Motion of an insulating solid particle near a plane boundary under the action of uniform ambient electric and magnetic fields

This work addresses the wall-particle interactions between a solid and insulating particle immersed above a plane wall in a conducting liquid when subject to ambient uniform electric and magnetic fields. Both for a perfectly conductingor for an insulating wall, attention is paid to the net electromagnetic force and torque exerted on the particle when itis held fixed and also to the particle rigid-body migration when it is freely suspended in the liquid. A new boundary approach is proposed to obtain those quantities whatever the particle shape and location. The advocated procedure actuallyreduces the task to the determination of a few surface quantities by inverting seven boundary-integral equations on the particle boundary. The entire procedure is then asymptotically worked out in the case of a perfectly conducting wall fora distant particle, i.e. when the wall-particle gap is much larger than the particle length scale. The derived asmptoticresults reveal that the magnitude of the wall-particle interactions deeply depends on the distant particle geometry. In that sense, the results previously obtained by other authors for a distant sphere interacting with an insulating plane wall are far from being general.