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

Abstract

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.