Abstract
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.
Highlights
An unbounded, electrically conducting, Newtonianfluid under the simultaneous application of an electric current density J and a non-collinear magnetic flux density B will undergo a magnetohydrodynamic flow in the direction perpendicular to both the applied fields
Equation (20) for the EMP migration of a spherical particle positioned at the center of a spherical cavity indicates that the velocity of the particle is bilinear in the applied electric current and magnetic flux density fields
The EMP migration of a spherical particle situated at the center of a spherical cavity filled with a conducting fluid subject to uniformly applied electric and magnetic fields is analyzed at the quasi-steady state
Summary
Electrically conducting, Newtonianfluid under the simultaneous application of an electric current density J and a non-collinear magnetic flux density B will undergo a magnetohydrodynamic flow in the direction perpendicular to both the applied fields This fluid flow is driven by the resulted Lorentz force density J × B , which plays as an additional term in the Navier-Stokes equation [1]-[3]. The EMP motion of a colloidal sphere in a concentric spherical cavity filled with a conducting fluid subject to uniformly prescribed electric and magnetic fields is analyzed with the consideration of the total force (including the Maxwell stress) exerted on the particle, where the particle and fluid may have arbitrary values in electric conductivity and magnetic permeability. The geometric symmetry in this model system allows closed-form formulas for the EMP force and migration velocity of the confined particle to be obtained in Equations (15) and (20), respectively
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