Bubble transitions in strongly collapsed elastic tubes

Abstract

The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elastic tube is investigated experimentally in a benchtop model of airway reopening. Localized regions of strong collapse are likely in the lung, because collapsing fluid-elastic instabilities promote extensive deformation of the airway cross-section beyond the point of opposite wall contact. We find that radical changes in the reopening mechanics occur at this point. We build on the recent identification by Heap & Juel (Phys. Fluids, vol. 20, 2008, article no. 081702) of three different steadily propagating bubbles (asymmetric, double-tipped and pointed) that are selected successively for increasing values of the capillary number (Ca, ratio of viscous to surface tension forces) in tubes initially collapsed beyond the point of opposite wall contact. The asymmetric bubble is also observed in less collapsed tubes for small values of Ca, and we show that it bifurcates super-critically from the usual parabolic-tipped bubble as Ca increases. We also characterize the mechanisms underlying the discontinuous transitions between asymmetric and double-tipped bubbles, and double-tipped and pointed bubbles. In particular, we find that the tube must reopen to a critical height for double-tipped bubbles to be selected. The length of the precursor fingers in the double-tipped bubble decreases with Ca, and the bubble loses stability to pointed bubbles when this length is less than the height of the tube at the point where the fingers merge. By contrast with the asymmetric and double-tipped bubbles, the pointed bubble infiltrates the most collapsed part of the tube to yield the rapid reopening of the airway at low pressure, with the potential to reduce ventilation-induced lung damage.