Calculus of Variations and Geometric Measure Theory

S. Dipierro - F. Maggi - E. Valdinoci

Asymptotic expansions of the contact angle in nonlocal capillarity problems

created by maggi on 01 Oct 2016
modified on 25 Apr 2018



Inserted: 1 oct 2016
Last Updated: 25 apr 2018

Journal: J. Nonlinear Science
Year: 2017


We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels $
^{-n-s}$, with $s\in(0,1)$ and $n$ the dimension of the ambient space. The fractional Young's law (contact angle condition) predicted by these models coincides, in the limit as $s\to 1^-$, with the classical Young's law determined by the Gauss free energy. Here we refine this asymptotics by showing that, for $s$ close to $1$, the fractional contact angle is always smaller than its classical counterpart when the relative adhesion coefficient $\sigma$ is negative, and larger if $\sigma$ is positive. In addition, we address the asymptotics of the fractional Young's law in the limit case $s\to 0^+$ of interaction kernels with heavy tails. Interestingly, near $s=0$, the dependence of the contact angle from the relative adhesion coefficient becomes linear.