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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