Illustrated Physics
physics, drawn
Concept

Meniscus — where it appears

The curved surface a liquid takes where it meets a solid wall, whose shape is set by the contact angle and by the balance of surface tension against gravity. Its curvature is what supplies the pressure difference that drives capillary rise.

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

Four tubes, four heights. Water in tubes of radius 0.2, 0.4, 0.8, 1.6 mm, with each meniscus drawn as the spherical cap a 20° contact angle forces and each height computed from it. The narrowest rises 70 mm and the widest 9 mm — in inverse proportion to the radius, with nothing about the glass or the volume of water entering it.

How high water will climb

Water rises up a narrow tube against gravity, and the narrower the tube the higher it goes. The height is set by a curved surface pulling on a circumference while gravity pulls on an area, and the two scale differently — which is the whole of it.

fluids · Capillarity One line decides whether it climbs for ever. The wetting condition for a corner, drawn as a map. The horizontal axis is the corner's half-angle and the vertical axis the liquid's contact angle with the walls; the diagonal is θ + α = 90°. Below it the meniscus in the corner curves into the liquid, the capillary pressure grows without bound as the corner narrows, and the liquid wicks along it indefinitely. Above it the curvature has the other sign and the liquid stays put. The boundary is tested by evaluating the meniscus a millionth of a degree either side of it at seventeen half-angles, and it wicks on one side and not the other every time. water on clean glass, right-angled corner: α = 45°, θ = 5° — wicks; water on glass, a 20° groove: α = 10°, θ = 40° — wicks; water on plastic, right-angled corner: α = 45°, θ = 75° — does not. A right-angled corner needs a contact angle under 45°, which water on clean glass has and water on most plastics does not.

The corner a liquid never stops climbing

A narrow tube lifts a liquid to a definite height because it has a smallest width. A corner has none, so the capillary suction it can develop is unbounded — and whether the liquid takes advantage is decided by a single inequality between the contact angle and the corner's own angle.

fluids · Surface tension

Named alongside it

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

CapillarityContact angleLaplace pressureSurface tensionWettingCapillary lengthCurvatureGeometryHydrostatic equilibriumHydrostaticsScaling

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