Capillarity problems with nonlocal surface tension energies

TL;DR

This paper investigates nonlocal surface tension energies in capillarity problems, deriving new equilibrium conditions and connecting them to classical theories and a nonlocal isoperimetric problem.

Contribution

It introduces a nonlocal modification to the classical capillarity energy functional and derives the resulting equilibrium conditions, extending classical theory.

Findings

New equilibrium conditions for nonlocal capillarity energies

Connection to classical mean curvature and Young's law

Recovery of a nonlocal isoperimetric problem

Abstract

We explore the possibility of modifying the classical Gauss free energy functional used in capillarity theory by considering surface tension energies of nonlocal type. The corresponding variational principles lead to new equilibrium conditions which are compared to the mean curvature equation and Young's law found in classical capillarity theory. As a special case of this family of problems we recover a nonlocal relative isoperimetric problem of geometric interest.