Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems

Research output: Contribution to journalArticle

1 Citation (Scopus)

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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Capillarity
Contact Angle
Contact angle
Asymptotic Expansion
Fractional
Adhesion
kernel
Free energy
Heavy Tails
Surface tension
Coefficient
Interaction
Surface Tension
Gauss
Free Energy
Model
Family

Cite this

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title = "Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems",
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.",
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Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems. / Dipierro, Serena ; Maggi, Francesco ; Valdinoci, Enrico .

In: Journal of Nonlinear Science, Vol. 27, No. 5, 2017, p. 1531-1550.

Research output: Contribution to journalArticle

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AU - Maggi, Francesco

AU - Valdinoci, Enrico

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N2 - 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.

AB - 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.

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