Memory effects in contact line friction

When a drop of liquid comes into contact with a solid surface, it relaxes toward an equilibrium configuration, either wetting the surface or remaining in a droplet-like shape with a finite contact angle. The force driving the process toward equilibrium is the corresponding out-of-balance Young's force. However, the speed with which the liquid front advances depends strongly on an opposing friction force arising from dissipative processes due to the moving solid-liquid-gas contact line. In analogy to the treatment of hydrodynamic friction, we present an exact method, based on the Mori-Zwanzig formalism, to extract this friction from equilibrium fluctuations. We find that the contact line exhibits long-lasting memory with a characteristic power-law decay due to coupling to the systems hydrodynamic modes. For the systems studied in this work, the majority of the friction emerges due to this coupling. Within the linear response regime, we obtain the frequency-dependent dissipative and elastic response of the contact line to an external perturbation, including a frequency-dependent friction coefficient.