A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.

In this article, we have discussed extensively electrokinetic ion transport and fluid flow through a slit polymer-grafted nanochannel filled with power-law fluid. The rigid walls of the channel are coated with the ion and fluid penetrable polymer layer containing a pH-regulated zwitterionic functional group (e.g., succinoglycan). The mathematical model is based on the non-linear Poisson–Boltzmann equation for electric double layer potential and the flow field within the polymer layer is governed by a modified Darcy–Brinkman equation; the Cauchy momentum equation governs the fluid flow outside of the polymer layer along with the equation of continuity for incompressible fluid. In order to consider a wide range of pertinent parameters, we adopt a finite difference based numerical tool to solve the coupled set of governing equations. We have analyzed several interesting features of electrokinetic transport phenomena through such a polymer-grafted nanochannel for a wide range of electrostatic and hydrodynamic properties of the polymer layer, parameters describing the non-Newtonian rheology of the background fluid, and the pH and concentration of the bulk electrolyte. In addition, we have also illustrated the ionic current across the undertaken nanochannel and observed that it can be either cation selective, anion selective or non-selective, depending on the critical choice of the pertinent parameters.