and shear-thinning rheology conspire in real time.

The Kaye effect versus two other classic jet-impact behaviours — same falling-stream setup, very different physics.

Feature	Kaye effect (shampoo)	Liquid rope coiling (honey)	Water-jet splash
Fluid rheology	Shear-thinning, non-Newtonian	Newtonian, high viscosity	Newtonian, low viscosity
Core mechanism	Air-film lubrication + local viscosity collapse redirect the jet	Viscous buckling of a compressed liquid thread	Inertial impact and cavity dynamics
Role of air	Essential — thin entrained film prevents merging	None	Bubbles entrained but incidental
Reynolds regime	Re < 1 in heap, rising to tens in sheared streamer	Re ≪ 1 (viscous)	Re ≫ 1 (inertial)
Visible outcome	Streamer leaps up and off the pile	Jet coils into a neat rope pile	Crown splash, no leap