Extensional/elongational viscosity

A. = ale, where A = extensional (elongational) viscosity, a viscosity coefficient when appHed stress is extensional stress (strain rate. This parameter is often used for characterising polymer solutions. 

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). 

Demonstrations are given of the importance of extensional or elongational viscosity in the foam process. New polypropylenes are compared in extensional flow and it is shown how rheological differences allow the prodnction of low density foam on tandem extrnsion equipment. 6 refs. 

At this point it is appropriate to define viscosity and how it is measured. In the text that follows, the shear viscosity is referred to as viscosity. It is important to realize that fluids also have an extensional or elongational viscosity when stretched however, this property is not dealt with here. The shear mode of deformation is assumed henceforth, such that the motion in the fluid is similar to the action of the blades of a pair of shears. 

Figure 2.37 presents plots of elongational viscosities as a function of stress for various thermoplastics at common processing conditions. It should be emphasized that measuring elongational or extensional viscosity is an extremely difficult task. For example, in order to maintain a constant strain rate, the specimen must be deformed uniformly exponentially. In addition, a molten polymer must be tested completely submerged in a heated neutrally buoyant liquid at constant temperature. 

Figure 3.32 The predictions of the Doi-Edwards integral model for the normalized uniaxial extensional (or elongational) viscosity rj and for the viscometric shear coefficients r)(y) and i(y). Also shown are the predictions of the differential model, Eq. (3-77). (From Larson, 1984b, with permission from the Journal of Rheology.)--------------------------------------------------...

When describing dilatant behavior, the maximum stretch rate, e, in the converging flow at the contraction is a better parameter, but more difficult to be calculated. Instead of the term stretch rate, other authors also used deformation rate (e.g., Chauveteau, 1981) or elongational rate (e.g.. Sorbic, 1991). The shear-thickening viscosity is also called elongational viscosity (often referred to as the Trouton viscosity Sorbie, 1991) or extensional viscosity in the literature. James and McLaren (1975) reported that for a solution of polyethylene oxide (a flexible coil, water-soluble polymer physically similar to HPAM), the onset of elastic behavior at maximum stretch rates was of the order of 100 s and shear rates of the order of 1000 s. In this instance, the stretch rate is about 10 times lower than the shear rate. However, some authors use shear rate instead of stretch rate in defining the Deborah number—for example, Delshad et al. (2008). 

While dynamic mechanical and steady shear measurements are frequently used in rheology studies of surfactant systems, extensional viscosity measurements are lacking. This can be attributed to the difficulties associated with such measurements and the lack of commercial laboratory instrumentation since the discontinuance of the Rheometric Scientific RFX rheometer. For many detergent compositions, the relatively low viscosity further complicates such measurements. There appear to be very few data on extensional or elongation viscosity for detergent consumer products and actives in the technical literature at this time. 

When a pendant drop forms slowly at the lower end of a capillary tube it ultimately falls and stretches the filament (which remains attached to the drop). For a Newtoiuan flmd the filament qmckly thins and breaks but long filaments can be formed from visco-elastic liqmds [Jones et al., 1990]. The forces acting on the falling drop are determined using a force balance, and the extensional stress determined as a function of time [Jones and Rees, 1982], The falling pendent drop technique is simple to set up and analyse, and provides consistent values of an apparent elongational viscosity. 

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