Normal stress coefficient oscillatory

In addition to relationships between apparent viscosity and dynamic or complex viscosity, those between first normal stress coefficient versus dynamic viscosity or apparent viscosity are also of interest to predict one from another for food processing or product development applications. Such relationships were derived for the quasilinear co-rotational Goddard-Miller model (Abdel-Khalik et al., 1974 Bird et al., 1974, 1977). It should be noted that a first normal stress coefficient in a flow field, V i(y), and another in an oscillatory field, fri(ct>), can be determined. Further, as discussed below, (y) can be estimated from steady shear and dynamic rheological data. 

Figure 3.15 The frequency-dependent in-phase and out-of-phase components of the dynamic viscosity, rj and rj in small-amplitude oscillatory shear, along with the shear-rate dependence of the first normal stress coefficient hi (y) for a 0.05 wt% solution of polystyrene of molecular weight 2.25 X 10 in a solvent of oligomeric styrene. The lines through the data show the predictions of the Zimm theory for r and 2r)"f(o and the Zimm theory for hi(y) modified to account for finite extensibility, as discussed in Section 3.6.2.2.I. The dashed lines are the contributions of the individual Zimm relaxation modes to 2rj"((o) /

Normal Stress Coefficients and Oscillatory Viscometric Measurements... 

However, dynamic measurements, such as the oscillatory tests, are preferred in practice over the steady shear measurements for determining the viscoelastic properties of fluids. This is not only because of the difficulty in determining the first normal stress coefficient accurately, but the determination of a fluid s viscosity by steady shear measurement is only a partial characterization of a viscoelastic fluid s properties. 

A sinusoidally varying shear strain rate with small amplitude, such that 721 = 721 cos cor, evokes a sinusoidally varying normal stress difference symmetry considerations because of the proportionality to 721, is predicted by the phenomenological models previously quoted.5 -54 jj,g oscillatory stress difference is superposed on a constant stress and both are proportional to 721 if 721 is small. The coefficient is now defined as the ratio (ai i — ff22)/(72i) - It is the sum of a constant term and two oscillating terms ... 

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