Migrating and interacting micro-bubbles immersed in a conducting liquid under the action of uniform ambient electric and magnetic fields

This work addresses the slow viscous migration of two spherical bubbles immersed in a conducting liquid when subject to uniform electric and magnetic fields. Basic assumptions and resulting governing equations for the flow about the bubbles are given and a new analytical solution is established for a single bubble. The challenging case of two interacting bubbles is then treated by resorting to a so-called reflection technique. This permits one to asymptotically expand in terms of the normalized center-to-center distance of the bubbles the net hydrodynamic forces exerted on the bubbles when fixed and also the resulting velocities when freely suspended in the liquid. Depending upon the applied electric and magnetic fields, short-range or long-range bubble-bubble interactions are thereby predicted.