Numerical modelization of contact angle hysteresis of falling droplet under enhanced lubrication approximation

Moving contact lines are involved in several engineering applications: in in-flight icing phenomenon, the eventual transition from droplet to rivulet or continuous film regime is crucial for the prediction of ice accretion over the aircraft surface; absorption process through structured packing is also characterized by a thin film flowing over the corrugated sheets. Disjoining pressure together with the assumption of a thin precursor film is largely used in numerical simulations of thin films and moving droplets in order to model the dynamics of moving contact lines and the surface wettability properties, in terms of imposed static contact angle. The disjoining pressure model was largely validated in case of falling films with the well known Voinov-Hoffman-Tanner law. On the other side, the capability of the disjoining pressure to model the contact angle hysteresis, which is a crucial parameter for predicting moving droplets behavior, has not been discussed yet. Here, numerical simulations of both falling films and moving droplets under lubrication approximation are conducted and the disjoining pressure model is used to predict the contact line dynamics. After verification of the full curvature implementation for a 1D falling film, the effective contact angle hysteresis is estimated for a moving droplet under different flow conditions and the transition from droplet to rivulet regime detected.