Viscosity comparison with hard spheres

Harris, K. R. (1992). The self-diffusion coefficient and viscosity of the hard-sphere fluid revised A comparison with experimental data for xenon, methane, ethene and trichloromethane. Mol. Phys., 77,1153-1167. 

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

Figure 14.8 Generational dependence of relative viscosity, tv, on solution volume fraction for the first six generations, G, of PAMAM dendrimers in ethylenediamine (EDA) in comparison with theoretical predictions of Krieger (A), Eiler (B) and Mooney (C) hard sphere models (according to ref. [5])...

The concentration dependence of the zero shear viscosity, (normalized to the solvent viscosity, r/s], is given in Figure 37. The concentration is expressed as the effective hydrodynamic volume fraction, Hard sphere data, taken from the literature, are included for comparison. It is obvious that with increasing the star functionality the polymer behavior ranges from entangled polymers (f= 32) to soft colloidal spheres (f = 128).1 1... 

Fig. 18. A comparison of the experimental viscosity data for argon as a function of density with the predictions of the simple Enskog theory and of the modified Enskog theory. In the simple Enskog theory the effective hard-sphere diameter is determined by fitting the low-density limit of the viscosity to the Boltzmann equation result for hard spheres. Then x is calculated for all densities by using this diameter in Eq. (144). In the modified Enskog theory, both x nd the hard-sphere diameter are determined from the equation of state data. (Figure courtesy of J. V. Sengers.)...

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]... 

The influence of fillers has been studied mostly at hl volume fractions (40-42). However, in addition, it is instructive to study low volume fractions in order to test conformity with theoretical predictions that certain mechanical properties should increase monotonlcally as the volume fraction of filler is Increased (43). For example, Einstein s treatment of fluids predicts a linear increase in viscosity with an increasing volume fraction of rigid spheres. For glassy materials related comparisons can be made by reference to properties which depend mainly on plastic deformation, such as yield stress or, more conveniently, indentation hardness. Measurements of Vickers hardness number were made after photopolymerization of the BIS-GMA recipe, detailed above, containing varying amounts of a sllanted silicate filler with particles of tens of microns. Contrary to expectation, a minimum value was obtained (44.45). for a volume fraction of 0.03-0.05 (Fig. 4). Subsequently, similar results (46) were obtained with all 5 other fillers tested (Table 1). 

Figure 13.13. Comparison of the behavior predicted from Equation 13.35 with the data tabulated by de Kruif et al [43] for the viscosity of dispersions of sterically stabilized hard silica spheres in cyclohexane. There are no adjustable parameters in Equation 13.35. Relative viscosity denotes r (dispersion)/r (cyclohexane). Relative volume fraction denotes 0/0. Couette and parallel refer to measurements with a Couette rheometer and a parallel plate rheometer, respectively. Zero and infinite refer to the limits y —>0 and y- < >, respectively.

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