Effect of the Surface Charge-Dependent Boundary Slip on the Electrophoresis of a Hydrophobic Polarizable Rigid Colloid

The electrophoresis of a hydrophobic charged rigid colloid is studied by considering the lateral movement of the adsorbed surface charge. The slip velocity condition at the hydrophobic surface is modified to take into account the impact of the frictional and electric forces created by the adsorbed laterally mobile surface charge. Though the dependency of the surface charge on the slip velocity in the context of electrophoresis has been addressed before, the effect of the laterally mobile adsorbed surface charge on the electrophoresis of hydrophobic colloids has not been studied. The dielectric colloid is considered to polarize and create an induced immobile surface charge when subjected to an imposed electric field. The impact of the mobile surface charge along with the immobile induced surface charge on electrophoresis of a hydrophobic colloid is elucidated by numerically solving the governing electrokinetic equations in their full form. We have also developed a simplified model under a weak applied field consideration, which can be further reduced to a closed-form analytic expression for the mobility under the Debye-Hu''ckel approximation. This analytic model for mobility is in excellent agreement with the exact numerical solution for an entire range of the Debye length when the zeta-potential is in the order of the thermal potential. One of the notable features of this closed-form mobility expression is that it accounts for the mobile adsorbed surface charge on the hydrodynamic slip condition and the dielectric polarization of the particle. We find that the mobility of the surface charge decreases the electrophoretic mobility of the hydrophobic dielectric colloid. However, the mobile surface charge enhances the mobility of a conducting hydrophobic colloid.