Continuous-Flow Capillary Rheometry

In this section, we present another experimental method that also employs a capillary die. However, this method allows one to determine not only shear viscosity but also normal stress differences in steady-state shear flow by continuously supplying a polymeric 

When a fluid enters a tube from a large reservoir section, the velocity profile becomes fully developed at a certain distance from the die entrance. A conventional criterion, such as the constant pressure gradient in the tube, is not sufficient to determine whether a viscoelastic fluid has attained fully developed flow in a cylindrical die because the relaxation time of a viscoelastic fluid is much greater than that of a Newtonian fluid. The criteria for determining fully developed flow in viscoelastic fluids have been discussed in the literature (Han and Charles 1970). 

Of course, the measurement of T (R, z) precisely at the exit of a die is not possible mechanically. Therefore, the extrapolation of the measurement taken nearest to the exit of the die must be justified if one wishes to use the exit pressure as a means of interpreting the flow properties of the fluid tested. This is because the extrapolation tacitly assumes that the flow remains fully developed to the die exit. We will elaborate on this further later in this section. 

We now present the theory (Davis et al. 1973 Han 1974) that enables one to determine both shear viscosity and normal stress differences for viscoelastic fluids from measurements of z) in a long capillary die. For steady-state fully developed flow in the cylindrical die, the equations of motion are given by 

In view of the fact that Reynolds numbers in polymer melt flow are very low (say, 10 to 10 2) in almost all practical situations and the contribution of the thrust Ti) terms in Eqs. (5.59) and (5.61) may be considered negligibly small compared with that of other terms for polymer melt flows, from Eq. (5.61) we have 

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Figure 5.15 gives logA j versus logy plots for an LDPE at three different temperatures, which were obtained, via Eq. (5.64), from the Pp j, measurements given in Figure 5.14. Later in this chapter we compare the values of determined from continuous-flow capillary rheometry with those obtained from cone-and-plate rheometry.

Another experimental method that is as important as continuous-flow capillary rheometry is slit rheometry. The basic idea of slit rheometry is the same as that of continuous-flow capillary rheometry insofar as the measurement of wall normal stress along the die axis is concerned. But, there is a significant theoretical difference between the two methods, as we will make clear, and also in the die design. The slit rheometer has some advantages over the continuous-flow capillary rheometer in the way that transducers can be mounted on the die wall, but there are also some disadvantages. 

When a very viscous molten polymer is forced to flow through a slit or capillary die, viscous shear heating can become significant above a certain critical value of y or ct. Under such situations, nonlinear profiles of wall normal stress in a slit or capillary die may be observed, as described in the preceding section. Therefore, continuous-flow capillary/slit rheometry is limited to y or a, below which viscous shear heating can be neglected. 

Another method is to use continuous-flow capillary (or slit) rheometry, as discussed in Chapter 5. Han and coworkers (Han and Ma 1983a, 1983b Han and Villamizar 1978 Han et al. 1976) were the first to use a continuous-flow capillary (or slit) rheometer to determine the viscosity of polymer melts with solubilized gaseous components. Later, other investigators (Elkovitch et al. 1999 Lee et al. 1999 Royer et al. 2000, 2001) employed the same method. 

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