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Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. I: General theory. (English) Zbl 1013.76096

Summary: We examine the behaviour of an insulating particle suspended in a liquid metal and subject to the influence of locally uniform electric and magnetic fields \((E,B)\). The electric field drives a current \(J\) which is perturbed by the presence of the particle, and the resulting Lorentz force drives a flow. It is assumed that both the Reynolds number and the Hartmann number based on particle size are small. If the particle is fixed, it experiences a force and couple that are each bilinear in \(J\) and \(B\); if it is freely suspended, then it moves with translational velocity \(U\) and angular velocity \(\Omega\) each similarly bilinear in \(J\) and \(B\). We determine the general form of these bilinear relationships, with particular attention to three types of particle symmetry: (i) isotropy; (ii) axisymmetry; and (iii) orthotropy.

MSC:

76T20 Suspensions
76W05 Magnetohydrodynamics and electrohydrodynamics
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