Electrophoretic Mobility of Nonuniformly Charged Spherical Particles with Polarization of the Double Layer

A model is developed to simultaneously account for both a nonuniform zeta potential (ζ) on the surface and polarization of the double layer in computing the electrophoretic motion of a spherical particle. The double layer is assumed thin (κ R ⪢ 1 where κ is the Debye parameter and R the particle's radius) but effects of ion transport within it are included; this work extends the previous theory for nonuniformly charged particles which neglects ion transport within the double layer. The model is generally valid for symmetrically charged electrolytes and any distribution of ζ along the surface of a particle as long as the surface gradient is O( R -1). Sample calculations for the electrophoretic mobility are made for a particle when its axis of charge distribution is aligned with the applied electric field. When polarization is important, the mobility depends on the details of the ζ-distribution and not just on the monopole and quadrupole moments as is the case without polarization. Several examples demonstrate that particles having the same mobility at infinite κ R (no polarization) but different ζ-distributions can have significantly different mobilities at finite κ R.