Jurin's law
Halve the bore, double the rise
Height rises in exact inverse to the tube's radius. A half-millimetre bore lifts water
near thirty millimetres; open the bore to a full millimetre and the climb falls by half.
The bank reads the law directly — the thinnest tubes stand tallest.
h = 2γ·cosθ / (ρ·g·r) · h ∝ 1/r
The meniscus
A surface that curves to the wall
Because glass wets, water is highest where it touches the wall and lowest in the middle —
a concave dish. That curvature is the skin under tension, and the tighter the bore the
deeper the dish. The bright line along each top is light catching the taut surface.
contact angle θ ≈ 0° on clean glass
Coalescence
Two drops become one, at once
Let a bead grow at the rim and the moment it touches the column the skin cannot hold two
surfaces — they snap into one in under a millisecond, and the shock rings the whole column.
Tap the glass yourself and you set the same oscillation going.
merge time ~ 10⁻³ s · then damped ringing