Nonlinear effects on electrokinetics of a highly charged porous sphere

The motivation of the present study is to provide a correct estimate of the electrophoretic mobility of a charged porous particle for wide-range electrokinetic parameters, such as particle charge density, permeability, and Debye length. Based on the Nernst–Planck equation, which takes into account the external electric field and fluid convection on ion transport, we have estimated the mobility of the particle by establishing a force balance. We have validated our results with the linear model due to Hermans and Fujita (K Nederl Akad Wet Proc Ser B 58:182–187, 1955) and the computed solution based on perturbation of the Poisson–Boltzmann model as obtained by Hsu and Lee (J Colloid Interface Sci 390:85–95, 2013). For the case of thin double layer, our computed results agree with the linear model even for large values of charge density of the particle. The linear model overpredicts our computed solution for mobility when the thick Debye layer is considered. However, a large discrepancy of the present model from the results based on the perturbation of the Boltzmann model is observed for all the cases considered. We have analyzed the double-layer polarization and counterion condensation through the distribution of counterions, net charge density, and the effective charge density of the particle.