Angular parallel-plate

Fig. 1 a, b. Schematic diagram of a flow of fluid under combined shear conditions a — between flatly parallel plates under the action of pressure difference AP = P -P2 (the upper plane moves in the direction transverse to the main flow) b — between two coaxial cylinders rotating towards one another at angular velocities flj and fi2... 

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

The velocity field between the cone and the plate is visualized as that of liquid cones described by 0-constant planes, rotating rigidly about the cone axis with an angular velocity that increases from zero at the stationary plate to 0 at the rotating cone surface (23). The resulting flow is a unidirectional shear flow. Moreover, because of the very small i//0 (about 1°—4°), locally (at fixed r) the flow can be considered to be like a torsional flow between parallel plates (i.e., the liquid cones become disks). Thus... 

Suppose the upper plate is rotating with an angular speed of Q. Conventionally, one measures the stress by assuming the velocity field V0(z, r)=Qr(z/H), as shown in Fig. 7a throughout the sample in between the parallel plates. The free meniscus surface has the stress-free condition n a = 0 where n is the unit vec-... 

The reciprocal of the specimen resistance in the equivalent parallel circuit for a given frequency is sometimes called the specimen conductance GP. It is a combination of DC conductance, by which we mean any real flow of charge through the sample under the influence of the applied field, and the anomalous conductance due to any time-dependent polarisation processes. The contribution that a true DC conductivity dielectric loss at an angular frequency w can be readily calculated as follows for the material in a parallel-plate capacitor. If the capacitor plates have area A and separation s ... 

Fig. 16 Parallel plate system r = distance of a point from the center of the plates, = radius of the plates, H — gap between the plates, T — torque produced,

For a parallel plate capacitor with the sinusoidally modulated plate separation d(t) given by Eq. (2) (do=average distance between the parallel plates. Ad=vibration amplitude and ( =angular frequency of vibration), the time dependent capacitance C(t) is given by Eq. (3) with C(t) defined by Eq. (3). 

Figure 3 r as a function of temperature for PP cooled from 290 C (— —) and VB cooled from 330° (— —). Parallel plate fixtures used. Angular frequency = 10 rad/s. Strain = 5%. Cooling rate = 7°C/min. 

The polymers used were isotactic PP (Repol-HllOMA, Reliance, India) and PEH (940400-B, Futura Polymers, India). The properties of PP and PET are given in Tables 15.1 and 15.2. The dynamic viscosities of the polymers were measured at a temperature of 265°C using a parallel plate rheometer to estimate the viscosity ratio. The dynamic viscosity variation of the polymers with angular frequency (w) in log-log scale is delineated in Figure 15.1. The viscosity ratio of PET and PP Vpet/Vpp) is between 3.0 and 2.6 in the frequency range 100 to 200 rad/sec. 

A parallel-plate rheometer is sometimes used to determine linear viscoelastic properties of polymer liquids by oscillating one plate with a small angular amplitude or small strain amplitude. By measuring the torque amplitude, Mq, <5, and the dynamic viscoelastic functions are obtained by Eq. (48)-(52). In this case, the geometric constant A is given by... 

In this system, clearance is a small distance. Hence, the rotating cylinders can be represented by a system of parallel plates (Figure 5-6) with the top plate (outer cylinder moving with a velocity (the angular velocity times the radius) of... 

Using an Advanced Rheometric Expansion System (ARBS) with parallel plates of 2S mm diameter, we performed dynamic temperature sweep expo-iments under isochronal conditions with increasing temperature as well as decreasing temperature. The heating and cooling rate of these experiments was 0.5 °C/min. The strain amplitude (y,) and the angular frequency (ca) were low enough to satisfy a linear viscoelasticity. 

R = radius of sample (in cone and plate or parallel plate) a = angular displacement (radians)... 

Numerous less elaborate devices with parallel plate or cone and plate geometry have been described in the literature. " Application of torque by a torsion wire from which the rotating element of the apparatus is suspended can be quite satisfactory for creep if the torsional stiffness of the wire is small and the top is turned through a large angle then the torque remains essentially constant despite the small angular displacement at the bottom of the wire. It is difficult to perform creep recovery experiments with a torsion wire, but these can be accomplished if the... 

Most rheological measurements measure quantities associated with simple shear shear viscosity, primary and secondary normal stress differences. There are several test geometries and deformation modes, e.g. parallel-plate simple shear, torsion between parallel plates, torsion between a cone and a plate, rotation between two coaxial cylinders (Couette flow), and axial flow through a capillary (Poiseuille flow). The viscosity can be obtained by simultaneous measurement of the angular velocity of the plate (cylinder, cone) and the torque. The measurements can be carried out at different shear rates under steady-state conditions. A transient experiment is another option from which both y q and ]° can be obtained from creep data (constant stress) or stress relaxation experiment which is often measured after cessation of the steady-state flow (Fig. 6.10). 

Another type of viscometer which finds occasional use is the disk-plate viscometer (Fig. 16.8). A disk of radius R rotates with an angular velocity of CO relative to a parallel plate. The disk and plate are separated by a distance d(d R with the test fluid in between. The torque M on either the disk or plate is measured. This is known as torsional (twisting) flow, and is another example of a viscometric flow. 

The oscillatory shear measurements were performed with a Rheometrics mechanical spectrometer (RMS 800) with parallel plates. The angular frequency range was from 10 to 10 rad/s. The samples were tested at 30, 60,120, and 150 °C. In addition to the... 

In a parallel plate rheometer, shear flow is generated in a layer of fluid (thickness d) sandwiched between parallel discs (Figure 8.11). The fluid is retained in the gap by surface tension. Shear is created by rotating one disc at an angular speed Q, while the other is maintained stationary by applying a torque T. In this case, it does not matter which of the two discs is rotated, and in some designs both discs are rotated in opposite directions. Fluid elasticity creates a normal force F that attempts to separate the plates. T, Q, and F are the experimental measurables in this flow configuration. 

An Advanced Rheometric Expansion System (ARES, TA Instruments) was used in oscillatory shear mode with parallel plate geometry. Strain amplitude was fixed at 2% and dynamic frequency sweep experiments with angular frequency ( ) from 0.1 to 100 s were performed at 280°C. PET and all blends were tested under nitrogen atmosphere, while pure LCP, which was found not to degrade, was tested under air. The complex viscosity ( 7 ), dynamic storage (GO and loss (G") moduli were obtained. All rheological measurements are an average of four runs. 

The rheological behaviour of molten polymers is of prime importance as it relates to their microstructure and governs their processing characteristics [1]. Rotational rheometers, specifically cone-plate, parallel plate, and sliding plate rheometers are routinely used to characterize the linear viscoelastic properties of polymer melts. Small amplitude oscillatory shear experiments are employed to measure the storage (G ) and loss moduli (G"), which are related to the elastic and viscous character of the material, respectively, and the complex viscosity (77 ) as functions of angular frequency (a). 

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