Slit 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. 

We now present the theory (Davis et al. 1973 Han 1974) that allows one to determine shear stress and first normal stress difference in steady-state shear flow using wall normal stress measurements along the axis of a slit die. Consider a fluid flowing through a slit die having the height h and the width w, and assume that flow has become fully developed. Then, for steady-state fully developed flow, the equations of motion 

Therefore, measurements of wall normal stress along the die axis, T ib, z) in the fully developed region allows one to calculate dp/dz (see Eq. (5.55)), and thus cr and rj. Similar to the analysis of the capillary flow presented above, we have the following expression for y in slit flow (Han 1974, 1976)  

Integrating Eq. (5.67) from y = 0to y = b (half of the slit height), one obtains 

From the definition of the deviatoric (or extra) stress, for fully developed fiow one has 

Except for nummcal constants, the equations for calculating shear rate are the same as fOT the csq illary. The constant 0.79 in the representative shear rate equation can be obtained following the derivation given in Example 6.2.1 (see also Laun, 1983, Appendix A). Varying slit thickness, H, can be used like capillary radius to test for wall slip. In fact, the studies by Lim and Schowalter (1989) and by Geiger (1989) referred to in Section 6.2 were done with slit dies. Slip or melt fracture in polymer melts occurs at about the same wall shear stress as for capillaries, lO Pa. 

Shear heating can also affect slit data. Again the Nahme number can be used to estimate when significant viscosity errors will occur. For a rectangular charmel 

Similar to capillary, but no Bagley plots are needed if pressure transducers on the slit wall are used 

Utility (same advantages and limitations as capillary except) 

Obtain dp/dx directly from pressure transducers no entrance corrections N by pex and especially pi, more rigorous than capillary die swell, but obtaining accurate N values is difficult Effect of finite slit width Cleaning slit comers 

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In papers dealing with melt processing the oscillatory rheology and slit rheometry of polycarbonates are dealt with briefly. ... 

However, two other methods for obtaining normal stress data from slit rheometry have had reasonable success the exit pressure and particularly the pressure hole method. These are discussed in Sections 6.3.2 and 6.3.3. 

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. 

Note that capillary/slit rheometry is also very useful for determining the shear flow properties of heterogeneous polymer systems, including immiscible polymer blends which are discussed in Chapter 11, highly-filled molten polymers, which are discussed in Chapter 12, and molten polymers with solubilized gaseous component, which are... 

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. 

In analyzing the viscosity data at various temperatures and shear rates, which were obtained via slit rheometry for molten PS, PMMA, polypropylene (PP), and LDPE with solubilized CO2 at varying concentrations, Royer et al. (2000, 2001) used the following expressions, analogues of Eq. (13.13), for the concentration-dependent shift factor at temperatures below T + 100... 

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