A Finite Element Study of Low Reynolds Number Two-Phase Flow in Cylindrical Tubes

A finite element solution to the steady-state problem of an inviscid bubble flowing at low Reynolds number in a cylindrical tube occupied by a second viscous phase was obtained. Interfacial tension forces were balanced against the viscous and pressure forces in order to locate the position of bubble-liquid interface. Velocities, pressures, and film thicknesses were obtained as a function of the capillary number. Specific applications of these results include the description of multiphase flow in tubes and porous media, and blood cell movement in small capillaries. The numerical results are compared with published theories and experiments.