Feedback control of falling liquid films

Presented by Dr. Susana Gomes (University of Warwick) 

Abstract: 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 one wishes to explore the flow’s instabilities and drive the system towards a non- uniform state. In this talk, we will present a control methodology based on same-fluid blowing and suction at the wall. Given a desired interface shape, we apply controls which are proportional to the deviation between the current state of the system and the chosen solution. We study the effect of these controls on a hierarchy of models for the interface, which include a weakly nonlinear model (the Kuramoto-Sivashinsky equation), two long-wave models (the Benney equation and a first-order weighted residuals model) and the full Navier-Stokes equations. We show that we can use a finite number of point-actuated controls based on observations of the interface to stabilise both the flat solution and chosen nontrivial solutions. Furthermore, we investigate the robustness of the designed controls to uncertain observations and parameter values, as well as across the hierarchy of models.