Shear stress capillary rheometer measurement

A slit die is designed on the assumption that the material is Newtonian, using apparent viscous properties derived from capillary rheometer measurements, at a particular wall shear stress, to calculate the volumetric flow rate through the slit for the same wall shear stress. Using the correction factors already derived, obtain an expression for the error involved in this procedure due to the melt being non-Newtonian. Also obtain an expression for the error in pressure drop calculated on the same basis. What is the magnitude of the error in each case for a typical power law index n = 0.377... 

The cone and plate rheometers are useful at relatively low shear rates. For higher shear rates capillary rheometers are employed. They are usually constructed from metals. The molten polymer is forced through the capillary at a constant displacement rate. Also, they may be constructed to suit various specific shear stresses encountered in commercial operation. Their big disadvantage is that shear stress in the capillary tubes varies from maximum at the walls to zero at the center. On the other hand, stable operation at much higher shear rates is possible. Determination, however, of rjo is usually not possible due to limitations of the instruments. At low shear rates, one can determine the steady-state viscosity from measurements of the volumetric flow rates, Q and the pressure drop ... 

As a result of these difficulties, typical capillary rheometers measure pressure in or above the reservoir as indicated in Figure 6.2.1 or from the forces on a driving piston. (Different capillary rheometer designs are discussed further in Chapter 8.) To determine the true shear stress, a number of corrections must be considered. 

Reservoir diameter and capillary L/R influence the equilibrium swell ratio. If / ,// < 10 and L/R > 40, then swell measurements are independent of rheometer geometry (Han, 1976). Of course, the onset of melt distortion sets an upper limit on shear stress for swell measurements. 

This instrument is a commercially available Laboratory Capillary Rhometer called the LCR 7001. The instrument has a 9.5505 mm barrel diameter and a load cell capable of measurements to 10 kN. The capillary die diameters used in this study included the following 1 mm (L/D=30), 1 mm (L/D=5), 1 mm (L/D=20), and 2 mm (L/D=15). Shear rates on the rheometer were adjusted to get good test sensitivity and to provide improved correlation to the controlled stress capillary rheometer. Figure 2 shows the controlled rate capillary rheometer. 

Fig. 2 shows the flow curve for the neat exact 5361 at loot). The instability problem of the metallocene based polymers with narrow molecular distribution is well known. Fig. 3 shows the photographs of the extrudate samples with varying Dechlorane concentration collected during the capillary rheometers measurement. It is interesting to see that while the severe instabilities such as slip-stick and gross-melt fracture were observed at the shear rate from 177.8 s to 3162.2 s for the neat Exact resin, the severe instability appeared at the shear rate between 177.8 s and 562.2 s but disappeared at the shear rate above 1000.1 s for Exact/10% Dechlorane suspension. The shark-skin like instabilities were observed above the Dechlorane concentration of 20% and the shear rate at which the instability started to appear was decreased as the Dechlorane concentration was increased. Since the viscosity of the Dechlorane-filled systems was higher than that of the neat resin at all rates of shear, the instabilities are expected to develop the melt fracture at even lower shear rates. The shear viscosity vs. shear rate relationships measured with plate-plate rheometers and capillary rheometers are shown in Fig. 4. In this figure it is seen that both sets of data are reasonably matched. It is observed that at low shear rate range the viscosity increment due to the increase in the filler concentration is more pronounced than that at high shear rate. Both plate-plate and capillary measurements were carried out with constant shear rate (CSR) mode. While the capillary rheometer could accurately follow the preset shear rate values the plate-plate rheometer couldn t keep up with the preset shear rate values. Above two observations are due to the yield stress developed at low shear rate. At low shear rate particle-particle interaction dominates the flow phenomena and the yield stress was observed. At high shear rate hydrodynamic effect dominates the flow phenomena.

There are a number of techniques that are used to measure polymer viscosity. For extrusion processes, capillary rheometers and cone and plate rheometers are the most commonly used devices. Both devices allow the rheologist to simultaneously measure the shear rate and the shear stress so that the viscosity may he calculated. These instruments and the analysis of the data are presented in the next sections. Only the minimum necessary mathematical development will he presented. The mathematical derivations are provided in Appendix A3. A more complete development of all pertinent rheological measurement functions for these rheometers are found elsewhere [9]. 

Melt flow rheology measurements were obtained on the MBAS polymer using an Instron capillary rheometer. The data reported were obtained using an 0.056-inch capillary, 90° included angle, with an L/D of 36. In Figure 5 the maximum shear stress (lb/in2) is plotted vs. the apparent shear rate (sec 1). The apparent viscosity (lb-sec/in2) vs. tem-... 

Steady shear viscosities can be measured with two different instruments. The System IV can measure polymer viscosities from about 0.001 to 10 sec 1 while the Gottfert Capillary Rheometer is capable of obtaining viscosities from 0.1 to 100,0001/s. In steady shear, the strains are very large as opposed to the dynamic measurements that impose small strains. In the capillary rheometer, the polymer is forced through a capillary die at a continuously faster rate. The resulting stress and viscosity are measured by a transducer mounted adjacent to the die. A schematic of the system is illustrated in Figure 5. 

Many of the comments in the previous chapter about the selection of grade, additives and mixing before moulding apply equally in preparation for extrusion. It is important of course that the material should be appropriate for the purpose, uniform, dry, and free from contamination. It should be tested for flow and while many tests have been devised for this it is convenient to classify them as either for low or high rates of shear. The main terms used in such testing ( viscosity , shear rate , shear strain , etc.) are defined in words and expressed as formulae in ISO 472, and it is not necessary to repeat them here. Viscosity may be regarded as the resistance to flow or the internal friction in a polymer melt and often will be measured by means of a capillary rheometer, in which shear flow occurs with flow of this type—one of the most important with polymer melts—when shearing force is applied one layer of melt flows over another in a sense that could be described as the relationship between two variables—shear rate and shear stress.1 In the capillary rheometer the relationship between the measurements is true only if certain assumptions are made, the most important of which are ... 

This section will be devoted to the Newtonian viscosity i]0, that is to situations where the shear rate is proportional to the shear stress. This is the case under steady-state conditions at low shear rates. Although rj0 may be directly measured at low shear rates in a cone and plate rheometer, it is in general not measured directly but found by extrapolation of viscosity values, as measured in a capillary rheometer, as a function of shear rate ... 

The rheological behaviour of the two polymers was determined using classical techniques of rheometry, already described in Chapter II. 1 (rotational and capillary rheometers for shear viscosity and first normal stress difference measurements CogsweU method for the elongational viscosity). 

In order to facilitate rapid melt viscosity measurement and data analysis a modified Gflttfert capillary rheometer has been interfaced to a Hewlett-Packard data acquisition system. All test parameters (temperature, barrel pressure, etc) are monitored automatically and the data is stored on magnetic tape. After testing is complete, raw data is entered into an analysis program used to compute tables and draw plots of shear stress, shear rate, and apparent viscosity. Examples of the application of this system to commercial polymers are discussed. 

To calculate shear stress, shear rate and melt viscosity, the melt pressure and piston velocity must be monitored. The former is measured using a 0 to 20,000 psi pressure transducer mounted in the rheometer barrel just above the capillary. A linear potentiometer is used to monitor piston position during the test. Utilizing the piston displacement data and the HP real time clock, the piston velocity is calculated. 

Capillary rheometers can usually measure over a range of shear stresses from lO to 10 N m and shear rates from 0.001 to 500,000s. ... 

Fundamentally it is the same as the capillary rheometer, but the shear. stress is kept constant from an applied load in the form of a weight, and instead of measuring the shear... 

The measured values of polymer flow taken by capillary rheometers are often presented as plots of shear stress versus shear rate at certain temperatures. These values are called apparent shear stress and apparent shear rate at the tube wall. Corrections must be applied to these values in order to obtain true values. The corrected value of shear stress is determined by the Bagley correction [20]... 

A systematic study of the basic rheological properties for a wide variety of polypropylene melts has been made by Minoshima et al. [89]. These authors measured shear viscosities at low shear rates in a Rheomatrics mechanical spectrophotometer and at high rates in an Instron capillary rheometer. The principal normal stress difference, Ni, was measured in the mechanical spectrophotometer with a cone and plate device. The elongational viscosity, of special importance to fiber formation, was measured in an apparatus built by Ide and White [90],... 

Simplified versions of capillary rheometers are melt flow testers, which are especially suitable for laboratory use since they are relatively easy to handle and represent a fast measure. However, they only give information about the fluidity at a certain shear rate which however for chemists in most cases is enough to judge the material s fluidity. Using a melt flow tester the measure of fluidity is not expressed in terms of the melt viscosity but as the amount of material extruded in a given time (10 min). The amount of extrudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MF//2 (190 C) = 9.2 g/10 min means that at 190 C and 2 kg load, 9.2 g of polymer melt are extruded through a standard nozzle in 10 min. Today the expression melt flow index is often replaced by the melt flow rate (MFR)... 

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