An analytical study on interfacial wave structure between the liquid film and gas core in a vertical tube

A model has been derived for interfacial wave propagation for a liquid film on the wall of a vertical pipe and for a flowing gas in the central core. An analytical study is presented for the stability of a flat interface, and for traveling waves on the interface. Long wave theory is applied to both phases and the resulting conservation equations are of the same form as a two-fluid model. Two situations are examined: the interface between a Taylor bubble and the liquid film, where the gas velocity is small, and the interface for cocurrent annular flow where the gas velocity is relatively large. The interface between a Taylor bubble and a liquid film was found to be dominated by waves, which can be destabilized by the inertia of the liquid phase. For annular flow the interface is subject to a Kelvin–Helmholtz instability. When the gas flow rate is small, and surface tension is negligible, the traveling wave has a shape similar to that of a Taylor bubble except near the tip and trailing edge. When surface tension is dominant, the solution is a soliton. This region and the receding part of the soliton appears to be related to the ripple waves seen near the trailing edge of Taylor bubbles.