Effects of gravity, inertia, and surfactant on steady plug propagation in a two-dimensional channel

Abstract

Liquid plugs may form in pulmonary airways during the process of liquid instillation or removal in many clinical treatments. Studies have shown that the effectiveness of these treatments may depend on how liquids distribute in the lung. Better understanding of the fundamental fluid mechanics of liquid plug transport will facilitate treatment strategies. In this paper, we develop a numerical model of steady plug propagation driven by gravity and pressure in a two-dimensional liquid-lined channel oriented at an angle α with respect to gravity. We investigate the effects of gravity through the Bond number, Bo, and α; the plug propagation speed through the capillary number, Ca, or the Reynolds number, Re; the plug length LP, and the surfactant concentration C0. Without gravity, i.e., Bo=0, the plug is symmetric, and there are two regimes for the flow: two wall layers and two trapped vortices in the core. There is no flow interaction between the upper and lower half plug domains. When Bo≠0 and α≠0, π, fluid is found to flow from the upper precursor film, through the core and into the lower trailing film. Then the number of vortices can be zero, one, or two, depending on the flow parameters. The vortices have stagnation points on the interface when C0=0, however when the surfactant is present (C0>0), the vortices detach from the interface and create saddle points inside the core. The front meniscus develops a capillary surface wave extending into the precursor film. This is where the film is thinnest and thus the wall shear stress is highest, as high as ∼100dyn∕cm2 in adult airways, which indicates a significant risk of pulmonary airway epithelial cell damage. Adding surfactant can decrease the peak magnitude of the shear stress, thus reducing the risk of cell damage. The prebifurcation asymmetry of the plug is quantified by the volume ratio, Vr, defined as the ratio of the liquid above to that below the center line of the channel. Vr is found to increase with LP, Ca, Re, and C0, while it decreases with Bo. The total mass left behind in the trailing films increases with Bo for any α at α>2π∕5, Ca and α for any value of Bo>0.