Curvature-Driven Interface Motion
Allen-Cahn equation — mean curvature flow, shrinking droplets
Parameters
Interface width ε:
4.0
Mobility M:
1.0
Speed (dt):
0.3
Initial shape:
Single Circle
Ellipse
Multiple Droplets
Random Blobs
Pause
Interface area
—
Largest droplet R
—
Step
0
Phase +1 fraction
—
Allen-Cahn equation:
∂_t φ = M(ε²∇²φ − W'(φ))
W(φ)=¼(φ²−1)², W'=φ(φ²−1)
Interface moves with normal velocity v_n=M·κ (mean curvature).
Circular droplet radius: R(t)=√(R₀²−2Mt).
Onsager variational principle: minimizes free energy.