Cahn-Hilliard diffusion — Fick's law and spinodal decomposition
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Cahn-Hilliard equation: ∂c/∂t = ∇·[M∇μ], where chemical potential μ = a(2c³−c) − κ∇²c. The double-well free energy f = a(c²−1)²/4 drives spinodal decomposition: a homogeneous mixture separates into two equilibrium phases. The κ∇²c term penalizes sharp interfaces, selecting a characteristic length scale for domain coarsening.