Viscous film-flow coating the interior of a vertical tube. Part 2. Air-driven flow. (27th July 2017)

• Record Type: Journal Article
• Authors: Camassa, Roberto; Ogrosky, H. Reed; Olander, Jeffrey
• Is Part Of: Journal of fluid mechanics. Volume 825(2017)
• Page Start: 1056
• Page End: 1090
• Publication Date: 2017-07-27
• Subjects: gas/liquid flows, -- interfacial flows (free surface), -- thin films; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2017.409
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : The flow of a viscous liquid film coating the interior of a vertical tube is studied for the case when the film is driven upwards against gravity by a constant volume flux of air through the centre of the tube. A nonlinear model exploiting the slowly varying liquid–air interface is first developed to estimate the interfacial stresses created by the airflow. A comparison of the model with both experiments and previously developed theoretical results is conducted for two geometrical settings: channel and pipe flow. In both geometries, the model compares reasonably well with previous experiments. A long-wave asymptotic theory is then developed for the air–liquid interface taking into account the estimated free-surface stresses created by the airflow. The stability of small interfacial disturbances is studied analytically, and it is shown that the modelled free-surface stresses contribute to both an increased upwards disturbance velocity and a more rapid instability growth than those of a previously developed 'locally Poiseuille' model. Numerical solutions to the long-wave model exhibit saturated waves, whose profiles and velocities show substantial improvement with respect to the previous model predictions. The theoretical results are compared with new experiments for a modified version of the set-up described in Part 1.