A simultaneous measurement technique based on planar laser-induced fluorescence imaging (PLIF) and particle image/tracking velocimetry (PIV/PTV) is described for the investigation of the hydrodynamic characteristics of harmonically excited liquid thin-film flows. The technique is applied as part of an extensive experimental campaign that covers four different Kapitza (Ka) number liquids, Reynolds (Re) numbers spanning the range 2.3 -320, and inlet-forced/wave frequencies in the range 1 -10 Hz. Film thicknesses (from PLIF) for flat (viscous and unforced) films are compared to micrometer stage measurements and analytical predictions (Nusselt solution), with a resulting mean deviation being lower than the nominal resolution of the imaging setup (around 20 μm). Relative deviations are calculated between PTV-derived interfacial and bulk velocities and analytical results, with mean values amounting to no more than 3.2% for both test cases. In addition, flow rates recovered using LIF/PTV (film thickness and velocity profile) data are compared to direct flowmeter readings. The mean relative deviation is found to be 1.6% for a total of six flat and nine wavy flows. The practice of wave/phase locked flow-field averaging is also implemented, allowing the generation of highly localized velocity profile, bulk velocity and flow rate data along the wave topology. Based on this data, velocity profiles are extracted from 20 locations along the wave topology and compared to analytically derived ones based on local film thickness measurements and the Nusselt solution. Increasing the waviness by modulating the forcing frequency is found to result in lower absolute deviations between experiments and theoretical predictions ahead of the wave crests, and higher deviations behind the wave crests. At the wave crests, experimentally derived interfacial velocities are overestimated by nearly 100%. Finally, locally non-parabolic velocity profiles are identified ahead of the wave crests; a phenomenon potentially linked to the cross-stream velocity field.

We offer new insights and results on the hydrodynamics of solitary waves on inertiadominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

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We present results from the simultaneous application of planar laser-induced fluorescence (PLIF), particle image velocimetry (PIV) and particle tracking velocimetry (PTV), complemented by direct numerical simulations, aimed at the detailed hydrodynamic characterization of harmonically excited liquid-film flows falling under the action of gravity. The experimental campaign comprises four different aqueous-glycerol solutions corresponding to four Kapitza numbers (Ka = 14, 85, 350, 1800), spanning the Reynolds number range Re = 2.3-320, and with forcing frequencies f w = 7 and 10 Hz. PLIF was employed to generate spatiotemporally resolved film-height measurements, and PIV and PTV to generate two-dimensional velocity-vector maps of the flow field underneath the wavy film interface. The latter allows for instantaneous, highly localized velocity-profile, bulk-velocity, and flow-rate data to be retrieved, based on which the effect of local film topology on the flow field underneath the waves is studied in detail. Temporal sequences of instantaneous and local film height and bulk velocity are generated and combined into bulk flow-rate time series. The time-mean flow rates are then decomposed into steady and unsteady components, the former represented by the product of the mean film height and mean bulk velocity and the latter by the covariance of the film-height and bulk-velocity fluctuations. The steady terms are found to vary linearly with the flow Re, with the best-fit gradients approximated closely by the kinematic viscosities of the three examined liquids. The unsteady terms, typically amounting to 5%-10% of the mean and peaking at approximately 20%, are found to scale linearly with the film-height variance. And, interestingly, the instantaneous flow rate is found to vary linearly with the instantaneous film height. Both experimental and numerical flow-rate data are closely approximated by a simple analytical relationship with only minor deviations. This relationship includes terms such as the wave speed c and mean flow rate Q, which can be obtained by relatively simple and inexpensive methods, thus allowing for spatiotemporally resolved flow-rate predictions to be made without requiring explicit knowledge of the full flow-field information underneath the wavy interface.

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We propose the first consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re = 20 − 120 and surface tension coefficients σ = 0.0512 − 0.072 N m −1 on substrates with inclination angles β = 19 • − 90 • . Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e. height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by non-linear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

Annular flows are employed in numerous engineering and industrial processes relating to the chemical, oil and gas, solar and nuclear energy industries. Yet, the reliable time-and space-resolved measurement of film thickness in these flows still eludes us, as the moving and wavy interface renders the application of optical diagnostics, such as planar laser-induced fluorescence (PLIF), particularly challenging. In this research article, we present a novel adaptation of PLIF, which we refer to as structured PLIF (S-PLIF), and with which we seek to suppress the errors in PLIF-derived film thickness measurements due to total internal reflection (TIR) of the emitted fluorescence at the phase boundary. The proposed measurement approach relies on a periodic modulation of the laser-light intensity along the examined region of the flow in order to generate fluorescence images with alternating bright and dark regions. An image-processing methodology capable of recovering the location of the true gas-liquid interface from such images is presented, and the application of S-PLIF is demonstrated in liquid films in a vertical pipe over the Reynolds number range Re L ≈ 150 − 1500. The results from this technique are compared to simultaneously recovered, "conventional" (uncorrected) PLIF data, as well as data from other techniques over the same range of conditions, demonstrating the efficacy of S-PLIF. A comparison amongst S-PLIF data obtained with the observation angle between the laser-sheet plane and the camera's observation axis set to β = 70°and 90°is also performed, showing that the employment of β = 70°is highly advantageous in avoiding distortions caused by reflections of the emitted fluorescence at the film free-surface. The instantaneous and average film-thickness uncertainties of S-PLIF are estimated to be below 10% and 5%, respectively, when measuring smooth films; an improvement over the other optical measurement techniques considered in this work. Finally, the application of S-PLIF is demonstrated in the presence of a gas-shear flow with gas entrainment in the liquid, and simultaneously with particle image velocimetry (PIV).