• Pixel-art sticker of Capillum, personifying Capillary Rise, with the caption “Thinner Tube, Higher Rise.”

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Capillum

Capillary Rise Physics

\[h = \frac{2\gamma\cos\theta}{\rho g r}\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

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

Meet Capillum, a thin glass tube who lifts water up inside herself with no pump at all.

Water molecules are attracted to glass more strongly than to each other, so water climbs the walls of a narrow tube. Surface tension pulls the column up until its weight balances the upward pull. This rise is described by Jurin's law, named after James Jurin, who studied it in 1718.

The narrower the tube, the higher the water goes. For clean glass, the contact angle is close to 0, so cos θ ≈ 1. With water's surface tension of 0.0728 N/m, a tube of radius 0.5 mm gives h ≈ 2 × 0.0728 / (1000 × 9.81 × 0.0005) ≈ 0.030 m, about 3 cm.

Mercury does the opposite. It is attracted to itself more than to glass, so its contact angle is greater than 90°, cos θ is negative, and the level in the tube sits below the level outside.

Paper towels, candle wicks and soil all draw water up through tiny gaps. In tall trees, capillary action helps, but most of the lift comes from water evaporating at the leaves.

Equations

\[h = \frac{2\gamma\cos\theta}{\rho g r}\]
Symbols
SymbolMeaningUnit
\(h\) height of rise \(\mathrm{m}\)
\(\gamma\) surface tension of the liquid \(\mathrm{N/m}\)
\(\theta\) contact angle between liquid and tube \(\mathrm{rad}\)
\(\rho\) density of the liquid \(\mathrm{kg/m³}\)
\(g\) gravitational field strength \(\mathrm{m/s²}\)
\(r\) radius of the tube \(\mathrm{m}\)