Secondary 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 secondary electroviscous effect is the enhancement of the viscosity due to particle-particle interactions, and this of course will control the excluded volume of the particles. The most complete analysis is that due to Russel30 and we may take this analysis for pair interactions as the starting point. Russel s result gives the viscosity as... 

The secondary electroviscous effect refers to the change in the rheological behavior of a charged dispersion arising from interparticle interactions, i.e., the interactions between the electrical double layers around the particles. 

The secondary electroviscous effect is often interpreted in terms of an increase in the effective collision diameter of the particles due to electrostatic repulsive forces (i.e., the particles begin to feel the presence of other particles even at larger interparticle separations because of electrical double layer). A consequence of this is that the excluded volume is greater than that for uncharged particles, and the electrostatic particle-particle interactions in a flowing dispersion give an additional source of energy dissipation. 

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. 

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. 

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.

In concentrated suspensions, the motion of particles is cmcially affected by hydrodynamic interaction between neighbouring particles, which strongly depends on the interparticle distances, i.e. on the suspension structure (cf. Overbeck et al. 1999 Watzlawek and Nagele 1997, 1999). This structure is clearly influenced by the inteiparticle forces, in particular by the forces that occur when the EDL of two particles overlap (e.g. Russel 1978 Quemada and Berli 2002). When a suspension contains only a single particulate component, such a double layer overlap leads to repulsions and, thus, decreases the particle mobility and increases the suspension viscosity (Fig. 3.5). This effect is called secondary electroviscous effect. Its... 

Fig. 3.5 Secondary electroviscous effect strong repulsion between similarly charged particles reduces their mobility since the overlap of EDL (indicated by dotted lines) would require additional energy and, as a result, the suspension is not randomly ordered the decisive parameter is the double layer thickness, which can be controlled via the electrolyte concentration...

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... 

Generally speaking, the viscosity increase due to the electroviscous effect is not very large, mostly within a factor of two. It is non-comparable to the ER effect, which would gives a ten-thousand times increase in the rheological property. Since the first and secondary electroviscous effects are actually observed without an external electric field in aqueous systems, those two topics will not be explored further. 

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