Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 2. Boundary formulation and ellipsoidal particles

Antoine Sellier 1, *
Abstract : This paper examines the low-Reynolds-number migration of an insulating and rigid particle that is freely suspended in a viscous liquid metal and subject to uniform ambient electric and magnetic fields E and B. Under the same physical assumptions as Part 1, a whole boundary formulation of the problem is established. It allows the determination of the particle rigid-body motion without calculating the modified electric field and the flow induced by the Lorentz body force in the fluid domain. The advocated boundary approach, well-adapted for future numerical implementation, makes it possible to obtain an analytical expression for the translational velocity of any ellipsoidal particle (the simplest case of non-spherical orthotropic particles). The behaviour of a spheroid is carefully investigated and discussed both without and with gravity. The migration of this simple non-spherical particle is found to depend on both its nature (prolate or oblate) and the ambient uniform fields E and B. The spheroid translates without rotation, and not necessarily parallel to E ? B. For adequately selected fields E and B, the spheroid may either migrate parallel or anti-parallel to a sphere and even be motionless.
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Antoine Sellier. Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 2. Boundary formulation and ellipsoidal particles. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2003, july (488), pp.335-353. ⟨10.1017/s0022112003004944⟩. ⟨hal-01024937⟩

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