Nonlinear electrophoresis of ideally polarizable particlesE. Yariv
Faculty of Mathematics, Technion-Israel Institute of Technology - Haifa 32000, Israel
received 29 November 2007; accepted in final form 19 April 2008; published June 2008
published online 27 May 2008
An initially charged ideally polarizable spherical particle is placed under a uniformly imposed electric field. The ensuing electrokinetic transport in the thinDebye-layer limit is characterized by three voltage scales, associated with the respective effects of initial charge, applied field, and ionic thermal motion. The magnitude of these three scales affects the asymmetric zeta-potential distribution along the particle surface, and then also the electrophoretic velocity engendered by the accompanied electro-osmotic slip. An analysis is presented for arbitrary (non-small) zeta-potentials, thus extending the smallzeta-potential prevailing models. The evaluation of the zeta-potential distribution is made non-trivial by its dependence upon the (uniform) value of the particle potential. This value, which is not a priori prescribed, is determined using global charge conservation arguments. Due to the nonlinear Debye-layer capacitance, the electrophoretic mobility of the particle differs from that of a comparable non-polarizable particle possessing the same net electric charge. Specifically, it decreases monotonically with both initial particle charge and applied-field magnitude. Extensions to non-spherical particles are also described.
47.57.jd - Electrokinetic effects.
47.65.-d - Magnetohydrodynamics and electrohydrodynamics.
41.20.Cv - Electrostatics; Poisson and Laplace equations, boundary-value problems.
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