A double-well free energy f(c) = a·c²/2 + c⁴/4 with a = −(quench depth) drives the Cahn-Hilliard equation:
μ = f'(c) − κ∇²c
∂c/∂t = M∇²μ
Below the spinodal edge c_s = √(depth/3), f''(c) < 0: any tiny composition fluctuation lowers the free energy further, so the flat mixture is linearly unstable and decomposes everywhere at once into a fine, bicontinuous pattern — no energy barrier, no waiting. That's spinodal decomposition.
Between c_s and the binodal c_b = √(depth), the mixture is metastable: it sits in a local minimum and stays uniform until a rare fluctuation nucleates a droplet big enough to overcome interfacial energy — nucleation and growth, seeded here as occasional random droplets that either shrink back or grow.
Beyond c_b the single-phase mixture is thermodynamically stable and nothing separates. However you enter it, once separated, domains coarsen — bigger regions swallow smaller ones to cut interfacial area, with characteristic size ξ growing roughly as t^(1/3). This flat 2D map plots the composition field c(x,y) directly instead of the 3D version's height-displaced mesh — same solver, top-down view.
- c̄ slider — average composition of the quenched melt, off from 50/50.
- Depth slider — how far below the critical temperature the quench goes; sets well depth and both c_s, c_b.
- Speed slider — how many Cahn-Hilliard integration substeps run per rendered frame.
- Quench now — resets the field to c̄ + small noise and restarts the clock.