What you are looking at
Four glass tubes of decreasing bore dipped into the same reservoir. The liquid's surface acts like a taut
membrane; where it meets the wall it pulls, and in a wetting liquid that pull lifts a column up each tube.
Watch the narrowest tube climb the highest — the tell-tale of
capillary action.
Surface tension and the contact angle
Surface tension γ is the energy cost per unit area of a liquid surface (equivalently, a force per unit
length along its edge). Where the surface meets the solid it makes a
contact angle θ:
θ = 0 means perfect wetting (water on clean glass), θ > 90° means the liquid beads and is pushed
down (mercury on glass, θ ≈ 140°).
Jurin's law
The surface tension acts around the circle where liquid meets glass (length 2πr), lifting with the vertical
component γcosθ. That force supports a column of weight ρg·πr²·h. Setting lift equal to weight:
2πr·γcosθ = ρg·πr²·h ⇒ h = 2γcosθ / ρgr
The height goes as
1/r — halve the tube's radius and the liquid climbs twice as high. When
θ exceeds 90° the cosine flips sign and h is negative: the liquid is
depressed below the reservoir,
exactly what mercury does.
The pressure jump underneath
The curved meniscus is a little pressure valve. Across it the pressure jumps by the
Young–Laplace amount, set by the curvature radius R = r/cosθ:
ΔP = 2γcosθ / r = 2γ / R
That lowered pressure just under a concave meniscus is what the atmosphere pushes the column up to restore —
the same physics that inflates a soap bubble and holds a water droplet round.
The capillary length
Surface tension wins over gravity only below a natural scale, the capillary length √(γ/ρg) — about 2.7 mm
for water. Tubes and drops smaller than this are ruled by surface tension (spheres, tall capillary rise);
much larger, and gravity flattens everything into puddles.
Things to try
Shrink the tube radius and watch every column shoot up as 1/r. Switch to mercury: γ is huge but its contact
angle is ~140°, so cosθ is negative and all four columns dip
below the reservoir. Dial the contact
angle up through 90° with water and watch the rise fall to zero and then reverse.