Primary electroviscous effect

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The primary electroviscous effect occurs, for a dilute system, when the complex fluid is sheared and the electrical double layers around the particles are distorted by the shear field. The viscosity increases as a result of an extra dissipation of energy, which is taken into account as a correction factor pi" to the Einstein equation ... 

The increasing dilution of flexible polyelectrolytes at low ionic strength, the reduced viscosity may increase first, reach a maximum, and then decrease. Since a similar behavior can also be observed even for solutions of polyelectrolyte lattices at low salt concentration, the primary electroviscous effect was thought as a possible explanation for the maximum, as opposed to conformation change. 

Ohshima H. Primary Electroviscous Effect in a Dilute Suspension of Soft Particles. Langmuir 2008, 24, 6453-6461. 

Rubio-Hernandez F.J., Carrique F., Ruiz-Reina E. The primary electroviscous effect in colloidal suspensions. Advances in Colloid and Interface Science 107 (2004) 51-... 

Rubio-Hernandez F. J., Ruiz-Reina E., and Gomez-Merino A. I. Primary Electroviscous Effect with a Dynamic Stern Layer Low Ka Results. Journal of Colloid and Interface Science 226,180-184 (2000). 

Three electroviscous effects have been noted in the literature.27 The primary electroviscous effect refers to the enhanced energy dissipation due to the distortion of the diffuse layer from spherical symmetry during flow. The analysis for low diffuse layer potentials has been clearly reviewed by van de Ven28 and the result for the intrinsic viscosity with Ka—> oo is ... 

Figure 3.18 The primary electroviscous effect estimated from Equation (3.59) for spherical particles dispersed in 10 2 M KCl...

The first analysis of the primary electroviscous effect dates to 1916 when Smoluchowski presented the following equation for the intrinsic viscosity ... 

A corrected and more general analysis of the primary electroviscous effect for weak flows, i.e., for low Pe numbers (for small distortions of the diffuse double layer), and for small zeta potentials, i.e., f < 25 mV, was carried out by Booth in 1950. The result of the analysis leads to the following result for the intrinsic viscosity [rj] for charged particles in a 1 1 electrolyte ... 

The variations in the intrinsic viscosity predicted by the primary electroviscous effect are often small, and it is difficult to attribute variations in the experimentally observed [17] from the Einstein value of 2.5 to the above effect since such variations can be caused easily by small amounts of aggregation. Nevertheless, Booth s equation has been found to be adequate in most cases. Further discussions of this and related issues are available in advanced books (Hunter 1981). 

The intrinsic viscosity [17] in the above expression includes the primary electroviscous effect. The experimental data of Stone-Masui and Watillon (1968) for polymer latices seem to be consistent with the above equation (Hunter 1981). Corrections for a for large values of kRs are possible, and the above equation can be extended to larger Peclet numbers. However, because of the sensitivity of the coefficients to kRs and the complications introduced by multiparticle and cooperative effects, the theoretical formulations are difficult and the experimental measurements are uncertain. For our purpose here, the above outline is sufficient to illustrate how secondary electroviscous effects affect the viscosity of charged dispersions. 

In this chapter, we first present a theory of the primary electroviscous effect in a dilute suspension of soft particles, that is, particles covered with an ion-penetrable surface layer of charged or uncharged polymers. We derive expressions for the effective viscosity and the primary electroviscous coefficient of a dilute suspension of soft particles [26]. We then derive an expression for the effective viscosity of uncharged porous spheres (i.e., spherical soft particles with no particle core) [27]. 

Electroviscous Effect Any influence of electric double layer(s) on the flow properties of a fluid. The primary electroviscous effect refers to an increase in apparent viscosity when a dispersion of charged colloidal species is sheared. The secondary electroviscous effect refers to the increase in viscosity of a dispersion of charged colloidal species that is caused by their mutual electrostatic repulsion (overlapping of electric double layers). An example of the tertiary electroviscous effect would be for polyelectrolytes in solution where changes in polyelectrolyte molecule conformations and their associated effect on solution apparent viscosity occur. 

As outlined earlier (Chapter 3), electrically charged colloidal particles are surrounded by an electrical double layer. This leads to important rheological effects. The primary electroviscous effect is a consequence of the fact that the electrical double layer [Figure 8.10(a)] is deformed from its spherical shape by the shear field. Construction of the double layer ahead of the particle and its disintegration behind the particle take a finite time [Figure 8.10(b)], This causes an increase in the intrinsic viscosity, which for low zeta-potentials ( < 25 mV) is proportional to the square of this potential ... 

Figure 8.10 Origin of electroviscous effects (a) electrical double layer round a particle at rest, (b) distortion of the electrical double layer in a shear field, leading to the primary electroviscous effect, (c) trajectories of repelling particles caused by double-layer repulsion, leading to the secondary electroviscous effect, (d) effect of ionic strength (or pH) on the extension of a charged adsorbed poly electrolyte, causing a change of the effective diameter of the particle, and the tertiary electroviscous effect.

We shall see that for these reversal of charge concentrations the simple rules no longer hold, which we met in studying the suppression of the electroviscous effect at very low salt concentrations, (see p. 203 Ch. VII 5b) Indeed the valency of the cation is no longer the only factor of primary importance, as very marked specific differences occur between cations of the same valency. Other properties of the cations viz., volume and polarising action come into play next to valency. 

The primary electroviscous effect is the retardation of the particle velocity (or the fluid flow in pores) due the polarisation of the EDL, which is a consequence of the relative motion between diffuse layer and the particle surface (Fig. 3.4). The polarisation, in turn, causes a flux of ions and solvent that opposes and decelerates the relative motion. This kind of deceleration affects particle sedimentation (von Smoluchowski 1903 Ohshima et al. 1984 Keh and Ding 2000) capillary flow... 

Bull 1932, Levine et al. 1975), the hydrodynamic drag on single particles (Booth 1954) or the viscosity of a suspension (Booth 1950 Ruiz-Reina et al. 2003). Note that the primary electroviscous effect is related to individual particles and surfaces any double layer interaction is excluded. It is essentially a second-order effect which —to first approximation—obeys the following equation ... 

It is of interest to determine whether this large electroviscous effect observed in ion-exchanged latex A-2 is a primary effect, i.e., due to distortion of the electric field around the particle by the flow, or a secondary effect, i.e, due to double layer interaction (more detailed studies of electroviscous effects in latexes have been made by Stone-Masui and Watillon (40) and Wang (41)). Booth s treatment of the primary electroviscous effect (42), when applied to our results, accounts for only 1-5% of the observed increase in viscosity, depending upon the value selected for the zeta potential. Therefore, the secondary effect is predominant, as is also expected from the non-Newtonian viscosity behavior (see ref. 43). 

A systematic review on the primary, secondary and tertiary electroviscous effect has been presented by Conway and Dobry-Duclaux [IJ in 1960. A brief review on some of those cITccts has been given by Dukhin [50] and Saville [51], and a more unified review has been presented by Hunter [4], In a dilute suspension, the apparent viscosity will increase with the particle volume fraction and the surface charge of the particle. A viscosity equation first published by Smoluchowski without proof [52] for describing such a system is... 

Particles dispersed in an aqueous medium invariably carry an electric charge. Thus they are surrounded by an electrical double-layer whose thickness k depends on the ionic strength of the solution. Flow causes a distortion of the local ionic atmosphere from spherical symmetry, but the Maxwell stress generated from the asymmetric electric field tends to restore the equilibrium symmetry of the double-layer. This leads to enhanced energy dissipation and hence an increased viscosity. This phenomenon was first described by Smoluchowski, and is now known as the primary electroviscous effect. For a dispersion of charged hard spheres of radius a at a concentration low enough for double-layers not to overlap (d> 8a ic ), the intrinsic viscosity defined by eqn. (5.2) increases... 

Chan, F.S. and Goring, D.A.I. 1966. Primary electroviscous effect in a sulfonated polystyrene latex. J. Colloid Interface Sci. 22 371-381. 

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