Polymer melts constitutive equations

Polymer Melt Constitutive Equations Based on Continuum Mechanics, 100... 

POLYMER MELT CONSTITUTIVE EQUATIONS BASED ON CONTINUUM MECHANICS... 

A measure Which is frequently used in polymer melt constitutive equations is the Hencky strain measure, related to the stretch ratio by ... 

Many industrially important fluids cannot be described in simple terms. Viscoelastic fluids are prominent offenders. These fluids exhibit memory, flowing when subjected to a stress, but recovering part of their deformation when the stress is removed. Polymer melts and flour dough are typical examples. Both the shear stresses and the normal stresses depend on the history of the fluid. Even the simplest constitutive equations are complex, as exemplified by the Oldroyd expression for shear stress at low shear rates ... 

R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworths, Boston (1988). 

Larson RG (1988) Constitutive equations for polymer melts and solutions, Butter-worths, Boston, p 256... 

Molecular Constitutive Equations for Polymer Melts in Viscoelastic Flow Solvers... 

So in the world of polymer melts, the intermediary of a constitutive equation, or equation set, albeit molecularly derived, would seem unavoidable at present. The success of the branched-polymer model discussed above would suggest that... 

J. P. W. Baaijens, Evaluation of Constitutive Equations for Polymer Melts and Solutions in Complex Flows, Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands (1994). 

There is a multitude of constitutive equations proposed for polymer melts. However, only a few have been used to solve actual polymer processing problems. Nevertheless, we feel, as we did in the first edition of this book, that it is instructive to trace their origin and to indicate the interrelationship among them. We will do this quantitatively, but without dealing in detail with the mathematical complexities of the subject. The following three families of empirical equations will be discussed ... 

We have tried to give a quick glimpse of the interrelationships among some commonly used constitutive equations for polymer melts and solutions. None predicts quantitatively the entire spectrum of the rheological behavior of these materials. Some are better than others, becoming more powerful by utilizing more detailed and realistic molecular models. These, however, are more complex to use in connection with the equation of motion. Table 3.1 summarizes the predictive abilities of some of the foregoing, as well as other constitutive equations. 

TABLE 3.1 Selected Constitutive Equations that Have Been Used for Polymer Melts, and Comments on Their Predictive Abilities3... 

GNF-based constitutive equations differ in the specific form that the shear rate dependence of the viscosity, t](y), is expressed, but they all share the requirement that the non-Newtonian viscosity t](y) be a function of only the three scalar invariants of the rate of strain tensor. Since polymer melts are essentially incompressible, the first invariant, Iy = 0, and for steady shear flows since v = /(x2), and v2 V j 0 the third invariant,... 

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