WIAS Preprint No. 2315, (2016)

Asymptotic expansions of the contact angle in nonlocal capillarity problems



Authors

  • Dipierro, Serena
  • Maggi, Francesco
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 76B45 76D45 45M05

Keywords

  • nonlocal surface tension, contact angle, asymptotics

Abstract

We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting a family of fractional interaction kernels The fractional Young's law (contact angle condition) predicted by these models coincides, in the limit, 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 it is positive. In addition, we address the asymptotics of the fractional Young's law in the limit case s close to 0 of interaction kernels with heavy tails. Interestingly, forsmall s, the dependence of the contact angle from the relative adhesion coefficient becomes linear.

Appeared in

  • J. Nonlin. Sci., 27:5 (2017) pp. 1531--1550.

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