Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems

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Abstract

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.
Original languageEnglish
Pages (from-to)1531-1550
Number of pages20
JournalJournal of Nonlinear Science
Volume27
Issue number5
DOIs
Publication statusPublished - 2017
Externally publishedYes

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