Control-based continuation maps out unstable equilibria in laboratory two-phase flow

We apply control-based continuation, an experimental method used to explore the bifurcation structure of nonlinear systems, to a spatially extended system by examining the equilibrium configurations of a bubble placed at the center of a straining flow. Feedback control is delivered by injecting/withdrawing fluid at actuation points and chosen according to real-time observations of the bubble as viewed from above. The amplitude of actuation is used to locate its unstable equilibria, and thus enable their observation. We map the unstable steady shapes of the bubble as a function of straining flow rate and demonstrate excellent agreement of the resulting experimental bifurcation diagram with numerical predictions.