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Ion steric effects on electrophoresis of a colloidal particle

Published online by Cambridge University Press:  13 November 2009

ADITYA S. KHAIR  and
TODD M. SQUIRES
ADITYA S. KHAIR*
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
TODD M. SQUIRES
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
*
†Email address for correspondence: [email protected]
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Abstract

We calculate the electrophoretic mobility Me of a spherical colloidal particle, using modified Poisson–Nernst–Planck (PNP) equations that account for steric repulsion between finite sized ions, through Bikerman's mean-field model (Bikerman, Phil. Mag., vol. 33, 1942, p. 384). Ion steric effects are controlled by the bulk volume fraction of ions ν, and for ν = 0 the standard PNP equations are recovered. An asymptotic analysis in the thin-double-layer limit reveals at small zeta potentials (ζ < kBT/e ≈ 25 mV) Me to increase linearly with ζ for all ν, as expected from the Helmholtz–Smoluchowski (HS) formula. For larger ζ, however, it is well known that surface conduction of ions within the double layer reduces Me below the HS result. Crucially, however, in the PNP equations surface conduction becomes significant precisely because of the aphysically large and unbounded counter-ion densities predicted at large ζ. In contrast, ion steric effects impose a limit on the counter-ion density, thereby mitigating surface conduction. Hence, Me does not fall as far below HS for finite sized ions (ν ≠ 0). Indeed, at sufficiently large ν, ion steric effects are so dramatic that a maximum in Me is not observed for physically reasonable values of ζ(≤ 10 kBT/e), in stark contrast to the PNP-based calculations of O'Brien & White (J. Chem. Soc. Faraday Trans. II, vol. 74, 1978, p. 1607) and O'Brien (J. Colloid Interface Sci., vol. 92, 1983, p. 204). Finally, by calculating a Dukhin–Bikerman number characterizing the relative importance of surface conduction, we collapse Me versus ζ data for different ν onto a single master curve.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 640 , 10 December 2009 , pp. 343 - 356
Copyright
Copyright © Cambridge University Press 2009

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