Viscosity-volume fraction

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... 

Disordered solutions of spherical micelles are not particularly viscoelastic, or even viscous, unless the volume fraction of micelles becomes high, greater than 30% by volume. Figure 12-7, for example, shows the relative viscosity (the viscosity divided by the solvent viscosity) as a function of micellar volume fraction for a solution of hydrated micelles of lithium dodecyl sulfate in water. Qualitatively, these data are reminiscent of the viscosity-volume-fraction relationship for suspensions of hard spheres, shown as a dashed line (see Section 6.2.1). The micellar viscosity is higher than that of hard-sphere suspensions because of micellar ellipsoidal shape fluctuations and electrostatic repulsions. 

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

HETP derived from the coupling theory contribution to the HETP from diffusion contribution to the HETP from flow dispersion viscosity volume fraction... 

AK Das, D Mukesh, V Swayambunathan, DD Kotkar, PK Ghosh. Concentrated emulsions. 3. Studies on the influence of continuous phase viscosity, volume fraction, droplet size and temperature on emulsion viscosity. Langmuir 8 2427— 2436, 1992. 

As discussed in the introduction, the bulk rheology of emulsion systems can be investigated using steady-state (shear stress as a function of shear rate), constant stress, and oscillatory techniques. These methods are the same as those described for interfacial rheology. In this section, some results on various emulsion systems will be described to illustrate the use of rheological measurements in investigating the interaction between emulsion droplets. First, the viscosity-volume fraction relationship for o/w and w/o emulsions... 

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.

Viscosity-Volume Fraction Relationship for Oil/Water and Water/Oil Emulsions... 

Figure 4.4 Changes of the complex viscosity, volume fraction and weight percent of PES in the DCEBA/DDM/PES mixture with 10wt% PES at different isothermal curing...

Russel [26] developed a model for the shear-thinning behavior at arbitrary Peclet number for the case of Rk > 1. An equation for the viscosity-volume fraction dependence up to second order can be found in reference [27],... 

A number of methods are available for production of maximum packing efficiency from particle characteristics but the accuracy with which such procedures could predict for the purpose of predicting viscosity of suspensions is questionable. Note that the denominator in equation 2, as in other relative viscosity-volume fraction relationships for use at high volume fractions, is a function of the free volume fraction of organic vehicle over and above that needed to fill the interstices between contacting particles. 

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