Illustrated Physics
physics, drawn
Concept

Cohesion — where it appears

The attraction of a material for itself, which in a granular medium comes from moisture, van der Waals forces or electrostatics rather than from anything structural. It is what allows a sand heap to stand steeper than its dry angle of repose and what makes a fine powder flow badly.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Surface at fixed volume. Four shapes of identical volume with their surface areas evaluated. The sphere's is the smallest at 4.836; the flattest shape drawn carries 1.91 times as much. Surface tension is an energy per unit area, so a free drop of liquid has an incentive to be the first of these and none at all to be any of the others.

The skin that is not a skin

A drop of water behaves as though it were wrapped in a stretched membrane, and there is no membrane. What there is instead is an energy cost per unit of surface, and almost everything the apparent skin does follows from a liquid trying to have less of one.

fluids · Surface tension The slope a heap of grains settles at. The steepest slope a cohesionless heap can hold, against the friction between its grains. A slab of thickness h on a slope is pushed down it by the weight's along-slope component and held by friction acting on the weight's across-slope component, and both are proportional to the same ρgh — so the thickness cancels and the criterion is tan θ = μ. Checked here at thicknesses of 2 mm, 50 mm, 2000 mm, the ratio of driving to holding stress differs by 2.2e-16, which is zero. That is why the quantity is an angle: nothing about the size of the pile, the size of the grains, the density or the strength of gravity survives into it, and a heap of sand on the Moon stands at the same slope as one on Earth. The marked materials are glass beads at 24°, dry sand at 33°, crushed gravel at 40°. The band between the two curves is the hysteresis: a slope steeper than 31.0° will keep flowing once started, and one shallower than 35.0° will not start — so a pile has a range of stable angles rather than one, and which it is found at depends on how it was built.

The angle that does not know the size of the heap

Pour sand and it makes a cone with a definite slope, and pouring more makes a larger cone with the same slope. The reason the answer is an angle rather than a length is a cancellation — the force pulling a surface layer downhill and the friction holding it back are both proportional to its weight, so everything about the size of the pile divides out — and everything that puts a length back in is a story about cohesion.

fluids · Granular matter The force that does not count the water. The force of a water bridge between two touching spheres of radius R, in units of 2πRγ, against the bridge's volume on a logarithmic scale running over six decades, for three contact angles. Each curve is nearly flat: from a millionth of R³ to a thousandth, the force on a wetting grain falls only from 0.99 to 0.92 of 2πRγ, and it stays close to cos θ for the others. A droplet between two grains of sand pulls almost as hard as one a thousand times larger. This is the reason sand wet with one per cent of water and sand wet with ten per cent hold together with about the same strength. The curves fall where a bridge is large enough for its neck to stop being small compared with the grain, and bridges of that size merge with their neighbours.

The sandcastle a spoonful of water holds

A dry heap of sand stands at thirty degrees and no steeper. Add a spoonful of water to a bucketful, and the same grains will stand in a vertical wall and carry a person's weight. Add ten times as much water and the wall is no stronger, because a bridge of water between two grains pulls with almost the same force whatever its size. Its strength belongs to the grain and the surface tension, and the amount of water hardly enters.

fluids · Granular matter

Named alongside it

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

Surface tensionAngle of reposeBond numberCapillary bridgeCapillary lengthDilatancyForce chainsFrictionGranular matterIntermolecular forcesInternal frictionLaplace pressure

All concepts