UNC-CH Physics and Astronomy PhD Defense

Jeff Olander

“Newtonian and non-Newtonian flows in a simple model of the human trachea”

The dynamics of fluid flow in a simplified model of the human trachea is described both experimentally and theoretically. Two configurations of this model are presented. In the first, viscous silicone oils are driven upward by a constant volume flux of air inside of a 1 cm I.D. x 20 cm smooth glass tube. In the second, viscous Newtonian and non-Newtonian liquids are pumped into longer 1 cm I.D. smooth glass tubes and allowed to drain under gravity. In all experiments, the liquids are initially flat and thin moving films which quickly develop periodic, long wave surface instabilities. In the gravity-driven case, these instabilities grow unchecked into liquid plugs separated by large bullet-shaped bubbles that move in lock-step with the plugs. On the theory side, low-Reynolds, long wave models of the Newtonian flows are presented. Linear stability analysis for these models are shown and results are compared with experiments.

For the non-Newtonian experiments, a pair of PIB(polyisobutylene)-PB(polybutene) Boger fluids were prepared. They were tested in a cone-and-plate rheometer, and sample results and their measured relaxation times are given. An Upper Convected Maxwell constitutive stress model is coupled to the Newtonian equations without the long wave assumption to describe these fluids’ flows. From this coupling, a small-amplitude, linear Weissenberg model was derived and is presented. It predicts an elasticity-enhanced Rayleigh-Plateau instability. However, experiments show a reduction in the growth of interfacial instabilities compared with Newtonian liquids. An explanation for this discrepancy is offered.