The flow of a highly viscous film lining the interior of a tube with time-dependent radius is studied using a long-wave asymptotic model. The base flow, arising due to pressure-driven core flow and/or gravity, is studied first. The impact of tube expansion and contraction in time on net transport is explored mathematically through prescribing the tube radius and air volume flow rate as a function of time. First-order model corrections—which incorporate the growth (and its saturation) of long-wave disturbances arising due to the Plateau-Rayleigh instability—are then added to the model. Linear stability analysis of this periodically forced model show that tube contractions and expansions enhance instability growth compared to a rigid tube. Simulations of the full nonlinear model equation highlight the role of free-surface waves in enhancing transport. Parameter values used here are motivated by the human lung and airway system.

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• Core-annular flows
• Instability of free-surface flows
• Lubrication theory
• Pulmonary fluid mechanics
• Thin fluid films
• Waves and free surface flows