The influence of gravity on the steady propagation of a semi-infinite bubble into a flexible channel

Motivated by discrepancies between recent bench-top experiments [A. Juel and A. Heap, J. Fluid Mech. 572, 287 (2007)] and numerical simulations [A. L. Hazel and M. Heil, ASME J. Biomech. Eng. 128, 573 (2006)] we employ computational methods to examine the effects of transverse gravity on the steady propagation of a semi-infinite, inviscid air finger into a two-dimensional elastic channel filled with a Newtonian fluid. The special case of propagation in a rigid channel is also discussed in Appendix. The coupled free-surface, fluid-structure-interaction problem is solved numerically using the object-oriented multiphysics finite-element library OOMPH-LIB. In the absence of gravity the relationship between the applied pressure and the propagation speed of the finger is nonmonotonic, with a turning point at small values of the propagation speed. We demonstrate that the turning point disappears when a modest gravitational force is applied and conjecture that it is this effect of gravity rather than any instability of the zero-gravity solution, as postulated in previous studies, that explains why the turning point has never been observed in experiments. At large propagation speeds, the presence of transverse gravity is shown to increase the pressure required to drive the air finger at a given speed, which is consistent with the observed discrepancies between previous zero-gravity simulations and the experimental results. Finally, we briefly discuss the possible implications of our results for the physiological problem of pulmonary airway reopening. © 2008 American Institute of Physics.