Publication 16-CNA-030

Stability Of Contact Lines In Fluids: 2D Stokes Flow

Yan Guo
Division of Applied Mathematics
Brown University
Providence, RI 02912, USA
guoy@dam.brown.edu

Ian Tice
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
ian.tice@andrew.cmu.edu

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 in 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 fast.

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