The motion of Taylor bubbles in vertical tubes. I. A numerical simulation for the shape and rise velocity of Taylor bubbles in stagnant and flowing liquid

A numerical method has been developed for computing the velocity field adjacent to a free surface along with the surface shape for situations where both the inertial and viscous terms are important. The method is used to predict the shape and rise velocity of a Taylor bubble in stagnant or flowing liquid. Multiple theoretical solutions are shown to exist and the criterion for selecting the physically observable solution is indicated.