Emulsions relative viscosity

Mooney- or Pal-Rhodes-type correlations can be used to correlate emulsion relative viscosities with the dispersed-phase volume fraction. 

The emulsion relative viscosity increases in the A regions in the direction of higher internal phase ratio (at constant formulation), so that the viscosity maximum is located near the vertical branches of inversion line (see Fig. 3c). This high viscosity, which is due to a high internal phase content, is... 

The different microstructures, shown in Fig. 3, are highly dynamic aggregates. They can be detected by well established scattering techniques, like X-ray, light or neutron scattering [ 13]. Beside scattering techniques, the transitions between the microstructures can be detected from the changes of the viscosity of w/o-micro emulsion. For a diluted dispersion of spherical droplets without interactions, the relative viscosity is expected to obey the Einstein-relation ... 

Figure 6.21 The influence of emulsifier concentration on the relative viscosity of sorbitan mono-oleate stabilised W/O emulsions in paraffin. The emulsions had dispersed phase volume fractions in the range 0.37 to 0.68 and mean droplet diameters, am, as plotted along the x-axis. From data in Sherman [215].

Figure 10. The relative viscosity of an emulsion depends on the droplet concentration. The emulsion viscosity increases linearly at small droplet concentrations and increases nonlinearly at droplet concentrations above 10%.

The viscosity of an emulsion is directly proportional to the continuous-phase viscosity (rjc), and therefore, all the viscosity equations proposed in the literature are written in terms of the relative viscosity (17 )- If an emulsifying agent is present in the continuous phase, as is the case with emulsions, 17 Is then the viscosity of the emulsifier solution rather than the viscosity of the pure fluid phase (i.e., oil or water alone). When an emulsion is prepared, some of the emulsifying agent becomes adsorbed at the oil-water interface this adsorption tends to lower the original concentration of emulsifier in the continuous phase and cause an associated decrease in 7], However, the amount of emulsifier adsorbed is usually very low compared with the total amount present, and therefore any decrease in concentration of the emulsifier can easily be neglected (23). 

For monodisperse or unimodal dispersion systems (emulsions or suspensions), some literature (28-30) indicates that the relative viscosity is independent of the particle size. These results are applicable as long as the hydrodynamic forces are dominant. In other words, forces due to the presence of an electrical double layer or a steric barrier (due to the adsorption of macromolecules onto the surface of the particles) are negligible. In general the hydrodynamic forces are dominant (hard-sphere interaction) when the solid particles are relatively large (diameter >10 (xm). For particles with diameters less than 1 (xm, the colloidal surface forces and Brownian motion can be dominant, and the viscosity of a unimodal dispersion is no longer a unique function of the solids volume fraction (30). 

Figure 13 illustrates another very interesting point. Here the relative viscosity of a bimodal suspension is plotted as a function of volume percent of small spheres in total solids. At any given total solids concentration, the relative viscosity decreases initially with the increase in volume percent of small spheres, and then it increases with further increase in small spheres. The minimum observed in the relative viscosity plots of a bimodal suspension is quite typical. There are no fundamental reasons why a similar behavior would not be true for emulsions. 

On the basis of the analogy with the influence of variable pressure on a material that obeys Hooke s law, Richardson 44) calculated the compressibility of an emulsion whose dispersed-phase volume concentration is increased from + A. From this calculation he derived the following expression for the relative viscosity of concentrated emulsions ... 

Figure 15. Relative viscosity vs, correlation for emulsions. (Reproduced...

Effects of Solids Size. The effect of solids size on the viscosity of the emulsion-solids mixtures is shown in Figure 19 for synthetic OAV emulsions. The oil concentration (solids-free basis) is 60% by volume, and the solids used are silica sand. The comparison is made at shear stresses of 6 and 14 Pa. The viscosity is expressed as the relative viscosity (t7ows/ 7ow)t lhat is, the viscosity of the emulsion-solids mixture divided by the viscosity of the solids-free emulsion. At low solids volume fraction (<0.1), solids size has little effect. 

As the size ratio of the sand particle to the oil droplets d d increases to about 2, there is less dependence on the oil concentration, as shown in Figure 21b. When the size ratio increases to about 3, as shown in Figure 21c, the relative viscosity becomes independent of the oil concentration this result indicates that the emulsions act as a continuous phase toward the solids. Under this condition, the solids and the droplets behave independently, and no interparticle interaction occurs between the solids and the droplets. Yan et al. (64) showed that when the emulsions behave as a continuous phase toward the solids, the viscosity of the mixtures can be predicted quite accurately from the viscosity data of the pure emulsions and the pure solids suspensions. The viscosity of an emulsion-solids mixture having an oil concentration of Pq (solids-free basis) and a solids volume fraction of 0s (based on the total volume) can be calculated from the following equation ... 

Relative Viscosity In emulsions, the viscosity of the emulsion divided by the viscosity of the continuous phase = 7]/7]q). 

The influence of phase volume on the flow properties of an emulsion is shown in Fig. 7.26. In this diagram the relative viscosity of the system increases with increasing 4>, and at any given phase volume increases with decreasing mean particle size, D. These and other factors which affect emulsion viscosity are listed in Table 7.6. 

Figure 7.26 The relative viscosities of w/o emulsions stabilised with sorbitan trioleate four emulsions have been studied with different mean particle diameters, D ,.

In describing the viscosity of an emulsion, the volume fraction of the dispersed phase is the most important parameter. A model suggested by M. Mooney (15) in 1951 for solid suspensions and emulsions with highly viscous dispersed phase described the relative viscosity as a function of volume fraction and a coefficient, k, called the self-crowding factor. 

For emulsions containing no salt the relative viscosities increased and the average particle sizes decreased with increasing NaOH content. However, once a sufficient quantity of NaOH was presented to form stable emulsions (4.0 x 10 moles NaOH/gram of oil for the Shell crude) further increases in NaOH content gpve only small increases in apparent viscosity and moderate decreases in particle size. 

These effects can be illustrated by estimating values of < from the Sherman model [3 ] from values of relative viscosity and average particle diameter. In Table II we can see the influence of NaCl concentration on a for the two emulsions shown in Figure 6. At the NaCl concentrations of minimum viscosity, values of a also show minima. 

Figure 11 shows all of the fresh emulsion data obtained in this study compared with Sherman s model. Values of a for these emulsions ranged from 0.60 to 0.62. The 1.0% NaCl emulsions generally had the highest relative viscosities and the highest [Pg.484]

Figure 11. Relative Viscosity vs. Particle Diameter for 607 Fresh Shell Crude Emulsions.

Steady-state shear stress-shear rate curves were used to obtain the relative viscosity (//,.)-volume fraction () relationship for the latex and emulsion. The results are shown in Figure 11.19 which also contains the theoretically predicted curve based on the Dougherty-Krieger equation [14],... 

Einstein s treatment of suspensions was extended to emulsions by Taylor [1932, 1934] who derived the following expression for the relative viscosity of emulsions ... 

For the relative viscosity of emulsions, in the absence of deformation and coalescence, Eqs 7.24-7.30 may also be used, provided that the intrinsic viscosity is calculated from Eq 7.50 and that the maximum packing volume fraction is treated as an adjustable parameter, dependent on the interphase. This pragmatic approach has been successfully used to describe [r]] vs. (() variation for such complex systems as industrial lattices (at various stages of conversion), plastisols and organosols. 

The rheological consequences of these changes can be predicted from a model system. The emulsion model indicates that making the interface more rigid causes the intrinsic viscosity of the emulsion to increase (see Eq 7.50). Similarly, an increase of the apparent volume of the dispersed phase causes the relative viscosity to increase (see Eqs 7.24-7.25). Furthermore, enhanced interactions between the phases will reduce the possibility of the interlayer slip, and increase formation of associative network formation, which may result in the yield stress. In short, compatibilization is expected to increase melt viscosity, elasticity and the yield stress. 

The ratio of the emulsion viscosity to the external phase viscosity is often called relative viscosity, and it is noted tv instead of/(). 

Figure 30 Relative viscosity as a function of fines volume fraction (size ratio =10) for lubricant oil-in-water emulsions of an internal phase volume of 0.65. (Adapted from Ref. 20.)...

Many empirical formulas have been proposed to render the effect of internal phase ratio on the emulsion viscosity, but they are only valid in specific cases. Pal and Rhodes (84, 85) proposed and used a semi-empirical equation, that makes use of experimental data O qq as the internal phase fraction O at which the relative viscosity qj. = 100. This experimental value must be attained in the same formulation and emulsification conditions, particularly stirring characteristics, which is maybe why it significantly embodies the overall effects of all remaining variables ... 

For a similar system, the shear viscosity was found to follow the power law model with yield (Pal et al. 1986). Owing to the presence of yield stress, the flow of concentrated emulsion was found to be facilitated by superposition of 10 Hz oscillation on the steady-state shear flow - up to 40 % energy saving was reported (Jezequel et al. 1985). More recently, the relative viscosity of emulsions was described in terms of scaling parameters (Pal 1997). Ten principal variables were incorporated into six dimensionless groups X, k, reduced time, h = t/(r n,dV8 kB T), relative density, = pd/pm> Peclet number, Pe = ti yd /SkeT, and Reynolds number. Re = p yd /4rin,. For the steady-state flow of well-stabilized emulsions, it was argued that the relative viscosity of emulsions should depend only on two... 

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