Feedback control and continuation for deformable bubbles

Abstract: In this talk, I explore how feedback control and control-based continuation (CBC) can be used to both stabilize and detect unstable steady states in physical experiments. CBC aims to create experimental equivalents of numerical methods such as tracking steady states and bifurcations which would otherwise not be possible in experiments. Here I describe our recent work on using CBC to explore bubble deformation in Hele-Shaw cells – the first such application of CBC in free-surface fluid mechanics. For the case of a propagating bubble (a Saffman-Taylor bubble), we use a numerical simulation of the system to develop a control strategy and act as a numerical experiment. We show how CBC protocols can be used to detect the unstable double-tipped propagating bubble state in nonlinear simulations, for both moving actuators and a more realistic setup involving an array of fixed-position actuators. Finally, I will also discuss some of our recent laboratory experimental results for using CBC for non-propagating bubbles placed in a straining flow, where we have successfully tracked both singly- and doubly-unstable steady branches connected via a limit point associated with bubble breakup.

Mathematics

Audience: researchers in the topic

Fluids and Structures Seminar @ UEA