Gas-assisted fluid displacement in a circular tube and a rectangular channel

In this paper the amount of liquid left inside of a circular tube and a rectangular channel when displaced by another immiscible fluid are determined by solving the full creeping-motion equations. The exact continuity of stress on the fee surface is employed with a finite difference method. In order to solve the equations, the steady-state shape of the interface is guessed and the normal stress boundary condition is dropped. The equations based on a stream function-vorticity formulation are solved with the aid of elliptic grid generation. The computed results are compared with the experimental results of Taylor (J. Fluid Mech. 1961; 10:161), the theoretical results of Reinelt and Saffman (SIAM J. Sci. Stat. Comput. 1985; 6:542) and our experimental data. The computed results are in close agreement with our experimental data and those of previous investigators.