Illustrated Physics
physics, drawn
Concept

Evaporation — where it appears

The loss of molecules from a liquid surface to the vapour above it, limited in still air by how fast the vapour diffuses away. Because only the fastest molecules escape, what is left behind is cooler — which is the whole of why sweating works.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Two ways to weaken a surface. Surface tension is a property of a surface rather than a constant of a liquid, and this shows how far it moves. The steep curve is water with ethanol dissolved in it, against ethanol mole fraction, through nine measured points: two per cent of ethanol takes the tension from 72 to 56.4 mN/m, a fall of 22% for a change of composition small enough to taste and not to see. The initial slope is 837 mN/m per unit of mole fraction, because ethanol collects preferentially at the surface and a little of it covers a great deal of area. The gentle line is pure water against temperature, read on the same horizontal axis as degrees rather than fraction: about 0.15 mN/m per degree, so a difference of ten degrees across a surface is worth about a millinewton per metre. Neither dependence would be interesting if surfaces were uniform. What makes them matter is that a difference in tension across a surface is a force along it, and nothing in the liquid prevents such a difference from existing.

The surface that pulls toward the stronger side

Surface tension is usually treated as a constant of a liquid, and it is not — it depends on temperature and on what is dissolved, and a difference in it along a surface is a force along that surface — which drags the liquid underneath and needs no pressure difference at all.

fluids · Surface tension Where a drying drop loses its liquid. The rate at which liquid leaves the surface of a drying drop, against distance from the centre in units of the drop's radius, for 5 contact angles. The flux is not uniform, and it is not a property of the liquid: it is set by how vapour diffuses away from a lens-shaped object, which is the same boundary-value problem as the field around a charged lens and has the same answer — a power law in the distance from the rim, with an exponent that depends only on the contact angle. at 10° the exponent is 0.471, and the loss has doubled by 87.8 per cent of the way out, at 40° the exponent is 0.357, and the loss has doubled by 92.5 per cent of the way out, at 70° the exponent is 0.182, and the loss has doubled by 98.9 per cent of the way out, at 90° the exponent is 0.000 and the drop dries evenly everywhere, at 120° the exponent is -0.500 and the flux falls toward the rim. Below a right angle the flux diverges at the contact line; at exactly a right angle it is uniform; above it the edge is the slowest-drying part of the drop. Since a pinned edge must be resupplied from the interior, that sign decides which way the liquid inside the drop flows — and therefore whether everything suspended in it ends up in a ring at the rim or in a spot at the centre.

The ring the drop leaves behind

A drop of coffee dries into a ring rather than a disc, and nothing about coffee is responsible. The pattern is produced by a boundary condition — an edge that cannot move — and it survives replacing the coffee with anything else that will stay suspended.

fluids · Surface tension The distance at which the air takes over. Evaporation of water at 20 °C into dry air, in kilograms per square metre per second, against the thickness of the layer the vapour must cross before it is carried away, both on logarithmic scales, with the kinetic and diffusive resistances added in series: 1/u + δ/D, where u = √(RT/2πM) is the speed at which the kinetic flux carries vapour off and D the diffusion coefficient. Dashed, the kinetic ceiling. At one atmosphere the two resistances are equal at δ = D/u = 0.17 μm, about two and a half mean free paths of the air; a layer much thinner than that leaves the surface at its ceiling, and a layer much thicker throttles it in proportion to its thickness. At a tenth of an atmosphere diffusion is ten times faster and the crossover moves out to 1.7 μm. Only in vacuum, or across gaps shorter than a mean free path, does the liquid itself set the rate.

The puddle that could dry in a second

A liquid in equilibrium with its vapour loses molecules exactly as fast as the vapour delivers them, and kinetic theory says how fast that is. For water at room temperature it is two and a half kilograms per square metre every second — a puddle two and a half millimetres deep gone in a second. Puddles take hours because almost every molecule that leaves is knocked back by the air within a fraction of a micrometre. The ceiling binds only where the vapour can escape in a single free flight: in vacuum, where water freezes itself, in the smallest droplets, and on the filament of a lamp.

thermodynamics · Kinetic theory

Named alongside it

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

DiffusionMarangoni effectSurface tensionWettingBoundary conditionBoundary conditionsCapillarityContact angleDetailed balanceEffusionGradientInterface

All concepts