The phenomenon of backflow in the capillary wave region of laminar falling liquid films is studied in detail. For the first time, the mechanism leading to the origination of the phenomenon is identified and explained. It is shown that backflow forms as the result of a separation eddy developing at the bounding wall similar to the case of classical flow separation. Results show that the adverse pressure distribution causing the separation of the flow in the capillary wave region is induced by the strong third-order deformation (i.e. change in curvature) of the liquid–gas free surface there. This deformation acts on the interfacial pressure jump, and thereby the wall pressure distribution, as a result of surface tension forces. It is shown that only the capillary waves, owing to their short wavelength and large curvature, impose a pressure distribution satisfying the conditions for flow separation. The effect of this capillary separation eddy on momentum and heat transfer is investigated from the perspective of modelling approaches for falling liquid films. The study is centred on a single case of inclined liquid film flow in the visco-capillary regime with surface waves externally excited at a single forcing frequency. Investigations are based on temporally and spatially highly resolved numerical data obtained by solving the Navier–Stokes equations for both phases. Computation of phase distribution is performed with the volume of fluid method and the effect of surface tension is modelled using the continuum surface force approach. Numerical data are compared with experimental data measured in the developed region of the flow. Laser-Doppler velocimetry is used to measure the temporal distribution of the local streamwise velocity component, and confocal chromatic imaging is employed to measure the temporal distribution of film thickness. Excellent agreement is obtained with respect to film thickness and reasonable agreement with respect to velocity.

A low-dimensional model capturing the fully coupled dynamics of a wavy liquid film in interaction with a strongly confined laminar gas flow is introduced. It is based on the weighted residual integral boundary layer approach of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369) and accounts for viscous diffusion up to second order in the film parameter. The model is applied to study two scenarios: a horizontal pressure-driven water film/air flow and a gravity-driven liquid film interacting with a co- or counter-current air flow. In the horizontal case, interfacial viscous drag is weak and interfacial waves are primarily driven by pressure variations induced by the velocity difference between the two layers. This produces an extremely thin interfacial shear layer which is pinched at the main and capillary wave humps, creating several elongated vortices in the wave-fixed reference frame. In the capillary wave region preceding a large wave hump, flow separation occurs in the liquid in the form of a vortex transcending the liquid–gas interface. For the gravity-driven film, a twin vortex (in the wave-fixed reference frame) linked to the occurrence of rolling waves has been identified. It consists of the known liquid-side vortex within the wave hump and a previously unknown counter-rotating gas-side vortex, which are connected by the same interfacial stagnation points. At large counter-current gas velocities, interfacial waves on the falling liquid film are amplified and cause flooding of the channel in a noise-driven scenario, while this can be delayed by forcing regular waves at the most amplified linear wave frequency. Our model is shown to exactly capture the long-wave linear stability threshold for the general case of two-phase channel flow. Further, for the two considered scenarios, it predicts growth rates and celerity of linear waves in convincing agreement with Orr–Sommerfeld calculations. Finally, model calculations of nonlinear interfacial waves are in good agreement with film thickness and velocity measurements as well as streamline patterns in both phases obtained from direct numerical simulations.

In a previous publication, Dietze, Leefken & Kneer (J. Fluid Mech., vol. 595, 2008, p. 435) showed that flow separation takes place in the capillary wave region of falling liquid films. That investigation focused on the mechanistic explanation of the phenomenon mainly on the basis of numerical data. The present publication for the first time provides clear experimental evidence of the phenomenon obtained by way of highly resolving velocity measurements in a specifically designed optical test set-up. Characteristically, the refractive index of the working fluid was matched to that of the glass test section to provide optimal access to the cross-section of the film for the employed optical velocimetry techniques, namely, laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Using LDV, time traces of the streamwise velocity component were recorded in high spatial (0.025 mm) and temporal resolutions (0.4 ms) showing negative velocity values in the capillary wave region. In addition, simultaneous film thickness measurements were performed using a Confocal Chromatic Imaging (CCI) technique enabling the correlation of velocity data and wave dynamics. Further, using PIV the spatio-temporal evolution of the velocity field in the cross-section of the film was measured with high spatial (0.02 mm) and temporal (0.5 ms) resolutions yielding insight into the topology of the flow. Most importantly these results clearly show the existence of a separation eddy in the capillary wave region. Due to the high temporal resolution of the PIV measurements, enabled by the use of a high-speed camera with a repetition rate of up to 4500 Hz, the effect of wave dynamics on the velocity field in all regions of the wavy film was elucidated. All experiments were performed using a dimethylsulfoxide (DMSO)–water solution and focused on laminar vertically falling liquid films with externally excited monochromatic surface waves. Systematic variations of both the Reynolds number (Re = 8.6–15.0) and the excitation frequency (f = 16–24 Hz) were performed. Results show that an increase in the wavelength of large wave humps, produced either by an increase in the Reynolds number or a decrease in the excitation frequency, leads to an increase in the size of the capillary separation eddy (CSE). Thereby, the CSE is shown to grow larger than the local film thickness, assuming an open shape with streamlines ending at the free surface.