Polymer rheology extensional viscosity

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

Extensional viscosity that results purely from shear deformation seems to be of less interest, but has been measured (108). The rheology of several different polymer melts in terms of shear viscosity and uniaxial and biaxial extensional viscosity has been compared (231). Additional information on the measurement of extensional viscosity are also available (105,238—240). 

Since homogenous melts are covered in a later account of pressure build-up and power input in the extruder (Chapter 7), this chapter confines itself to the flow behavior of homogenous unfilled polymer melts and on the introduction of the most important rheological parameters such as viscosity, shear thinning, elasticity, and extensional viscosity. The influence of these rheological properties on simple pressure- and drag flows is demonstrated, while the influence of rheological parameters on pressure build-up and power input in the extruder is described in more detail in Chapter 7. 

These conclusions are not surprising. A novel point, however, is the important adhesional role of roughness of the solid in wear, in addition to its obvious role in plowing wear. Another point is the source of the local heating which leads to enhanced wear the work that is done in drawing the craze fibrils of the polymer. Extensional viscosity is an importnat rheological property that... 

In this section, only measurements of shear viscosity have been addressed. However, some other devices are available that can assist in the characterization of the rheology of polymer melts under different types of deformation, other than shear. For instance, extensional viscosities can... 

Various instruments are available to measure the viscosity of polymer melts and solutions, and more generally their rheological behavior, which include capillary and rotational viscometers. The former can be used to measure parameters such as shear viscosity, melt fracture, and extensional viscosity, which are important for many polymer processes. The latter type of device can be used in either steady or oscillatory mode, thus providing a measure of the viscosity as well as viscoelasticity (G", G, and tan 5) as a function of frequency and temperature. 

Kennedy, J.C., Meadows, J. and Williams, PA. (1995) Shear and extensional viscosity characteristics of a series of hydrophobically associating polyelectrolytes. /. Chem. Soc. Faraday Trans., 91,911-916. Andrews, N.C., McHugh, A.J. and Schieber, J.D. (1998) Polyelectrolytes in shear and extensional flows conformation and rheology. /. Polym. Sei., PartB Poly. Phys., 36,1401-1417. 

The uniaxial extensiometers described so far are suitable for use with viscous materials only. They cannot, for example, be used to measure the steady extensional viscosity of such commercially important polymers as nylons and polyesters used in the textile industry, and which may have shear viscosities as low as 100 Pa sec at processing temperatures. As a consequence, other techniques are needed but these invariably involve nonuniform stretching. Here one cannot require that the stress or the stretch rate be constant. Also, the material is usually not in a virgin (stress-free) state to begin with. One can therefore not obtain the extensional viscosity directly from these measurements. Nonetheless, data from properly designed non-uniform stretching experiments can be profitably analyzed with the help of rheological constitutive equations. In addition, such data provide a simple measure of resistance that polymeric fluids offer to extensional deformation. 

As mentioned in Sections 1 and 3, a rheological constitutive equation relates the components of the three-dimensional extra-stress (matrix) to the components of the strain (matrix) or the rate of strain (matrix) in any given flow field. Extensional viscosity data of the kind shown in Figure 5 should therefore be explainable on the basis of a proper constitutive equation. Unfortunately, there is no simple constitutive equation that accurately predicts the behavior of a polymer melt in all the commonly encountered flow situations. Some equations do a remarkably good job... 

S. Soyles, D.A. Dinga, G.P. Glass, J.E. Dynamic Uniaxial Extensional Viscosity. Response in Spray Applications, Polymers as Rheology Modifiers, ACS 462 (1991)... 

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