Overlap volume fraction viscosity

The effective volume fraction increases with a relative increase of the dispersant layer thickness. Even at 10% volume fraction, a maximum packing (< = 0.67) is soon reached, with an adsorbed layer thickness that is comparable to the particle radius. In this case, overlap of the steric layers wiU result in significant increases in viscosity. Such considerations may help to explain why solids loading can be severely Hmited, especially with small particles. In practice, soUds loading curves can be used to characterize the system, and take the form of those illustrated in Figure 11.6... 

It has been shown (and made plausible from theory) that a general relation exists between relative or specific viscosity at very low shear rate and dimensionless concentration of polymer c[j ]0. This relation is shown in Figure 6.15 as a log-log plot. The critical concentration for chain overlap c would equal about 4/[ ]0 at that concentration, (jjsp)0 x 10 or r] x 11 (at very low shear rate), c is mostly expressed in g/100 mL. It may not exactly correspond to the critical volume fraction specific viscosity versus concentration. 

A small amount of fractal material increases the viscosity noticeably just as it increases osmotic pressure noticeably. The same concentration C that doubles the osmotic pressure is roughly the concentration that doubles the viscosity. As we noted above, this is the overlap concentration at which the distance between fractals Cp is comparable to their size R, and the overall volume fraction 4> in the solution is comparable to the (small) internal volume fraction i within a fractal. Fractals, including polymers, are potent viscosifiers. Many thick fluids in everyday life such as motor oil, or bottled sauces owe their thick consistency to a small proportion of polymers. 

Concentrated suspensions can have significantly elevated viscosities (relative to hard spheres at the same volume fraction) due to the interaction between overlapping EDLs. For particles to push past each other the double layer must be distorted. This effect is known as the secondary electro-viscous effect (Hunter, 2001). Similar effects occur when the repulsion is by steric mechanism. 

At high particle volume fractions there are considerable double layer overlappings in the system. Experimental evidences [29,63] suggest that the viscosity or yield stress of such a system decreases with the decrease of the particle volume fraction and with the increase of electrolyte concentration. It doesn t depend on the type and valency of ions. 

The low shear viscosity, rj, was measured using capillary and, at higher concentrations, a cone-plate rheometer [4], The two techniques gave equivalent results in the overlapping concentration range. The variation of the normalised low shear viscosity rj/rjo, where rjo is the water solvent viscosity, with the hard-sphere volume fraction Hs is shown in Fig. 5. For comparison, we have also plotted data from van der Werff and de Kruif [18] for hard-sphere silica dispersions of three different sizes. As can be seen, there is a perfect agreement between the microemulsion and silica data. The solid line in Fig. 5 shows the Quemada expression [19]... 

Here rjs is the viscosity of the pure solvent. is an effective volume fraction which also takes into account the hydration of the molecules. It can be up to three times the true volume fraction. But also in this case the viscosity of a 10 wt% surfactant solution is only about twice as high as the solvent viscosity. The same is true if anisometric micelles are present in the solutions as long as their rotational volumes do not overlap. 

---