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Boundary effects on electro-magneto-phoresis

Published online by Cambridge University Press:  10 March 2009

EHUD YARIV  and
TOUVIA MILOH
EHUD YARIV*
Affiliation:
Faculty of Mathematics, Technion – Israel Institute of Technology, Technion City 32000, Israel
TOUVIA MILOH
Affiliation:
School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
*
†Email address for correspondence: yarive@technion.ac.il
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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 O(λ3); it is directed along the leading-order force and tends to augment it.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 195 - 207
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Bentwich, M. & Miloh, T. 1978 On the exact solution for the two-sphere problem in axisymmetric potential flow. J. Appl. Mech. 45, 463–468.CrossRefGoogle Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242–251.Google Scholar
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, 637–651.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365–400.Google Scholar
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), 109–120.Google Scholar
Keh, H. J. & Anderson, J. L. 1985 Boundary effects on electrophoretic motion of colloidal spheres. J. Fluid Mech. 153, 417–439.CrossRefGoogle Scholar
Keh, H. J. & Chen, S. B. 1989 Electrophoresis of a colloidal sphere parallel to a dielectric plane. J. Fluid Mech. 194, 377–390.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics. Butterworth-Heinemann.Google Scholar
Kolin, A. 1978 Some current and potential uses of magnetic-fields in electrokinetic separations. J. Chromatogr. 159 (1), 147–181.Google Scholar
Kolin, A. & Kado, R. 1958 Fractionation of cell suspensions in an slectromagnetic force field. Nature 182 (4634), 510–512.Google Scholar
Leal, L. G. 1992 Laminar Flow and Convective Transport Processes. Butterworth-Heinemann.Google Scholar
Leenov, D. & Kolin, A. 1954 Theory of electromagnetophoresis. I. Magnetohydrodynamic forces experienced by spherical and symmetrically oriented cylindrical particles. J. Chem. Phys. 22 (4), 683–688.CrossRefGoogle Scholar
Magnaudet, J., Takagi, S. & Legendre, D. 2003 Drag, deformation and lateral migration of a buoyant drop moving near a wall. J. Fluid Mech. 476, 115–157.Google Scholar
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, 279–286.Google Scholar
O'Neill, M. E. 1964 A slow motion of a viscous liquid caused by a slowly moving solid sphere. Mathematika 11, 64–74.CrossRefGoogle Scholar
Sellier, A. 2003 a Migration of a conducting ellipsoid subject to uniform ambient electric and magnetic fields. C. R. Mécanique 331 (2), 127–132.Google Scholar
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, 335–353.CrossRefGoogle Scholar
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.Google Scholar
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, 317–326.Google Scholar
Solomentsev, Y., Velegol, D. & Anderson, J. L. 1997 Conduction in the small gap between two spheres. Phys. Fluids 9, 1209–1217.Google Scholar
Stimson, M. & Jeffery, G. 1926 The motion of two spheres in a viscous fluid. Proc. Roy. Soc. A 111 (757), 110–116.Google Scholar
Watarai, H., Suwa, M. & Iiguni, Y. 2004 Magnetophoresis and electromagnetophoresis of microparticles in liquids. Anal. Bioanal. Chem. 378 (7), 1693–1699.Google Scholar
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, 1104–1110.Google Scholar
Yariv, E. & Brenner, H. 2003 Near-contact electrophoretic motion of a sphere parallel to a planar wall. J. Fluid Mech. 484, 85–111.Google Scholar
Yariv, E. & Miloh, T. 2007 Electro-magneto-phoresis of slender bodies. J. Fluid Mech. 577, 331–340.CrossRefGoogle Scholar