Numerical study of bubble rise and interaction in a viscous liquid

In this article, the flow instabilities during the rise of a single bubble in a narrow vertical tube are studied using a transient two-dimensional/axisymmetric model. To predict the shape of the bubble deformation, the Navier-Stokes equations in addition to an advection equation for liquid volume fraction are solved. A modified volume-of-fluid technique based on Youngs' algorithm is used to track the bubble deformation. To validate the model, the results of simulations for terminal rise velocity and bubble shape are compared with those of the experiments. The effect of different parameters such as initial bubble radius, channel height, liquid viscosity and surface tension on the shape and rise velocity of the bubble is investigated.