Effects of Inertia and Gravity on Liquid Plug Splitting at a Bifurcation

Liquid plugs may form in pulmonary airways during the process of liquid instillation or removal in many clinical treatments. During inspiration the plug may split at airway bifurcations and lead to a nonuniform final liquid distribution, which can adversely affect treatment outcomes. In this paper, a combination of bench top experimental and theoretical studies is presented to study the effects of inertia and gravity on plug splitting in an airway bifurcation model to simulate the liquid distributions in large airways. The splitting ratio, $Rs$⁠, is defined as the ratio of the plug volume entering the upper (gravitationally opposed) daughter tube to the lower (gravitationally favored) one. $Rs$ is measured as a function of parent tube Reynolds number, $Rep$⁠; gravitational orientations for roll angle, $ϕ$⁠, and pitch angle, $γ$⁠; parent plug length $LP$⁠; and the presence of pre-existing plug blockages in downstream daughter tubes. Results show that increasing $Rep$ causes more homogeneous splitting. A critical Reynolds number $Rec$ is found to exist so that when $Rep⩽Rec$⁠, $Rs=0$⁠, i.e., no liquid enters the upper daughter tube. $Rec$ increases while $Rs$ decreases with increasing the gravitational effect, i.e., increasing $ϕ$ and $γ$⁠. When a blockage exists in the lower daughter, $Rec$ is only found at $ϕ=60deg$ in the range of $Rep$ studied, and the resulting total mass ratio can be as high as 6, which also asymptotes to a finite value for different $ϕ$ as $Rep$ increases. Inertia is further demonstrated to cause more homogeneous plug splitting from a comparison study of $Rs$ versus $Cap$ (another characteristic speed) for three liquids: water, glycerin, and LB-400X. A theoretical model based on entrance flow for the plug in the daughters is developed and predicts $Rs$ versus $Rep$⁠. The frictional pressure drop, as a part of the total pressure drop, is estimated by two fitting parameters and shows a linear relationship with $Rep$⁠. The theory provides a good prediction on liquid plug splitting and well simulates the liquid distributions in the large airways of human lungs.