Solitary waves on falling liquid films in the inertia-dominated regime

Abstract

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.

Experimental investigations of liquid falling films flowing under an inclined planar substrate

“…These include, among others, wetted-wall absorbers, heat exchangers, film condensers, evaporators or reactors, and microcooling schemes. Commonly studied flows include gravity-driven liquid films falling over inclined plates [3][4][5][6], gaseous shear-driven liquid films over horizontal plates [7], and liquid films falling down the inner or outer surfaces of tubes or pipes (annular or annulus flows) with or without a co-or countercurrent gas-shear flow in the core of the cross section [8][9][10].…”

Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity

“…The heat transfer properties of a wavy film on a heated substrate have also been tested [52][53][54], although without examining the effect of thermocapillarity on the fluid flow in particular. Experiments on two-dimensional pulses have been restricted to the isothermal case [55,56], where favorable comparisons of the wave speed and profile have been made between experiments, computations of the full Navier-Stokes system, and reduced-order (WRIBL) models. In these experiments, waves are created by flowing liquid down a tilted plate (of about 30 cm length) by oscillating the inlet flux at the upper side of the plate.…”

Direct Effect of Solvent Viscosity on the Physical Mass Transfer for Wavy Film Flow in a Packed Column

“…The present study involves a complex problem of the physical mass transfer via absorption in wavy film flow in a packed column. Accordingly, preliminary simulations were conducted for validation against experimental studies for wavy film flow 19,52 and physical mass transfer in wetted wall column 38 .…”