Nonlinear dynamics and control of evolving fluid interfaces
File(s)
Author(s)
Tomlin, Ruben
Type
Thesis
Abstract
In the present work, we consider the nonlinear dynamics of thin liquid films controlled by either external electric fields or fluid-mass actuators located on the substrate surface. For the former, we investigate two canonical cases, in which we are able to destabilise or stabilise a liquid film interface depending on the set-up of the electric field. We construct hierarchies of reduced-order models for the two problems, which predict and provide insight into novel electrohydrodynamic phenomena, such as multidimensional electropatterning and electrostatically-induced rivulet formation, and enable us to approximate the critical electric field strength required to prevent dripping of hanging films. For our consideration of a film influenced by fluid-mass actuators, we investigate both optimal (open-loop) and feedback (closed-loop) control methodologies for the stabilisation of multidimensional interfacial states. The optimal control problem we consider is amenable to both analysis and numerical simulation. For the feedback control problem, we consider sparsely located actuators which provide localised forcing on the interface. Proportional and model-based feedback controllers are constructed, and utilised to stabilise unstable travelling waves, synchronise chaotic dynamics, and inhibit Rayleigh–Taylor instabilities.
Version
Open Access
Date Issued
2019-09
Date Awarded
2020-02
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Papageorgiou, Demetrios
Pavliotis, Greg
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)