Abstract
The hydrodynamic equations for contact line motion are typically amended with different models to alleviate the stress singularity associated with the no-slip condition on the substrate. Using the spreading of a two-dimensional droplet as a prototype for a moving contact line, we study the dynamics of slip and precursor film models that are commonly used to cure the singularity. By considering the quasistatic spreading limit we establish equivalence relations that connect the slip and precursor film models. We examine these relations via numerical experiments and we show that they appear to persist even when the motion can no longer be treated as quasistatic. However, significantly different behaviors may be observed under certain conditions, particularly when multiple droplet equilibria are possible.