Slender bubbles: Inertial effects and stability

Abstract

The influence of inertia on the deformation and breakup of a slender bubble embedded in a Newtonian liquid in an axisymmetric extensional flow has been theoretically studied. The steady-state problem is governed by two dimensionless parameters: The capillary number and the Reynolds number for the external flow. The calculated stationary deformation reveals the existence of multiple solutions. A stability analysis of these results is used to distinguish between stable and unstable solutions and to establish the break-up point.