Moving contact line

Abstract
Although the contact angle between a liquid /vapor interface and a flat homogeneous solid at equilibrium is well explained at equilibrium, the motion of the triple line line is still not well understood. A mobility equation relates the deviation of the contact angle out of its equilibrium value and its speed on the solid. As the line moves on the solid thanks to an evaporation/condensation process, this introduces a dynamical Arrhenius factor small enough to make the mobility of the contact line the limiting factor of the dynamics, the smallness of the mobility being a well known experimental fact. Outside of the neighborhood of the moving contact line, the liquid-vapor interface is at equilibrium for capillary forces. This approach predicts well the cusps observed on the rear edge of droplets sliding on a tilted plane. A more microscopic theory is sketched that couples van der Waals phase field and Stokes-like fluid equations. For very small Arrhenius factors, this set of equations yields a dynamical change of the functions in the van der Waals phase field equation. The motion of the contact line may thus even lead to a wetting transition, that is to a continuous variation of the contact angle from a finite to a zero value as the receding velocity increases. This may be related to the observation of a limit contact angle in liquid flowing down a plate [l], [7] as well as to the known sensitivity of contact line mobility to vapor pressure.