Presets
Playback
Solution and crystals
Cooling rate, seeds, surface energy and the nucleation prefactor act on the next restart or live as marked in the labels.
Model checks
The science
Supersaturation and solubility
A solution holds at most the equilibrium concentration C*(T). The supersaturation ratio is S = C / C*(T); cooling lowers C* (here C* = 50 mol/m³ · exp(0.04 (T - 25 °C))), so S rises even if no salt is added. Nothing crystallises at S = 1: a metastable zone lets a solution stay supersaturated until nuclei appear.
Classical nucleation theory
A spherical cluster of radius r has free energy ΔG(r) = 4π r² γ - (4/3) π r³ (kT ln S)/v, with interfacial energy γ and molecular volume v. It peaks at the critical radius r* = 2 γ v / (kT ln S) with barrier ΔG* = 16 π γ³ v² / (3 (kT ln S)²). Clusters larger than r* grow, smaller ones dissolve. The nucleation rate is J = J0 exp(-ΔG*/kT) per m³ and second: extremely steep in S, which is why crystallisation switches on suddenly.
Growth and depletion
A crystal grows by dr/dt = kg (S - exp(l/r)), with the Gibbs-Thomson length l = 2 γ v / kT, so tiny crystals are more soluble. Every grown volume leaves the solution: C V + ρc ∑ wi (4/3) π ri³ = constant (solute moles are conserved), with the crystal molar density ρc = 1/(v NA). When there are many crystals, S falls back toward 1 and nucleation stops; seeding gives growth a head start so the burst never happens.
Honest simplifications: a well-mixed 1 cm³ batch of a hypothetical model salt (v = 5×10-29 m³, C* = 50 mol/m³), homogeneous nucleation only (real crystallisers mostly nucleate on dust and walls), no secondary nucleation, breakage, agglomeration or settling, a single growth law, spherical size as a stand-in for shape, and each drawn grain stands for a weighted group of identical crystals. Crystal shapes in the picture are schematic hexagons.
What to try
- Run Fast cooling: S climbs past 3 and a burst of tiny crystals appears, then S collapses.
- Run Slow cooling or Seeded: fewer, larger crystals form.
- Raise the surface energy gamma and watch the metastable zone widen (nucleation starts later at higher S).
- Compare the size distribution of the two presets: the same salt gives very different products.