Spinodal Decomposition — Cahn-Hilliard Coarsening
Phase separation via CH equation: ∂φ/∂t = M∇²[f'(φ) − κ∇²φ] — coarsening follows t^(1/3)
Free Energy
Temperature τ = (T−T_c)/T_c:
-0.3
Gradient penalty κ:
1.0
Mobility M:
1.0
Simulation
Time step dt:
0.5
Noise amplitude:
0.05
Run / Pause
Reset
Step:
0
Theory
Cahn-Hilliard equation:
∂φ/∂t = M∇²[f'(φ)−κ∇²φ]
Free energy: f(φ)= τφ²/2+φ⁴/4
Spinodal: τ < 0 → unstable
Linear instability: σ(q) = −Mq²(τ+κq²)
Max growth: q* = √(|τ|/2κ)
Coarsening: ⟨R(t)⟩ ~ t^(1/3)
Lifshitz-Slyozov-Wagner (LSW) theory