Hydrodynamic Characterization of Harmonically Excited Falling-Films: A Detailed Experimental and Computational Study

We investigate the hydrodynamic characteristics of harmonically excited liquid-films flowing down a $20~\degree$ incline by simultaneous application of Particle Tracking Velocimetry and Planar Laser-Induced Fluorescence (PLIF) imaging, complemented by Direct Numerical Simulations. By simultaneously implementing the above two optical techniques, instantaneous and highly localised flow-rate data were also retrieved, based on which the effect of local film topology on the flow-field underneath the wavy interface is studied in detail. Our main result is that the instantaneous flow rate varies linearly with the instantaneous film-height, as confirmed by both experiments and simulations. Furthermore, both experimental and numerical flow-rate data are closely approximated by a simple analytical relationship, which is reported here for the first time, with only minor deviations. This relationship includes the wave speed $c$ and mean flow-rate $\overline Q$, both of which can be obtained by simple and inexpensive measurement techniques, thus allowing for spatiotemporally resolved flow-rate predictions to be made without requiring any knowledge of the full flow-field from below the wavy interface.