Elongation and Shear Flows

MIXING OF HIGHLY VISCOUS FLUIDS, POLYMERS, AND PASTES 

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Accordingly, given the necessity from equilibrium coil dimensions that bt> 1, the shear rate and frequency departures predicted by FENE dumbbells are displaced from each other. Moreover, the displacement increases with chain length. This is a clearly inconsistent with experimental behavior at all levels of concentration, including infinite dilution. Thus, finite extensibility must fail as a general model for the onset of nonlinear viscoelastic behavior in flexible polymer systems. It could, of course, become important in some situations, such as in elongational and shear flows at very high rates of deformation. 

Lodge and Meissner have recently examined in detail the stresses during start-up of steady elongational and shear flows (374). The Lodge equation [Eq.(6.15)], with its flow-independent memory function, described the build-up of stress rather well (even for rapid deformations) until a critical strain was reached. Beyond the critical strain (which differed somewhat in shear and... 

N. J. Inkson, T. C. B. McLeish, O. G. Harlen, and D. J. Groves, Predicting Low Density Polyethylene Melt Rheology in Elongational and Shear Flows with Pom-pom Constitutive Equations , J. Rheol., 43, 873-896 (1999). 

Chain conformation in elongational and shear flow as seen by SANS... 

Table 9.1 Elongational and shear flow yield values for some filled polystyrene systems at 180°C...

Finally, a comment needs to be added for the difference in rheological responses under elongation and shear flow. 

The purpose of the present chapter is to introduce the techniques of birefringence, to define the validity of the stress optical law (i.e. the linear relationship between stress and birefringence) in both simple (simple shear and uniaxial elongation) and complex (flow in abrupt contraction) deformations, and to propose some examples of the interest of these techniques for the study of the flow of molten polymers. 

Melt Viscosity. The study of the viscosity of poljmier melts (47-62) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus, melt viscosity as a fimction of temperature, pressure, rate of flow, and poljmier molecular weight and structure is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extrusion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. Theoretical developments include a constitutive equation that correctly captures nonlinear behavior in both elongation and shear (63,64). 

IV zone complex divergent flow with elongation and shearing. 

Laminar flow conditions are usually caused by high liquid viscosities. Despite considerable agitation, the flow rates are much reduc, so that the overall circulation a) is slower than under turbulent conditions. Much more important, however, is the fact that there is no turbulence. The size reduction of liquid volume elements is brought about mostly by elongation and shear b), combined with folding and rupturing. The thickness of the smallest volume elements may be on the order of severed mm, resulting in diffusion times d) that can be several minutes. 

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