HYDRODYNAMIC CHARACTERISTICS OF INERTIA DRIVEN WAVY LIQUID FILM FLOWS

We investigate the hydrodynamic characteristics of two-dimensional, nonlinear evolution of inertia-driven wavy liquid films over flat surfaces using two dimensional numerical simulations. In this study, a constant monochromatic perturbation is applied to the velocity field at the inlet to enforce the film. We explore two control parameters: the Reynolds number ( Re = 15 - 60) and the wall inclination angle (θ = 10°- 90°), while maintaining a fixed vertical Kapitza number (Ka = 240). The wavy film flows reveal the existence of a critical Reynolds number, Re_c, such that both the maximum film height, h_max and discharge, q_max show inverse variations for Re > Re_c compared to Re < Re_c. For all the inclinations, both the film characteristics initially increase with Re up to Re_c and then decrease. This behavior is attributed to the relatively higher effective inertia, which shifts the recirculations beneath the center of the wavefront interface to the region of steeper interface (front of the wave) dictated by surface tension. Additionally, the asymmetry of the interface shape decreases rapidly with Re < Re_c, becoming asymptotically constant for Re >> Re_c for all inclinations. The wave speed and maximum discharge both vary linearly with h_max for all angles, but with different slopes in the two regions separated by Re_c. At any Re value, the streamwise velocity profile shows a semiparabolic nature at both the wave crest and wave tail, with increasing magnitude as orientations increase. However, the region of the front (steeper part) of the wave exhibits a deviation in the parabolic nature.These findings provide insights into the intricate interplay of effect of inertia and orientation in the Kapitza films, highlighting the importance of the critical Reynolds number, Re_c, in determining the film behavior and characterizing the interface asymmetry.