Viscosity-volume fraction curves

Viscosity-volume fraction curves Fig.2 shows the viscosity as a function of volume fraction of particles. The results are typical of those usually obtained with concentrated dispersions (6), showing a rapid increase in viscosity above a critical volume fraction of the dispersed phase. When the volume fraction reaches the so-called packing fraction, g (see Discussion Section), the viscosity reaches a very high value, gp may be obtained from a plot of versus and extrapolation to... 

Figure 12.8 Viscosity-volume fraction curves for W/O emulsions stabilised with PHS-PEO-PHS block copolymer.

The relative viscosity-volume fraction curve for water-in-oil emulsions (42) is shown in Figure 12. Isoparaffinic oil (Isopar M) was used in this case and the emulsions were prepared using an A-B-A block copolymer of PHS-PEO-PHS (Arlacel P135, supplied by ICI PHS refers to poly-12-hydroxystearic acid and PEO refers to polyethylene oxide). 

Figure 12 Viscosity-volume fraction curve for w/o 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],... 

Figure 20. Universal low and high shear limit viscosity vs. solid volume fraction curve for monodisperse and hidisperse systems (130).

Figure 6.38 gives relative viscosity (j/J-volume fraction ( ) curves for paraffin oil/ water emulsions. 

The use of the nomograph is as follows Find the intersecting point of the curves of continuous phase and dispersed phase viscosities on the binary field (left side of nomograph). A line is drawn from this point to the common scale volume fraction of dispersed phase and continuous phase liquids. The intersection of this line with the Viscosity of Emulsion scale gives the result. 

Figure 4.12a shows plots of the intrinsic viscosity —in volume fraction units —as a function of axial ratio according to the Simha equation. Figure 4.12b shows some experimental results obtained for tobacco mosaic virus particles. These particles —an electron micrograph of which is shown in Figure 1.12a—can be approximated as prolate ellipsoids. Intrinsic viscosities are given by the slopes of Figure 4.12b, and the parameters on the curves are axial ratios determined by the Simha equation. Thus we see that particle asymmetry can also be quantified from intrinsic viscosity measurements for unsolvated particles. 

The concept of a unique hydrodynamic volume for all rodlike polymers was derived from examination of the Mark-Houwink constants, K and a, of the equation [rj ] = KMa. Macromolecules with values of a greater than unity are commonly accepted to be stiff or rigid rods. However, it was also found that such molecules (even for values of a less than unity) obey a relation illustrated by close concordance with the curve in Fig. lb (13) flexible, branched or otherwise irregular polymers, on the other hand, show dispersion around the upper part of the curve. The straight line curve in Fig. lb implies that the constants K and a are not independent parameters for the regular macromolecules to which they apply. Poly (a- and polyQJ-phenylethyl isocyanide) fall on this line the former has a value of a > 1 while the latter has a value a < 1 (14) both polymers give linear concentration dependence of reduced specific viscosity for fractionated samples... 

Studies of the effect of particle size on viscosity suggest that Eqn. (1) is obeyed in the limit as cf> goes to zero. As the volume fraction of particles increases, the relative viscosity increases at a faster rate than linear rate, approaching infinity as the packing density of the suspension approaches that of densely packed solid particles Fig. 4.S.66 Regardless of particle size, all data in Fig. 4.8 scatter about a common curve. An empirical fit for this type of curve has been discussed by Kitano et al. 67... 

FIGURE 4.18 (Continued) (c) Predicted particle volume fraction for 35% weight CaCOs powder in a 75-mm hydrocyclone, (d) Experimental and predicted size selectivity curves for 35% weight CaCOg powder in a 75-mm hydrocyclone (the interactions correspond to viscosity corrections made for the particle volume fraction distribuiuBi within the hydrocyclone). From Rcgamani and Mifai [48]. 

In Brownian suspensions, as (p increases, the slope of the viscosity-shear rate curve in the shear-thickening regime typically increases, and for electrostatically stabilized suspensions at high-volume fractions, it can even become a discontinuous jump. At shear rates above the shear-thickening regime, there is typically a second shear-thinning regime (see... 

A similar, and even more dramatic, viscosity enhancement was observed by Buscall et al. (1993) for dispersions of 157-nm acrylate particles in white spirit (a mixture of high-boiling hydrocarbons). These particles were stabilized by an adsorbed polymer layer, and then they were depletion-flocculated by addition of a nonadsorbing polyisobutylene polymer. Figure 7-9 shows curves of the relative viscosity versus shear stress for several concentrations of polymer at a particle volume fraction of 0 = 0.40. Note that a polymer concentration of 0.1 % by weight is too low to produce flocculation, and the viscosity is only modestly elevated from that of the solvent. For weight percentages of 0.4-1.0%, however, there is a 3-6 decade increase in the zero-shear viscosity ... 

Assuming that Ci, C2, and C3 are not affected by temperature, pressure, and dissolution of CO2, they can be determined from a viscosity-shear rate curve of the neat polymer. Namely, the coefficient, Ci, which is equivalent to n - 1, can be determined by the slope of the viscosity and shear rate curve. The values of C2 and C3 can be determined from data of viscosity vs. free volume fraction of the neat polymer. The data of free volume fraction required for determining C2 and C3 can be obtained from PVT data of the neat polymer at temperatures and pressures where the viscosity measurements of the neat polymer are performed. 

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