solid surface [@furmidge1962], transport of liquid water in fuel cells [@zhu2008], liquid infused surfaces [@wexler2015], and coating [@vandre2013], contact line behavior is still not well understood.

The physics of a static contact angle between a liquid and a gas on a smooth solid surface is well established [@young1805; @gauss1830]. However, real surfaces are not completely smooth. They are not chemically homogeneous, and/or have roughness. This causes static contact angle hysteresis and contact line pinning, both of which are difficult to model. When looking at a moving contact line instead of a static contact angle things get even more complicated. Dynamic contact angle behavior is not well understood, even on a completely smooth solid surface. The origin of this poor understanding of the moving contact line is twofold: there is the contact line singularity problem, and the question of how the contact angle depends on contact line velocity.

The contact line singularity problem was first identified by @huh1971. While normally it is a good approximation to use the no-slip condition as boundary condition on the wall, for corner flow this assumption causes the viscous stress and pressure to scale as $r^{-1}$ and thus to diverge as $r \to
0$ at the 