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Motivated by the desire to understand complex transient behaviour in fluidflows, we study the dynamics of an air bubble driven by the steady motion of asuspending viscous fluid within a Hele-Shaw channel with a centred depthperturbation. Using both experiments and numerical simulations of adepth-averaged model, we investigate the evolution of an initially centredbubble of prescribed volume as a function of flow rate and initial shape. Theexperiments exhibit a rich variety of organised transient dynamics, involvingbubble break up as well as aggregation and coalescence of interactingneighbouring bubbles. The long-term outcome is either a single bubble ormultiple separating bubbles, positioned along the channel in order ofincreasing velocity. Up to moderate flow rates, the life and fate of the bubbleare reproducible and can be categorised by a small number of characteristicbehaviours that occur in simply-connected regions of the parameter plane.Increasing the flow rate leads to less reproducible time evolutions withincreasing sensitivity to initial conditions and perturbations in the channel.Time-dependent numerical simulations that allow for break up and coalescenceare found to reproduce most of the dynamical behaviour observed experimentallyincluding enhanced sensitivity at high flow rate. An unusual feature of thissystem is that the set of steady and periodic solutions can change duringtemporal evolution because both the number of bubbles and their sizedistribution evolve due to break up and coalescence events. Calculation ofstable and unstable solutions in the single- and two-bubble cases reveals thatthe transient dynamics are orchestrated by weakly-unstable solutions of thesystem termed edge states that can appear and disappear as the number ofbubbles changes.

The life and fate of a bubble in a geometrically-perturbed Hele-Shaw channel