INSTABILITY OF A GRAVITY-DRIVEN LIQUID FILM CONFINED IN AN INCLINED RECTANGULAR DUCT

This study deals with the confinement effects due to top and side walls on the stability of a falling liquid film flowing down an incline. To this aim, we consider a liquid film flowing between two infinite plates and in rectangular ducts in the presence of an adjacent gas phase, focusing on the case of zero net gas flow rate. A rigorous linear stability analysis is conducted for three gas-liquid systems of particular interest in applications. This enables us to demonstrate the effect of the gas-liquid density ratio and viscosity ratio in small channels/ducts and shallow downward inclinations. Although the analysis considers all wave numbers, the neutral stability boundary is found to be defined mainly by long-wave perturbations in the two-plate (TP) geometry, as well as in the rectangular ducts. The decrease of the channel height for the considered liquid-gas systems always stabilizes the liquid film. However, the Kapitza criterion for the onset of Kapitza waves on the surface of a falling liquid film can either overpredict or underpredict the stability limits of the channel/duct flows, depending on the channel height, its aspect ratio, and the viscosity and density ratios of the phases. The falling liquid film, bounded by the side walls, becomes unstable at larger flow rates with the decrease of the duct aspect ratio. The presence of recirculating gas in the channel/duct is found to affect the stability through the dynamic shear stress components at the gas-liquid interface. Therefore, its presence must be taken into account.