Motion of a semi-infinite bubble in a liquid filled channel using the level set method

The study of plug propagation in lung airways is of interest in the treatment of medical conditions such as asthma and in drug delivery. The problem of a semi-infinite bubble steadily displacing a liquid in a 2D channel (planar Bretherton problem) is computed using a fractional-step method on a Cartesian grid to solve the Navier-Stokes equations and a level-set formulation for resolving the air-liquid interface. We matched with available literature the geometry of the front and rear menisci of this semi-infinite bubble, stresses on the channel walls, and the maximum pressure drop as a function of the Capillary number -- the ratio of viscous to surface tension effects. Furthermore, we present preliminary results for flows within tapered walls to address area expansion near airway bifurcations.