Stabilising falling liquid film flows using feedback control

TL;DR

This paper demonstrates that feedback control using fluid injection and suction can effectively stabilize and manipulate falling liquid film flows, with potential for practical industrial applications.

Contribution

It introduces a robust control strategy for stabilizing falling liquid films using feedback based on interface observations, applicable with limited sensors and actuators.

Findings

Feedback controls can drive the system to arbitrary steady states and traveling waves.

Control effectiveness is independent of the flow model details.

Successful control achieved with limited observations and localized actuators.

Abstract

Falling liquid films become unstable due to inertial effects when the fluid layer is sufficiently thick or the slope sufficiently steep. This free surface flow of a single fluid layer has industrial applications including coating and heat transfer, which benefit from smooth and wavy interfaces, respectively. Here we discuss how the dynamics of the system are altered by feedback controls based on observations of the interface height, and supplied to the system via the perpendicular injection and suction of fluid through the wall. In this study, we model the system using both Benney and weighted-residual models that account for the fluid injection through the wall. We find that feedback using injection and suction is a remarkably effective control mechanism: the controls can be used to drive the system towards arbitrary steady states and travelling waves, and the qualitative effects are independent of the details of the flow modelling. Furthermore, we show that the system can still be successfully controlled when the feedback is applied via a set of localised actuators and only a small number of system observations are available, and that this is possible using both static (where the controls are based on only the most recent set of observations) and dynamic (where the controls are based on an approximation of the system which evolves over time) control schemes. This study thus provides a solid theoretical foundation for future experimental realisations of the control of falling liquid films.