Mesoscopic hydrodynamics of contact line motion

We review the paradoxes of the problem of a moving gas–liquid–solid contact line, and the ways to eliminate them by modifying both hydrodynamic equations at mesoscopic distances and boundary conditions at the solid surface. Two kinds of applicable models are represented by the Stokes equation amended by intermolecular forces and a diffuse interface model where the fluid density enters as an additional dynamic variable. The boundary conditions must be modified, either phenomenologically or by introducing a kinetic slip, in order to eliminate the viscous stress singularity in the sharp interface theory. In the diffuse interface theory the singularity is relaxed in a natural way, due to a gradual change of both fluid density and transport properties. In all cases, a properly defined “apparent” contact angle turns out to be dependent on both molecular-scale and macroscopic factors, as well as on the velocity.