Unsteady bubble propagation in a flexible channel: predictions of a viscous stick-slip instability

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Abstract
We investigate the unsteady motion of a long bubble advancing under either prescribed pressure ) loses stability at long times to a novel instability leading to spontaneous relaxation oscillations of increasing amplitude and period, for which the bubble switches abruptly between slow unsteady pushing and rapid quasi-steady peeling. This stick–slip motion is characterized using a third-order lumped-parameter model which in turn is reduced to a nonlinear map. Implications for the inflation of occluded lung airways are discussed.

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