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The opening of lung airways from a collapsed, flooded state is an important process in many medical conditions including asthma, cystic fibrosis, emphysema and respiratory distress syndrome. Airway opening also plays a pivotal role in one of the most critical respiratory events in life - the first breath. As a simple physical model of the opening process, one may consider a bubble that propagates down a two-dimensional, flexible-walled channel. Previous workers have investigated the behaviour of this system when the channel walls are impermeable and the bubble advances with constant speed, U. They demonstrated the existence of two steady solution branches: one at low U for which the bubble pressure, p<SUB>b</SUB>, decreases with increasing U, contrary to experimental observations; and one at larger U for which p<SUB>b</SUB> increases with U. Two potentially important extensions of this model are investigated in this dissertation. First, the walls of lung airways are known to be permeable to small molecules such as water, so the model is extended to include the effects of weak wall permeability. This problem is solved asymptotically by dividing the solution domain into a number of different regions. These include a long region (described by lubrication theory) which extends far ahead of the bubble tip, a Landau-Levich region where the fluid pressure readjusts to allow for the pressure drop across the advancing meniscus, and another long region where the fluid behind the bubble tip slowly drains through the permeable wall. Unlike the impermeable-wall case, it is shown that at low U, p<SUB>b</SUB> generally increases with increasing U. The solution also exhibits a receding contract line for which wall permeability eliminates the usual stress singularity.

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