Nonlinear electrophoresis of a dielectric particle in a non-polar media. Part I. Intermediate Debye numbers

The electrophoresis of a charged dielectric particle in a low conductivity non-polar media is numerically investigated over a wide range of parameters. Association/dissociation reactions that may alter the concentration of free charge carriers in weak non-polar media are not included in the present model. The results are compared with previously published experimental data, revealing a universal relaxation behaviour of the ionic cloud. We describe an electrophoretic regime observed at intermediate Debye numbers and relatively high Dukhin numbers. In this regime, non-equilibrium effects become important and the Smoluchowski formula is no longer applicable. Two charged layers with high tangential fluxes of counterions and coions are identified. The first layer is thin and corresponds to the electric double layer, whereas the second one is thicker and contains an extended space-charge region. This two-layer structure, with the maximum charge density located far from the surface, deviates from the classical Gouy–Chapman distribution and resembles the charge distribution near an ion-selective surface described by Rubinstein & Shtilman (1979 J. Chem. Soc. Faraday Trans. 2 , vol. 75 , pp. 231–246). A physical interpretation of the calculated ion concentration is provided for the first time using ion-flux streamfunctions for extreme parameter sets. Fluxes in both layers are aligned with the external field and eventually form a charged jet near the particle pole.