Asymptotic expansions of the contact angle in nonlocal capillarity problems

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 ? is negative, and larger if ? 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. © 2017, Springer Science+Business Media New York.