Rheological Material Functions

Simple shear flow is identical with the pattern depicted In Fig. 9.15. The velocity field is given by 

The only parameter included is the shear rate j. There is an instrument that is widely used because it realizes simple shear flow conditions in a manner convenient for experiments. This is the cone-and-plate rheometer sketched on the left-hand side of Fig. 9.16. The polymer melt is placed in the gap and, if the gap angle is kept small, then the shear rate is the same everywhere. With the aid of this apparatus, various experiments may be carried out, as for example, 

The properties of melts under extensional flows can be studied with the aid of a tensile rheometer. The basic experimental arrangement is sketched on the right-hand side of Fig. 9.16. A cylindrical rod of polymer melt, usually floating on a liquid substrate, is drawn by two pairs of ribbed rollers. One of the rollers is mounted on a leaf spring, so that the force required for the 

The process thus differs from a drawing where clamps attached to the two ends of a sample move with a constant relative speed, as this leads to 

The constant in Eq. (9.148) is known as the Hencky rate of extension and we choose for it the symbol ch 

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These flow features are of importance in a great number of technical processes, especially for high process velocities when extremely high shear rates can be observed. For polymeric systems this can lead to a so-called non-Newtonian behaviour, i.e. the rheological material functions become dependent on the shear or elongational rate. 

Rheological Behavior, Rheometry, and Rheological Material Functions of Polymer Melts, 80... 

It is important to note that the rheological material functions obtained experimentally, using rheometers, are evaluated in simple flows, which are often called viscometric or rheometric. A viscometric flow is defined as one in which only one component of the velocity changes in only one spatial direction, vx (y). Yet these material functions are used to describe the more complex flow situations created by polymer processing equipment. We assume, therefore, that while evaluated in simple flows, the same rheological properties also apply to complex ones. 

RHEOLOGICAL BEHAVIOR, RHEOMETRY, AND RHEOLOGICAL MATERIAL FUNCTIONS OF POLYMER MELTS... 

PIB/PDMS The morphology evolution and the rheological material functions in shear fiow both under transient and steady-state conditions Deyrail et al. 2007... 

In oil deposits with an average temperature of 80 C, the temperature dependence of the rheological material functions cannot be neglected. In all cases, a loss of the viscosity with increasing temperature is observed. Polysaccharides (e.g. xanthan) exhibit only a minor... 

We now introduce the major rheological material functions, with illustrations provided by typical experimental results. Figure 7.15 depicts data obtained for low density polyethylene under steady shear flow conditions, employing a cone-and-plate rheometer. Curves display both the shear rate dependence of the viscosity, with similar results as in Fig. 7.1, and the shear rate dependence of the first normal stress difference. The stresses arising for simple shear flows may be generally expressed by the following set of equations... 

Equations include and thus define three rheological material functions... 

Further, it is shown how the unification technique can be extended to other rheological material functions, such as normal stress difference, dynamic viscoelastic parameters, and extensional viscosity, to obtain coalesced curves which are grade and temperature invariant. 

Vlachopoulos (1981) and Tanner (1988a) have reviewed the various efforts to relate B to rheological material functions. The simplest and most widely used is Tanner s (1970a), which foilows from Lodge s work (1964) on recoverable strain. It assumes unconstrained recovery after steady shear and applies an integral model of the BKZ type (4.4.2) with one relaxation time. The result is... 

Because MFI is used so widely, there is interest in quantitatively relating it to rheological material functions. Michaeli (1984) gives a nomogram to relate MFI to melt viscosity. Such calculations generally ignore reservoir and entrance pressure losses. 

But the question for the rheologist is Can squeezing flow measure rheological material functions Strictly speaking, the answer is no. The flow is so complex that the squeezing force can be related to the gap change only through a constitutive equation. In fact, the flow has been used as a model to evaluate constitutive... 

More than 40 years qfter Weissenberg s pioneering proposal [Figures 4.1.1 and 8.1.1] for die measurement of shear and normal stresses during shear flow of elastic Uquids, the determination of the rheological material functions of polymers in simple shear flow is still a nightmareforthe experimenter. J. Meissner et al. (1989)... 

Chapters 5-7, which describe shear and extensional rheometry, give the most important deformation geometries and derive the working equations for each. These equations permit conversion of measured quantities like force, torque, pressure, and angular velocity to stress and strain on the sample. Such stress and strain data allow us to determine rheological material functions, which are needed to evaluate the parameters in particular constitutive equations. 

A) Models based on an empirical transformation from rheological material function to molecular weight distribution (viscosity models and modulus models)... 

Currently, there is no theory for concentrated suspensions that accounts for fiber contact. However, semidilute theory has been used to some extent to model their stress behavior, in which case A is fit to the rheological material functions of a fluid instead of calculating A from theory. In the majority of fiber composites of industrial significance, the matrix is polymeric and exhibits nontrivial viscoelastic behavior, which increases the complexity of modeling such suspensions. The first attempts ignore the fiber and treat the suspension as a homogeneous viscoelastic fluid. 

However, for non-Newtonian fluids, even though continuity equation and the equation of motion written as Equation 11.2 remain valid, the Newtonian constitutive equation is not correct and a different constitutive equation is needed. To find constitutive equations, experiments are performed on materials using standard flows described above. The functions of kinematic parameters that characterize the rheological behavior of fluids are called rheological material functions. Standardized material functions are shown in Table 11.1 [2-4]. 

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