• Pinchette – Plateau–Rayleigh physics T-shirt
  • Pinchette – Plateau–Rayleigh physics T-shirt
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PinchettePlateau–Rayleigh Instability

Pinchette – Plateau–Rayleigh Instability Physics T-Shirt

$29.99 USD
$29.99 USD
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Color
White · Black
Size
S–5XL
Made
To order · shipping times

Why does a thin stream from a tap break into drops? Surface tension pulls a liquid column toward less surface area. Ripples longer than the column’s circumference reduce that area, so they grow until the stream pinches into beads. Joseph Plateau and Lord Rayleigh worked it out, and Pinchette pours it. Pixel-art unisex tee; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

ShippingFree US

Free US shipping · $10 flat shipping outside the US. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A thin stream from a tap does not stay a cylinder. It ripples, pinches and breaks into a line of drops.

Surface tension wants the least surface area for the volume. Joseph Plateau found that any ripple longer than the stream's circumference lowers the area and so grows; Lord Rayleigh showed in 1878 that the fastest-growing one is about 4.5 diameters long, which sets the size of the drops.

Pinchette breaks into beads.

Equations

\[\lambda > 2\pi R\;\;\Rightarrow\;\;\text{unstable}\]
\[\sigma^{2} = \frac{\gamma}{\rho R^{3}}\,kR\,\left(1 - k^{2}R^{2}\right)\frac{I_1(kR)}{I_0(kR)},\qquad kR\big|_{\max}\approx 0.697\]
SymbolMeaningUnit
\(\lambda\) wavelength of a ripple along the stream \(\mathrm{m}\)
\(R\) radius of the liquid cylinder \(\mathrm{m}\)
\(\sigma\) growth rate of the ripple (inviscid jet) \(\mathrm{s^{-1}}\)
\(\gamma\) surface tension \(\mathrm{N/m}\)
\(\rho\) density of the liquid \(\mathrm{kg/m^3}\)
\(k\) wavenumber (2\pi/\lambda) \(\mathrm{rad/m}\)
\(I_0, I_1\) modified Bessel functions of the first kind \(\mathrm{–}\)

Sources

  1. Eggers (1997) Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys. 69, 865
  2. Rayleigh (1878) On the Instability of Jets, Proc. London Math. Soc. 10, 4
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