Effect of Gravity on Liquid Plug Transport Through an Airway Bifurcation Model

Many medical therapies require liquid plugs to be instilled into and delivered throughout the pulmonary airways. Improving these treatments requires a better understanding of how liquid distributes throughout these airways. In this study, gravitational and surface mechanisms determining the distribution of instilled liquids are examined experimentally using a bench-top model of a symmetrically bifurcating airway. A liquid plug was instilled into the parent tube and driven through the bifurcation by a syringe pump. The effect of gravity was adjusted by changing the roll angle $(ϕ)$ and pitch angle $(γ)$ of the bifurcation (⁠$ϕ=γ=0deg$ was isogravitational). $ϕ$ determines the relative gravitational orientation of the two daughter tubes: when $ϕ≠0deg$⁠, one daughter tube was lower (gravitationally favored) compared to the other. $γ$ determines the component of gravity acting along the axial direction of the parent tube: when $γ≠0deg$⁠, a nonzero component of gravity acts along the axial direction of the parent tube. A splitting ratio $Rs$⁠, is defined as the ratio of the liquid volume in the upper daughter to the lower just after plug splitting. We measured the splitting ratio, $Rs$⁠, as a function of: the parent-tube capillary number $(Cap)$⁠; the Bond number (Bo); $ϕ$⁠; $γ$⁠; and the presence of pre-existing plugs initially blocking either daughter tube. A critical capillary number $(Cac)$ was found to exist below which no liquid entered the upper daughter $(Rs=0)$⁠, and above which $Rs$ increased and leveled off with $Cap$⁠. $Cac$ increased while $Rs$ decreased with increasing $ϕ$⁠, $γ$⁠, and Bo for blocked and unblocked cases at a given $Cap>Cac$⁠. Compared to the nonblockage cases, $Rs$ decreased (increased) at a given $Cap$ while $Cac$ increased (decreased) with an upper (lower) liquid blockage. More liquid entered the unblocked daughter with a blockage in one daughter tube, and this effect was larger with larger gravity effect. A simple theoretical model that predicts $Rs$ and $Cac$ is in qualitative agreement with the experiments over a wide range of parameters.