Derivation of continuum models for the moving contact line problem based on thermodynamic principles

Contact lines arise as the boundaries of free boundaries in fluids.This problem is interesting and important, not only because it arises in many applications, but also because of the distinct mathematical and physical features it has, such as singularities, hysteresis, instabilities, competing scaling regimes, etc.For a long time, this area of study was plagued with conflicting theories and uncertainties regarding how the problem should be modeled.In the present paper we illustrate how continuum models for the moving contact line problem can be derived using simple thermodynamic considerations.Both the sharp interface models and diffuse interface models are derived.