Illustrated Physics
physics, drawn
Concept

Jurin law — where it appears

The rule that a liquid rises in a narrow tube to a height inversely proportional to the tube's radius, set by surface tension against the weight of the column. It assumes rigid walls, and a millimetre tube lifts water about fifteen millimetres.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The column that overshoots its own height. The height of water in a vertical glass tube, as a fraction of Jurin's equilibrium height 2γ/ρgr, against time for tubes of radius 0.2, 0.4, 1, 2 mm, integrated from the capillary pull, the weight and the Poiseuille drag with the inertia of the rising column. The 0.2 mm tube (Jurin height 74.4 mm) creeps up without overshooting; the 0.4 mm tube (Jurin height 37.2 mm) creeps up without overshooting; the 1 mm tube (Jurin height 14.9 mm) overshoots to 1.33 of it; the 2 mm tube (Jurin height 7.4 mm) overshoots to 1.46 of it. The linearised motion about the equilibrium is underdamped when the radius exceeds (32η²γ/ρ³g²)^(1/5) = 0.48 mm for water: wider tubes ring, narrower ones do not.

The pore that lifts highest fills slowest

Jurin's law says how high water climbs in a tube and nothing about how long it takes. The rise has three laws in succession — the column's inertia, then its viscous drag, then its weight — and the same narrowness that lifts water highest throttles it hardest, so for any deadline there is a best pore. A wide enough tube does something Jurin's law cannot: it overshoots and rings. And whatever the route, exactly half the energy the surface releases is lost.

fluids · Capillarity The pull of a meniscus against the stiffness of a wall. For two neighbouring lines of a wet pattern leaning towards each other, the net Laplace pressure pulling them together (heavy curve) and the bending stiffness pushing them back (straight lines), against the lean as a fraction of the half-gap. The pull grows faster than linearly, because narrowing a gap raises its suction, and it diverges as the gap closes. The stiffness is a straight line whose slope falls as the fourth power of the line's height; the lines drawn are for 0.8 times, 1 times, 1.25 times the critical height. At 0.8 of the critical height the straight state is stable and an unstable balance lies at a lean of 0.77 of the half-gap, a barrier the lines must be pushed over; at the critical height the two start with the same slope and the straight state is marginal; at 1.25 times the straight state is unstable and the pair collapses.

The walls a rinse pulls together

Every result about capillary rise assumes the walls hold still. Make them thin enough and they do not. The water between two walls is below atmospheric pressure, so it pulls them together, and as the gap narrows the suction grows. Beyond a critical height or length the walls cannot push back and they snap shut. It is why wet hair clumps, why a paintbrush comes out of water as a point, and why a chip factory cannot rinse lines of resist taller than about three times their width without laying them flat.

fluids · Capillarity

Named alongside it

The objects these essays reach for when they reach for this one.

Bending stiffnessCapillarityCapillary riseCritical dampingDissipationElastic instabilityElastocapillarityInertiaLaplace pressurePattern collapsePoiseuille flowSupercritical drying

All concepts