Kayella: Kaye Effect

Mechanics, Chaos & Fluids arc, page 100 of 193. Back to The Pixelated Physics Universe

Who they are

Kayella pours a ribbon of shampoo, and it leaps back up off the heap.

Kayella is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

Shampoo is shear-thinning: the faster it is sheared, the runnier it gets. A falling stream builds a heap, cuts a dimple in it, and slides out of the dimple on a thin, highly sheared lubricating layer, leaping back up. Each leap lasts about a second before it collapses. A. Kaye described it in 1963, and Versluis et al. explained the stable effect in 2006.

$$ \begin{gathered} \eta = K\,\dot{\gamma}^{\,n-1}, \qquad n < 1 \ (\text{shear-thinning}) \end{gathered} $$

Symbol Meaning SI unit
$\eta$ apparent (shear) viscosity Pa·s
$K$ consistency index Pa·sⁿ
$\dot{\gamma}$ shear rate 1/s
$n$ flow-behaviour index (n < 1 shear-thinning, n = 1 Newtonian) 1

Honest caveat: It is not an elastic bounce: the stream slides out on a lubricating layer.

Sources

Crossovers

Kayella meets Ayrtha (Hertha Ayrton, the Electric Arc and Sand Ripples). Ayrtha also studied sand ripples formed by moving water. Kayella's shampoo stream leaping off its own heap is another fluid surprise, where the flow builds the shape that then redirects it.

Kayella meets Clustrelle (Cheerios Effect). Kayella's shampoo is shear-thinning, so it gets runnier as it is sheared. Clustrelle's floating bubbles attract because surface tension bends the liquid surface. Both are everyday puzzles where the fluid's own shape drives the motion.

Kayella meets Flagella (Corkscrew Escape). Flagella swims at a low Reynolds number, where viscosity wins completely. Kayella's shampoo has a viscosity that depends on shear. Both live where the fluid's stickiness rules.

Wear the lore

Concept keywords: Kaye Effect, Kayella, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics