The effect of side walls on the stability of falling films

TL;DR

This study investigates how side walls affect the stability of falling liquid films, combining theoretical stability analysis with experiments, revealing that lateral confinement stabilizes the flow and introduces new stability modes.

Contribution

It introduces a combined theoretical and experimental approach to analyze the stabilizing effects of side walls on falling film flow and identifies a new wall-mode instability.

Findings

Lateral confinement stabilizes falling film flow.

A new wall-mode instability is identified.

Flow stability depends on channel width and wavenumber.

Abstract

We study the influence of side walls on the stability of falling liquid films. We combine a temporal biglobal stability analysis based on the linearized Navier-Stokes equations with experiments measuring the spatial growth rate of sinusoidal waves flowing downstream an inclined channel. Very good agreement was found when comparing the theoretical and experimental results. Strong lateral confinement of the channel stabilises the flow. In the wavenumber-Reynolds number space, the instability region experiences a fragmentation due to selective damping of moderate wavenumbers. For this range of parameters, the three dimensional confined problem shows several prominent stability modes which are classified into two categories, the well known Kapitza hydrodynamic instability mode (H-mode), and a new unstable mode, we refer to it as wall-mode (W-mode). The two mode types are stabilised differently, where the H-modes are stabilized at small wavenumbers, while the W-modes experience stabilization at high wavenumbers, and at sufficiently small channel widths, only the W-mode is observed. The reason behind the unique H-modes stabilisation is that they become analogous to waveguide modes, which can not propagate below a certain cut-off wavenumber. The spatial structure of the eigenmodes experiences significant restructuring at wavenumbers smaller than the most damped wavenumber. The mode switching preserves the spatial symmetry of the unstable mode.