A fast numerical method for the interfacial motion of an electrically conducting bubble in a Stokes flow

There is a great need for efficient numerical methods when solving interfacial motion problems involving coupled physical processes. To this end, a fast numerical method is developed for tracking the motion of an electrically conducting fluid bubble in a Stokes flow subject to an electric field.The motion of a two-dimensional bubble immersed in an infinite expanse of viscous fluid is examined. The Stokes equations governing the fluid dynamics and Laplace's equation governing the electrostatics are recast as integral equations. The electrohydrodynamic free boundary problem is reduced to the solution of integral equations along the bubble interface. The integral equations are discretized and solved with an iterative solver accelerated by the fast multipole method. Results from the numerical method are compared with published results of a simplified, analytical model and are found to be in good agreement.