Nonlocal capillarity for anisotropic kernels

TL;DR

This paper investigates a nonlocal capillarity problem with anisotropic, non-scale-invariant kernels, deriving a nonlocal Young's law for contact angles and analyzing the solvability based on kernel properties and adhesion.

Contribution

It introduces a model for nonlocal capillarity with anisotropic kernels and different fractional exponents, extending classical theories to more complex, non-scaling invariant interactions.

Findings

Derived a nonlocal Young's law for contact angles.

Established conditions for unique solvability of the model.

Analyzed effects of anisotropy and scale invariance breaking.

Abstract

We study a nonlocal capillarity problem with interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In particular, the lack of scale invariance will be modeled via two different fractional exponents $s_1, s_2\in (0,1)$ which take into account the possibility that the container and the environment present different features with respect to particle interactions. We determine a nonlocal Young's law for the contact angle and discuss the unique solvability of the corresponding equation in terms of the interaction kernels and of the relative adhesion coefficient.