Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-07-01T17:33:50.814Z Has data issue: false hasContentIssue false

Electrophoresis of slender particles

Published online by Cambridge University Press:  26 April 2006

Yuri Solomentsev
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
John L. Anderson
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Abstract

The hydrodynamic theory of slender bodies is used to model electrophoretic motion of a slender particle having a charge (zeta potential) that varies with position along its length. The theory is limited to systems where the Debye screening length of the solution is much less than the typical cross-sectional dimension of the particle. A stokeslet representation of the hydrodynamic force is combined with the Lorentz reciprocal theorem for Stokes flow to develop a set of linear equations which must be solved for the components of the translational and angular velocities of the particle. Sample calculations are presented for the electrophoretic motion of straight spheroids and cylinders and a torus in a uniform electric field. The theory is also applied to a straight uniformly charged particle in a spatially varying electric field. The uniformly charged particle rotates into alignment with the principal axes of ∇E; we suggest that such alignment can lead to electrophoretic transport of particles through a small aperture in an otherwise impermeable wall. The theory developed here is more general than just for electrophoresis, since the final result is expressed in terms of a general 'slip velocity’ at the surface of the particle. Thus, the results are applicable to diffusiophoresis of slender particles if the proper slip-velocity coefficient is used.

Type
Research Article
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acrivos, A., Jeffrey, D. J. & Saville, D. A.1990 Particle migration in suspensions by thermocapillary or electrophoretic motion. J. Fluid Mech. 212, 95.Google Scholar
Anderson, J. L.1985 Effect of nonuniform zeta potential on particle movement in electric fields. J. Colloid Interface Sci. 105, 45.Google Scholar
Anderson, J. L.1989 Colloid transport by interfacial forces. Ann. Rev. Fluid Mech. 21, 61.Google Scholar
Anderson, J. L. & Solomentsev, Y.1994 Electrophoresis of nohuniformly charged chains. In Macro-ion Characterization: From Dilute Solutions to Complex Fluids (ed. K. S. Schmitz). American Chemical Society Symposium Series, no. 548.
Batchelor, G. K.1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419.Google Scholar
Cole, J. D.1968 Perturbation Methods in Applied Mathematics. Waltham, Massachusetts: Blaisdell.
Cox, R. G.1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791.Google Scholar
Daoudi, S. & Brochard, F.1978 Flows of flexible polymer solutions in pores. Macromolecules 11, 751.Google Scholar
Dukhin, S. S. & Derjaguin, B. V.1974 Surface and Colloid Science, vol. 7 (ed. E. Matijevic). Wiley.
Fair, M. C.1990 Electrophoresis of nonspherical and nonuniformly charged colloidal particles. PhD thesis, Carnegie Mellon University.
Fair, M. C. & Anderson, J. L.1989 Electrophoresis of nonuniformly charged ellipsoidal particles. J. Colloid Interface Sci. 127, 388.Google Scholar
Fair, M. C. & Anderson, J. L.1990 Electrophoresis of dumbbell-like colloidal particles. Intl J. Multiphase Flow 16, 663, 1131.Google Scholar
Fair, M. C. & Anderson, J. L.1992 Electrophoresis of heterogeneous colloids: doublets of dissimilar particles. Langmuir 8, 2850.Google Scholar
Happel, J. & Brenner, H.1973 Low Reynolds Number Hydrodynamics. Noordhoff.
Henry, D. C.1931 The cataphoresis of suspended particles. Part I. The equation of cataphoresis. Proc. R. Soc. Lond. A 133, 106.Google Scholar
Hunter, R. J.1981 Zeta Potential in Colloid Science. Academic.
Johnson, R. E.1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411.Google Scholar
Johnson, R. E. & Wu, T. Y.1979 Hydrodynamics of low-Reynolds-number flow. Part 5. Motion of a slender torus. J. Fluid Mech. 95, 263.Google Scholar
Keller, J. B. & Rubinow, S. I.1976 Slender-body theory for slow viscous flow. J. Fluid Mech. 75, 705.Google Scholar
Keh, H. J. & Chen, S. B.1993 Diffusiophoresis and electrophoresis of colloidal cylinders. Langmuir 9, 1142.Google Scholar
Keh, H. J. & Yang, F. R.1991 Particle interactions in electrophoresis. IV. Motion of arbitrary three-dimensional clusters of spheres. J. Colloid Interface Sci 145, 362.Google Scholar
Kelman, R. B.1965 Steady state diffusion through a finite pore with an infinite reservoir. Bull. Math. Biophics 27, 57.Google Scholar
Mangelsdorf, C. S. & White, L. R.1992 The electrophoretic mobility of a spherical colloid in an oscillating electric field. J. Chem. Soc. Faraday Trans. 88, 3567.Google Scholar
Melcher, J. R.1981 Continuum Electromechanics. MIT Press.
Newman, J. S.1966 Resistance for flow of current to a disk. J. Electrochem. Soc. 113, 501.Google Scholar
O'Brien, R. W.1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 92, 204.Google Scholar
O'Brien, R. W.1990 The electroaccoustic equations for a colloidal suspension. J. Fluid Mech. 212, 81.Google Scholar
O'Brien, R. W. & White, L. R.1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday Trans. 74 (2), 1607.Google Scholar
O'Brien, R. W. & Ward, D. N.1988 The electrophoresis of a spheroid with a thin double layer. J. Colloid Interface Sci. 121, 402.Google Scholar
Pawar, Y.1993 Electrophoresis of heterogeneously charged colloidal particles. PhD thesis, Carnegie Mellon University.
Russel, W. B., Saville, D. A. & Schowalter, W. R.1989 Colloidal Dispersions. Cambridge University Press.
Saville, D. A.1977 Electrokinetic effects with small particles. Ann. Rev. Fluid Mech. 9, 321.Google Scholar
Sherwood, J. D.1982 Electrophoresis of rods. J. Chem. Soc. Faraday Trans. 2 78, 1091.Google Scholar
Solomentsev, Y., Pawar, Y. & Anderson, J. L.1993 Electrophoretic mobility of nonuniformly charged spherical particles with polarization of the double layer. J. Colloid Interface Sci. 158, 1.Google Scholar
Teubner, M.1982 The motion of charged colloidal particles in electric fields. J. Chem. Phys. 76, 5564.Google Scholar
Yoon, B. J.1991 Electrophoretic motion of spherical particles with a nonuniform charge distribution. J. Colloid Interface Sci. 142, 575.Google Scholar
Yoon, B. J. & Kim, S.1989 Electrophoresis of spheroidal particles. J. Colloid Interface Sci. 128, 275.Google Scholar