Why does water climb a paper towel?
Touch a paper towel to water and watch water climb its tiny gaps. No pump lifts it: water is attracted to the fibers, and its surface tends to pull tight. Together, these effects help it rise.
Look at the surface inside a fine tube: it curves upward along the wall. An upward pull supports the water while gravity pulls down. The level stops when the two balance. With the same water and wall material, a narrower tube usually lets water rise higher.
A wall that water does not wet easily changes the surface shape and can reverse the rise. Follow the surface and compare where it stops.
Three observations with towels and straws
You need a glass of dyed water (so levels are visible), a few paper towels and straws of different bores. Change one thing at a time:
- Towel bridge. Twist a towel into a rope, dip one end into the tall glass of water and drape the other into an empty, lower glass. After half an hour, water has travelled over the rim, drop by drop, into the lower glass—exactly chapter one of the demonstration.
- Change the bore. Stand a wide straw and a thin one (or a coffee stirrer) in the same glass. Guess which level rises higher, then compare the two columns side by side.
- Change the wall. Put a drop of water on glass and another on waxed paper: compare spreading with beading. Ordinary plastic straws may already repel water, and coating their insides evenly is difficult; use clean fine glass tubes for a classroom level comparison.
While observing, keep your eye on the meniscus: the deeper it hollows and the higher it climbs the wall, the higher the column stands. The shape changes first; the height follows.
Jurin’s law: five quantities decide the height
More: a closer explanation
Touch a towel’s corner to the water and the water starts climbing. Nobody pushes it and no pump is involved—the upward pull hides in the water’s own surface.
Water molecules attract one another. Molecules at the surface are pulled inward, so the surface behaves like a taut elastic film always trying to shrink: that contractile pull is surface tension. When water meets a solid it likes—glass, paper fibres—its molecules rush to hug it; this is wetting. The hugging water drags the surface upward, forming an upward-hollowed meniscus in a narrow tube.
Once the meniscus curves, the whole surface film hauls the column up along the wall: the pull points up while the column’s weight points down. Water stops at the height where the two exactly balance. The finer the tube, the wall pull decreases, but the column area decreases even faster, so the water climbs higher—the height runs inverse to the tube’s radius.
Coat the wall with wax, and water no longer cares to cling. The contact angle passes 90°, the meniscus bulges upward, and the level inside ends up below the cup’s. Climb or press down—it all depends on whether water wants that wall.
Open: from the pull–weight balance to the formula
Let surface tension be γ, the contact angle θ, the density ρ, gravity g and the tube radius r. Around the wall, the upward component of surface tension is 2πr·γcosθ; the column’s weight is ρg·πr²h. Balancing the two:
With teaching values γ = 0.0728 N/m (water), ρ = 1000 kg/m³ and g = 9.81 m/s², water in a 1 mm glass tube (θ≈0°) rises about 14.8 mm; at 0.1 mm, about 148 mm. The radius sits in the denominator—halve the gap and the climb doubles. Alcohol’s surface tension is roughly a third of water’s, so it climbs visibly lower under the same conditions; on waxed walls θ≈105°, cosθ turns negative and the formula returns a depression instead of a rise.
Open: what the contact angle measures
The contact angle is measured at the meeting point of liquid, wall and air; it says how eagerly the liquid hugs that wall. Water on clean glass has θ≈0° and spreads completely; on paraffin θ≈105° and it beads up. Within one formula, a change of sign in cosθ turns climbing into pressing down—material choice matters as much as gap size.
The model’s limits: capillarity is not a lift for tall trees
Shrink r to 0.05 mm—paper-towel pore territory—and the formula still offers only about 30 cm; this is a result for that radius, not a universal height limit. Finer ideal pores can lift water higher, though flow becomes slower. A forty-metre tree raises water on transpiration’s negative pressure from its leaves, plus the tensile strength of the water column itself; wetting and cohesion support the continuous pathway together with the transpiration pull; they are not a separate lift confined to the tree base. To follow that road, see the plant-water scene. The rigorous treatment of surface tension and capillarity follows OpenStax College Physics, surface tension; water’s travel through soil and plants is explained by USGS on capillary action.
Next time you watch a wick burn, a wall dampen or a pen write, try naming which of the quantities dominates: the fineness of the gap, or the wall’s appetite for water.