We consider a two-phase core annular flow in a cylindrical pipe in this talk. The inner core is assumed to be a pressure driven gas flow. The other phase is highly viscous fluid lining the inner wall of the pipe. Several models are presented, including the classic Poiseuille solution for two-phase flows, to predict the mean thickness of the liquid layer in the experiment by Kim et al. , where a fixed flow rate of gas drags the liquid upward in a vertical pipe, in which the liquid is injected into the pipe at a fixed feed rate.

We derive a nonlinear evolution equation based on the lubrication approximation for the interface. The equation incorporates the strong pressure-driven gas flow as a forcing term into the equation for the liquid, with an effective viscosity for turbulent flow replacing the molecular viscosity of the gas. We study numerically the interface evolution of an initially axisymmetric disturbance of the annular film of viscous liquid. The mean height of the liquid layer in the experiment can be accurately predicted using this model, and the existence of the ring-like waves reported in the experiments is confirmed by the interfacial dynamics of the model.