Impact of Ion Steric and Ion Partitioning Effects on the Electrophoresis of Soft Particles in Power‐Law Fluid

The electrophoretic behavior of soft particles suspended in a power-law electrolyte medium is investigated by accounting for the combined effects of ion steric interactions and ion partitioning. The former effect arises from the finite size of the electrolyte ions, and its impact plays a significant role in the particle motion. On the other hand, the latter effect arises due to a contrast in dielectric permittivity of the polyelectrolyte layer (PEL) and the surrounding electrolyte. Note that both these effects significantly modify the distribution of mobile ions within the PEL and consequently modify the electrostatic potential and thus the electrophoretic velocity of the particle. A flat-plate formalism, valid when the particle size well exceeds the thickness of the electric double layer (EDL), is employed to develop the mathematical model. The electrostatic potential is governed by the modified Poisson-Boltzmann equation incorporating the Carnahan-Starling equation of state to represent ion steric effects. The electrohydrodynamics is described by the Darcy-Brinkman equation within the PEL and the Cauchy momentum equation in the electrolyte region, together with an appropriate constitutive relation for power-law fluids. The electrophoretic velocity of the soft particle is deduced herein through a generalized framework that accommodates arbitrary charge density of the PEL as well as a broad range of other model parameters. Furthermore, the analytical expressions for electrophoretic velocity are derived by incorporating the ion partitioning effect while neglecting steric interactions for both weak and arbitrary electrostatic potentials. The computed numerical results are further validated with the analytical results deduced in this work as well as available experimental results in the literature. The impact of pertinent parameters on the electrostatic potential as well as the electrophoretic velocity of the particle is further illustrated. The findings of this study provide a more precise framework for calculating the intrinsic parameters that govern soft particle electrophoresis within power-law microenvironments.