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Boundary effects on electro-magneto-phoresis

  • EHUD YARIV (a1) and TOUVIA MILOH (a2)
Abstract

The effect of a remote insulating boundary on the electro-magneto-phoretic motion of an insulating spherical particle suspended in a conducting liquid is investigated using an iterative reflection scheme developed about the unbounded-fluid-domain solution of Leenov & Kolin (J. Chem. Phys., vol. 22, no. 4, p. 683). Wall-induced corrections result from velocity reflections, successively introduced so as to maintain the no-slip condition on the wall and particle boundaries, as well as from the Lorentz forces associated with comparable reflections of the electric field. This method generates asymptotic expansions in λ (≪1), the ratio of particle size to particle–wall separation. The leading-order correction to the hydrodynamic force on the particle appears at O3); it is directed along the leading-order force and tends to augment it.

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Corresponding author
Email address for correspondence: yarive@technion.ac.il
References
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Bentwich, M. & Miloh, T. 1978 On the exact solution for the two-sphere problem in axisymmetric potential flow. J. Appl. Mech. 45, 463468.
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242251.
Goldman, A. J., Cox, R. & Brenner, H. 1967 Slow viscous motion of a sphere parallel to a plane wall – I. Motion through a quiescent fluid. Chem. Engng Sci. 22, 637651.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365400.
Jeffery, G. 1912 On a form of the solution of Laplace's equation suitable for problems relating to two spheres. Proc. Roy. Soc. Lond. A 87 (593), 109120.
Keh, H. J. & Anderson, J. L. 1985 Boundary effects on electrophoretic motion of colloidal spheres. J. Fluid Mech. 153, 417439.
Keh, H. J. & Chen, S. B. 1989 Electrophoresis of a colloidal sphere parallel to a dielectric plane. J. Fluid Mech. 194, 377390.
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics. Butterworth-Heinemann.
Kolin, A. 1978 Some current and potential uses of magnetic-fields in electrokinetic separations. J. Chromatogr. 159 (1), 147181.
Kolin, A. & Kado, R. 1958 Fractionation of cell suspensions in an slectromagnetic force field. Nature 182 (4634), 510512.
Leal, L. G. 1992 Laminar Flow and Convective Transport Processes. Butterworth-Heinemann.
Leenov, D. & Kolin, A. 1954 Theory of electromagnetophoresis. I. Magnetohydrodynamic forces experienced by spherical and symmetrically oriented cylindrical particles. J. Chem. Phys. 22 (4), 683688.
Magnaudet, J., Takagi, S. & Legendre, D. 2003 Drag, deformation and lateral migration of a buoyant drop moving near a wall. J. Fluid Mech. 476, 115157.
Moffatt, H. K. & Sellier, A. 2002 Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 1. General theory. J. Fluid Mech. 464, 279286.
O'Neill, M. E. 1964 A slow motion of a viscous liquid caused by a slowly moving solid sphere. Mathematika 11, 6474.
Sellier, A. 2003 a Migration of a conducting ellipsoid subject to uniform ambient electric and magnetic fields. C. R. Mécanique 331 (2), 127132.
Sellier, A. 2003 b Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 2. Boundary formulation and ellipsoidal particles. J. Fluid Mech. 488, 335353.
Sellier, A. 2005 Migration of a solid conducting sphere immersed in a liquid metal near a plane boundary under the action of uniform ambient electric and magnetic fields. In The 15th Riga and 6th PAMIR International Conference on Fundamental and Applied MHD, pp. 311–314.
Sellier, A. 2006 Migration of a solid conducting sphere immersed in a liquid metal near a plane conducting solid wall under the action of uniform ambient electric and magnetic fields. Magnetohydrodynamics 42, 317326.
Solomentsev, Y., Velegol, D. & Anderson, J. L. 1997 Conduction in the small gap between two spheres. Phys. Fluids 9, 12091217.
Stimson, M. & Jeffery, G. 1926 The motion of two spheres in a viscous fluid. Proc. Roy. Soc. A 111 (757), 110116.
Watarai, H., Suwa, M. & Iiguni, Y. 2004 Magnetophoresis and electromagnetophoresis of microparticles in liquids. Anal. Bioanal. Chem. 378 (7), 16931699.
Xu, Z. M., Li, T. X. & Zhou, Y. H. 2007 Continuous removal of nonmetallic inclusions from aluminum melts by means of stationary electromagnetic field and dc current. Metall. Mater. Trans. A 38A, 11041110.
Yariv, E. & Brenner, H. 2003 Near-contact electrophoretic motion of a sphere parallel to a planar wall. J. Fluid Mech. 484, 85111.
Yariv, E. & Miloh, T. 2007 Electro-magneto-phoresis of slender bodies. J. Fluid Mech. 577, 331340.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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