3D computational simulations and mathematical modeling of non-Newtonian plug flow in straight and bifurcating capillary tubes

Liquid plug flow in capillary tubes is a classical problem in fluid mechanics with far reaching applications, especially in the medical field. Particularly, in surfactant replacement therapy (SRT), liquid plugs are instilled into the airway to treat preterm infants with respiratory distress syndrome. There is a growing body of literature dedicated to understanding the physics of targeted surfactant delivery, e.g., plug film deposition and plug splitting at bifurcations. However, most mathematical models and fluid simulation have only looked at the propagation of Newtonian plugs, when in practice, the surfactant used in SRT is of non-Newtonian behavior. To address this gap, we have developed a novel numerical method capable of capturing the complex interaction between a non-Newtonian fluid, Newtonian liquid, and gas. Using an in-house 3D flow solver and the Volume-of-Fluid framework, we simulate plug propagation and splitting at airway bifurcations. In addition, we quantify the asymmetry of plug splitting and compare the simulation results to a new mathematical model for non-Newtonian plugs.