Motion of arbitrary 2-bubble clusters immersed in a conducting liquid when subject to uniform ambient electric and magnetic fields

Abstract : This work examines the slow viscous migration of two insulting spherical bubbles freely suspended in a conducting Newtonian liquid when subject to superposed uniform and steady electric and magnetic fields. Assuming vanishing Reynolds and Hartmann numbers makes it possible to end up with decoupled problems for the disturbed electric field and the Stokes flow about the 2-bubble cluster. Such problems are efficiently addressed by resorting to a boundary approach, which finally reduces the determination of each bubble velocity to the calculation of a very few and carefully selected surface quantities at the cluster boundary. Relevant boundary-integral equations governing these required surface quantities are derived and the associated numerical implementation is tested against the analytical solution and the asymptotic predictions derived in a previous paper for a single bubble and two widely-separated bubbles, respectively. Numerical results for close bubbles reveal strong bubble-bubble interactions deeply depending upon the applied electric and magnetic fields.