Electrophoresis of a rigid particle in a weakly non-Newtonian Carreau fluid with ion steric interactions

The electrophoresis of a rigid particle in a weakly non-Newtonian viscoelastic fluid accounting the ion steric interactions of finite-sized ions is studied. Under the weakly non-Newtonian fluid consideration, which assumes a small deviation of the shear rate-dependent viscosity from the baseline Newtonian viscosity, the mobility can be expressed as a linear superposition of the Newtonian part and a non-Newtonian correction. We consider a modified form of the standard point-charge based Nernst–Planck–Poisson (PNP) model to incorporate the ion steric interactions arises due to the finite-sized ion consideration. The ion steric interactions is accounted through the excess electrochemical potential, which is modeled based on the Boublik–Mansoori–Carnahan–Starling–Leland equation of state. This modification of the PNP-model is relevant for a higher surface charge. The modified Nernst–Planck–Poisson model is solved numerically supplemented by a theoretical analysis under a thin Debye layer consideration. Under the thin Debye layer consideration with arbitrary ζ-potential the non-Newtonian correction of the mobility is expressed in terms of relaxation time and flow behavior index as well as the electrokinetic parameters, such as Debye length and ζ-potential. Ion steric interaction enhances the non-Newtonian part of the mobility in a similar manner as the Newtonian part. This makes the non-Newtonian part more significant in the particle motion at a higher ionic concentration or surface charge density. The nonlinear dependence of mobility on particle surface charge density at high charge levels arises from enhanced surface conduction. This effect is quantified by the Dukhin number, which measures the relative importance of surface to bulk conduction and thereby assesses the nonlinear dependence of mobility on the ζ-potential. Ion steric interactions decreases the Dukhin number by suppressing counterion accumulation near the surface, indicating counterion saturation.