Influence of Double-Layer Overlap on the Electrophoretic Mobility and DC Conductivity of a Concentrated Suspension of Spherical Particles

Abstract

In this paper, the specific effect of the overlapping of electrical double layers on the electrophoretic mobility and the electrical (DC) conductivity of concentrated suspensions of spherical colloidal particles is considered. Previous work has dealt with the study of such physical quantities for general conditions, including arbitrary zeta potentials, particle volume fractions, double-layer thicknesses (overlapping of double layers was allowed), and ionic properties of the solution. However, the large number of variables involved screened to some extent the specific role and, in many cases, the extraordinary magnitude of the overlapping contribution by itself. This is the reason that we are concerned here with the analysis of the latter effect in more detail. Thus, we present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus the zeta potential and particle volume fraction for different electrolyte concentrations, specially in the region where overlapping effects are more relevant. Numerical results corresponding to the same theoretical conditions but where the overlapping correction is neglected are also shown for comparison. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. The results show that neglecting double-layer overlapping corrections leads in most cases to an important underestimation of the true values of both the electrophoretic mobility and the electrical conductivity. The differences between both treatments are more pronounced the larger the double layer thickness and/or particle volume fraction are. Concerning DC conductivity, the overlap of double layers might help in interpreting discrepancies generally found between experimental data and standard theoretical values, even in suspensions with particle volume fractions that are typically considered to be dilute.

Recent developments in electrokinetics of salt-free concentrated suspensions

“…Unlike dilute suspensions, for which successful theoretical models have been derived [1][2][3][4][5], for concentrated ones the analysis is complicated by the existence of important electro-hydrodynamic particleparticle interactions, very difficult to manage from the theoretical point of view. To overcome these limitations, some macroscopic (i.e., continuum-) descriptions have been developed that consider interactions in an average sense by mean field approaches [6][7][8][9][10][11][12][13][14][15][16][17]. Other macroscopic descriptions also account for ionic excluded volume effects, in very good agreement with Monte Carlo simulations considering explicitly the study of particle-ion or ion-ion correlations [18][19][20][21][22][23][24], mainly in equilibrium.…”

Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles

“…This is the Shilov-Zharkikh [27] boundary condition used in [11,25], which does not coincide with the condition of LevineNeale [26]:…”

“…This boundary condition, used in [11,18,22,23,25], is common to both the Kuwabara [29] and Happel [30] cell models, which differ in the second boundary condition as noted later.…”

“…This condition used in [11,18,19,23,25], is related to the requirement that the perturbation of the concentration at the mid point between two particles aligned with the field must be zero by symmetry. In some works [24] a different condition is used:…”

“…For the cell model, the boundary conditions are fairly well established [11,18,[22][23][24][25] except for the condition on the electric potential. The earlier works used the Levine-Neale condition [26] that was partly superseded in more recent works by the condition of ShilovZharkikh [27].…”