Numerical Solution of the Electrokinetic Equations for Multi-ionic Electrolytes Including Different Ionic Size Related Effects

Abstract

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.

Applicability of the Linearized Poisson-Boltzmann Theory to Contact Angle problems and Application to the Carbon Dioxide-Brine-Solid Systems

“…The table generally shows decreased surface potential with decreased pH, which is consistent with Fig. 2 of the research work of López et al, (2018).The increased positive surface potential of mica after pH of 3.43 shows increased protonation of surface functional groups leading to the development and increase surface positive potential.…”

Analytical modeling of micelle growth. 3. Electrostatic free energy of ionic wormlike micelles – Effects of activity coefficients and spatially confined electric double layers

“…Here, to calculate (hs) i γ we will use the expression for the activity coefficient of a hard-sphere fluid composed of several components of different radii. This expression, which is derived from the BMCSL equation of state [12,13], reads [14]:…”

“…Alargova et al [8,9] and Srinivasan and Blankschtein [10] demonstrated that the effect of counterion binding has to be taken into account in order to achieve agreement between theory and experiment, especially in the case of multivalent counterions. Koroleva and Victorov [11] took into account the effect of the finite size of the ions by using the Boublik−Mansoori−Carnahan−Starling−Leland (BMCSL) equation for a mixture of hard spheres of different radii [12][13][14]. Note, however, that all these studies are still using some of the simplifying assumptions adopted in Refs.…”

“…(ii) hard-sphere [12][13][14] and (iii) specific interactions [34] between the ions, and exactly describe the experimental dependencies of γ ± = (γ + γ − ) 1/2 on the salt concentration for uniform solutions [35]. Furthermore, to describe the electrostatic potential and the ionic distributions in the EDL, we combine the Poisson equation with the equation for electrochemical equilibrium (with γ i ≠ 1), rather than with the conventional Boltzmann equation, which presumes γ i = 1.…”

Editorial for the Special Issue on AC Electrokinetics in Microfluidic Devices

“…The influence of finite ionic size on the dielectric and electrokinetic properties of colloidal suspensions is analyzed by López-García et al [6]. They extended previous works to systems made of three or more ionic species with different ionic sizes and found qualitative and quantitative differences with respect to the standard electrokinetic model.…”