We consider a family of nonlocal capillarity models, where surface tension is
modeled by exploiting the family of fractional interaction kernels
∣z∣−n−s, with s∈(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→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 σ is
negative, and larger if σ is positive. In addition, we address the
asymptotics of the fractional Young's law in the limit case s→0+ of
interaction kernels with heavy tails. Interestingly, near s=0, the dependence
of the contact angle from the relative adhesion coefficient becomes linear