Four tubes, four heights

At its defaults it draws 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.

capillary-rise is one function in lib/figures/fluids.js — matter that will not hold a shape, and the forces in it. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

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.

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.

Capillary rise against tube radius on logarithmic axes: a straight line of slope minus one, because the pull acts on the circumference and the weight lifted grows with the area. A tube a tenth the radius lifts water ten times as far, which is why the effect is invisible in a drinking glass and decisive in a soil, a wick and a sheet of paper.

Water in tubes of radius 0.15, 0.3, 0.6 mm, with each meniscus drawn as the spherical cap a 0° contact angle forces and each height computed from it. The narrowest rises 99 mm and the widest 25 mm — in inverse proportion to the radius, with nothing about the glass or the volume of water entering it.

4 drops of the same 5 µL of liquid, on 4 solids it meets at 20°, 60°, 90°, 140°. Each is the spherical cap that volume and that angle force, so the footprint radius is computed rather than chosen: 20° gives 2.61 mm, 60° gives 1.71 mm, 90° gives 1.34 mm, 140° gives 0.69 mm. At every contact line the three interfacial tensions are drawn to scale, and only their horizontal components balance — γsv = γsl + γlv cos θ. The vertical pull of the liquid surface is taken up by the solid, which is why the angle belongs to three interfaces at once and to no single liquid: change the solid and nothing about the water has changed.

2 drops of the same 5 µL of liquid, on 2 solids it meets at 30°, 110°. Each is the spherical cap that volume and that angle force, so the footprint radius is computed rather than chosen: 30° gives 2.26 mm, 110° gives 1.10 mm. At every contact line the three interfacial tensions are drawn to scale, and only their horizontal components balance — γsv = γsl + γlv cos θ. The vertical pull of the liquid surface is taken up by the solid, which is why the angle belongs to three interfaces at once and to no single liquid: change the solid and nothing about the water has changed.

physicscheck asserts something about capillary-rise that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.