Oldroyd three-constant model

Figure 3.3 gives logarithmic plots of n/r] versus predicted from three models (1) the ZFD model, (2) the Oldroyd three-constant model, and (3) the Spriggs model. It is seen in Figure 3.3 that the predicted viscosities from all three models decrease at a much faster rate than those observed experimentally (see Figure 3.2) with increasing shear rate, and that the viscosities predicted from the Oldroyd three-constant model level off as shear rate is increased, which is seldom observed experimentally. 

Small-amplitude oscillatory analysis can readily be applied to any nonlinear constitutive equation. For instance, applying Eq. (3.79) to the Oldroyd three-constant model, Eq. (3.21), we obtain... 

Figure 3.11 gives plots of n /irjo versus A.jC that are predicted from two constitutive equations (1) the upper convected Maxwell model, and (2) the Oldroyd three-constant model. It is seen in Figure 3.11 that both models predict values of increasing very rapidly without bound as e increases, in contrast to the experimental results given in Figure 3.10. As a matter of fact, all the expressions summarized in Table 3.3 predict similar elongational behavior, which is considered to be physically unrealistic.

The three constant Oldroyd model is a nonlinear constitutive equation of the differential corrotational type, such as the Zaremba-Fromm-Dewitt (ZFD) fluid (Eq. 3.3-11). [For details, see R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Second Edition, Vol. 1, Wiley, New York, 1987, Table 7.3-2.]... 

Three-constant Oldroyd model for viscoelastic fluids. Phys. Fluids. 5,... 

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