Abstract
The dynamics of a gas bubble suspended in an axisymmetric straining flow is examined with modern tools of global stability analysis. The complete bifurcation diagram of a bubble constrained to remain trapped at the stagnation point is determined. It is made of a stable branch, along which the bubble oscillates, and an unstable branch along which it develops non-oscillating waisted shapes prefiguring breakup. Two unstable non-oscillating modes also allow a free bubble to drift away from the stagnation point, not only along the elongation axis but also within the compressional plane thanks to a specific self-propulsion mechanism.
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