| The flow of a viscous liquid film coating the inside of a vertical tube is studied theoretically and experimentally. As the film flows, small perturbations to the free surface grow in time and space due to the Rayleigh-Plateau instability mode. In the simplest case, the flow of a highly viscous Newtonian film falling due to gravity is considered, and a single model equation is derived using long-wave asymptotics to study the evolution of the free surface. Both linear stability analysis and nonlinear solutions are studied and shown to give excellent agreement with experiments performed in the Joint Fluids Lab.;In the second case, the core of air is forced to flow at a constant volume flux due to an imposed pressure gradient. The stress exerted on the film by the airflow at the interface contributes to the transport of the fluid; at a high enough (upwards) air volume flux, the liquid is transported upwards against gravity. The free surface again exhibits instability growth which in many regimes saturate as a series of traveling waves. We alter the model developed in the first section to include the interfacial stress exerted by the airflow using two different methods, and compare the results of each through linear stability analysis and numerical solutions. The flow of the fluid inside the layer is also studied using streamlines in a traveling reference frame and again compared to experiments.;A comparison is also made between long-wave and thin-film modeling approaches for the problems described above. Qualitative differences in the behavior of numerical solutions to each class of models are explored. Finally, the flow of a non-Newtonian liquid film with shear-thinning properties is briefly studied theoretically for gravity-driven flow. |
