Torqued cylinder apparatus

Various methods (1-1) have used to determine the dynamic mechanical properties of polymers. Many of the instruments described are well known and are widely used (torsional pendulum, rheovibron, vibrating reed, and Oberst beam ASTM D4065-82). Newer instruments like the torqued cylinder apparatus (4), resonant bar apparatus (5) and Polymer Laboratories Dynamic Mechanical Thermal Analyzer (6) are becoming more popular in recent times. 

The frequency range of the torqued cylinder apparatus is 50 Hz to about 1500 Hz. The temperature range of the experiment is -40 C to 70 C. The maximum temperature is limited by the durability of the shaker diaphragms. 

Measurements on the torqued cylinder apparatus are made isothermally, from 50 to 1500 Hz, in 5 C intervals starting at -40 C. Thermal equilibrium time between temperature changes is about 1.5 hours. Typically, a material can be evaluated in about 20 hours using this method. 

PARAMETER RANGE COMPARISON. Table I summarizes the parameter ranges of the torqued cylinder apparatus, the resonance apparatus and the DMTA. Since the bulk moduli of the materials under consideration in this paper are much larger than the Young s or shear moduli, the materials are considered incompressible. For incompressible materials, the shear modulus is one third of Young s modulus. Comparisons are then made by converting Young s modulus to shear modulus for the data measured by the resonance apparatus and the DMTA. 

Figure 7 contains the shifted data of the resonant bar apparatus for HOI. The data obtained at each temperature with this device covers a slightly broader frequency range than the torqued cylinder apparatus, resulting in overlapping of the data when shifted. The G data contains very little scatter, but there is moderate scatter in the loss factor data. 

In this instrument a liquid is caused to rotate in an outer cylinder, and it causes a torque to be applied to the torsion wire attached to the inner cylinder. The. viscosity is calculated from the torque, the apparatus being calibrated. Another device for measuring viscosity is the falling-ball viscometer (Figure 11.16e). The viscosity is calculated from the time reciuired for the ball to fall from one position to another. 

In this apparatus the polymer melt is sheared between concentric cylinders. The torque required to rotate the inner cylinder over a range of speeds is recorded so that viscosity and strain rates may be calculated. 

The same apparatus was used, but quantities of paste were removed to give an air space in the vessel. On rapid agitation the volume increased, dependent on the air content required. Paste viscosities were measured, using a Stormer viscometer, which is a type of concentric cylinder viscometer. Although it is possible to obtain results in absolute terms, for comparative purposes the times for 100 revolutions of the rotor under a fixed applied torque were recorded. 

A viscometer is an apparatus that measures the viscosity of a fluid. A common style consists of an outer fixed cylinder with an inner rotating cylinder. One that is being used has an outer cyhnder radius of 15 cm, an inner radius of 14.25 cm, and a height of 22 cm. It takes a torque (force time radius) of 0.07 N-m to maintain an angular speed of 50 rpm at 4°C. What is the viscosity of the fluid that fills the annular region of the cylinders What fluids could this be ... 

It is also possible to calculate the flow path in a Couette apparatus for non-Newtonian liquids (flowing between rotating cylinders Fig. 31) (see page 56). If an inner cylinder rotates at an angular velocity co and a shear deformation takes place in the gap between the internal and external cylinder (R — i a) we observe a torque M ... 

Another group of possible errors arises from the characteristics of apparatus, evaluation of rotation velocity of cylinders and torque, measured as net torque [15]. These problems do not appear in the case of Newtonian or Bingham fluids, while the tixotropic one reveal several problems because the gradient of velocity in the space between the cylinders depends on the paste rheological properties which ate to be tested. There are different ways to resolve this problem Nagataki and Kawano [17] measured directly the distribution of velocity gradient in the space between the cylinders. The assumption that this gradient is linear is not a correct approach, particularly when it appears later that this is not true it is an error and not the approximation [15]. 

CFD-simulations of the measurement apparatus were carried out using a computational mesh with a near-wall refinement on the surface of the rotating cylinder. The simulations reported here were done without the additional baffle at the bottom of the tank (see Fig. 1). Computations with different /rvalues were first conducted in order to find out the dependence of the drag reduction on k. Drag reduction was calculated from the torque on the rotating cylinder due to wall shear forces. 

Example 5. a. Neglecting end eSects, determine the shear stress as function of radius in terms of the measured torque on the stationary inner cylinder (bob), M(Ri), and the geometry of the apparatus as the outer cylinder (cup) is rotated with an angular velocity ta (radians/s). 

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