Feedback control of thin film flows

Dr Susana Gomes (Imperial College London)

Frank Adams 1,

The flow of a thin film down an inclined plane is unstable when the Reynolds number is larger than a critical value depending on the slope angle. These flows are important for many industrial applications, including coating and heat transfer. While some applications benefit from a flat film, in many cases, such as heat transfer, one wishes to explore the flow’s instabilities and drive the system towards a non-uniform state. Given a desired interface shape, we propose a control methodology based on same-fluid suction/injection at the wall. The controls are proportional to the deviation between the current state of the system and the chosen solution (feedback controls). We apply these controls to three partial differential equations (PDEs) which model the interfaces of thin film flows in different limits: two long-wave models - the Benney equation and a first-order weighted residuals model - and in the weakly nonlinear regime - the Kuramoto-Sivashinsky (KS) equation. We show that in the simplest model (the KS equation) we can use a finite number of point-actuated controls based on observations of the full interface, and investigate the robustness of the designed controls to the more general models, and also to uncertain/limited observations.

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