Cahn-Hilliard — Spinodal Decomposition

Binary mixture phase separation: ∂c/∂t = M∇²(f'(c) − κ∇²c)
Coarsening dynamics — domains grow as L(t) ~ t^(1/3)

Parameters

Initial conc c₀: 0.50 Noise amplitude: 0.05 Mobility M: 1.00 Interface κ: 0.50 Color: Phase

Step: 0

Free energy: —

Domain scale: —

Cahn-Hilliard 1958.
f(c) = c²(1−c)² (double well)
κ penalizes interfaces.
Spinodal: ∂²f/∂c² < 0 region.

Coarsening: small domains
merge → big domains. L ~ t^(1/3)
(Lifshitz-Slyozov-Wagner theory)