Plate rheometer

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

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. 

A sliding plate rheometer (simple shear) can be used to study the response of polymeric Hquids to extension-like deformations involving larger strains and strain rates than can be employed in most uniaxial extensional measurements (56,200—204). The technique requires knowledge of both shear stress and the first normal stress difference, N- (7), but has considerable potential for characteri2ing extensional behavior under conditions closely related to those in industrial processes. 

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],... 

Sliding angle (a), contact angle and drop size and, 22 113-114 Sliding plate rheometer, 22 738, 740 Slightly toxic substances, 23 113... 

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... 

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

This section will present the derivations for a cone and plate rheometer. A schematic of the device is shown in Fig. A3.2. The main discussion is presented in Section 3.6.2. 

The velocity in vector format for the above cone and plate rheometer is ... 

The flow behaviour of polymeric electrophotographic toner systems containing carbon black varying in surface area and concentration were determined using a cone and plate rheometer [51]. As the concentration of carbon black was increased, the viscosity at low shear rates become unbounded below a critical shear stress. The magnitude of this yield stress depended primarily on the concentration and surface area of the carbon black flller and was independent of the polymer (polystyrene and polybutyl methacrylate) and temperature. It was postulated that at low shear rates the carbon black formed an independent network within the polymer which prevented flow. 

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