Cell Model of the Direct Current Electrokinetics in Salt-Free Concentrated Suspensions:  The Role of Boundary Conditions

Abstract

In this paper, a general electrokinetic theory for concentrated suspensions in salt-free media is derived. Our model predicts the electrical conductivity and the electrophoretic mobility of spherical particles in salt-free suspensions for arbitrary conditions regarding particle charge, volume fraction, counterion properties, and overlapping of double layers of adjacent particles. For brevity, hydrolysis effects and parasitic effects from dissolved carbon dioxide, which are present to some extent in more "realistic" salt-free suspensions, will not be addressed in this paper. These issues will be analyzed in a forthcoming extension. However, previous models are revised, and different sets of boundary conditions, frequently found in the literature, are extensively analyzed. Our results confirm the so-called counterion condensation effect and clearly display its influence on electrokinetic properties such as electrical conductivity and electrophoretic mobility for different theoretical conditions. We show that the electrophoretic mobility increases as particle charge increases for a given particle volume fraction until the charge region where counterion condensation takes place is attained, for the abovementioned sets of boundary conditions. However, it decreases as particle volume fraction increases for a given particle charge. Instead, the electrical conductivity always increases with either particle charge for fixed particle volume fraction or volume fraction for fixed particle charge, whatever the set of boundary conditions previously referred. In addition, the influence of the electric permittivity of the particles on their electrokinetic properties in salt-free media is examined for those frames of boundary conditions.

Salt concentration and particle density dependence of electrophoretic mobilities of spherical colloids in aqueous suspension

“…[7][8][9][10][11][12][13]28,29]. Here we use a version allowing for arbitrary zeta potential and κa and thus double-layer overlap, but not including a dynamic Stern layer allowing for specific adsorption/desorption processes nor for conductance behind the hydrodynamic slip plane.…”

“…For more concentrated suspensions, cell model calculations and in particular those with Shilov-Zharkikh boundary conditions have been proven quite successfull (SECM-SZ) [6][7][8][9][10][11]. With the exception of a few very recent attempts made on strictly salt-free systems [12,13], SECM-BZ neglects the contribution of any counterions stemming from the particles themselves. Thus, no dependence on particle concentration of the mobility due to an enhanced effective salt concentration nor due to a changed composition of the electrolyte is expected, even in models including a dynamic Stern layer.…”

Factors affecting the pH and electrical conductivity of MgO–ethylene glycol nanofluids

“…Further increment in the volume fraction only increases the amount of counterions, which feeds the condensation regions (regions close to the particle surface) and leaving the bulk charge and potential virtually unchanged, thereby reducing the electrical conductivity incremental slope or sometimes cause the electrical conductivity to plateau. 36,59 Regarding the effect of size of nanoparticles on the pH, the relative pH plot of figure 11 shows that the smaller the particle size, the higher the pH value. The shaded rectangles in figure 11 correspond with those in figure 10 at the point of counterion condensation.…”

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

“…If the suspension is concentrated [5], the particle-particle electrohydrodynamic interactions introduce severe limitations when dealing with the response to external fields, not only for the mathematical difficulties of dealing with many-body interactions, but also for the additional numerical problems raised when it comes to solve the equations, no matter the approximation chosen. The authors have addressed this problem by using a cell model approach to deal with electrokinetic and rheological properties in concentrated suspensions [10][11][12][13][14][15][16][17][18].…”