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Stability of Contact Lines in Fluids: 2D Stokes Flow

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Abstract

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially quickly.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George St., Providence, RI, 02912, USA

    Yan Guo

  2. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Ian Tice

Authors
  1. Yan Guo
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  2. Ian Tice
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Correspondence to Ian Tice.

Additional information

Communicated by A. Bressan

Y. Guo was supported in part by NSFC Grant 10828103 and NSF Grant DMS-Grant 1209437.

I. Tice was supported by a Simons Foundation Grant (#401468) and an NSF CAREER Grant (DMS #1653161).

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Guo, Y., Tice, I. Stability of Contact Lines in Fluids: 2D Stokes Flow. Arch Rational Mech Anal 227, 767–854 (2018). https://doi.org/10.1007/s00205-017-1174-4

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