Primary electroviscous effect particles

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 ... 

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

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

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 ... 

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]. 

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.

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). 

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... 

The slopes of the different curves correspond to the fuU electrohydrodynamic effect, ( ) + ( ) pj, where the first term expresses the hydrodynamic effect, and the second is the consequence of the distortion of the electrical double layer that surrounds the particles. To determine this second term and, more exactly, the primary electroviscous coefficient, pi. 

Approximate results calculated via Eq. (27.57) are also shown as dotted lines in Fig. 27.2. It is seen that Ka > 100, the agreement with the exact result is excellent. The presence of a minimum of L Ka, la, alb) as a function of Ka can be explained qualitatively with the help of Eq. (27.57) as follows. That is, L Ka, la, alb) is proportional to 1/k at small Ka and to k at large Ka, leading to the presence of a minimum of L Ka, la, alb). As is seen in Fig. 27.3, for the case of a suspension of hard particles, the function L ko) decreases as Ka increases, exhibiting no minimum. This is the most remarkable difference between the effective viscosity of a suspension of soft particles and that for hard particles. It is to be noted that although L Ka, la, alb) increases with Ka at large Ka, the primary electroviscous coefficient p itself decreases with increasing electrolyte concentration. The reason is that the... 

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... 

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