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

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...