Continuation of Capillary Surfaces with Topological Change via the Van der Waals–Cahn–Hilliard Theory
Abstract
Abstract. We study the capillary energy functional via the van der Waals–Cahn–Hilliard theory. Our study is motivated by how two droplets are connected as the volume increases. We deal with 2-dimensional case and the perturbation theory for the capillary energy functional and the continuous deformation of the critical point of the capillary energy functional allowing singularities when the area changes are discussed. Numerical computations based on the above theory are performed, and the results suggest that critical points consisting of two connected components and one connected component are connected by a continuous 1-parameter family of sets bounded by curves with a singularity, and hysteresis also can be seen in the dynamics.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Fluid Dynamics and Heat Transfer
Solidification and crystal growth phenomena
Publication details
- Journal / source
- SIAM Journal on Applied Mathematics
- Volume
- 86
- Issue
- 2
- Pages
- 506–531
- Publication date
- 6 March 2026
- Language
- EN