Spinodal decomposition: a binary mixture separates into domains. The Cahn-Hilliard equation drives coarsening — domains grow as t^(1/3). Watch the characteristic spinodal pattern emerge then coarsen.
Cahn-Hilliard equation: ∂c/∂t = M∇²[f'(c) - κ∇²c], where f(c)=c²(1-c)² is the double-well free energy. Spinodal decomposition occurs when ∂²f/∂c²< 0; the fastest-growing mode has wavelength λ* = 2π√(2κ/|f''|). Domain coarsening follows t^(1/3) (Lifshitz-Slyozov).