Illustrated Physics
physics, drawn
Concept

Supersaturation — where it appears

The excess of a vapour's pressure, or a solute's concentration, over the value at which it is in equilibrium with its condensed phase. Air saturated over supercooled water droplets is supersaturated over ice, which is why ice crystals in clouds grow.

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

The barrier a new phase has to climb. The free energy of a droplet against its radius, at four supersaturations. Two terms compete: the volume term is a gain and goes as r³, the surface term is a cost and goes as r². At small radius the surface wins, so a droplet that forms by chance is more expensive than the vapour it came from and evaporates again; past a critical radius the volume wins and the droplet grows without limit. The maximum between them is the barrier. At S = 1.5 the critical radius is 2.66 nm and the barrier 533.8 kT, S = 2 the critical radius is 1.56 nm and the barrier 182.6 kT, S = 3 the critical radius is 0.98 nm and the barrier 72.7 kT, S = 5 the critical radius is 0.67 nm and the barrier 33.9 kT. The critical radius contains a few hundred molecules at low supersaturation and a handful at high, which is the first sign that a theory built on a surface tension and a bulk free energy is being applied outside its comfort. Both the critical radius and the barrier are located here by searching the drawn curve and checked against the closed forms 2γ/|Δg| and 16πγ³/3Δg², which agree to a part in a thousand.

The barrier a new phase has to climb

Water vapour three times supersaturated is thermodynamically desperate to condense and will sit there indefinitely if it is clean enough. The obstacle is that a droplet has to start small, and a small droplet is nearly all surface — so the first nanometre of every phase transition costs energy rather than releasing it, and what decides whether anything happens is the height of that cost divided by kT.

thermodynamics · Phase change How supersaturated a cloud is, to an ice crystal. The supersaturation over ice of air that is just saturated over liquid water, eᵥᵥ/eᵢ − 1, in per cent, against temperature; dashed, the same computed from the chemical potentials, exp(LΔT/RT·Tₘ) − 1, with L the latent heat of melting per mole, ΔT the supercooling and Tₘ the melting point. A supercooled cloud is in balance with its droplets, so to any ice crystal inside it the air is 5.1 per cent supersaturated at −5 °C, 10.5 at −10, 22.0 at −20 and 41.2 at −35. Over the droplets themselves it is exactly saturated, so they neither grow nor shrink by vapour. The excess is the chemical-potential difference between supercooled water and ice, 217 J per mole at −10 °C, expressed as a pressure ratio.

The ice that grows by stealing from the droplets

Most clouds colder than freezing are not made of ice. They are made of droplets of liquid water, some tens of degrees below their freezing point, waiting for something to start them freezing. When a few ice crystals do appear among them, the crystals grow and the droplets shrink, without touching, because supercooled water has a higher chemical potential than ice and so a higher vapour pressure: air balanced with the droplets is ten per cent supersaturated, to an ice crystal, at minus ten degrees. A few crystals among a hundred thousand droplets each take everything, grow heavy enough to fall, and that is how most of the rain outside the tropics begins — as snow.

thermodynamics · Chemical potential

Named alongside it

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

Bergeron processThe Boltzmann factorChemical potentialCritical radiusDiffusion growthFree energyHeterogeneous nucleationIce nucleationMetastabilityNucleationPrecipitationSupercooling

All concepts