Jose′ Juan López-García

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.

The electric AC response of electrolytic cells with DC bias is analyzed solving numerically the Poisson–Nernst–Planck equations and avoiding the commonly used infinite solution approximation. The results show the presence of an additional low-frequency dispersion process associated with the finite spacing of the electrodes. Moreover, we find that the condition of fixed ionic content inside the electrolytic cell has a strong bearing on both the steady-state and the frequency response. For example: the characteristic frequency of the high-frequency dispersion decreases when the DC potential increases and/or the electrode spacing decreases in the closed cell case, while it remains essentially insensitive on these changes for open cells. Finally, approximate analytic expressions for the dependences of the main parameters of both dispersion processes are also presented.

The transport properties in nanochannels are examined using a modified electrokinetic model (MEM) that takes into account the finite ion size by modeling the hydrated ions as charged dielectric spheres so that the electrolyte solution becomes a non-homogeneous fluid characterized by permittivity and viscosity values that are both functions of the local ionic concentrations. We show that the simultaneous consideration of ionic size, permittivity, and viscosity effects always improve on the predictions of the standard electrokinetic model for point-like ions (SEM), with corrections that are significant in the nanofluidic systems parameter range. The results reported herein are expected to provide a deeper understanding of the ion transport and fluid flow in nanofluidic devices.

A modified electrokinetic model is presented in which hydrated ions are represented as charged dielectric spheres so that the electrolyte solution becomes a nonhomogeneous fluid characterized by permittivity and viscosity values that are both functions of the local ionic concentrations. This modifies both the Poisson-Nernst-Planck and the Navier-Stokes equations and also introduces additional Born and dielectrophoretic forces acting on the ions. The model is numerically solved for a plane charged interface both in equilibrium and under the action of an applied tangential DC electric field, which makes it possible to determine the electrophoretic mobility of a suspended particle in the Smoluchowski limit. The obtained results show that the strong increase of the electrophoretic mobility due to steric and permittivity related effects is countered by the viscosity dependence on the ionic concentrations leading to values that are moderately higher than those predicted by the standard electrokinetic model. This behavior suggests that the proposed model may be used to improve the interpretation of experimental electrophoretic mobility data.

One of the main assumptions of the standard electrokinetic model is that ions behave as point-like entities. In a previous work (López-García, et al., 2015) we removed this assumption and analyzed the influence of finite ionic size on the dielectric and electrokinetic properties of colloidal suspensions using both the Bikerman and the Carnahan–Starling equations for the steric interactions. It was shown that these interactions improved upon the standard model predictions so that the surface potential, electrophoretic mobility, and the conductivity and permittivity increment values were increased. In the present study, we extend our preceding works to systems made of three or more ionic species with different ionic sizes. Under these conditions, the Bikerman and Carnahan–Starling expressions cease to be valid since they were deduced for single-size spheres. Fortunately, the Carnahan–Starling expression has been extended to mixtures of spheres of unequal size, namely the “Boublik–Mansoori–Carnahan–Starling–Leland” (BMCSL) equation of state, making it possible to analyze the most general case. It is shown that the BMCSL expression leads to results that differ qualitatively and quantitatively from the standard electrokinetic model.

The structure of the diffuse part of the electric double layer at solid-electrolyte solution interfaces is examined using a theoretical model that takes into account the finite ion size by...

The structure and differential capacitance of the diffuse part of the electric double layer at solid‐electrolyte solution interfaces are examined using a theoretical model that takes into account the finite ion size by modeling the solution as a suspension of polarizable insulating spheres in water. This formalism is applied to binary and mixed electrolyte solutions using the “Boublik–Mansoori–Carnahan–Starling–Leland” (BMCSL) theory for the steric interactions among ions. It is shown that the ionic size differences have a strong bearing on the diffuse part of the electric double layer structure, as well as on the differential capacitance dependence on the surface potential for mixed electrolytes.