On the application of a three-dimensional boundary integral method to compute distortion of magnetic drops

In this work, a new general three-dimensional hydrodynamic-magnetic boundary integral formulation for the magnetic free surface in viscous flows at low Reynolds numbers is presented. We use an extension of the Lorentz reciprocal theorem for the incompressible flow of a magnetic fluid combined with the fundamental solution of a creeping flow in order to obtain the integral representation of the flow in terms of hydrodynamic and magnetic potentials. The proposed boundary integral formulation could be used to simulate three-dimensional deformations of polar droplets in magnetic fields.