Cone rheometer

Again the reader must be warned that a large proportion of the Je° data in the correlation, summarized in Eqs. (5.26) and (5.27) and Tables 5.2 and 5.5, are based on normal stress measurements (total thrust in plate-cone rheometers) with attendant uncertainties about whether limiting behavior was attained. Also, in... 

Fig. 3.22 Shear rate dependence of the molecular breakdown of polyisobutylene at 37 "C. The data were obtained with single-cone rheometer [7].

MODELS BASED ON DECOUPLED FLOW EQUATIONS -SIMULATION OF THE FLOW INSIDE A CONE-AND-PLATE RHEOMETER... 

Using the described algorithm the flow domain inside the cone-and-plate viscometer is simulated. Tn Figure 5.17 the predicted velocity field in the (r, z) plane (secondary flow regime) established inside a bi-conical rheometer for a non-Newtonian fluid is shown. 

Petera, J. and Nassehi, V., 1995. Use of the finite element modelling technique for the improvement of viscometry results obtained by cone-and-plate rheometers. J. Non-Newtonian Fluid Mech. 58, 1-24. 

Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

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. 

FIG. 4 Viscosity (cone-plate rheometer, D = 3.23 s1, at 25°C) and clear point of 10% sodium lauryl ether (2 EO) sulfate solutions with 0.5% of added NaCl vs. percentage of dialkanolamide [77],... 

When compared to standard (open cavity) cone-plate or parallel disks rheometers, closed cavity torsional rheometers such as the RPA or the PPA have unique high-strain capabilities, which prompted us to modify the instmment in order to investigate the promises of FT rheometry, as outlined a few years ago by the pioneering works of Wilhelm. The technique consists of capturing strain and torque signals and in using FT calculation algorithms to resolve it into their harmonic components, as detailed below. 

Gel formation was monitored using a controlled-stress rheometer (Carri-Med CS 50, TA Instruments, Guyancourt, France) with cone-and-plate geometry (cone diameter 4 cm, angle 3°58 ). The bottom plate was fitted with a Peltier temperature controller that... 

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]. 

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. 

The rheometer most often used to measure viscosity at low shear rates is the cone and plate viscometer. A schematic of a cone and plate rheometer is found in Fig. 3.24. The device is constructed with a moving cone on the top surface and a stationary plate for the lower surface. The polymer sample is positioned between the surfaces. Two types of experiments can be performed the cone can be rotated at a constant angular velocity, or it can be rotated in a sinusoidal function. The motion of the cone creates a stress on the polymer between the cone and the plate. The stress transferred to the plate provides a torque that is measured using a sensor. The torque is used to determine the stress. The constant angle of the cone to the plate provides an experimental regime such that the shear rate is a constant at all radii in the device. That is, the shear rate is independent of the radial position on the cone, and thus the shear stress is also independent of the position on the cone. 

Using the cone and plate rheometer the angle Q is forced in a sinusoidal manner, leading to linear strain being introduced in the polymer. The shear strain, y, is a sinusoidal function of time t with a shear rate amplitude of % as follows ... 

Here t is the resulting shear stress, 6 is the phase shift often represented as tan(d), and (O is the frequency. The term 6 is often referred to as the loss angle. The in-phase elastic portion of the stress is To(cosd)sin(wt), and the out-of-phase viscous portion of the stress is To(sind)cos(complex modulus and viscosity, which can be used to extend the range of the data using the cone and plate rheometer [6] ... 

Figure 3.26 Complex viscosity measured using a cone and plate rheometer. The data are for a GPPS resin with an MFR of 1.5 dg/min (5 kg, 200 °C) measured at 225 °C. The data are from Fig. 3.22...

G storage modulus as measured using a cone and plate rheometer G" loss modulus as measured using a cone and plate rheometer J(t) creep compliance... 

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

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