Phase Ordering & Ostwald Ripening

Cahn-Hilliard coarsening: ⟨R⟩ ~ t^(1/3) (LSW theory)

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LSW Theory

∂φ/∂t = M·∇²μ
μ = −εφ + φ³ − κ∇²φ
⟨R(t)⟩ ~ (M·γ·t)^(1/3)
Ostwald ripening: smaller droplets have higher curvature → higher chemical potential (Gibbs-Thomson). Solute flows from small to large droplets. Large grow, small shrink and vanish.

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Time t0
Droplets
⟨R⟩
R_max
t^(1/3)
Free energy