| description abstract | 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. | |
