Investigation of the backflow phenomenon in falling liquid films

Abstract

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.