Constitutive instabilities

Fig. 2.8.11 Schematic constitutive relationship (shear stress versus shear rate) for a wormlike micelle system exhibiting constitutive instability. When the average shear rate exceeds yc the fluid subdivides into two coexisting shear bands residing on stable branches of the constitutive relationship.

One leading explanation attributes the anomalous melt flow behavior (i.e., flow discontinuity and oscillation) to constitutive instabilities [65]. In other words, the anomalies would be constitutive in nature and non-interfacial in origin. Such an opinion has not only been expressed phenomenologically by Tordella [9b] and many other rheologists but found support from several theoretical studies [65-67]. However, these theories only attempt to describe inherent bulk flow behavior. Thus, a connection between the anomalous flow phenomena and constitutive instabilities was often explored without any account for possible molecular processes in the melt/wall interfacial region. 

Extrudate distortion has been viewed as explicit evidence for melt flow instabilities or melt fracture. This is another calamitously misleading assertion in the massive literature of over 3000 papers on the subject. Because extrudate distortion was also observed even without any signature of slip, it was concluded by Blyler and Hart [32] that the slip process is not an essential part of the flow instability. This dilemma, that the flow anomalies including flow oscillation cannot be accounted for in terms of either a constitutive instability or interfacial slip mechanism, has persisted until very recently. Denn coined this plight the paradox [10b]. 

Constitutive Instabilities, Extrudate Distortions and Melt Fracture 11.1... 

Monodisperse melts appear to exhibit a plateau region in the stress vs shear rate flow curve [51,62,65]. The capillary flow behavior actually closely resembles the oscillatory shear behavior in the sense that the flow curve essentially overlaps on the absolute value of complex modulus G vs the oscillation frequency (0 [62]. Thus.it appears that the transition-like capillary flow behavior of highly entangled monodisperse melts reflects constitutive bulk properties of the melts and is not interfacial in origin. It remains to be explored whether this plateau indeed manifests a real constitutive instability, i.e., whether it is double-valued. 

Remark 5.2 The instability quoted in Theorem 5.3 is due to the aforementioned S-shaped curve. This constitutive instability—inherent to the model—has been questioned as unphysical by some authors. 

Greco F, Ball RC (1997) Shear-band formation in a non-newtonian fluid model with a constitutive instability. J Non-Newt Fluid Mech 69(2-3) 195-206... 

We noted in Section 11.3.1 that the prediction of a maximum in steady-state shear stress as a function of shear rate was a basic failure of the Doi-Edwards constitutive equation. Such a prediction implies that the same shear stress is produced by more than one shear rate. In such a situation, a uniform shearing flow at shear rates near or above the inverse of the reptation time Tj, would become unstable to a so-called constitutive instability, leading to spontaneous... 

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