Surface tension-modulated solitary waves on falling liquid films in the drag–inertia regime

We explore the impact of surface tension on the dynamical evolutions of traveling solitary waves of constant shape and speed on falling liquid films by investigating the previously unexplored coupling of the Reynolds number (Re) and the Capillary number (Ca) within the drag–inertia regime. Our study highlights the impact of Ca on the resulting flow recirculation patterns, influencing the surface wave characteristics, wave speed, and velocity profiles. A regime map on the Re−Ca plane and a film-depth averaged force balance model explain a signature asymmetry in the tail and front zones of the falling film. In the drag–inertia regime, three distinct film characteristics beneath the solitary wave hump are identified as Re increased, namely, moderate solitary waves without recirculation, strong solitary waves with recirculation near the transition line, and solitary waves with decreasing or saturated film amplitude depending on Ca. Recirculation zones are observed to appear for Re>30 at all Ca, growing stronger at high Ca and weakening at low Ca, influencing a selective decay in the film thickness with Re or its asymptotic saturation.