Effects of finite counterion size and nonhomogeneous permittivity and viscosity of the solution on the electrokinetics of a concentrated salt-free colloid

Abstract

In the present work, a general model of the electrokinetics and dielectric response of a concentrated salt-free colloid is developed which includes consideration of the finite size of the counterions released by the particles to the solution, a non-homogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and specially the fact that the solution viscosity and diffusion counterion coefficient are allowed to be functions of the local counterion concentration. These effects have recently been discussed by J. J. López-García et al. [J. J. López-García, J. Horno and C. Grosse, Ionic size, permittivity, and viscosity-related effects on the electrophoretic mobility: A modified electrokinetic model, Phys. Rev. Fluids 4, 103702 (2019)] in the case of dilute colloids in general electrolyte solutions. The objective of this work is to explore the new effects and their influence on the electrokinetic response of concentrated salt-free systems. Present results confirm previous findings regarding the important increases of the DC electrophoretic mobility and DC electrical conductivity, as well as huge increments of the dynamic electrophoretic mobilities at high frequencies when finite ion size effects were taken into account. In addition, consideration of the viscosity of the solution and of the counterion diffusion coefficient as functions of the local counterion concentration, leads to a decrease of the magnitude of the previous electrokinetic results. A comparison is elaborated between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of point-like counterions and following with the inclusion of finite counterion size, non-homogeneous electrical permittivity with associated Born and dielectrophoretic effects, and finally position-dependent viscosity and diffusion counterion coefficient effects.