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

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 nonhomogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and especially 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. [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. The theory incorporates a more convenient hard-sphere hydrodynamic model to account for the nonhomogeneous viscosity of the solution than others proposed in previous works in the literature. A comparison is elaborated on between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of pointlike counterions and following with the inclusion in sequence of additional aspects such as finite counterion size, nonhomogeneous electrical permittivity with associated Born and dielectrophoretic effects, and, finally, position-dependent viscosity and diffusion counterion coefficient, and clearly shows the influence of individual effects on the general electrokinetic response and especially the relevant role the nonhomogeneous viscosity on the dc and ac electrokientic behavior of salt-free colloids.