Soft matter · PDF notes
Cahn–Hilliard dynamics
A short derivation of conserved phase-separation dynamics, linear instability, coarsening, and the scaling picture.
The Cahn–Hilliard equation is a minimal model for phase separation when the order parameter is conserved. These notes connect its thermodynamic construction to the patterns and growing length scales seen during coarsening.
What the notes cover
- Free-energy functionals for a conserved order parameter
- Chemical potential and the Cahn–Hilliard equation
- Linear instability of a homogeneous state
- Domain growth, coarsening, and scaling
The presentation is meant to bridge the formal derivation and the physical picture of domains forming and merging over time.