Colloidal Gel — Arrested Spinodal Phase Separation

When phase separation freezes mid-way: Cahn-Hilliard with gelation

Parameters

Colloidal particles with short-range attraction undergo spinodal decomposition: phase-separated into dense (gel) and dilute regions via Cahn-Hilliard:

∂φ/∂t = ∇²(−∇²φ + f'(φ))


When local density exceeds φ_gel, gelation arrests the coarsening — the network freezes into a disordered, stress-bearing solid (colloidal gel).


This creates bicontinuous networks with fractal dimension ~2.4, unlike macro-phase-separated fluids. Applications: food gels (yogurt), aerogels, tissue scaffolds, battery electrodes.


Color: bright = dense/gelled phase, dark = dilute phase. Gelled regions (white outline) are frozen.