Rivulet cascade from falling liquid films with side contact lines
Résumé
We investigate the dynamics of films of partially wetting liquids falling down a vertical plane in the presence of air. We focus on the little-studied case where the film is not in contact with lateral walls and thus has two side contact lines. By way of 3D direct numerical simulations, we study the fingering instability and the distribution of rivulets. Our results show that the instability develops as a cascade: two twin rivulets first develop at the free sides, followed by a series of twin rivulets growing closer to the center. This self-sustained fall is caused by the formation of stagnation zones at the front contact line as the liquid behind the ridge escapes toward a newly created rivulet. We also show that the established rivulet distance follows the prediction of linear instability, despite the cascade. The dynamics of the cascade is modified by inertial and film thickness effects, as well as by initial shape perturbations of the contact line. On the contrary, varying the contact angle does not affect the development of the cascade, apart from the average wavelength.