English

Surfactants in the Two Gradient Theory of Phase Transitions

Analysis of PDEs 2025-09-17 v2

Abstract

We investigate the influence of surfactants on stabilizing the formation of interfaces in solid-solid phase transitions. The analysis focuses on singularly perturbed van der Waals-Cahn-Hillard-type energies for gradient vector fields, supplemented with a term that accounts for the interaction between the surfactant and the solid. Assuming the potential term to have only two rank-one connected wells, we prove that the effective energy for the formation of an interface decreases when the surfactant segregate to the interface.

Keywords

Cite

@article{arxiv.2401.03840,
  title  = {Surfactants in the Two Gradient Theory of Phase Transitions},
  author = {Marco Cicalese and Tim Heilmann},
  journal= {arXiv preprint arXiv:2401.03840},
  year   = {2025}
}

Comments

correction of typo: Proof of Proposition 3.5, Step 2: added the definition of the density g