On the relationship between the thin film equation with weak slippage and Tanner's law

In this talk we will introduce two models for the movement of a small droplet over a substrate: the thin film equation and the quasi static approximation. By tracking the motion of the support of solutions to the thin film equation, we connect this two models. This connection was expected from experimental data which suggested Tanner's law: the edge velocity of a spreading thin film on a pre-wetted solid is approximately proportional to the cube of the slope at the inflection. This is joint work with Prof. Antoine Mellet.