Capillary rheometers

A capillary rheometer is basicaiiy a ram extruder with a capillary die at the end see Fig. 6.18. 

As the piston moves down, it forces the molten polymer through the capillary. The shear stress in the capiiiary at the wait can be related to the pressure drop along the capillary (APJ by the following equation  

If the piston diameter is much larger than the capillary diameter (Dp DJ and if entrance effects are neglected, then  

The apparent shear rate at the capillary wall can be determined from the flow rate V through the capillary. This can be determined from Eqs. 6 and 13 in Appendix 5.1. 

The flow rate is determined by the area and the velocity of the piston  

This appendix contains the detailed development for the equations that are presented in Chapter 3. Full understanding of these developments is not required for detailed analysis and troubleshooting of the extrusion process. They are presented here for those who desire a deep understanding of the mathematics involved with the screw rotation analysis. Some of the equations and figures are duplicated in this appendix for clarity. The nomenclature used here is consistent with that used earlier. The reader is directed to Chapter 3 for nomenclature. 

This section will present the derivations for a capillary rheometer. A schematic of the device is shown in Fig. A3.1. The main discussion is presented in Section 3.6.1. The assumptions for the derivations are as follows  

The capillary in the die has a diameter of 2R and a length in the z direction (axial) of i. The pressure gradient is considered to be constant over the length of the capillary. Since the z direction velocity is not a function of z and it is not a function of 0, the z component of the cylindrical coordinate equation of motion reduces to an ordinary differential equation [1]  

Where // is referred to as the Newtonian viscosity. The apparent shear rate is often used when deaiing with a non-Newtonian poiymer  

As pointed out by Morrison [1], there is nothing apparent about t that is, this is the shear rate that is obtained when it is assumed that the poiymer behaves iike a Newtonian fluid. 

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Capillary Rheometry Galaxy III, V Automated Capillary Rheometers Galaxy I... 

Melt Index Tester MTS Capillary Viscometer Automatic Capillary Rheometer ProcessibiLity Tester... 

HVA 6 Automated CapiUary/Sht Viscometer MFM Melt Flow Rheometer Automatic Melt Flow Indexer AK Continuous Capillary Rheometer Han Slit Rheometer... 

J The viscosity characteristics of a polymer melt are measured using both a capillary rheometer and a cone and plate viscometer at the same temperature. The capillary is 2.0 mm diameter and 32.0 mm long. For volumetric flow rates of 70 x 10 m /s and 200 x 10 m /s, the pressures measured just before the entry to the capillary are 3.9 MN/m and 5.7 MN/m, respectively. 

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 shear viscosity, especially as measured with capillary rheometers characterized by high shear rates, is hardly sensitive to material structure since the investigator usually has to deal with the substantially destroyed structure in the molten sample. Melt stretching experiments would normally provide much more information [33]. 

Understanding the melt rheology of rubber nanocomposites is crucial from the processing perspective. Bandyopadhyay et al. [37] have studied the melt flow behavior of rubber-silica hybrid nanocomposites in a capillary rheometer. 

A capillary rheometer is another type of instmment, in which the uncured mbber is extmded through a small orifice and the change in dimensions of the extmdate is measured with a laser [2]. This instmment generates high shear rates, compared to Mooney rheometer. The capillary rheometer can thus represent flow of compounds on mbber processing machinery, such as injection molds. 

Experimental polymer rheology data obtained in a capillary rheometer at different temperatures is used to determine the unknown coefficients in Equations 11 - 12. Multiple linear regression is used for parameter estimation. The values of these coefficients for three different polymers is shown in Table I. The polymer rheology is shown in Figures 2 - 4. 

Alpha Technologies) Oscillating Disc Rheometer. Other rheometers are the Yarsley piston rheometer and the capillary rheometer. 

Capillary rheometers are in the form of a barrel where the operator puts the polymer sample. After heating to equilibrate its temperature, the sample is pushed by a piston through a die at chosen rates. Various sizes and shapes of dies are available. Capillary rheometers measure the rheological properties under broad ranges of conditions of temperature, pressure, stress, strain and time, allowing the adoption of parameters near to those for processing. 

Figure 3.6 Solution capillary rheometers a) Ubbelohde-type rheometer (courtesy of Cannon Instrument Company, USA), and b) a schematic of an Ostwald viscometer...

Real polymers are more complex than these simple mechanical models. Qualitatively, when a real polymer is forced to flow through a contraction or expansion in an extrusion screw, it will exhibit viscoelastic behaviour. The polymer molecules will be elongated if forced through a contraction, or they will retract when they flow into an expansion. The effect of viscoelastic behavior in a capillary rheometer is observed in the form of recirculation flow just before the polymer enters the... 

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]. 

Capillary rheometers are used extensively to measure viscosity in the intermediate to high shear rate range. The rheometer has for all practical purposes a lower limit in viscosity measurement because of the plunger seals. These seals are shown on the bottom of the plunger in Fig. 3.16, and they induce a frictional resistance when they are pushed through the rheometer barrel. The piston force can be evaluated without polymer in the barrel, but it is always a source of error at low viscosities because of experimental variability. Moreover, barrel friction is one of the critical corrections that must be made when evaluating viscosity measurements... 

A new polymer was developed by the polymer scientists in a company. A sample has been provided to the process development laboratory to determine the viscosity of the polymer as a function of shear rate and temperature. The instrument available is an old capillary rheometer. The piston has a diameter of 9.525 mm, and a series of capillaries that fit the rheometer barrel have a diameter of 2.54 mm and lengths of 25.4, 50.8, 76.2, and 101.6 mm. The rheometer temperature was set at 270 °C. Shear viscosity data are needed to estimate process performance. 

There would be a minimum of 80 data sets needed to generate this data for one temperature. Because of the time involved, usually about 10 to 15 shear rate data points are generated at each temperature. The plot of the viscosity as a function of shear rate at 270°C is presented in Fig. 3.22. The viscosity below a shear rate of 5 1/s would be best taken using a cone and plate rheometer. The wall friction for the capillary rheometer between the piston and the rheometer cylinder wall would likely cause a force on the piston of the same order as the force due to the flow stress. 

R radius of the capillary die flow path for a capillary rheometer or the radius of a cone and plate rheometer... 

Appendix A3 Rheological Calculations for a Capillary Rheometer and for a Cone and Plate Rheometer... 

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