Elongational/shear viscosities ratio stress dependence

Figure 19. The ratio of elongational to shear viscosities The theoretical dependence of the ratio of elongational to shear viscosity coefficients on the invariant of the additional stress tensor is calculated according to equation (9.71) and depicted by the dashed curve. The solid curves represent experimental data for systems listed in Table 3. Adapted from the paper of Pokrovskii and Kruchinin (1980).

Han and Funatsu [1978] studied droplet deformation and breakup for viscoelastic liquid systems in extensional and non-uniform shear flow. The authors found that viscoelastic droplets are more stable than the Newtonian ones in both Newtonian and viscoelastic media they require higher shear stress for breaking. The critical shear rate for droplet breakup was found to depend on the viscosity ratio it was lower for < 1 than for A, > 1. In a steady extensional flow field, the viscoelastic droplets were also found less deformable than the Newtonian ones. In the viscoelastic matrix, elongation led to large deformation of droplets [Chin and Han, 1979]. 

Very dilute solutions of axisymmetric rigid molecules exhibit not only frequency-dependent viscoelastic properties but also an apparent viscosity which depends on shear rate. This non-Newtonian flow is predicted by theory for elongated ellipsoids and rigid dumbbells,and the theoretical results have been widely applied for certain biological macromolecules. The shear-rate dependent viscosity r) is defined as the ratio of shear stress a to shear rate 7, and the intrinsic viscosity as defined by equation 5 with 77 substituted for rjo is then in general a function of 7. At low shear rates, the shear-dependent intrinsic viscosity has the form... 

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