Shear Flow Measurements

FIGURE 3.19 Plate-plate rheometer. The torque, T, and normal force, F, measurements are used to determine jj and — ilri- 

FIGURE 3.20 Capillary rheometer. Polymer is melted by conduction in the reservoir and then pushed through the capillary by the plunger. Viscosity data are obtained from AP and Q measurements. 

The capillary rheometer (Fig. 3.20) is commonly used to obtain r] at high shear rates. Basically the device consists of a barrel for melting the polymer and a plunger that pushes the melt through the capillary. The data obtained from this device consist of the pressure required to push the melt through the capillary and the volumetric flow rate (plunger speed and cross-sectional area). Two corrections are applied to this data. 

FIGURE 3.21 Pressure profile in a capillary rheometer. The various pressures are defined in the figure including the exit pressure, Pat. and the entrance pressure, APem- 

the pressure drop must be corrected for the additional pressure required for the melt to pass through the contraction between the barrel and the capillary. For any fluid, the wall shear stress is given by 

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There was little discussion of this perspective during the next 25 years, and only in the 1960s was there renewed attention. In 1962, Zakharenko et al. [Zl] in Moscow reported shear flow measurements of rubber-carbon black compounds. In 1972, Vinogradov et al. [V8], also in Moscow, reported similar results for other rubber-carbon black compounds and indicated the occurence of yield values. At the same time similar behavior was reported for talc-polypropylene compounds by Chapman and Lee [C8] of Shell and for titanium dioxide-polyethylene compounds by Minagawa and White [M29]. 

The instruments of Turner and Moore [T12] and Montes et al. [M38] are pressurized by an external reservoir. This allows shear flow measurements to be carried out at constant shear rates and conditions for the development of slippage in individual compounds to be determined. 

It should be pointed out that Eq. (4.124) was derived without invoking fluctuations of contour length (i.e., without considering the Rouse motion in a reptating chain). The main idea behind the derivation of Eq. (4.124) is that since experimental data for r)Q is usually obtained from shear flow measurements, stress effects must be included in the reptation model that is, when a polymer is subjected to shear flow, a relaxation of polymer chains to reptate around the entangled junctions must be taken into consideration, in addition to the reptation of the overall center-of-mass motion. 

Oscillatory shear flow properties (also referred to as dynamic viscoelastic properties) have long been used to investigate the viscoelastic properties of polymeric materials (Ferry 1980). Oscillatory shear flow measurement requires an instrument that can generate sinusoidal strain as an input to the fluid under test and record the stress resulting from the deformed fluid as an output. For such purposes, a parallel-plates flxture as well as a cone-and-plate flxture can be used the uniform shear rate in the radial direction that is necessary when conducting steady-state shear flow experiments is no longer necessary. 

The salient feature of oscillatory shear flow measurement is that it yields information on both the viscous property t] (co) and the elastic property G (o) of a fluid. 

Vega, J. F., Santamaria, A. Small-amplitude oscillatory shear flow measurements as a tool to detect very low amounts of long chain branching in polyethylenes. Macromol. (1998) 31, pp.3639-3647... 

We therefore conclude that for (d/R) 1, y (RQId), a result we might have guessed from the similarity of Couette shear flow with d/R 1 to planar Couette shear. Thus, Couette shear flow measurements performed using small cylinder spacings (typically shear stress Zg and shear rate y. 

Rheological Properties. Rheological studies of the nanocomposites were performed using a Rheometrics Mechanical Spectrometer model 800 on 25mm diameter samples punched from the injection molded plaques. Dynamic oscillatory shear flow measurements of the nanocomposites were made in the linear regime of strain in a frequency range of 0.1 to 100 rad/s under a continuous nitrogen atmosphere. 

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