Electromagnetophoresis of a Colloidal Sphere in a Spherical Cavity

The quasi-steady electromagnetophoretic motion of a spherical colloidal particle positioned at the center of a spherical cavity filled with a conducting fluid is analyzed at low Reynolds number. Under uniformly applied electric and magnetic fields, the electric current and magnetic flux density distributions are solved for the particle and fluid phases of arbitrary electric conductivities and magnetic permeabilities. Applying a generalized reciprocal theorem to the Stokes equations modified with the resulted Lorentz force density and considering the contribution of the magnetic Maxwell stress to the force exerted on the particle, which turns out to be important, we obtain a closed-form formula for the migration velocity of the particle valid for an arbitrary value of the particle-to-cavity radius ratio. The particle velocity in general decreases monotonically with an increase in this radius ratio, with an exception for the case of a particle with high electric conductivity and low magnetic permeability relative to the suspending fluid. The asymptotic behaviors of the boundary effect on the electromagnetophoretic force and mobility of the confined particle at small and large radius ratios are discussed.