Cycle-induced flow and transport in a model of alveolar liquid lining

Abstract

A simplified model is developed for an alveolar liquid lining undergoing cyclic stretching which mimics breathing motions. A thin, viscous film coats an extensible alveolar wall with small aspect ratio, $\varepsilon$ . Scaling analysis and asymptotic theory are used to describe the interface profile and surfactant distribution during the oscillation cycle for either insoluble or soluble surfactants. The flow consists of two distinct regimes: an outer region away from the rigid endwalls where flow is near-parallel and a boundary-layer region at the rigid endwalls where flow is non-parallel. The system is solved asymptotically in the limit of $\varepsilon\ll 1$ and small strain amplitudes, $\Delta \ll 1$ . For leading order in $\varepsilon$ , steady streaming vortical flows are found at $O(\Delta^2)$ and their size, number and flow direction depend on the system parameter values. This preliminary model can be useful for understanding alveolar transport characteristics for slowly diffusing molecules with large Peclet number, such as endogenous surfactants and proteins as well as delivered surfactants, drugs and genetic material that may occur in various therapies or partial liquid ventilation. The flow pattern also provides a pathway for cell–cell signalling within the alveolus.