Flow evolution and fingering instability of a thin water film on an inclined plate under shear airflow

One of the key issues affecting aircraft safety in the field of aircraft icing and anti-icing is the stability of shear-driven runback water films on component surfaces. This study investigates the flow evolution and fingering instability of thin water films on inclined plates under shear airflow, elucidating the coupled multi-physics mechanisms governing film rupture. A theoretical model, which integrates airflow shear stress and contact line forces, is established through the long-wave approximation of Navier-Stokes equations, enhanced by the precursor film model and dynamic contact angle model. A numerical solver (rivuletFoam) is developed to simulate interfacial evolution. The results of linear stability analysis combined with numerical simulation show that increasing inclination angle amplifies Kapitza instability by strengthening gravitational components, expanding the cutoff wavenumber by 24%. The airflow shear stress enhances the maximum temporal growth rate by 17 times and reduces the film rupture time by 96% through capillary ridge acceleration. Contact angle augmentation intensifies disjoining pressure gradients, decreasing maximum continuous film length by 92% while reducing rivulet count by 43%. Precursor film thinning amplifies intermolecular forces, extending the cutoff wavenumber range by 44%. The proposed model effectively captured the fingering-to-rivulet transitions and provided critical insights for interfacial instability prediction in multiphase flows, which is of significant engineering value for the optimization of the design of aircraft anti-icing systems.