Capillary Action: Jurin's Law and the Physics of Wicking

Surface tension, made visible in a narrow tube

Liquid molecules at a free surface are pulled inward by their neighbours, with nothing pulling back from above — this net inward pull is surface tension, and it makes the surface behave like a stretched elastic membrane trying to minimize its area. Dip a narrow glass tube into water and that membrane-like surface, where it meets the tube's inner wall, drags a thin film of liquid up the glass, and the bulk liquid below follows it — the water climbs the tube well above the level in the open dish. This is capillary action, and it is entirely a surface effect: it becomes negligible in wide vessels because gravity's pull on the extra liquid volume quickly outweighs the surface force, which is why capillarity only matters in narrow tubes, thin gaps and porous materials.

Wetting, contact angle, and the meniscus

How strongly a liquid wets a solid is measured by the contact angle θ, the angle between the solid surface and the liquid surface, measured through the liquid. Water on clean glass has θ near 0°-20° — it wets glass almost completely, and the liquid surface curves into a concave meniscus that dips at the tube's center. A liquid that does not wet a surface (θ > 90°) instead forms a convex meniscus that bulges upward at the center, and, as the next section shows, is pushed down rather than pulled up by the same tube.

Jurin's law

James Jurin quantified capillary rise in 1718 by balancing the upward force from surface tension acting around the tube's inner circumference against the weight of the liquid column it must support:

upward force   = 2πr · γ · cos(θ)     (tension along the wetted circumference)
weight of column = πr² · h · ρ · g       (liquid raised to height h)

setting them equal and solving for h:

h = 2γcos(θ) / (ρgr)

γ = surface tension,  θ = contact angle,  ρ = liquid density,
g = gravitational acceleration,  r = tube's inner radius

Rise height is inversely proportional to radius — halve the tube's radius and the liquid climbs roughly twice as high, because the lifting force scales with the wetted circumference (proportional to r) while the liquid weight to be lifted scales with cross-sectional area (proportional to r²). This is why capillary rise is dramatic in a hair-thin glass tube or the microscopic pores of a paper towel, and utterly unnoticeable in a drinking glass.

Mercury: the exception that proves the rule

Mercury does not wet glass — its contact angle with clean glass is around 140°, comfortably past 90°. Because cos(140°) is negative, Jurin's law predicts a negative rise height: mercury in a narrow glass tube is actually depressed below the level of the open reservoir, and its meniscus bulges upward into the characteristic convex dome familiar from any mercury thermometer or barometer. The same equation, the same physics, the opposite sign — because mercury's cohesive forces (mercury molecules attracting each other) dominate over its adhesive forces to glass, the reverse of water's situation.

Where capillary action actually does the work

A paper towel or a cotton wick is riddled with capillary-scale channels between fibres, which is why it draws liquid in so readily — the same Jurin's law mechanism, just in an irregular porous network instead of a single round tube. In plants, xylem vessels are narrow enough that capillary forces contribute to moving water, but Jurin's law alone would only predict a rise of centimetres for xylem-sized channels — nowhere near enough to explain water reaching the top of a tall tree. The dominant mechanism there is the cohesion-tension theory: evaporation from leaf surfaces pulls on a continuous, hydrogen-bonded column of water under tension, like sucking on a very long, very thin straw, with capillary forces in the narrow vessels helping keep that fragile, tensioned column from breaking apart.

Frequently asked questions

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