A note on the solution to the moving contact line problem with the no-slip boundary condition

When two immiscible fluids flow on a solid substrate, a moving contact line forms at the location where the fluid-fluid interface meets the solid surface. Under the no-slip boundary condition, the velocity field is necessarily multi-valued at the moving contact line. In this paper we show that the Stokes equation with the no-slip boundary condition does not admit such multi-valued solution when the fluid-fluid interface is assumed to be flat near the moving contact line.

Keywords

Stokes flow, no-slip boundary condition, moving contact line problem

2010 Mathematics Subject Classification

30E25, 35Q30, 76D05

Full Text (PDF format)

Received 14 April 2019

Accepted 3 September 2019

Published 25 October 2019